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Drying of hog fuel in a fixed bed Sheikholeslami, Roya 1990

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DRYING OF HOG F U E L FN A FIXED BED By ROYA SHEIKHOLESLAMI B.Sc,  The University of Kansas  M.A.Sc., The University of British Columbia  A T H E S I S S U B M I T T E D IN P A R T I A L T H E REQUIREMENTS DOCTOR  FULFILLMENT O F  FOR T H E DEGREE O F  O F PHILOSOPHY  in T H E FACULTY OF GRADUATE CHEMICAL  STUDIES  ENGINEERING  We accept this thesis as conforming to the required standard  T H E UNIVERSITY  O F BRITISH  COLUMBIA  January 1990 © ROYA SHEIKHOLESLAMI, 1990  In  presenting  degree at the  this  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  publication of  by  his  or  her  representatives.  for  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be It  is  granted  by the  understood  that  head of copying  my or  this thesis for financial gain shall not be allowed without my written  permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  Abstract  Hog fuel is increasingly becoming an alternative to alleviate the energy problems associated with the use of fossil fuels. To make adequate use of hog fuel, its moisture content should be reduced prior to combustion either in an external dryer or in the initial stages of a hog fuel boiler.  Therefore, this research project was undertaken to establish the  factors which govern the drying rate of wet hog fuel particles.  T h e convective drying  of wood-waste on the slow moving bed of hog fuel boilers was simulated in a packed bed. T h e information which was obtained can also be applied to approximate the drying behaviour in external dryers.  A n apparatus was constructed to accommodate the use of hot air, flue gas, superheated steam and a mixture of them as drying media.  Drying tests were carried out, over  the temperature range of 1 2 5 - 2 4 5 ° C , on 1.1 to 4 kg batches of Western Hemlock hog fuel of thicknesses from 2 to 12 mm. T h e relative effects of velocity ( V ) , temperature ( T ) , nature of the drying gas, bed depth (L), and initial moisture content of the hog fuel samples ( M ) on the drying process were investigated using a mixture of several thickness D  fractions having an average (sauter mean) particle thickness (d ) of 6.3 mm. p  Drying rates were determined through measurement of the change either in humidity of the drying gas, or flow rate of the superheated steam across the bed of hog fuel.  Gas  humidity was measured using an optical dew point sensor and steam flow was monitored using an orifice plate connected to a massflow transmitter.  ii  Drying rates have been quantified as functions of hog fuel particle thickness, initial moisture content and bed depth. T h e effects of gas temperature, velocity and humidity have also been quantitatively established.  T h e drying process was insensitive to CO2 content  of the drying gas.  T h e existence of an inversion temperature above which drying rates increase with humidity of the drying medium was both experimentally and theoretically confirmed and the locus of inversion points was determined.  Instantaneous  normalized drying rates, / , and characteristic moisture contents, $, have  been determined and the existence of a unified characteristic drying rate curve was verified. Using a receding plane model, / was formulated as a function of $, for d  p  = 6.3  m m and at L = 25 cm, for both superheated steam and relatively dry air.  Pressure drop measurements  were obtained for all the runs with the exception of the  superheated steam ones. Application of an accepted pressure drop equation permitted the sphericity of the hog fuel particles to be approximated.  A design equation for gas  pressure drop in beds of hog fuel particles was investigated.  T h e simultaneous heat and mass transfer processes in drying during the heat transfer controlled period was studied. Using the concept of volumetric evaporation, an empirical correlation for the overall heat transfer coefficient in a packed bed of hog fuel particles has been obtained.  T h e effects of different parameters on both the particle residence time required for drying and the grate heat release rate in hog fuel boilers were determined.  iii  Table of Contents  Abstract  ii  List of Figures  viii  List of Tables  xii  Acknowledgement  xiv  1  Introduction  1  2  Literature Review  7  2.1  Wood as a Fuel  7  2.2  Hog Fuel Boiler Systems  10  2.2.1  Predrying Hog Fuel  11  2.2.2  Change in the Method of Burning  12  2.3  Structure of the Wood  14  2.4  Moisture Transport in Wood  16  2.5  Vapour Transport within a Drying Medium  21  2.6  Drying Theories  24  2.6.1  Diffusion Theory  25  2.6.2  Capillary Theory  26  2.6.3  Moving Boundary Theory  26  2.7  Characteristic Drying Curve.  29  2.8  Batch Drying in a Packed Bed  31 iv  2.9 3  32  Methods and Materials  35  3.1  Overview  35  3.2  Experimental Apparatus  38  3.2.1  The Burner System  38  3.2.2  Heat Exchanger System  40  3.2.3  Drying Chamber  42  3.2.4  Preparation of The Drying Medium  42  3.3  4  Objectives of this Study  Drying Rate Measurements  45  3.3.1  Humidity Measurement  47  3.3.2  Mass Flow Measurement  49  3.4  Temperature and Flow Measurement  3.5  Hog Fuel Sample Preparation  3.6  Procedure for a Drying Run  Results and Discussion  • • •  :  °0 52 58  '  61  4.1  General Procedures  61  4.2  Particle Size  4.3  Bed Height  4.4  Hog Fuel Initial Moisture Content  87  4.5  Drying Temperatures  90  4.6  Gas Velocity . . .  93  4.7  The Nature of the Drying Medium  100  4.7.1  Flue Gas  100  4.7.2  Superheated Steam  107  4.7.3  Humidified Air  114  . . . :  v  73 79  4.7.4  5  A Comparison —Different Types of Drying Media  4.8  Characteristic Drying Curves  4.9  Pressure Drop Analysis  . .  123 138 152  4.10 Heat Transfer During Constant Drying Rate Period  154  4.11 Industrial Implications  182  Concluding Remarks  189  Nomenclature  195  References  207  A  Sample Calculations  224  A.l  224  Determination of Factors Affecting the Properties of the Fluid  A.2 Determination of the Drying Rate and the Related Properties  228  A.3 Parameters Determining Solid Properties  231  A.4 Factors Affecting Hydrodynamics of a Packed Bed  233  A.5 Determination of Heat and Mass Transfer Coefficients and Dimensionless groups during Constant Rate Period  B  235  A.6 Determination of the Factors Affecting Characteristic Drying Curve . . .  247  A.7 Determination of Friction Factor and the Related Properties  248  A.8 Parameters Determining the Falling Rate Behavior  249  A.9 Correction of the Maximum Drying Rate for Mass Flow of Gas . . . . . .  251  A.10 Correction of Run 26 for Both Temperature and Mass of Wet Solid . . .  251  A.11 Effect of Bed Height on the Grate Heat Release Rate  252  Drying Rate Curves  254  vi  C Tabulated Instantaneous Drying Rate Data D Tabulated Data on Maximum and Falling Drying Rates E  Calibration Curves and Equations  F  Computer Programs  vn  List of Figures  2.1  Combustion Zones and Degradation of Wood Constituents in Oxygen as Determined by Thermogravimetry (Courtesy of F. C. Beall [21])  8  2.2  Sloping/Reciprocating Grate, Jagerlund [38]  13  2.3  A Baretube Grate Furnace with a Reverse Grate, Jagerlund [38]  14  2.4  Structure of a Typical Hardwood [49]  15  2.5  The Evaporation of Free Water from Wood (Courtesy of C. Skarr) [49]  2.6  Movement of Free Water in Tangential Direction Due to Capillarity (Spolek  .  18  and Plum) [51]  19  2.7  Drying out of a Two-Pore System, Keey [46]  20  2.8  Concentration Gradient as a Function of the Diffusional Path  21  2.9  Moisture Transport in Drying a Porous Material, Keey [46]  30  2.10 Batch Drying of Thick Beds of Solids: (a) Drying Zone Resides within the Bed; (b) Drying Zone Passed through Drying Column  33  3.1  Photograph of the Apparatus  36  3.2  Flow Diagram of the Apparatus  37  3.3  Natural Gas Fired In-line Burner  39  3.4  A Photograph of the Heat Exchanger  41  3.5  A Photograph of the Drying Chamber  43  3.6  Sketch of the Line Connections for Steam Measurement with 1—| in orifice  3.7  plate  46  Electric Diagram, of the Dew Point Sensor  48  Vlll  3.8  A Schematic Diagram of Flow Metering Lines for Superheated Steam Runs 51  3.9  A Photograph of 2 - 4 mm Thick Particles  53  3.10 A Photograph of 4 - 6 mm Thick Particles  54  3.11 A Photograph of 6 - 8 mm Thick Particles  55  3.12 A Photograph of 8 - 10 mm Thick Particles  56  3.13 A Photograph of 10 - 12 mm Thick Particles  57  4.1  A Plot of Drying Rate versus Time  66  4.2  A Plot of Rate versus Moisture Content  67  4.3  A Plot of Moisture Content versus Time  69  4.4  A Plot of Characteristic Drying Curve  71  4.5  Drying Rates versus Time for Various Particle Sizes  76  4.6  Maximum Drying Rate versus Particle Thickness  77  4.7  Moisture Content versus Time for Various Particle Sizes  78  4.8  Drying Rates versus Moisture Content for Various particle sizes  80  4.9  Drying Rate versus Time for Various Bed Depths  81  4.10 Drying Rate versus Moisture Content for Various Bed Depths  83  4.11 Plot of Moisture Content versus Time for Various Bed Depths  84  4.12 Maximum Drying Rate versus the Bed Depth  86  4.13 A Plot of Drying Rates versus Time for Various Initial Moisture Contents  88  4.14 Moisture Contents versus Time for Various Initial Moisture Contents  89  . .  4.15 Drying Rates versus Moisture Content for Various Initial Moisture Contents 91 4.16 Drying Rates versus Time at Different Temperatures  92  4.17 Moisture Content versus Time at Different Temperatures  94  4.18 Drying Rates versus Moisture Content at Different Temperatures 4.19 Maximum Drying Rates as a Function of Temperature  IX  .  . . . .  95 96  4.20 Drying Rates versus Time at Different Mass Flow Rates  97  4.21 A Plot of Drying Rates versus Time at Various Velocities  99  4.22 Moisture Contents versus Time at Various Velocities  101  4.23 Moisture Contents versus Time at Various flow rates  102  4.24 Drying Rates versus Moisture Contents at Various Velocities  . 103  4.25 Drying Rates versus Moisture Contents at Various Flow Rates  104  4.26 Drying Rates versus Time for Various CO2 Concentrations  108  4.27 Drying Rates versus Moisture Content for Various CO2 Concentrations . 109 4.28 Superheated Steam Drying Rate versus Time at Various Temperatures  111  4.29 Moisture Content versus Time for Superheated Steam Drying  112  4.30 Drying Rate versus Moisture Content for Superheated Steam Drying  . . 113  4.31 Maximum Drying Rate versus Temperature for Superheated Steam Drying 115 4.32 Drying Rate versus Time at Different Air Humidities  116  4.33 Drying Rate versus Time for Run 23  117  4.34 Drying Rate versus Time for Run 29  118  4.35 Maximum Drying Rate versus Inverse of Absolute Humidity  120  4.36 Moisture Content versus Time at Different Air Humidities  121  4.37 Drying Rate versus Moisture Content at Different Air Humidities  . . . .  4.38 Maximum Drying Rate versus Temperature in Air and Steam  122 125  4.39 Adiabatic Saturation Temperature as a Function of Humidity at Various temperatures  129  4.40 Maximum Change in Gas Enthalpy versus Temperaure at Different Humidities  130  4.41 Locus of Inversion Point versus Humidity . .  132  4.42 Mean Specific Heat of the Mixture versus Humidity  134  4.43 Concentration Gradient versus Humidity at Various Temperatures . . . .  137  x  4.44  Moisture Profile in Solid at Onset of Falling Rate Period  140  4.45  Characteristic Drying Curves for Runs of Various Bed Depths  143  4.46  Characteristic Drying Curves for Various Particle Sizes  146  4.47  Characteristic Drying Curves for Runs at Different Air Humidities . . . .  147  4.48  Unified Characteristic Drying Curve  151  4.49  A Fit of the Experimental Hydraulic Euler Number to Ergun Equation  156  4.50  Sphericity as a Function of Voidage for Randomly Packed Beds, Courtesy of Brown [77]  157  4.51  A Plot of Modified Friction Factor as a Function of Reynolds number  . .  4.52  Adiabatic Humidification of a Gas  4.53  Drying in Relatively Deep Beds of Solids: (a) Humidity-Temperature Re-  158 167  lationships in the Gas Phase (case A ) ; (b) Humidity-Temperature Relationships in the Gas Phase (case B); (c) Number of Transfer Units versus Bed Height  174  4.54  State of Drying Gas Traveling Along the Column (case A )  175  4.55  A Plot of Modified Nusselt Number as a Function of Reynolds number  .  181  4.56  Effect of Wood Moisture Content on Boiler Efficiency ( R . L . Stewart), [39]  184  4.57  T h e Effect of Various Parameters on the Normalized Drying T i m e to Reach M  4.58  T h e Effect of Various Parameters on the Normalized Drying Time to Reach M  A.l  185  = 0.6  = 0.3  186  Schematic Diagrams of Gas Temperature along the Column with a Uniform (a) and a Non-uniform (b) Solid Temperature  241  A. 2  Plot of Temperature Distribution along the Bed  242  B. l  to  B.9  Plots of Drying Rates versus T i m e for Runs 1A to 46 . . . . 255 to 263  xi  List of Tables  1.1  End Use Energy Demand in Canada in 1985  1  1.2  End Use Industrial Energy Demand (in Petajoules) in 1985  2  1.3  Heat Contents and Typical Efficiencies of Fuels  3  4.1  Summary of Drying Experiments  62  4.2  Summary of Parameters Indicating the Reproducibility of the Data . . .  74  4.3  Summary of Runs with Varying Particle Size  74  4.4  Summary of Runs with Varying Bed Height  85  4.5  Summary of Runs with Varying Hog Fuel Initial Moisture Content . . . .  87  4.6  Summary of Runs with Varying Temperature  90  4.7  Summary of Runs at Different Velocities  98  4.8  Composition of Combustion Gases for Wood Material and Natural gas  106  4.9  Summary of Runs with Varying CO2 Content  106  4.10 Summary of Superheated Steam Drying Runs  110  4.11 Effect of Gas Humidity  119  4.12 Summary of Parameters Affecting the Relative Drying Rates  144  4.13 Summary of Pressure Drop Data  155  4.14 Summary of Physical Properties at Film Temperature  169  4.15 Heat Transfer Coefficients and Dimensionless Groups .  170  4.16 Mass Transfer Coefficients and Dimensionless Groups  171  4.17 Rates of Heat Flow at Different Heat Transfer Modes ( W )  177  4.18 Summary of Temperature and Humidity Data .  178  xii  4.19 Summary of data Determining the Analogy between the Transfer Processes 179 A.l  Heat Capacities of the Components of the Drying Medium  225  A.2 Enthalpy of various streams  237  A.3 Emissivities of C0  239  2  A. 4 Maximum Drying Rates at Various Temperatures at Mass Flow of 142  B. l  kg/hr  251  Parameters in the Fit of Drying Rate Curve  264  B. 2 Summary of Data Representing the Goodness of the fit C. l  to  C.34 Summary of Data for Runs 1A to 46  D. l  Maximum Drying Rate Data and the Confidence Intervals  265 267 to  D.2 Summary of Data on Drying Rates During the Falling Rate Period  330 332  . . .  333  D.3 Summary of Data Affecting the Slope of the Falling Rate Curve  334  D.4 Summary of Data on the Slope of the Falling Rate Curve  335  D. 5 Particle Residence Time Required to Reach Various Final Moisture Contents336 E. l  Calibration Equations for Flowmeters  338  E. 2 Calibration Equations for Thermocouples  339  F. l  341  Program to Calculate the Instantaneous Drying Rates  xm  Acknowledgement  I would like to thank my supervisor, Dr. A.P. Watkinson, for his conscientious guidance; and particularly, I am grateful to him for being very understanding and encouraging during the course of this study. This project was undertaken after discussions with Dr. B.R. Blackwell of Sandwell Swan Wooster and his continuous interest and helpful advice throughout this project is very much appreciated. The financial support by Science Council of British Columbia and a reseach operating grant to Dr. Watkinson and also some contributions made by Crofton Pulp and Paper Division of B.C. Forest Products and Babcock and Wilcox Canada are gratefully acknowledged. I would like to express my gratitude to my friends and the members of my family whose support in need has been immeasurable; and in particular, I am indebted to my mother as without her unrelenting support this job would have never been possible. Thanks are also due to Mr. J . Baranowski and the rest of the personnel in the Chemical Engineering workshop for constructing the equipment. My thanks also go to Dr. R . J . Kerekes for the use of Pulp and Paper Center facilities, to Dr. J . Hatton for providing access to the screening facilities in P A P R I C A N Vancouver Laboratory and to the C A N F O R Ltd. for supplying the hog fuel samples.  xiv  Chapter 1  Introduction  Canada has faced a costly energy problem since the 1973 oil crisis. According to national energy program statistics, the net oil imports in 1979 were over 200,000 barrels per day. Biomass contributes almost 3% of total energy supply. One objective of the national energy plan was to double the use of forest biomass by 1990 and to triple it by the end of the century [1]. A Canadian energy review in 1987 [2] indicated that hog fuel and pulping liquor contributed up to 6% of the total energy in Canada in 1985. This corresponds to 18.2% and 49.2% of the total industrial energy used in, respectively, Canada and British Columbia (Tables 1.1 and 1.2).  The study also showed that in 1984, 8% of the total  Canadian energy demand was supplied by renewable resources.  The Canadian pulp and  paper industry reduced the amount of purchased energy, which increased in cost from  Table 1.1: End Use Energy Demand in Canada in 1985 Sector Residential Commercial Industrial Transportation Other Total  Energy Petajoules 1275 850 2210 1700 765 6800  1  % Total 18.75 12.5 32.5 25.0 11.25 100.0  Chapter  1.  2  Introduction  Table 1.2: End Use Industrial Energy Demand 'in Petajoules) in 1985 Pulp &; Paper Region Hog Fuel Other Total Other Industrial & Pulping Liquor 402.2 Canada 344.8 1464 2210 British Columbia 198.8 85.2 119.5 403.5  0.72 to 5.33 $/GJ, by 28% from 18.5 to 13.2 GJ per tonne of product between 1972 and 1985 [3]. According to Christenson [4], wood residues can be classified into three categories: logging and  log handling, wood products manufacturing, and unharvested.  Hog fuel, which  typically has a moisture content of 50-70% wet basis, consists of the first two categories; the third category, which is the largest, is not used. In a study done on 79 sawmills in Oregon and California [5], it was reported that wood residues approximate 50-60% by volume of the logs processed for production of finished lumber. These residues include sawdust, shavings, bark, and coarse residues (i.e. slabs, edgings, sawmill trim, planter trim) and according to Resch [6] can be respectively broken down to 13.4%, 9.7%, 11.5% and 26.0% of the volume of a log. According to Moore [5], these residues, either are sold to:  1. pulpmills for pulp production, particle board industries, wood fuel industries, or agricultural industries for cattle bedding and landscaping purposes. otherwise they are: 2. burned in the incinerators, dumped in landfills, or used in the plant as a fuel in wood- fired boilers.  Chapter  1.  3  Introduction  Table 1.3: Heat Contents and Typical Efficiencies of Fuels Type of Fuel Unit Heat Content Cost" Cost" Typical $/unit $/GJ Efficiency GJ/unit Heavy fuel oil (#6 Oil ) m 108.21 2.60 41.6 80% Light fuel oil (#2 Oil ) m 39.1 216.00 5.52 75% Natural gas m 0.037 70% 0.10 ' 2.70 Steam coal mt 29.84 70.38 2.36 65% Wood (dry hardwood) mt dry 19.9 65% Douglas fir sawdust mt dry 20.8 66% Western hemlock sawdust mt dry 19.4 58% 23.4 Douglas fir bark mt dry 67% Western hemlock bark mt dry 22.7 10.00 0.44 66% Electricity kWh 0.0036 0.039 10.83 95% 3  3  3  6  c  c  "Average reported [9] values for 1988. ^Metric tonne. Reported [11] value for 1985. c  This study [5] indicates that, with the exception of coarse residues, a good portion of the residues (50% of sawdust and 80% of bark and any unused shavings) are used as a fuel within the plant. The survey shows that almost all the coarse residues and shavings are utilized; however, there is a need for a system, a dryer or an expedient hog fuel boiler, to utilize the unused sawdust and bark. Bridie [7] suggests that among all different types of wood fuels, bark is the least preferred due to its high silicon content (5.23% dry basis) which gives rise to slag formation and hence a need for the furnace to be cleaned out more regularly. The heating value of wood per unit weight is less than that of fossil fuels. Approximate values are reported by Kelleher [8] and by Resch [6] and shown in Table 1.3. Therefore, based on average higher heating value of 21.2 MJ per kg. dry wood, the heat content of 1 ton of moist wood (50% by weight moisture on a wet basis) equals one barrel of bunker  Chapter  1.  4  Introduction  C oil when utilized for steam production. Wood fired boilers are less efficient (65%) than both natural gas (70%) and oil fired (80%) boilers. However, due to the comparativelylower cost of wood fuel, for the production of the same amount of heat, the fuel cost with wood would be approximately l/5th of that with fossil fuels [10].  The cost of  heavy fuel oils which is generally utilized by coastal forest industries was reported, by Canadian Forestry Service [11], to be $170 /m ($27/Barrel) in 1983 and also speculated 1  3  to reach a value ranging from $186.90 to $247.70 per cubic meter by 2004. The study also indicated an average price of $10 per unit volume for hog fuel in B.C. coastal mills 2  in 1985. The above prices would result in an energy cost of $4.25 and $0.50 per gigajoule of energy respectively for heavy fuel oil and hog fuel. The authors [11] calculated an energy equivalent of hog fuel which is defined as "the maximum imputed value of hog fuel assuming it is displacing heavy fuel oil after taking into account differences in boiler efficiencies and capital charges". They determined that, excluding the capital costs, the energy equivalent value was $45 per volumetric unit of hog fuel in 1984, which would increase to an average value of $60 per unit of the fuel by 1990. If the capital costs were included, the 1984 value would drop to $26 per volumetric unit. It should be noted that the speculations for energy equivalent of hog fuel were overpredicted as is indicated in Table 1.3 the fossil fuel prices have been reduced since 1983.  In addition to wood being an inexpensive renewable source, the use of wood as an energy source has positive environmental effects; it reduces the disposal problem for logging operations and generates lower quantities of both SO2 and nitrogen oxides (80% less) compared to conventional fuels [12, 13, 14]. However, there are disadvantages associated with the use of wood waste as a fuel [12, 13] due to: Prices are in Canadian dollars 200 ft of bulk volume = 2 m of solid volume = 2 mt of wet wood based on 60% wet basis moisture content 1  2  3  3  Chapter  1.  Introduction  5  • a need for greater expertise in operating combustion units and a relatively higher rate of maintenance, • greater fuel processing and handling requirements, • production of particulate emissions, • and production of non-hazardous cinders, clinkers and ash which, however, are not as bulky as those from coal combustion.  The  major use of wood fuel in the pulp and paper industry is to feed hog fuel boilers.  Absence of impurities and foreign material, and uniformity in size and moisture content, reduce the handling problems and facilitate the optimization of boiler performance [15]. Therefore, ideally hog fuel should be processed and homogenized prior to its use; however, economic considerations often preclude this step. The amount of water that must be evaporated from the wet hog fuel limits the rate that wood fuel can be burned in a wood waste fired boiler. The boiler thermal efficiency also decreases as the wood fuel moisture content increases. A study done by Bursey [16] indicates that the boiler efficiency using bark decreases by one third (from 77% to 59%) as the fuel moisture content increases from 30% to 65% (wet basis). Fuel which is dryer, having a higher heating value, increases the boiler capacity and facilitates firing and emissions control. The problems associated with high moisture-content hog fuel can be alleviated by either installing an external dryer system as a retrofit to an existing boiler or by re-building the boiler and changing the method of burning to one which can utilize wood fuel up to 65-70% (wet basis) moisture content without the use of costly auxiliary fossil fuels. Drying technology and the drying of porous materials are not new [17]. Many experimental and numerical studies have been done on drying of wood, particularly lumber and  Chapter  1.  Introduction  6  veneer. A few studies have been made for small uniformly sized particles. However, there is virtually no quantitative scientifically-based design information on the drying of hog fuel sized particles. As Blackwell and MacCallum [18] suggest: "more specific scientific information is needed on the drying rates of hog fuel sized particles". The objective of this research program was therefore to investigate the drying rate of hog fuel and the factors affecting such a process. By developing the knowledge of the kinetics of the hog fuel drying process, design of either external dryers or hog fuel boilers themselves could possibly be improved. Nonhebel and Moss [19] have mentioned 34 parameters involved in a drying process and have categorized them with respect to the following four different groups:  • properties of the drying medium • properties of the solid • properties of solid-liquid system • the heat transfer properties of the system  In hog fuel drying the last two categories are not very controllable; therefore, it is the intention to investigate the drying rate of hog fuel with respect to both the moisture content and the size of the fuel feed, and to the characteristics of the drying medium such as source of heat, velocity, temperature, and humidity. Since the study is geared toward the application of inclined grate hog fuel boilers, the drying process was examined in a packed bed which can simulate the slow moving bed of these boilers.  Chapter 2  Literature Review  2.1  W o o d as a Fuel  Ultimate analysis of dry wood and bark indicates that on average they consist of 50% carbon, 42% oxygen, 6% hydrogen and 2% ash by weight.. Burning of wood can be considered to consist of three processes [20]: dehydration, pyrolysis, and combustion of volatiles and free carbon. Dehydration refers to evaporation of water, which is an endothermic process. Decomposition of wood into gaseous, liquid and solid components is called pyrolysis. This is also an endothermic process during the initial stages. Exothermic oxidation of these volatile species and of the solid char which is mainly fixed carbon, is called combustion. As reported by Browne [21], thermal decomposition of wood starts above temperatures as low as 95°C. However, ignition does not occur at temperatures below 220°C [22] as determined by thermogravimetric methods and shown in Figure 2.1. Duration of heating time and type of the environment are also controlling factors for the decomposition process. Meyer has reported [25] that decomposition proceeds faster in the presence of oxygen and air than in the presence of inert gases. His experimental data indicate that even though the activation energies in steam are low, the decomposition rate decreases with increases in the steam content of the gas since drying is delayed and hence the length of the decomposition period is reduced. Browne [21] indicates a wide range of  7  Chapter  2.  Literature  8  Review  Induced Sustained Spontaneous ignition burning ignition  500  270 300  400  -D-  500  (90%) •ignition  LI6NIN  (io%) (50%) iHEMICELLULOScT -potential ignition •ignition  CELLULOSE  Figure 2.1: Combustion Zones and Degradation of Wood Constituents in Oxygen as Determined by Thermogravimetry (Courtesy of F. C. Beall [21]) variation for the spontaneous ignition temperature; however, Fons [23] suggests a value of 340°C based on the particle surface temperature. His experimental data on 13.3 cm long wood cylinders of 9.5 mm in diameter heated in an electrical furnace indicate a nine-fold increase in the ignition time for a 27% drop in the furnace temperature. Combustion analysis [24] predicts that to some extent combustion of volatiles and chars take place simultaneously and the temperature effect is distinct during the former but not in case of the latter. Wood composition, size and moisture content are rate determining parameters in combustion of wood in air. Seventy to eighty percent of wood and bark consists of volatile material with the remainder as fixed carbon and ash; therefore the burning process mainly takes place in the gaseous state [26]. Compared to wood, bark usually has 10% more fixed carbon which burns in solid state at a lower rate and needs a higher residence time [27]. The smaller the size of the particle the larger would be the total exposed surface per  Chapter  2.  Literature  Review  9  unit weight and the higher would be the rate of combustion. Analysis of wood combustion in a stoker-type furnace at 1100 K [24], suggests that the reactivity of 10 mm wood specimens drops by 6% as the size is doubled. Smith [27] considers moisture content to be the critical parameter influencing the following areas:  • fuel handling and transport • net higher heating value • furnace design • combustion rate • handling of combustion process • particulate emissions • boiler efficiency  The heating value (as-received or wet basis) of wet fuel is lower than that of dry fuel since some energy is needed to evaporate the water. An increase in the moisture content of the wood typically necessitates an increase in the amount of excess air (drying gas) to ensure complete evaporation. Higher excess air would decrease boiler efficiency and increase the flue gas volume. High volumes of flue gas reduce the combustion temperature and hence the combustion rate [28, 41]. Higher temperatures result in a more complete combustion and reduce particulate emissions [29]. Increasing the excess air, at a given combustion temperature, also increases the formation of nitrogen oxides. According to McDermott et al. [30], to have a stable combustion of hog fuel, a furnace temperature of about 1000°C to 1100°C is needed. To achieve this condition, the fuel  Chapter  2.  Literature  Review  10  moisture content should not exceed 55% to 59% (wet basis), respectively, for unheated [31] or preheated [30] air. Therefore, when burning hog fuel with a wet basis moisture content of 58% or greater in a conventional furnace (static pile burning), auxiliary fuel must be utilized to sustain combustion.  2.2  Hog Fuel Boiler Systems  Fluidized bed, suspension, fuel bed and spreader stoker (which is a combination of the last two) firing methods are normally used for combustion of solid fuels [32]. In fuel bed firing all of the wood burns on a grate while in spreader stoker operation a portion of the fuel burns in suspension and the rest burns on a grate. The feed is introduced by gravity in the case of the former, and by revolving paddles in the case of the latter. The grates mostly employed in North American hog fuel boilers are horizontal with no, or extremely slow, movement (static grates) on which the three processes of drying, pyrolysis and combustion occur. In both cases mal-distribution of the fuel on the grate and bed-blanketting due to introduction of wet hog fuel restricts the performance of the furnace. The design of the commonly used travelling grate spreader stoker may be modified by addition of arches to reflect radiation and expedite the burning process. The rearrangement of both the wood fuel feeding system and the air inlet into the furnace can also be used as means to satisfy a particular plant's need. However, it was demonstrated that during normal day to day operation such a boiler can handle wood with a maximum of up to 60% wet basis moisture content in the absence of auxiliary fuel [33]. This limit is often exceeded as hog fuel which mainly consists of bark and sapwood, may contain moisture  2. Literature  Chapter  Review  11  contents up to 75%. Therefore, changes in the method of burning or predrying of hog fuel are usually necessary to increase the boiler performance and eliminate auxiliary fuel support.  2.2.1  Predrying H o g Fuel  The first alternative to alleviate the moisture problem is the use of external dryers. Rotary and flash dryers (hot hog, cascade, flash tube) use hot air or flue gas as a drying medium and are classified [34] to be applicable for use in drying hog fuel. In a rotary dryer, the drying process takes place through direct contact and co-current flow of hot flue gas and hog fuel-sized wet particles. The flash drying principle is based on the relatively short exposure of small-sized wet particles to a hot high velocity gas. To reduce the fire hazard a combination of flash and rotary dryer may be used [35]. Here the wet particles are first introduced to a hot and low retention time flash dryer for the removal of surface moisture, and subsequently to a relatively lower temperature and lengthy dwell time rotary dryer. In a hot conveyor system, the drying process takes place through contact of wet material located on a bin and steam heated ambient air or gas. The flow of gas in conjunction with slow movement or vibration of the conveyor result influidizationof material, enhancement of heat transfer and drying rates, and reduction of fire hazards due to the lower required temperature and retention time. Steam dryers recently used for drying of hog fuel [36, 37] use steam both as a transferring and a heating medium. The dryer consists of a tube and shell heat exchanger based on the counter-current flow of high pressure steam in the shell and low pressure steam conveying the wet wood in the tube. In addition to producing a fuel of lower moisture content, the ability of this system both to utilize extraction steam from a power generating turbine as  Chapter  2.  Literature  Review  12  an indirect heating medium, and to recover the latent heat of evaporated moisture which is transferred to the low pressure steam, makes this process advantageous [36, 38]. The start up and shut down procedures are also facilitated for steam dryers which require a shorter residence time of material in the dryer [38]. The advantages, disadvantages and the application of superheated steam to drying systems is discussed in detail by Beeby and Potter [39]. Predrying of hog fuel is justified if the heat used in the dryer cannot be of any use in the boiler. Even under these conditions predrying might not always be economically feasible as both the boiler and the dryer efficiencies are affected by the extent of drying. As the fuel moisture content is reduced, the thermal efficiency increases for the former and decreases in case of the latter; therefore, as Smith [27] has shown, there is an optimum amount of moisture which can be removed before the gain in the efficiency of the boiler is counter-balanced by the fall in efficiency of the dryer.  2.2.2  Change in the Method of Burning  Inclined grates were developed in Europe and in contrast to the situation with horizontal grates, it has been proven that they can burn wet hog fuel with moisture content in excess of 65% with no auxiliary fuel support [40]. In an inclined bed or a so-called dynamic fuel bed, the fuel is introduced through chutes or screws on the upper end of the grate and the three stages of burning take place on successive areas of the grate[41]. As the wood gets drier the angle of repose becomes smaller resulting in an easier flow of the material. Therefore, the angle of the sloping grate is designed to gradually decrease to provide a controlled and smooth movement of the fuel. The last stage of the burning can be accomplished on reciprocating grates which provide automatic removal of the ash  Chapter  2.  Literature  13  Review  Dump Grate  Figure 2.2: Sloping/Reciprocating Grate, Jagerlund [38] (Figure  2.2). In the absence of a reciprocating grate a reverse grate with automatic  mechanical scrapers is usually installed at the end of the fixed sloping grate to discharge the ash (Figure 2.3). Use of both drying and burn-out refractory arches facilitates the entire burning process by re-radiation and eliminates the use of auxiliary fuel for burning wood with 65-70% moisture content [41, 42, 43]. The smooth fuel entry to the furnace and even distribution of fuel on the grate reduces the suspension burning, provides complete burn-out of carbon, alleviates the problem of fly ash carry over and results in a more efficient combustion [42, 43]. In addition, according to MacCallum [42], these grates are highly reliable and low in cleaning and maintenance cost.  Chapter  2.  Literature  14  Review  Fuel  Drying Zone  -Burn-out Arch  and Burning Zone  Ash Dumping Zone Ash Rake  Final Burn-out Zone  F i g u r e 2.3: A B a r e t u b e G r a t e F u r n a c e w i t h a Reverse G r a t e , J a g e r l u n d  2.3  [38]  Structure of the W o o d  W o o d is a h y g r o s c o p i c , a n i s o t r o p i c , p o r o u s b u t n o t very p e r m e a b l e m a t e r i a l w h i c h m a i n l y consists of cells m a d e o f c e l l u l o s e , h e m i c e l l u l o s e a n d l i g n i n w i t h a h o l l o w a i r space, l u m e n , i n s i d e t h e m ( F i g u r e 2.4). T h e cell w a l l c o n t a i n s m i c r o v o i d s h a v i n g less t h a n 2 % of t o t a l cell v o l u m e [44]. W h e n d r y w o o d is p l a c e d i n a s t r e a m of h u m i d air, w a t e r v a p o r molecules strike the s o l i d surface, c o n d e n s e a n d release heat o f a d s o r p t i o n  [45]. A t a r e l a t i v e v a p o r  pressure ( p a r t i a l pressure o f the w a t e r v a p o r / v a p o r pressure o f t h e w a t e r at t h e d r y b u l b t e m p e r a t u r e ) of 0.995 t h e m i c r o v o i d s i n t h e cell w a l l b e c o m e c o m p l e t e l y s a t u r a t e d w i t h w a t e r [44].  W a t e r exists as l i q u i d i n the m i c r o v o i d s d u e t o f o r m a t i o n o f h y d r o g e n b o n d s  between  Chapter  2.  Literature  Review  15  G r o s s structure of a typical h a r d w o o d . radial surface, and T G is the tangential surface. elements are separated by scalariform and thick walls. tween the cells.  Plane T T  is the cross section.  RR  is the  T h e vessels or pores are indicated by P, and the  perforation plates, S C .  Pits in the walls of the fibers and vessels. K . The wood rays are indicated at W R .  AR  T h e fibers. F. have small caviiies provide  for the  flow  o f liquid be-  indicates one annual ring.  wood (springwood) is designated S. while the latewood (summerwood)  is S M .  The  lamella is located at M L . (Courtesy o f U . S . D . A . Forest Service.)  Figure 2.4: Structure of a Typical Hardwood [49]  T h e earlytrue  middle  Chapter  2.  Literature  Review  16  water molecules and hydroxyl groups of cellulose and hemicellulose [46]. This results in a wood moisture content of 28-30% (dry basis) and is referred to as the fiber saturation point. An increase in the relative vapor pressure (up to 1) and further capillary condensation will result in a complete take up of water by capillaries (up to 150% of the weight of wood) and a wetted surface [46]. The moisture content of wood below and above the fibre saturation point is, respectively, called bound (hygroscopic or sorbed) and unbound (free) water [47]. The moisture content in the sorption region also depends on whether the equilibrium is achieved through adsorption or desorption; there is a hysteresis effect. At a given relative vapor pressure the adsorption moisture content is always lower than the desorption one since in case of former the hydroxyl groups of wood substance are drawn closely to each other reducing the free sites for formation of hydrogen bonds between water and hydroxyl groups [44].  2.4  Moisture Transport in W o o d  Wood is a hygroscopic capillary porous material with a complex cellular-capillary stucture which is dimensionally unstable upon moisture removal [48]. The communication between the adjacent cell cavities takes place through pit membranes on the cell walls. As Siau [49] describes, pits are openings on the walls with chamber diameter ranging from 6 to 30 fim. In the soft woods, the relatively thicker membrane at the centre of the chamber, which is called the torus, has no or possibly very small opening. Diameter of the torus is about one-half to one-third of the chamber diameter and is connected to the periphery of the chamber by strands of microfibrils, known as margo. The size of aperture to the chamber is about one-half of the torus diameter. Hardwood pit membranes consist only of the strands of the microfibrils and there is no torus present.  Chapter  2.  Literature  Review  17  According to Stamm [50] the mechanism of movement of free water in the wood depends on both the size of pit membrane pores and the air content of the cell cavities. He suggests that in the case of fully water-filled cavities, the liquid evaporates from cut cavities and moves outward as a vapour until the air-water menisci reach pit membrane pores connecting the cut cavities to the uncut cavities. Water can evaporate from a pit membrane of pore size greater than 42 fim. If none of the pit membrane pores are that large, the capillary tension would exceed the compressive strength of the cell wall which will collapse resulting in flow of free water. However, if the cell cavities contain air bubbles larger than 42 fim, the bubbles will expand forcing the free water out without collapse of the wood stucture. These steps, shown in Figure 2.5, were illustrated by Skarr and presented by Siau [51]. It should also be mentioned that the collapse of the cell wall is not very likely due to the presence of either air bubbles or large enough pit membrane pores [50]. Spolek and Plumb [53] have also proposed a mechanism for the movement of water under capillary forces. Figure 2.6 shows that water first evaporates from the cylindrical section of the cell cavities and to a greater extent from the ones closer to the surface due to a more rapid drying process. Therefore, the air water miniscus recedes into a tapered zone which has a smaller radius and the liquid there is under greater tension as the distance to the outside surface increases. This would result in movement of water from within the wood toward the surface. Since wood has a complex structure, the movement of moisture or water vapor within the wood and the behaviour of the standard drying rate curve versus moisture content can be more easily described through simple models used for ideal moist solids, which are nonhygroscopic and highly capillary porous (pore radius > l//m) materials, where moisture  Chapter  2. Literature  Review  18  Chapter  2.  Literature  19  Review  L f / / / / / / 7~r  rl  «W*W"  4i  GAS  7—7—77,  Figure 2.6: Movement of Free Water in Tangential Direction Due to Capillarity (Spolek and Plum) [51] always exerts its full pressure. Keey [48] has used the following simplified mechanism of two-pore system:  • This simple process [48] is based on the movement of water within two joined capillaries of unequal diameter. During the course of drying, first the surface moisture of a completely sodden material is driven off under a constant rate of evaporation. Upon removal of the surface moisture the evaporation of water, brought to the surface by capillary action, takes place from a wider pore with a constant moisture level as a result of being continuously fed by the narrower pore. Although the rate of evaporation during this period is not constant, according to definition, the region from the start of the drying process up to the onset of withdrawal of the larger miniscus within the solid is called the constant-rate period. The constant-rate period is followed by a so called falling rate period which is controlled by diffusion and during which the rate of evaporation drops markedly. The average moisture content of the body at which the transition between these two regions occur is called the critical moisture content. Figure 2.7 represents the drying process in  Chapter  2.  Literature  20  Review  A CD  -t-  o cn  R  i\  CD >  !  / ' One-pore //evaporation  CD  / /  rr  1  i i  j •  ! Two-pore evaporation  !  0  Relative  filling  of  pores  .0  Superficial moisture  Figure 2.7: Drying out of a Two-Pore System, Keey [46] terms of relative drying rate (instantaneous drying rate/maximum drying rate) as a function relative filling of the pores.  In removal of moisture from a piece of water-saturated wood, first the saturated surface moisture and then a portion of the free (capillary) water is evaporated. In this region, the constant rate of evaporation is controlled by heat transfer and the saturated surface of the wood remains at the wet bulb temperature of the drying medium. When the rate of evaporation from the surface becomes higher than the rate at which moisture is brought to the surface, the falling rate period begins. The fibre saturation point and critical moisture content would coincide if wood were made of a highly porous material. However, due to the complex structure of the wood, the movement of free water within the wood is restricted. This results both in a higher value for the critical moisture content than for the fibre saturation point, and in a falling rate region which is controlled by  Chapter  2.  Literature  21  Review  w O  S  z  F i g u r e 2.8: C o n c e n t r a t i o n G r a d i e n t as a F u n c t i o n of the D i f f u s i o n a l  Path  c a p i l l a r y , diffusion or i n t e r n a l l i q u i d mass transfer.  2.5  Vapour Transport within a Drying Medium  If a p a r t i c l e o f w o o d is b e i n g d r i e d i n a gas, t h e v a p o u r b r o u g h t d i f f u s i o n a l processes or e v a p o r a t e d  to the surface  by  at the surface w i l l diffuse t h r o u g h t h e mass transfer  b o u n d a r y l a y e r s u r r o u n d i n g the p a r t i c l e to the b u l k of the d r y i n g gas, due to the h u m i d i t y gradient (Figure  2.8). T h e f l u x is d e s c r i b e d t h r o u g h F i c k ' s first l a w :  J  where  w  =  -D WG'  dC  w  (2.1)  dz  Jw  = diffusional flux ( k m o l / m - s )  DWG  = diffusivity of w a t e r v a p o u r t h r o u g h gas  Cw  = concentration of water vapour ( k m o l / m )  2  (m /s) 2  3  Chapter 2. Literature  22  Review  = distance along diffusional path (m)  The total efflux of vapour with respect to the surface of the solid would be the sum of diffusional flux and the bulk motion: N  = Jw + ^ ( N  w  W  (2.2)  + N) G  or ^  where  ~ — 1i  w  1  _  kML— C  V- ' 6  Nw = flux of mass transfer of water vapour (kmol/m -s) 2  NG  = flux of mass transfer of gas (kmol/m -s)  C  = total molar concentration of gas stream (kmol/m )  2  3  NQ is usually negligible when diffusion takes place at right angles to the surface and within a short diffusional path [48]; therefore, the molal flux of vapour would become:  c  1  Substituting for Jw would yield: N  = Z ^ S L ^ L  W  ( 2  .5)  o  Rearranging and applying Dalton's law to the above equation, and integrating over the thickness of the boundary layer, S, would result in: N  w  £°™ f±zSl  = [  ]]n  1  *  J  (1-Yi')  (2.6) V  '  Chapter 2.  Literature  23  Review  and N  where  =  w  M  CD WG  (RM  w  + Y) 1  (RM  + Y)  ln  ( 2  2  Y'  = mole fraction of water vapour ( ^-)  8  = mass transfer boundary layer thickness (m)  Y  = kg water vapour/kg dry gas  Nw  = flux of water vapour mass transfer (kg/m -s)  -  ? )  £  2  Mw, MQ = molecular weights of water and gas, respectively (kg/kmol) RM  = ratio of molecular weights  1,2  = represent properties at the start and end of diffusion path  (MW/MQ)  The term in the square bracket is an "F-type" [48] mass transfer coefficient which is minutely dependent upon humidity conditions. Manipulating the logarithmic term and multiplying and dividing Equation 2.7 by (RM + Y )(Y -Y ) 1  N  w  =  FM  RM G  RM  or  1  + Yi  (Yi - Y )  2  yields:  (Yi - Y ) 2  (2.8)  3  KY  4,  (2.9)  NwHFM^.Z^^-Y,) therefore, Nw =  K 4\Y -Y ) Y  1  2  (2.10)  and ky = Ky-<f>  (2.11)  Chapter  2.  Literature  24  Review  Y\ — Y = humidity potential  where  2  4>  = humidity potential coefficient  Ky  = humidity independent mass transfer coefficient (kg/m -s-( ^^™ ))  ky  = humidity dependent mass transfer coefficient (kg/m -s-("^^" ' ))  2  2  r  aler  1 er  As is indicated in Equation 2.8, <f>\ is almost one for very small humidity levels and </> 2  also approaches unity at low values of humidity potential. Under these conditions the mass transfer flux is a linear function of humidity potential; therefore, for mild drying conditions, it is customary to use the limiting value of: k  Y  ~ F.M  G  (2.12)  For more intense drying conditions, Equation 2.8 is used to express the flux of mass transfer.  2.6  Drying  Theories  The generalized system of heat and mass transfer equations is described by Luikov [54] to explain drying of porous solids during the falling rate period. However, due to problems in solving such a complex system, the transfer of mass in the presence of the temperature gradient is usually dealt with through simplified and less abstract theories. As reported by Kisakiirek and Gebizlioglu [55], among the different theoretical models applied to solve the drying problem only diffusion, capillary and moving boundary theories have been able to rather successfully explain the drying mechanism.  Chapter  2.6.1  2.  Literature  25  Review  Diffusion Theory  M a s s transfer m o t i o n [47].  takes p l a c e t h r o u g h m o l e c u l a r diffusion  i n fluids w i t h n o or very slow  M o l e c u l a r diffusion o c c u r s w i t h i n a p h a s e or b e t w e e n phases o f a s y s t e m  w h e r e t h e r m o d y n a m i c e q u i l i b r i u m does not p r e v a i l . T h e d r i v i n g force for the  diffusion  process is the c h e m i c a l p o t e n t i a l , /x;, w h i c h is defined b y the f o l l o w i n g r e l a t i o n s h i p [56]:  w = (§=r) where  (- ) 2 13  Gj, = G i b b s f u n c t i o n ( k J ) rii = k m o l e s of species i at a n y i n s t a n t  W i t h i n a p h a s e h o w e v e r , the c h e m i c a l p o t e n t i a l g r a d i e n t centration gradient.  c a n be r e p l a c e d b y the con-  I n m u l t i p h a s e systems, c o n c e n t r a t i o n gradient c a n also be used as  a m e a s u r e o f d r i v i n g force since i t is c u s t o m a r y t o d e a l w i t h diffusional forces i n each phase separately  [47]. S h e r w o o d [57] a n d G i U i l a n d [58] have a s s u m e d the diffusion of l i q -  u i d m o i s t u r e t h r o u g h a s o l i d p o r o u s m e d i u m to be a result of c o n c e n t r a t i o n g r a d i e n t a n d p r e d i c t e d u n s t e a d y c o n c e n t r a t i o n of w a t e r t h r o u g h F i c k ' s second l a w of diffusion.  There  was a g o o d agreement b e t w e e n the e x p e r i m e n t a l d a t a a n d t h e o r e t i c a l m o d e l s b o t h w h e n the effect of m o i s t u r e content  is i n c o r p o r a t e d i n the e v a l u a t i o n of diffusion  a n d at m o i s t u r e contents b e l o w the fibre s a t u r a t i o n p o i n t .  coefficient,  Chapter  2.6.2  2.  Literature  26  Review  Capillary T h e o r y  The capillary theory considers the flow of liquid moisture toward the surface through the capillaries due to solid-liquid molecular attraction and subsequent evaporation of water at the surface.  A model was originally developed by Krischer [59] who described the  mechanism of liquid transport with the following equation analogous to the Fickian law:  N = P.D^  where  N  = flux of mass transfer  p  = density of dry wood ( k g / m )  (2.14)  (kg/m -s) 2  3  a  D  = apparent moisture diffusivity through wet material ( m / s )  M  = moisture content (kg water/kg dry wood)  x  = mass transfer path (m)  a  2  Another model developed by Comstock [52] and used by Spolek and Plumb [53] was based on capillary transport due to capillary suction potential and used Darcy's law, which was also suggested by Siau [51] to be a good flow mechanism for wood, to predict the movement of moisture in wood.  2.6.3  Moving Boundary Theory  In the moving boundary model, the evaporation of water takes place at a moving interface which divides the solid into wet and dry zones. T h e movement of moisture is considered to be due to capillary action in the wet zone and vapor diffusion in the dry zone. Keey [48]  Chapter  2.  Literature  27  Review  has described the rate of evaporation by Equation 2.10 and used the following relationship to describe humidity-independent mass transfer coefficients within the porous body:  = F„M  K„ Y  D  v  = ^.M  G  (2.15)  G  = ^  (2.16)  = (|)  where  £ D  (2-17)  = diffusional path or depth of recession from surface (m) = vapor diffusivity in the dried material ( m / s ) 2  v  ip  = porosity of the solid ( m / m )  £  = tortuosity  fiD  = diffusion resistance  ss  = represent properties during subsurface evaporation  3  3  coefficient  B y considering the additive property of mass transfer gradients within the dry pores and across the boundary layer:  (Y„  - Y ) = (Y . - Y.) + (Y. - Y ) db  t  db  (2.18)  or N K-<t>ss  N  N r f — KY .<t> s K .<t>. ta  a  Ya  the following overall mass transfer coefficient is derived:  -, s (2.19) nin  Chapter  where  2.  Literature  28  Review  N  = flux of evaporation (kg/m -s)  Ky  = humidity-independent mass transfer coefficient (kg/m -s)  4>  = humidity potential coefficient  Y  = dry basis absolute gas humidity  K  = overall mass transfer coefficient (kg/m -s)  BIM  = mass transfer Biot No., ratio of the internal resistance of dry solid  2  2  2  to that of mass transfer boundary layer based on depth of recession ss, s, db = represent properties at the subsurface, surface and the bulk of gas, respectively  According to Fulford [60], the mathematical treatment of the diffusion theory is relatively easier than the capillary and moving boundary theories; however, the theoretical results are not in a very close agreement with the experimental ones. The latter models have, however, resulted in a closer prediction of the experimental data. Numerical solution to a system of differential equations [53] which is based on both capillary and diffusive processes and also mathematical solution to a theoretical model solely based on the capillary mechanism [55] are indicative of the presence of a complex mechanism during the falling rate period.  The results indicated that the capillary motion controls the  movement of moisture within the wood when the free liquid exists, while diffusion is the controlling factor upon depletion of the free moisture.  Chapter 2.  2.7  Literature  29  Review  Characteristic D r y i n g Curve  As is represented in Figure 2.9 the movement of moisture within porous solids can be described by the following [61]:  • The movement of the liquid water is accomplished by capillarity and the moisture is referred to as being in funicular state. As the drying process proceeds, the water in the originally full pores is being replaced by air pockets. • When the water withdraws to the waist of the pores and so called water bridges are formed, the moisture in a liquid state either creeps toward the surface along the capillary walls or reaches the surface through successive evaporations and condensations between liquid bridges. This is the start of the falling rate period where the capilliary motion ceases and the moisture is in the so-called pendular state. • The moisture flows as a vapour upon evaporation of the liquid bridges. The solid is left in hygrothermal equilibrium with its surroundings.  The depth of recession of water in the pores is a function of the fraction of the water rings remaining in the pores. As Suzuki [62] suggests, the depth does not exceed one pore layer depth until 80% of the moisture is removed. Morgan and Yerazunis [63] related the moisture efflux to the location of the evaporative plane through the following equation: N =  N  (2.21)  K .cf>.(Y -Y )  (2.22)  Y  max  where  K .<l>.(Y -Y ).f(C,Bi' )  Y  tu  aa  M  db  db  flux of evaporation (kg/m -s) 2  Chapter 2.  Literature  Stage I  30  Review  Stage 2 Capillary flow  Stage 3  Stage 4  Evaporation-condensation  Vapour flow  Drying  »»-  Figure 2.9: Moisture Transport in Drying a Porous Material, Keey [46] = maximum flux of evaporation (kg/m -s)  N 1  2  * max  Ky  = humidity independent mass transfer coefficient (kg/m -s) 2  = humidity potential coefficient = dry basis abs. humidity at adia. sat. & dry bulb temp.  f(C,Bi' ) M  c  = relative drying rate, representing the effect of the material = relative depth of evaporative plane, where £ = 1 represents evaporation at the surface  Bi'  M  = mass transfer Biot No. based on solid thickness  The comparison between the experimental data and Equations 2.21 and 2.22 also indicated that the evaporative plane remains close to the surface until 80% of the water is  2.  Chapter  Literature  31  Review  r e m o v e d [63]; therefore, suggesting t h a t for a g i v e n m a t e r i a l , t h e n o r m a l i z e d d r y i n g r a t e f =  N N 1  =  * max  R  (2.23)  iL„ max  Kj x  is a f u n c t i o n o f the extent of d r y i n g or, i n o t h e r w o r d s , a c h a r a c t e r i s t i c m o i s t u r e c o n t e n t , $ . T h i s p a r a m e t e r is d e n n e d for n o n - h y g r o s c o p i c m a t e r i a l s [64] as  M $ = —  (2.24)  a n d , for h y g r o s c o p i c b o d i e s b y :  M $ = T,  where M , M , CT  and M  e  represent,  M  e  TT  2  respectively, t h e i n s t a n t a n e o u s ,  -  2  5  critical, and equilib-  r i u m average d r y - b a s i s m o i s t u r e content of the b o d y . Therefore, for a m a t e r i a l u n c h a n g e d i n f o r m / = / ( $ ) . A p l o t of r e l a t i v e d r y i n g rate versus c h a r a c t e r i s t i c m o i s t u r e c o n t e n t is c a l l e d the c h a r a c t e r i s t i c d r y i n g curve. A s S c h l i i n d e r suggests [65], i n d u s t r i a l dryers are u s u a l l y designed b a s e d o n the e x p e r i m e n t a l d a t a o b t a i n e d f r o m l a b o r a t o r y - s c a l e  batch  tests p r e s e n t i n g the d r y i n g rate as a f u n c t i o n of m o i s t u r e content. Therefore, t h e d e s i g n a n d s i z i n g of large-scale dryers w i l l be f a c i l i t a t e d i f a c h a r a c t e r i s t i c d r y i n g c u r v e is o b t a i n e d for a d r y i n g process. H o w e v e v e r , for processes w h e r e the d r y i n g is n o t l i m i t e d b y k i n e t i c s a n d is r a t h e r e q u i l i b r i u m - l i m i t e d , s u c h as d r y i n g of disperse systems or s y s t e m s w i t h v e r y s m a l l or v e r y large mass transfer coefficients [66], t h i s does n o t h o l d .  2.8  Batch D r y i n g i n a Packed B e d  D u r i n g the b a t c h d r y i n g process i n a p a c k e d b e d , various d r y i n g zones are f o r m e d a l o n g t h e b e d height ( F i g u r e 2.10(a)).  T h e solid temperature  is i n c r e a s e d as t h e d r y i n g gas  travels a l o n g the c o l u m n . T h e h u m i d i f i c a t i o n process follows as the s o l i d surface t e m p e r a t u r e , T , approaches t h e wet b u l b t e m p e r a t u r e , s  T b, o f t h e d r y i n g gas. I n r e l a t i v e l y deep w  Chapter  2.  Literature  32  Review  beds of solids, the solid temperature and moisture content are non-uniform along the bed height. This would result in two distinct regions of drying, Z < Z , where T„ > T e  wb  and  of heating the solid or of condensation of evaporated moisture, Z > Z , where T < T . e  s  wb  The drying zone, Z , passes through the column as drying proceeds (Figure 2.10(b)). e  This section is called the desorption zone and is subdivided to a zone of drying unbound and one of drying bound moisture. Drying rate is constant and at its maximum while the desorption zone resides within the bed. Condensation of evaporated moisture takes place in the second zone if the drying gas leaving point Z is saturated at the prevailing temperature and pressure. However, for e  unsaturated drying gas at Z , the heat conduction to the solid is taking place at the e  expense of isobaric cooling of the gas out of contact with the fully wetted surface of the solid. For very deep beds, the second zone might contain both a region of heat conduction which is followed by a condensation region resulting in a completely saturated gas exiting the dryer.  2.9  Objectives of this Study  Moisture removal is a necessary step prior to combustion of hog fuel. Irrespective of whether drying occur in an external dryer or on the grate of a hog fuel boiler, an understanding of the drying process is required for intelligent design and operation. Therefore, the objectives of this study were  1. to investigate the effect of different parameters such as: •  Particle thickness (d ) p  Chapter  2.  Literature  Review  ^  33  (a)  zone of drying unbound  moisture  zone of drying bound  heat  conduction  to the  Figure 2.10:  moisture  solid  Batch Drying of Thick Beds of Solids: (a) Drying Zone Resides within the  Bed; (b) Drying Zone Passed through Drying Column  Chapter  2.  Literature  34  Review  H o g fuel i n i t i a l m o i s t u r e content  (M ) 0  B e d d e p t h (L) D r y i n g temperature Gas velocity Gas humidity CO2  (T; ) n  (Vi ) n  (Yi ) n  content of t h e d r y i n g gas  o n the k i n e t i c s o f t h e d r y i n g process d u r i n g the c o n s t a n t a n d the f a l l i n g r a t e p e r i o d s ;  2. to s t u d y heat a n d mass transfer processes d u r i n g t h e c o n s t a n t rate p e r i o d ; 3. to e x a m i n e t h e c o n c e p t o f t h e i n v e r s i o n p o i n t t e m p e r a t u r e  b o t h theoretically a n d  experimentally; 4. to i n v e s t i g a t e the p o s s i b i l i t y of the existence o f b o t h a u n i f i e d c h a r a c t e r i s t i c d r y i n g rate c u r v e a n d a m a t h e m a t i c a l e x p r e s s i o n for / as a f u n c t i o n of $ u s i n g a r e c e d i n g plane model; 5. to e v a l u a t e for h o g fuel t h e a p p l i c a b i l i t y of some d e s i g n e q u a t i o n s for pressure d r o p i n p a c k e d beds; 6. to i n v e s t i g a t e the effect o f t h e above m e n t i o n e d factors o n p a r t i c l e residence t i m e r e q u i r e d for d r y i n g , a n d o n the grate heat release r a t e i n h o g fuel b o i l e r s .  Chapter 3  M e t h o d s and Materials  3.1  Overview  T h e convective drying of wood-waste on a slowly moving bed of hog fuel boilers can very well be simulated in a packed bed (see Page 234)- T h e changes which occur simultaneously in both moisture content and temperature of the wood during this process depend on the drying condition and the nature of the material. T h e apparatus shown in Figure 3.1 was designed to investigate the effect of different factors on the kinetics of drying process.  T h e construction of the unit took place in the workshop of the Department of  Chemical Engineering.  Figure 3.2 shows the flow diagram of the apparatus. T h e study of the relative effect of the nature of the drying medium on the drying process was one of the objectives of this work. Therefore, to cover the range of conditions, the unit was designed to accommodate the use of hot air, flue gas, superheated steam and a mixture of them as drying gases with very little modification.  To minimize corrosion, the unit was built mainly of stainless  steel for hot streams and copper tubing for cold ones, except that several large mild steel valves were used rather than stainless steel due to cost reasons. T h e main items of  35  Chapter 3.  Methods and Materials  Figure 3.1: Photograph of the Apparatus  36  Chapter  3. Methods  and  2  Materials  <r>  CO  r-  t  37  N (O m v ro w h- H H H H H  uaA  *>  M — M — —  irrfjtiO  -  cn c o —  CM  I  o o <D X  Chapter  3. Methods  and  38  Materials  equipment are: 1  • a natural gas fired in-line excess air burner • a heat exchanger for generation of superheated steam and control of inlet drying medium temperature • a drying chamber • instrumentation to measure fluid flows, temperatures, gas humidities and pressure drops  The basic approach of the experiments was to place a hog fuel sample in a 20 cm diameter x 137 cm high column and measure the change in humidity or in flow rate of the drying medium across the bed under different operating conditions.  3.2  Experimental  3.2.1  Apparatus  T h e B u r n e r System  A photograph of the 84-10TBH Eclipse natural gas fired in-line burner used is shown in Figure 3.3. The burner has a capacity of 170 m /hr of heated air and operates at higher 3  than 200% excess air. Pressure taps across the nozzle provide a means for flow measurement. The absence of a separate combustion chamber is economically advantageous however it made the whole system very sensitive to changes in pressure. 1  Drawings can be obtained from the author or the Chemical Engineering Department.  Chapter 3.  Methods  and Materials  Figure 3.3: Natural Gas Fired In-line Burner  Chapter  3. Methods  and  40  Materials  The burner system includes: three safety pressure switches on both regulated air and gas lines; a spark plug; a motorized valve to shut the gas flow off in the absence of a flame; and a flame rod for flame detection. They are all connected to and monitored by a 5602 Tervcon flame safe-guard. The combustion temperature is measured by a chromel alumel (K-type) thermocouple and controlled by the flame safe-guard through monitoring the flow of natural gas using an automatic butterfly valve. This type of temperature control system has the advantage of producing a constant flow of gases leaving the burner. The combustion products can be used either as the drying medium or to superheat the steam. Within the temperature range investigated, the burner flue gas has a humidity of about 0.02 kg water/kg dry gas and contains about 1% C0  2  by volume. Therefore, it  can either approximate hot air or simulate stack gases from wood-fired boilers through addition  3.2.2  oiC0 . 2  Heat Exchanger System  The unit consists of a 3 m long U-shaped tubular heat exchanger as is shown in Figure 3.4. The exchanger, having a shell side interfacial area of 0.57 m , is made of a 2 in (I.D. 2  = 5.25 cm, O.D. = 6.03 cm ) and a 4 in (I.D. = 10.23 cm, O.D. = 11.43 cm ) stainless steel pipe, respectively, as the tube and the shell. The products of combustion enter the tube side of the exchanger at one end and flow counter-currently to the steam which enters the shell side of the exchanger at the opposite end. High pressure steam is produced by an LB-100 series electric steam generator, manufactured by Electro Steam Generator Corp., with a capacity of 156 kg/hr at 100°C. The supplied steam, after passing through a steam trap, is monitored by a regulating valve  Figure 3.4: A Photograph of the Heat Exchanger  Chapter  3.  Methods  and  42  Materials  and its pressure is measured by a 515 kPa Marsh pressure gauge.  The steam enters  the shell side of the exchanger via a 1-| in pipe after passing through an M-400 series Keiso rotameter and an orifice meter.The two measuring devices are to provide accurate measurement of the flow under different conditions.  3.2.3  Drying Chamber  The drying chamber, shown in Figure 3.5, is made of a 137 cm long, 8 in schedule 10 stainless steel pipe ( I.D. = 20.8 cm, O.D. = 21.9 cm )flangedto a 10.5cm long conical section connected to a l-|in pipe. A 3.2 mm thick perforated plate containing 127 3.2 mm diameter holes is used as an air distributor. The holes are centered 1.6 cm apart from each other giving rise to about 12-18 cm H 0 drop in pressure under the flow conditions 2  investigated. The column is provided with several 6.4 mm diameter openings along its opposite sides for temperature and pressure drop measurements. A tightly fitted basket is inserted in the column to both facilitate and speed the removal of the dried hog fuel sample at the end of the experiment. The basket is 90 cm high and made of 0.64 mm thick stainless steel sheet with a stainless steel screen of 3 mm mesh size at the bottom.  3.2.4  Preparation of The Drying Medium  The drying process takes place in one of the following media:  1. Hot, relatively dry air leaving the burner. This is the flue gas from the burner operated at high percent excess air.  Figure 3.5: A Photograph of the Drying Chamber  Chapter  3. Methods  and  44  Materials  2. Flue gas, which was simulated by adding CO2 to medium 1 above.  3. Humidified "air" which resulted from bleeding steam into medium 1 above.  4. Superheated steam  To cover the range of humidity variation, both streams leaving the heat exchanger can either exit the system at different quantities or be directed toward the drying chamber. Under the first three conditions the drying takes place in a medium fully or partially composed of the stream leaving the tube side of the exchanger. There is always a flow of steam in the shell to prevent damage due to thermal expansion of the metal. W h e n the humidity of air need not be altered , the steam flows out of the system through a 1 - | in pipe and the condensate produced is removed by a Clark No. 60 steam trap.  To have hot air , the required amount of the air leaving the exchanger is directed toward the packed bed through a 1—| in pipe.  T h e remainder of the air measured by a 2 in  orifice plate exits the system via a 2 in pipe. Addition of CO2 gas to the hot air flowing in the 1 - | in pipe will simulate dry flue gases from wood fired boilers which contain approximately 12% CO2 by volume. C0  2  is supplied from cylinders and metered using  a Fisher series 10A3500 flowrator.  To modify the humidity of air, the steam flow is diverted into the stream of air and directed toward the drying chamber via a 1 - |  in pipe.  T h e steam quantity is only  roughly measured by the Keiso rotameter since the meter is not very sensitive to minor fluctuations at flow rates less than 20% of the maximum. Therefore, the 1~  in orifice  plate in conjunction with a manometer is used for accurate measurement of the bleed flow. To eliminate the effect of static head produced by the condensate in the measuring lines, the pressure taps are connected via ^ in horizontal stainless steel tubing to two  Chapter  3. Methods  and  Materials  45  reservoirs as shown in Figure 3.6. Each reservoir is connected to the manometer from the openings at the top and equipped with a drainage system at the bottom. The ^ in ball valves on the horizontal lines separate the process stream during drainage period. For superheated steam drying the hot gases leaving the exchanger are vented out of the system through a 2 in pipe. The steam flows toward the column and is metered primarily by the Keiso rotameter and periodically checked by the 1-| in orifice plate. The drying medium, irrespective of the type, first passes through a heat exchanger which utilizes cooling water to make small adjustments in temperature. It then either enters the column through a 1~ in pipe or is by-passed during the introduction of wood into the bed. A 2 in check valve prevents the by-passed gas from entering the column. Down stream of the dryer, the gas is metered by a 3in orifice plate and then directed out of the system through a 3in pipe. In case of the first three drying media, a slip stream of the dryer outlet gas is directed to the sensor for humidity measurement (see Section 3.3.1) and the remainder is vented. In order to prevent condensation in the building ventilation lines for the superheated steam runs, the whole dryer outlet stream was first passed through a cooling heat exchanger and the condensate is discharged into the drain.  3.3  Drying Rate Measurements  The drying rate is determined through measurement of the change either in humidity or flow rate of the drying medium across the bed of hog fuel. The former method is used for the first three media mentioned in Section 3.2.4 while the latter is applied to drying in superheated steam. An 1151DP Rosemount mass flow transmitter is used for metering the flow rates. The transmitter is connected, via two three-way valves, to two orifice  Chapter  3. Methods  and  Materials  46  Figure 3.6: Sketch of the Line Connections for Steam Measurement with 1-| in orifice plate  Chapter  3. Methods  and  47  Materials  meters to provide the measurement of the flow of superheated steam exiting the drying chamber and that one of gas entering the humidity sensor. When drying with superheated steam, the instantaneous  drying rate of hog fuel  (kg water evaporated/s - kg dry solid) across the column is calculated through the following relationship: R  =  k  ^  = k  (  G  ^  G  "  i  )  (  3  1  )  Equation 3.2 is used for calculation of the rate of drying with the three other media. R = ^G'*Y  (3.2)  = ^G'{Y -Y ) out  in  where -yout —  3.3.1  * sam  Y i Tn i m x  m x  Y ni da  .  da  —  V"""/  Humidity Measurement  A recent review [67] summarizes the different parameters such as T , m0  Td  eW)  RH%,  etc.  and their required sensing elements which are used to determine the humidity of a gas mixture.  A dew point hygrometer ( General Eastern model 1100DP ) with a model  1111D condensation type sensor is used for humidity measurements which according to Wiederhold [67] are "the most accurate, reliable and wide range detectors available for humidity measurement". The sensor basically works based on the optical detection of the dew layer on an illuminated mirror. When the mirror is dry a photodetector equipped with an electrical bridge system is fully illuminated, producing an electrical current to drive a thermoelectric cooler resulting in formation of a dew layer. Light scattering on a wet mirror causes the bridge output and hence the cooling current to decrease.  Chapter  3. Methods  and  Materials  48  Figure 3.7: Electric Diagram of the Dew Point Sensor The temperature of mirror is measured by a platinum resistance temperature transducer embedded within the mirror. Figure 3.7 illustrates the principle of operation. The sensor accuracy was tested by placing it in a loop, containing an ice bath, in which humid air recirculates. After the steady state condition is reached, the instrument should read the dew point temperature of 0° C. To check the system accuracy at higher dew point temperatures, humidified gas leaving the sensor is cooled to sub-zero temperatures by passing through a cooling heat exchanger. The condensate is collected in a flask and the dry gas volume determined by a dry gas meter. A comparison between the humidity value measured by using the condensate and the instrument reading gives an indication of system accuracy. The calibration was checked every 2 to 3 weeks. The unit includes a balance adjustment knob which is used to zero the sensor under the dry conditions before each operation. The presence of enough contaminants on the mirror surface will prevent zeroing the unit and indicates the necessity for cleaning of the mirror.  However, as  Chapter  3. Methods  and  49  Materials  suggested by the manufacturer, the mirror should be cleaned as infrequently as possible. The sensor measures dew point temperatures ranging from -40 °C to 80 °C ; however, it has a process temperature requirement of less than 80 °C. To both meet this restriction and also prevent condensation in the connecting lines, a side stream of the exit gas from the drying chamber is diluted with air before introduction into the sensor. The gas sample flow is measured by a 1 inch orifice plate connected to the Rosemount mass flow transmitter. The diluting air is metered by a Fisher series 10A3500 flowrator after passing through an F45-421-AODA Norgren filter for removal of oil and water. A bleed of this mixture is metered by a Matheson rotameter (which was calibrated by a Matheson model 8160 mass flow meter) and directed toward the sensor with the remainder being vented.  3.3.2  Mass Flow Measurement  The mass flow of the superheated steam exiting the drying chamber is measured by a 3 inch orifice plate connected to the mass flow transmitter. To alleviate the condensation problem in connecting lines, the whole distance that the steam travels once its contact with the hog fuel is over, is electically heated well above the boiling point temperature of water at the system pressure.  To meet the temperature requirements of the mass  flow transmitter, the sensing element is separated from the process stream by filling the vertical transparent connecting lines with Miriam blue oil (sp. = 1.75) topped by 1Octadecene (sp. = 0.789) which also provides a visual means to insure the absence of static head due to condensate formation. A schematic diagram of the connecting lines is shown in Figure 3.8. The three-way valves, which are disconnected from 1 inch orifice, are used to separate the meter from the process lines and connect it to the atmosphere  Chapter  3. Methods  and  50  Materials  during a run. This provides a check of the accuracy of the meter as it should read zero in the absence of a pressure gradient across the sensing diaphram.  3.4  Temperature and Flow Measurement  Temperature is measured along the process lines. For high accuracy the chromel constantan (E-type) thermocouples are mainly used except where some chromel alumel (K-type) thermocouples were used to measure the heated air temperature in the vicinity of the burner. All the thermocouples are calibrated (see Appendix  E)  over the range 0-250°C  in glycerine using a Haake model TP-41 temperature bath and a Hewlett Packard model 2801A quartz thermometer. Flow measurement is accomplished either by a rotameter or by an orifice meter connected to either a manometer or the mass flow transmitter.  The gas metering devices are  calibrated with a dry gas meter. The steam metering devices are calibrated by measuring the rate of change in the weight of a tank of water into which the steam flow is discharged. The calibration equations are provided in Appendix E (Page  337). Calibrations were  checked periodically and found to remain constant. The 1 inch orifice and the Rosemount transducer measuring the undiluted sample flow toward the sensor, and the diluting air rotameter were checked more frequently as there was greater care needed for an accurate measurement to reduce the possibility of error due to sample preparation. During the course of the experiments all the temperatures and majority of the flow measurements are logged on an A T & T I B M A T compatible computer. Data acquisition takes place through 2 E X P - 1 6 Metrabyte expansion sub-multiplexer board serially connected to a DASH-8 Metrabyte A / D converter interface (see Appendix  F, Page  340).  Chapter  3. Methods  and  Materials  51  Figure 3.8: A Schematic Diagram of Flow Metering Lines for Superheated Steam Runs  Chapter  3.5  3. Methods  and  52  Materials  Hog Fuel Sample Preparation  Western Hemlock hog fuel samples were supplied by CANFOR Ltd. in Vancouver. The average moisture content of the samples was determined to be 58% wet basis (1.41 kg 2  water/kg dry wood). This value was obtained using a microwave oven which according to Harris [68] provides results within 1% less than the ones obtained using conventional methods. Application of a microwave oven in moisture content determination has been investigated using prototype equipment which is being marketed [69]. After removal of the over-large particles the samples were screened for thickness using a Wennberg classifier [70, 71] at the Vancouver Laboratory of PAPRICAN. The average weight fractions, ((f>i) , of the different thicknesses, 6;, of the accepts is shown below: wt  Thickness  Weight Fraction  2mm-4mm  0.25  4mm-6mm  0.30  6mm-8mm  0.25  8mm-10mm  0.14  10mm-12mm  0.07  To simulate the fractions in the accepts, a 40, 35 and 25 weight percent mixture, respectively, of the 4mm-6mm, 6mm-8mm and 8mm-10mm particles was chosen for the majority of the runs. Using the following relationship: 1 .(*) (kg water/kg wet wood) x 100  (3.4)  Chapter  3. Methods  and  Materials  53  Figure 3.9: A Photograph of 2 - 4 mm Thick Particles this mixture would result in a Sauter mean thickness of 6.3mm, which is used as the particle size. However; this is a crude approximation to the particle size since the shape and length of the particles vary considerably even within a thickness fraction as is shown in Figures 3.9 to 3.13.  The classified hog fuel samples were kept in a cold room at  approximately 3°C. The moisture contents of samples were checked over time on a random basis and seemed not to change. To study the effect of initial moisture content of hog fuel on the drying process, samples of 4mm-6mm, 6mm-8mm and 8mm-10mm were separately soaked in water for more than  Chapter  3. Methods  and  Materials  Figure 3.10: A Photograph of 4 - 6 mm Thick Particles  54  Chapter  3. Methods  and  Materials  5 cm  Figure 3.11: A Photograph of 6 - 8 mm Thick Particles  Chapter  3. Methods  and  Materials  Figure 3.12: A Photograph of 8 - 10 mm Thick Particles  Chapter  3. Methods  and  Materials  Figure 3.13: A Photograph of 10 - 12 mm Thick Particles  Chapter  3. Methods  and  Materials  58  four weeks. The moisture content of the sodden samples was checked periodically. There was no appreciable change after the first month. The maximum attainable moisture contents of the above samples were, respectively, 2.00, 1.92, and 1.85 kg water/kg dry wood giving rise to an average value for the blended sample of 1.92 kg water/kg dry wood (66% wet basis). To check the uptake of moisture by the wood, a small sample of the blend was hung inside a vaccum chamber (100 kPa) partially filled with water. After an evacuation period of about 15 minutes, the chamber was turned upside-down, resulting in the sample being immersed in the water.The sample was removed after 3hrs and its moisture content was measured to be 1.84 kg water/kg dry wood (65% wet basis). This test shows that even the absence of air resistance in the cavities would only speed the uptake of moisture and result in an approximately the same maximum attainable moisture content of 1.92 kg water/kg dry wood (66% wet basis) observed for the sample soaked in water over a period of approximately 4 weeks.  3.6  Procedure for a D r y i n g R u n  The major steps taken during a drying run with flue gas as the drying medium are itemized below:  1. The hog fuel sample is weighed, and its bulk volume determined. 2. The steam flow is turned on into the heat exchanger with the exit flow directed toward the drain.  Chapter  3. Methods  and  Materials  59  3. The burner is fired allowing the desired amount of heated air to pass through the process Hne. Temperatures, pressures and flow rates are continuously monitored. 4. The dew point meter is zeroed and diluting air humidity is measured. A side stream of the exit drying gas is directed toward the sensor and the humidity of the mixture is determined. 5. After the steady state is achieved throughout the system which takes about 3 hours, the composition of the drying medium is fixed by addition of CO2 or steam depending upon the desired operating condition. Twenty to thirty additional minutes are needed for steady conditions to be reached. 6. The data acquisition system is switched on and the initial conditions are recorded. 7. The gas flow is by-passed. The lid of the column is then removed, and the hog fuel sample is dumped into the chamber and lid fastened. The column is not tapped, therefore solids should be very close to their loose-packed density (see Page 234 f  or  additional  comments).  The flow is diverted back to the chamber for the hog fuel  drying to proceed. 8. The drying time is typically about 40 minutes but it can go as high as 85 minutes for thick particles in deep beds and as low as 13 minutes for shallower beds at higher temperatures. During this period all the temperature, flow rate and pressure measurements are logged. 9. Constant outlet gas humidity, or a steady temperature along the bed normally indicates the end of the experiment. However, at higher temperatures, spontaneous ignition of wood may occur.  Chapter  3. Methods  and  Materials  60  10. At the end of the run the gas flow to the drying chamber is by-passed and it is purged with nitrogen gas to prevent fire. 11. The thermocouples along the bed are first removed, and then the basket containing the dried sample is removed from the drying chamber, weighed and its bulk volume is then determined. 12. The burner and the data acquisition system are switched off, and the drying gas and steam flow valves are shut.  For the runs in which superheated steam is used as the drying medium, some changes in procedure were required. Thus between steps 5 and 6: • The electrical tapes are switched on. To prevent condensation anywhere in the system, a side flow of the drying gas is directed toward the by-pass line. After the whole system has approached the operating temperature, the flue gas flow leaving the heat exchanger is vented and the by-pass Hne turned off. The steam flow exiting the heat exchanger is re-routed to pass through the system. The temperature is monitored along the process Hne to ensure the absence of condensation. And between steps 10 and 11: • The steam flow is directed toward the drain and some hot air leaving the heat exchanger is re-routed toward the by-pass Hne.  Chapter 4  Results and Discussion  4.1  General Procedures  Thirty four successful experiments, summarized in Table 4.1, were carried out to determine the effect of different factors on the kinetics of the drying process in the fixed bed of hog fuel particles. Following is the list of parameters which were investigated:  1. Particle size 2. Hog fuel initial moisture content 3. Bed depth 4. Drying temperature 5. Gas velocity 6. Nature of the drying gas • Flue gas • Superheated steam • Humidified air  61  Chapter  4. Results  and  62  Discussion  Table 4.1: Summary of Drying Experiments*  WOOD  DRYING MEDIUM  RATE  HATER  RUI  RUH MASS M.C. SIZE HEIGHT VOID VOID kg  d.b.  ran  PRE 3. 54 1. 14  cm  in f i n l  23.13 .565  FLOW  TEMP  HUMID  kg/hr  oC  d.b.  195.0  C02 Vin Vave '/, m/s  m/s  Re  Rep  DEN. kg/cu.m  MAX. TIME 1/s  s  RATIO fit/me as  82.3 .0021  0.0 1.40 1.38 18845 522  1.19  0.49 6240  1  4. 18 1.14  8-10 32.31 .632  156.0 151.8 .0114  1.0 1.43 1.37 11278 499  0.93  0.74 4285  0.84  1  3  3.00 1.41  6.3  25.97 .708  140.4 241.3 .0263  1.7 1.57 1.44  8894 278  0.77  1.81 1370  fire  3  4  3.00 1.41  6.3  28.00 .709  183.3 155.7 .0308  1.0 1.77 1.64 13183 411  0.89  1.37 1621  0.96  4  8  3.00 1.,41  6.3  25.39 .702  175.5 204.0 .0248  1.2 1.84 1.,70 11749 367  0.82  1.46 1149  0.78  8  9  2.00 1.,41  6.3  16.11 .686  140.2 154.8 .0168  1.0 1.34 1.,28 10084 315  0.90  1.37 2587  0.98  9  10  1.50 1.,41  6.3  12.34 .693 .623  141.4 158.1 .0233  1.0 1.36 1.,32 10112 318  0.89  1.75 2924  1.02  10  11  3.00 1.,41  6.3  23.99 .684 .641  142.0 147.8 .0139  1.0 1.33 1.,26 10339 323  0.91  1.09 3292  1.00  11  12  3.00 1.,41  6.3  27.04 .720 .611  152.5 126.3 .0261  1.0 1.37 1.,31 11570 381  0.96  1.02 4163  0.98  12  13  4.00 1.,41  6.3  32.95 .693 .602  140.9 158.5 .0239  1.0 1.35 1.,27 10072 314  0.89  0.97 3205  1.03  13  14  3.00 1..41  4-6  26.86 .718 .651  142.0 150.7 .0212  1.0 1.35 1..27 10287 253  0.90  1.05 3262  1.00  14  15  3.00 1..41 10-12 24.51 .691 .584  142.3 151.2 .0139  1.0 1.34 1..29 10295 557  0.91  0.84 4510  0.92  15  16  3.00 1..41  6-8  24.10 .686 .806  141.7 152.0 .0233  1.0 1.35 1,.29 10243 353  0.90  0.98 3160  1.03  16  17  3.00 1,.41  2-4  30.18 .749 .888  141.7 148.5 .0201  1.0 1.33 1,.24 10305 152  0.91  1.18 2195  0.98  17  18  3.00 1.41  8-10 25.27 .700 .622  141.0 153.9 .0211  1.0 1.37 1,.30 10160 460  0.88  1.00 3595  0.98  18  19  3.00 1,.41  6.3  25.27 .700 .634  126.8 204.8 .0210  1.5 1.39 1,.28  8471 283  0.78  1.25 2149  0.97  19  20  3.00 1,.41  6.3  26.43 .713 .658  141.8 154.0 .0145  1.0 1.37 1,.30 10213 317  0.89  1.04 3723  0.97  20  22  3.00 1,.41  6.3  24.51 .691  126.7 220.7 .0205  1.5 1.41 1,.25  8268 258  0.77  1.41  955  fire  22  23  3.00 1,.41  6.3  26.82 .717 .661  123.2 198.5 .1422  1.5 1.32 1,.20  8328 258  0.80  1.41 1286  0.98  23  26  1.,50 1.41  6.3  12.49 .697  117.8 246.8 .0460  2.0 1.35 1,.24  7411 230  0.75  2.40  819  fire  26  29  3.,00 1 .41  6.3  25.00 .697 .643  125.9 202.2 .1347  1.5 1.36 1,.25  8444 262  0.79  1.25 1561  0.94  29  30  3.,00 1 .41  6.3  25.58 .704 .856  125.5 201.7 .2856  2.0 1.39 1 .29  8142 252  0.75  1.68 1502  1.02  30  31  3.,00 1.92  6.3  18.86 .668 .594  143.9 154.4 .0195  1.0 1.30 1 .22 10357 321  0.95  1.34 2760  1.03  31  32  3.,00 1 .92  6.3  21.48 .709 .592  142.9 156.2 .0226  1.0 1.33 1 .26 10252 318  0.92  1.41 2802  0.94  32  34  3.,00 1.41  6.3  24.50 .691 .631  14S.8 148.2 .0130 11.7 1.25 1 .20 10643 330  1.00  1.23 4049  1.02  34  36  3..00 1 .41  6.3  24.42 .690 .853  144.1 148.2 .0114  6.1 1.32 1 .26 10500 326  0.94  1.25 3410  0.98  36  38  1..50 1 .41  6.3  12.05 .685  85.6 250.8  0.0 0.86 0 .83  8073 250  0.85  2.42 1634  fire  38  39  3,.00 1 .41  6.3  25.13 .698 .641  97.9 170.9  0.0 0.79 0 .77 10876 337  1.08  0.93 4082  0.96  39  41  3..00 1 .41  6.3  27.32 .723 .597  91.7 220.5  0.0 0.80 0 .75  9193 285  0.98  1.56 1991  0.93  41  42  3,.00 1 .41  6.3  27.89 .726 .639  95.5 189.5  0.0 0.81 0 .78 10194 316  1.01  1.00 2833  0.97  42  43  3 .00 1 .41  6.3  22.94 .670 .577  86.3 245.7  0.0 0.82 0.76  8218 255  0.90  1.73 1809  0.95  43  44  3 .00 1 .41  6.3  23.78 .681 .818  90.0 221.3  0.0 0.81 0 .76  9001 279  0.96  1.86 1991  0.93  44  45  3 .00 1 .41  6.3  24.76 .694 .611  93.6 206.9  0.0 0.82 0.78  9635 299  0.98  1.37 2215  0.98  45  46  3 .00 1 .41  6.3  25.18 .699 .634  94.4 204.7  0.0 0.82 0 .78  9762 303  0.98  1.41 1811  0.94  46  * See next page f o r the legends  PRE  Chapter  4. Results  and  Discussion  Legends to Table 4.1 1.  M A S S is the mass of wet sample.  2.  M . C . is the initial moisture content of wood in kg H 2 O / kg dry wood.  3.  SIZE is either the thickness fraction or the Sauter mean thickness.  4.  H E I G H T is initial bed height (see Appendix A).  5.  V O I D is the loose packed voidage where "in" is the initial voidage, "final" is the voidage after the experiment.  6.  F L O W is the time average of the total mass flow of the inlet gas.  7.  T E M P is the time average of the gas inlet temperature.  8.  H U M I D is the inlet gas humidity in kg H^O/kg dry air.  9.  C O 2 is the volumetric percentage of C O 2 in the inlet drying gas  10.  V { is the time average superficial velocity of the inlet gas.  11.  V  n  a v e  is the time average superficial velocity at the mean inlet and outlet  gas temperature. 12.  R e and R e are the inlet gas Reynolds numbers based on the diameter p  of the column and the particle size. 13.  D E N is the average inlet gas density.  14.  R A T E is defined by Equations 3.2 and 3.1  15.  M A X is the maximum drying rate.  16.  T I M E is the total drying time.  17.  R A T I O is the ratio of evaporated water found from the fitted curve to the one found through measurement of change in the weight of the sample.  18.  D R Y I N G M E D I U M consists of mainly hot air for Runs 1 to 36 and of superheated steam for Runs 38 to 46.  63  Chapter  4.  Results  and  64  Discussion  To discuss the relative effect of each parameter on the process, the conditions of Run 11 and Run 20 were chosen as the base case for comparison. The bracketed values show the range of variation covered in the study. Variable Investigated  Base Case  Type of species  Western Hemlock  Bed depth" (cm)  25  (12-33)  Initial wet bed weight (kg)  .3  (1.5-4.0)  Particle thickness (mm)  6.3  (2-4 to 10-12)  Hog fuel initial moisture content (d.b. )  1.41  (1.14-1.92)  Inlet gas temperature (°C)  150  (62-250)  Inlet gas superficial velocity (m/s)  1.35  (0.79-1.77)  Inlet gas C 0 content (%Vol.)  1  (0-11.7)  Inlet gas humidity  0.02  (O-002-oo)  b  C  d  2  6  Degrees of superheat of steam (°C)  Range Studied  (50-125)  "Measured by weight of wet sample. *Corrsponds to 3 kg of wet hog fuel. Denotes a 40, 35 and 25 wt% mixture of, respectively, 4-6, 6-8 and 8-10 mm thick particles. kg H20/kg dry solid. kg H 0 / k g dry air. c  d  e  2  To analyze the results, the following steps were taken for all runs:  1. The drying behaviour of the transient batch drying process is represented through the instantaneous average drying rate across the bed depth. This assumption has been made even though there is a wave of M (instantaneous moisture content) through the bed with time and regardless of the the bed height which might exceed height of the desorption zone (see Section 2.8).  Chapter 4. Results and Discussion  65  2. The rate of drying is calculated by either the change in humidity or mass flow of the drying medium across the bed of solids (Equations 3.2 or 3.1) and plotted versus time. The data points have very little scatter for majority of the runs; however, some scatter is present for some others due to operating conditions (see Appendix B, Page 254, f  or  the plots of all runs). Figure 4.1, representing the conditions of  the base case, shows a typical plot of drying rate as a function of time; it consists of an initial heat up or induction period, a so called constant rate period and a falling rate period. The duration of each period depends upon the operating conditions. The induction period is defined here as the time to reach the beginning of the constant rate period. The constant rate region is typically very short, and the rate during this period is really represented by a maximum rather than a sustained constant value. 3. To determine the average instantaneous moisture content (M) of the sample, the drying rate (R = d(M — M)/d8) is fitted to the following expression. The fitting a  parameters, the sum of square of residuals and the variance of the fit are tabulated and included in Tables B.l and B.2, and in Appendix C.  M^M}^± ^.>  (4.!)  d R=  a  i= l  The rate function is numerically integrated to give M which will be used to produce a plot of R versus moisture content as is shown in Figure 4.2. The critical (M^) and equilibrium (M ) moisture contents which respectively represent the end of e  the constant and the falling rate periods are operating-condition dependent. M  CT  is determined graphically and represents the intercept of the two tangents to the drying rate curve at maximum and at just after the appearance of the knee-shape transition. M is the solid moisture content when in equilibrium with the drying e  gas which is essentially zero for the runs; however, an approximate value of 0.02 kg  Chapter  4.  Results and  Discussion  66  T—r  0.0028  T—P  o 0.0024  E x p e r i m e n t a l Fitted  R u n  7)  11  I  O  147.8°C 0.0020  o  v,»  1.33m/s  L  24.0cm  M (-1  -  0.0016  1.41d.b.  0  dp  6.3  co  m m  1.0 v o l %  2  0.0139d.b.  0.0012  -  •  -  — -  d  > 0.0008 O) 4->  0.0004  rX  0.0000CB--  1  -0.0004 0  800  1  '  •  1600  2400  0  •  •  3200  (s)  Figure 4.1: A Plot of Drying Rate versus Time  _L 4000  4800  Chapter 4.  Results and  Discussion  67  0.0022 0.0020 h 7)  ' 0.0018  O O  £ 0.0016 £ 0.0014 OS  0.0012  0.0010 h  £ 0.0008 £ 0.0006 0.0004 h 0.0002 h 0.0000 0.0  0.2 0.4 0.6 0.8  1.0  1.2  1.4 1.6  M (kg w a t e r / k g dry wood)  Figure 4.2: A Plot of Rate versus Moisture Content  Chapter  4. Results  and  68  Discussion  l/^O/kg dry wood is taken from the experimental values of Luikov [72] on spruce at different temperatures and relative humidities. The magnitude of the constant rate is representative of convective processes, while the slope of the curve during the falling rate period represents the movement of water or water vapor within the particle. 4. A plot of moisture content versus time is also prepared as shown in Figure 4.3. The slope of the linear part of the curve was calculated by linearly fitting the experimental data points measured in the time interval where exit gas temperature remained approximately constant. This value was found to be, for all runs, within ±3% of the magnitude of the maximum drying rate, R ax] thus, showing that m  the latter is a good approximation of the constant rate value. For design, values of drying rate to moisture content of about 0.6 kg H 0/kg 2  dry wood are needed,  since at this moisture content, the hog fuel boiler efficiency approaches that of fossil fuels (see Page 184)- Rmax gives a good estimate of the drying rate at this moisture content. 5. The drying behaviour during the early stages of the falling rate period has been examined. The slope, LU, of the drying rate curve versus moisture content ( Figure 4.2 ) is calculated at four different moisture content values ranging from 0.3 to 0.6 with an increment of 0.1 kg H 0/kg 2  dry wood. The results are tabulated  in Appendix D, Page 331, and due to the proximity of their magnitude within the above mentioned interval, their mean value is used throughout the text to study the drying rate mechanism during the falling rate period. A comparison between the mean value and the slope of the line connecting M = 0.3 to M = 0.6 points on the drying rate curve confirms the semi-linearity of the curves within this region (Table D.4).  Chapter 4.  0  Results and  Discussion  69  600 1200 1800 2 4 0 0 3000 3 6 0 0 4 2 0 0 4 8 0 0  e  (s)  Figure 4.3: A Plot of Moisture Content versus Time  Chapter  4.  Results  and  70  Discussion  6. To elucidate the relative effect of the external and the internal mechanisms, the characteristic drying curve is plotted as is shown in Figure 4.4. The ordinate is the relative rate of drying (/ = R/Rmax) content, $ = (M - M )/(M e  cr  and abscissa is the characteristic moisture  - M ). e  7. The modified friction factor, f f , proposed by Leva [76] and represented by Equam  tion 4.2 is calculated using the experimental average bed voidage and pressure drop data. The sphericity,  was tested using the Equation 4.3 proposed by Ergun [77]  for pressure drop in packed beds, and compared to that expected from the voidagesphericity relationship of Brown [78].  = Vml  '> = ^  e>w - ef+  °  <">  ™  8. An attempt was made to obtain an empirical equation for the Nusselt number during the heat transfer period. Such a relationship in conjunction with the possibility of the existence of a unified characteristic drying curve would provide more information on drying kinetics during the falling rate period. 9. The accuracy of the measured drying rates are determined through the accuracy of measuring devices. In general, maximum drying rates are within ±2.5% (see  Appendix  A, Page 229 for more  accurate  details).  10. A check of the reproducability of the data has been made through several replicate runs. The sample, a , and the sample estimate of the population, cr _ , standard n  n  1  deviations are calculated and shown in Table 4.2. The magnitude of the population standard deviations due to experimental errors within a 95% confidence band, S , ee  and the corresponding relative deviations, S , are determined using the "Student's ee  er 4.  Results  and  72  Discussion  t test". The results indicate that the average value of, 6 , is within ±7% for the ee  maximum drying rate and within ±11% for the slope during the falling drying rate. The accuracy of the fitted curve ( R vs 6 ) is examined using the BMD  P-series of  statistical programs [73] for a nonlinear regression. The observed and the predicted drying rates and the standard deviation of the predicted values, cr , are included in p  Appendix C, Page 266. The slope of the typical drying rate curve, Figure 4.2, is a function of R, M and 9; therefore, for an exact 9, the variance and the standard deviation of the slope, LU, is determined [74] through, respectively, Equations 4.4 and  4.5: 2  (  d  u  N2  j  2  , /  9  u  2  J  r- 8LU  The gradient in Equation 4.5 is calculated at four moisture contents and reported along with their average value in Table D.3. The results indicate that P( )  A  U  =  1A(T  P(R)  ( - ) 4  6  can be used to approximate the standard deviation of the slope of the falling rate curve for 0.3 < M < 0.6. There is a very little variation in the magnitude of the standard deviations during the constant rate period; therefore, the average value is used for calculation [74] of standard deviations of the predicted maximum drying rates within 95% confidence limits (6 ). The same procedure is used to determine the deviations on the rate, P  within a 95% confidence band, during the falling rate period. According to Equation 4.6, ^p( ) = l-4<^p() would, with 95% confidence, determine the error on the slope. w  fl  The sum of square of residuals, SR = ^ (RE ~ Rp) , shown in Table B.2, represents 2  pure experimental error, SEE, p l  u s  the error associated with the lack of fit, SL, [75]  Chapter  4.  Results  and  73  Discussion  as shown by: SR = SEE  +  (4.7)  SL  The mean square of pure experimental errors, o" , can be approximated from a 2  ee  number of genuine replicate runs. A comparison between <r  2 ee  and mean square of  residuals, o~ , can be used to approximate the lack of fit [75]. 2  r  12. In a linear fit of the form: Yi = a + b(  Xi  '  - x)  (4.8)  the variance of predicted (fitted) value, cr , is calculated [74] through mean square 2  p  of the residuals, cr via Equation 4.9: 2  r  1  (Xj-Xf  |  Tn(xi-x)  2  (4.9)  In a nonlinear fit, the predicted values can be grossly approximated [75] to be bounded by a sum of squares, Sp, for a 1 - a' joint confidence region using the following expression: Sp  where F i(p,n a  — p)  =  SR l +  n — p  —^F ,(p,n-p) a  (4.10)  is the significance point of F-distribution with p and n — p  degrees of freedom.  4.2  The  Particle Size  drying process was investigated with respect to size of hog fuel particle and the  results are summarized in Table 4.3. The effect of particle size on the drying process during the heat transfer controlled period is attributed to the contributions made by the  Chapter  4.  Results  and  Discussion  Table 4.2: Summary of Parameters Indicating the Reproducibility of the Data Parameter  Run 11&20 31&32 41&44 45&46 Average 11&20 31&32 41&44 45&46 Average  •^"max  xlO  3  is' ) 1  xlO  3  Repl  Re 2  1.09 1.34 1.56 1.37  1.04 1.46 1.65 1.41  1.071.40 1.61 1.39  1.15 1.30 1.57 1.35  1.02 1.36 1.41 1.42  1.09 1.33 1.49 1.38  P  Rep  8 %  0~n-l  0.03 0.06 0.05 0.02 0.04 0.07 0.03 0.08 0.03 0.05  0.04 0.08 0.06 0.03 0.05 0.09 0.04 0.11 0.05 0.07  ee  0.04 0.06 0.04 0.02 0.04 0.08 0.03 0.07 0.04 0.06  Table 4.3: Summary of Runs with Varying Partic Run 15 18 16 14 17  L  a  cm 24.5 25.3 24.1 26.9 30.2  T•*- in  °C 151.2 153.9 152.0 150.7 148.5  "Weight of wet hog fuel = 3 kg.  v  in  m/s 1.34 1.37 1.35 1.35 1.33  d  p  mm 10-12 8-10 6-8 4-6 2-4  •^max  xlO s0.84 1.00 0.98 1.05 1.18 3  0.08 0.15 0.12 0.06 10 0.18 0.08 0.21 0.10 0.14  7 11 7 4 7 15 6 14 7 11  Size x 10 s"  S  3  1  Rmax  Rfall  0.03 0.03 0.03 0.03 0.03  0.02 0.02 0.02 0.02 0.03  p  1  xlO s0.89 1.21 0.89 1.29 1.31 3  1  4.  Chapter  Results  and  75  Discussion  size on the interfacial surface area and gas phase turbulence.  For a given weight of  sample, smaller particles provide larger surface areas for transfer processes resulting in an increase in the magnitude of the drying rate. For the reported values of particle size and tube diameter the data indicate [78, 80, 90] that in a randomly packed bed, the smaller the dimensions of the solid material, the tighter would be the packing and the larger would be the interstitial velocity. However, Grassmann [80] indicates, the main factor determining the porosity of the bed is the shape and the orientation of the particles relative to each other. The experimental results indicate (Table 4.3) that the height of the packing is larger for the two smaller sizes compared to the larger particle sizes, which represents a looser packing for the smaller sizes. This is due to the presence of shives and sliver-like pieces of wood which in a random packing prevents particles from easily sliding over each other, and form a close packing. This effect would result in a lower interstitial velocity; however, the turbulence is apt to increase due to the packing orientation. Figure 4.5 represents a plot of drying rates versus time for different particle sizes. As is indicated by the figure, the maximum drying rate increases from 0.84xlO xl0~ s 3  _1  -3  s  _1  to 1.18  with decreasing particle thickness from an average value of 11 mm to 3 mm.  The maximum drying rate is plotted as a function of average particle thickness in Figure 4.6 and is fitted to the following relationship: Rmax = 0.1505 x 10~ - 0.1976 x l O " ^ 2  3  (4.11)  0 4 8  where d is the particle size in mm and Rmax is the maximum drying rate in s . _1  p  An increase in the thickness of the particle reduces the rate of heat conduction within the particle and hence increases the induction period. The effect is particularly evident for thicker particles, and as is seen in Figure 4.7 there is a 3.5 fold increase in the induction period for the thickest particle in comparison to the thinner ones.  Chapter  4.  Results  and  76  Discussion  0.0022 0.0020 I  0.0018  o % 0.0016 £  0.0014  X  0.0012  d l> 0 . 0 0 1 0 0.0008 0.0006 N  —'  0.0004 0.0002 0.0000  0  600  1200 1800 2400 3000 3600 4200 4 8 0 0  e  (s)  Figure 4.5: Drying Rates versus Time for Various Particle Sizes  Chapter  4.  Results  0.0014  a,nd  T-T  I  T  I O O  77  Discussion  i n  0.0013 i n  =  I  T—T  I  I  I  I  I  I"  151° C  1.35  m / s  0.0012  T3 0 . 0 0 1 1 O  0.0010  o  CD  £ 0.0009 o  0.0008 0.0007 0.0006  '  0  4 dp  6 8 (mm)  10  Figure 4.6: Maximum Drying Rate versus Particle Thickness  1  12  Chapter  4.  Results  and  Discussion  78  2.0  1  Run  1.8 O O  1.6 1.4 1.2  \  1.0  CD  -  —— —  Y •  :  V  17 14 16 18 15  • 1 . • dp  mm 2 - 4 4 - 6 6-8 8-10 10-12  :  "  \ V*  -  \\\\  Vs. W  -  \ \  0.4  \  0.2 0.0  — —•—  -  0.8 0.6  1 1-1  x  ;  \ \  -  -  0  6 0 0 1200 1800 2 4 0 0 3000 3 6 0 0 4 2 0 0 4 8 0 0 6  (s)  Figure 4.7: Moisture Content versus Time for Various Particle Sizes  Chapter  Due  4.  Results  and  79  Discussion  to a larger specific surface area and thus a higher percentage of surface moisture  at a given average moisture content, the critical moisture content also decreases as the particle thickness decreases.  A plot of drying rate versus moisture content shown in  Figure 4.8 is indicative of such a relationship. The movement of moisture within the particle is also hindered by an increase in the thickness of the particle. Therefore, the rate of drying is lower for a thicker particle during the internal moisture controlled region. As the particle thickness increases, the drying rate approaches zero at higher values of the average moisture content. The thinnest hog fuel particles show a finite drying rate value even at essentially zero moisture content. This could partly be due to relatively negligible internal diffusional resistance resulting in semi surface evaporation, and partly due to the fit of experimental data. As the particle size decreases there is a greater possibility of fire hazard under a given operating condition; therefore, the samples were removed from the drying chamber as soon as the drying rate approached zero. This resulted in fewer data points at the end of the run for thinner particles (see Appendix B, Page 254)  a n  d  a  fitted curve which is more sensitive to the fluctuations in the rate of drying toward the end of the run to meet the convergence criteria.  4.3  Bed Height  Thermal capacity is one of the main factors affecting design and sizing of hog fuel boilers. For a given thermal capacity, it is desirable to minimize the size of the boiler and operate at a high fuel throughput. However, the fuel throughput and hence the grate heat release rate (rate of energy delivered per unit surface area of the boiler hearth) are limited by the fuel moisture content. To study the effect of the grate heat release rate on the extent of drying, the height of the bed of sample was varied. Figure 4.9 shows the change in drying  Chapter  4.  Results  and  80  Discussion  0.0022 0.0020 en  ' 0.0018  O O  £ 0.0016  I  I  I  I  I  I  Run  I  I  '  '  '  i  i  i  I  i  i  i  dp  17 14 16 18 15  m  m  2 4 6 8 10  -  4 6 8 10 12  £Cut) 0.0014 0.0012 > 0.0010  £ 0.0008 £ 0.0006 GO  0.0004 0.0002 0.0000 0.0  I  0.2 0.4  I  I  I  0.6 0.8  I  1  1.0  1.2 1.4  M (kg w a t e r / k g dry wood)  Figure 4.8: Drying Rates versus Moisture Content for Various particle sizes  1.6  Cha.pter  4.  Results  0.0022  and  81  Discussion  i i i i i i i  j i  i  1  J  i  l  i  Run  0.0020  |  I  l i  i  l  l  1  1  I  l  l  i  L cm  0.0000  10  12  9  16  11&20  25  13  33  1  0  600  1  1  1200 1800 2 4 0 0 3000 3600 4 2 0 0 4 8 0 0  0  (s)  Figure 4.9: Drying Rate versus Time for Various Bed Depths  Chapter  4. Results  and  82  Discussion  rate versus time for batches of wet hog fuel ranging from 1.5 kg to 4 kg which represent bed heights of 12.3 cm to 33 cm, respectively. The change of rate with respect to average moisture content is shown in Figure 4.10. The maximum drying rate controlled by heat transfer decreases,as expected, from 1.75x10~ s 3  -1  to 0.97x10~ s 3  _1  as the bed height  increases from 12.3 cm to 33 cm due to the reduction of the average thermal gradient between the solid and the drying medium across the bed, and the change in thermal properties of the fluid along the bed height. A similar trend is also seen with respect to evaporation of partially bound water in the region between the critical moisture content and fiber saturation point. However, there is not an appreciable change in the slope of the falling rate period during the diffusion controlled region since the movement of water within the wood is not greatly affected by such a small change in gas temperature along the column. The plot of moisture content with respect to time is shown in Figure 4.11. A comparison between these runs shows that 65% more time is needed to reach the average moisture of 0.5 kg water/kg dry wood for the sample of greatest height (Run 13) than the shallowest one (Run 10). The maximum drying rate plotted versus the bed height shown in Figure 4.12 indicates a nonlinear relationship between the two parameters which could be fitted to the following form: Rmax =  where Rmax is in s  _1  + 0.85 x IO"  3  (4.12)  and the bed height, L, is in cm. The results, summarized in Table  4.4, show a 39% drop in maximum drying rate upon about doubling (from and 12.3 cm to 25.2 cm) the bed height and a 9% drop in the rate due to 1.3 fold increase (from 25.2 cm to 33.0 cm) in the height for mixed samples at 155±4 °G and 1.35 m/s. For Runs 38 and 43, at 248±3 °C and 0.84 m/s, a 27% drop in rate occurs upon doubling the bed height. For thicker particles at 153±1 °C and 1.4 m/s (Runs 1 and 18) a 26% decrease is  Chapter  4.  Results  and  83  Discussion  0.0022 0.0020  Run  ' 0.0018 O O  £ 0.0016 £ 0.0014 0.0012 > o.ooio £ 0.0008 rt £ 0.0006 CK)  0.0004 0.0002 0.0000 0.0  0.2 0.4 0.6 0.8  1.0  1.2  1.4 1.6  M (kg w a t e r / k g dry wood)  Figure 4.10: Drying Rate versus Moisture Content for Various Bed Depths  Chapter  4.  Results  and  Discussion  84  2.0 1.8  ' ''' .  Run •  o o £ 1.4 k  —  10 9 11&20 13  L cm 12 16 25 33  -  -  \> 1.2 X  \»\\  1.0 -  \\  CD  \\  "£ 0.8  \  -  -  S 0.4 0.2 0.0  0  SJ=Jr.i . l 1 , , , "  6 0 0 1200 1800 2 4 0 0 3 0 0 0 3 6 0 0 4 2 0 0 4 8 0 0  e  (s)  Figure 4.11: Plot of Moisture Content versus Time for Various Bed Depths  Chapter  4.  Results  85  and Discussion  Table 4.4: Summary of Runs with Varying Bed Height Run 10 9 ll&20 13 18 1 38 43  W  a  L  kg 1.50 2.00 3.00 4.00 3.00 4.18 1.50 3.00  d  cm 12.3 16.1 25.2 33.0 25.3 32.3 12.1 22.9  T-  p  mm 6.3 6.3 6.3 6.3 8-10 8-10 6.3 6.3  J  v  in  - in  °C  158.1 154.8 150.9 158.5 153.9 151.8 250.8 245.7  m/s 1.36 1.34 1.35 1.35 1.37 1.37 0.86 0.82  p  xlO s1.75 1.37 1.07 0.97 1.00 0.74 2.42 1.76 3  1  xlO s1.62 1.28 1.09 0.88 1.21 1.19 2.81 1.71 3  x 10 s" 3  S  Rmax 1  1  Rfall  0.12 0.07 0.02 0.07 0.03 0.04 0.20 0.06  0.06 0.03 0.01 0.03 0.02 0.03 0.13 0.04  "Where two runs are listed, the average results are given.  observed due to 1.3 fold increase in bed height. These comparisons are tabulated below:  Case  Runs  T ave  dp  L  % Drop  Compared  °c  mm  cm  111 Rrnax  A  10 - 11&20  155  6.3  12.3 -*25.2  39  B  11&20 - 33  155  6.3  25.2 -^33.0  9  C  38 - 43  248  6.3  12.1 ->22.9  27  D  18 - 1  150  8-10  25.3 ^32.3  26  Therefore, the effect of bed height on the maximum drying rate is more pronounced as the bed gets shallower (cases A and B), for the lower inlet temperatures (cases A and C) and for the larger particles (cases B and D). Thus where the thermodynamics is not the limiting factor, the effect of bed height on maximum drying rate increases with decreasing mass transfer rates.  Chapter  4.  Results  and  86  Discussion  0.0022  i  ^ 0.0020  T  O  V  i  i n  i n  i  i  i  i  i  i  i  i  i  i  i  |  i  i  = 156 ° C = 1.35 m / s  £ 0.0018 T3 0 . 0 0 1 6 >0.0014 M  0)  £ 0.0012 Qi)  0.0010 (3 0 . 0 0 0 8  0.0006  1  10  1  i  14  . . .  i  i  18  i  22 L  i  j  .  26  •  30  (cm)  Figure 4.12: Maximum Drying Rate versus the Bed Depth  •  1  34  Chapter  4. Results  Table 4.5: Summary of Runs with Varying Run w L TW *' ws cm m/s °C kg kg 31&32 3.00 1.03 20.17 155.3 1.32 3.00 1.24 25.21 150.9 1.35 11&20 11A&20A 2.48 1.03 20.17 155.0 1.32 9 2.00 0.83 16.11 154.8 1.34 da  0  a  87  and Discussion  Hog Fuel Initial Moisture Content M UJ x 10 S x 10 sd.b. xlO ss" Rmax Rfall 1.92 1.44 1.38 0.12 0.07 1.41 1.07 1.09 0.02 0.01 1.41 1.18 1.41 1.37 1.17 0.07 0.03 3  0  3  1  p  3  1  1  A = adjusted data.  4.4  H o g Fuel Initial Moisture Content  Due to the variations in the initial moisture content of hog fuel and its effect on the performance of the wood fired boilers, the effect of that parameter on the drying process was also studied. Figure 4.13 shows how the drying rate varies with respect to time for batches of hog fuel samples for identical mass of wet wood and different initial moisture contents.  As the figure shows the maximum drying rate increases by 30% for a 36%  increase in the dry basis initial moisture content. It should be noted that the conditions are not identical with respect to the height of the bed in all runs. In other words the mass of dry wood is not constant. Therefore, the average of Runs 11&20 is corrected for the height and temperature using Equations 4.12 and 4.13, respectively, and the corrected values which represent a mid point between Runs 11&20 and 9 are reported in Table 4.5. As the table indicates, the maximum drying rate increases by 19% for a 36% rise in the initial moisture content under otherwise identical conditions. Comparison of the curves of moisture contents versus time shown in Figure 4.14, indicates that 27% more time is needed for the initially wetter sample of hog fuel to reach the average moisture content of 0.5 kg water/kg dry wood. Under the condition tested, the initial moisture content of the sample is expected to affect the drying process only when  Chapter  4.  Results  0.0022  cn  1 TJ O O  1  f-i  1  1  I  Discussion  i  i  i  j  i  88  r i  0.0020  Run  0.0018  31&32 9 11&20  £ 0.0016 >>  TJ  and  j  i  i  i  Mo d.b. 1.92 1.41 1.41  w kg 3.0 2.0 3.0  i  • ' • i  i  • • i  1  r  i  L cm 20 16 25  W8  0.0014  0.0012 ft CD  <D  0.0010 0.0008  «S  0.0006  tt  0.0004 0.0002 0.0000  T1 r  0  T  -L  •  1  1  1  1  •  1  600 1200 1800 2400 3000 3600 4200 4800 0  (s)  Figure 4.13: A Plot of Drying Rates versus Time for Various Initial Moisture Contents  Chapter  4.  Results  and  Discussion  89  i  Run  — 31&32 9 11&20  0  Mo  W  d.b. 1.92 1.41 1.41  w a  kg 3.0 2.0 3.0  i  i i i i i I i i  i  L  cm 20 16 25  _I_J_  600 1200 1800 2400 3000 360042004800 6  ( s )  Figure 4.14: Moisture Contents versus Time for Various Initial Moisture Contents  Chapter  4. Results  90  and Discussion  Table 4.6: Summary of Runs with Varying Temperature y. LO 8 x 10 sRun vin Rmax in in dry basis m/s xlO sxlO s°C •^max Rfall 22 1.41 220.7 1.41 .0205 0.03 0.03 1.32 0.02 19 204.8 1.39 .0210 1.25 0.01 .0142 0.02 1.07 1.09 0.01 11&20 150.9 1.35 12 1.02 126.3 1.37 .0261 0.99 0.03 0.01  T-  3  1  P  1  3  1  3  1  a  "No data available for to due to spontaneous ignition of wood.  the surface evaporation is the rate determining factor. This is evident in a plot of drying rates as a function of instantaneous average moisture content shown in Figure 4.15 where there is virtually no change in the slope or magnitude of the curves during the diffusion controlled region.  4.5  D r y i n g Temperatures  Drying experiments were also carried out on 25.5 cm deep batches of hog fuel at an average inlet velocity 1.38 m/s with relatively dry air which contained 0.0204 kg water/kg dry air, at different inlet gas temperatures ranging from 126 °C to 221 °C. The results are summarized in Table 4.6 and plotted as rate versus time in Figure 4.16.  As the plot  shows, the maximum drying rate increases with temperature and the effect is much more pronounced at higher inlet temperatures ; this is evident by comparing Run 12 with Run 11&20 and Run 22 with Run 19. The table indicates that increasing the temperature by 25°C from 126°C to 151°C would result in 5% rise in the maximum drying rate while increasing the temperature only by 16°C from 205°C to 221°C would increase the maximum drying rate by 13%. Change of moisture content with respect to time, shown in Figure 4.17, indicates that within the temperature range tested, the induction period is independent of temperature; however, the total drying time decreases with increasing  Chapter  4.  Results  0.0022  i  and  i i i • • • i • ••  TJ O  I '  0 .0018  o  I  i  i i i  ii  w  31&32  1.92  3.0  20  9  1.41  2.0  16  1.41  3.0  25  11&20  * 0 .0016  1 1  Mo d.b.  Run  0.0020 I  91  Discussion  W8  kg  i  iiii  i i i  L cm  !>>  u  0 .0014  em  0 .0012 ft  * 0 .0010 (>  fn 0.0008 £ 0.0006 0.0004 Ph  0.0002 0.0000 0.0  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.8  2.0  M (kg w a t e r / k g dry wood)  Figure 4.15: Drying Rates versus Moisture Content for Various Initial Moisture Contents  Chapter  4.  Results  and  92  Discussion  0.0022  0  600  1200 1800 2400 3000 3600 4 2 0 0  e  (s)  Figure 4.16: Drying Rates versus Time at Different Temperatures  4800  Chapter  4. Results  and  93  Discussion  temperature. A plot of drying rates versus moisture content, Figure 4.18, shows that the maximum drying rate is approached at lower moisture contents as the inlet temperature increases due to the existence of a higher degree of evaporation during the induction period. The slope of the falling rate period also increases with increases in temperature. The rate of increase seems to be linear as the slope is 0.99 x 10  -3  s  _1  for a drying temperature  of 126°C and increases by 10% and by 33% for inlet temperatures of 151°C and 205°C, respectively. There are no data available for the inlet temperature of 221°C during the falling rate period at moisture contents below 0.4 kg water/kg dry wood, as the figure shows, due to spontaneous ignition of the hog fuel sample. The maximum drying rate values are plotted versus temperature in Figure 4.19, and were fitted to a second degree polynomial by the following relationship: R  = -0.314 x 10~ + 0.135 x 10~ T - 0.272 x 10" T 3  max  where T is in °C and R  4.6  4  7  2  (4.13)  is in s . -1  m a x  Gas Velocity  The effect of velocity on the drying process was also examined in several runs with an average bed height of 25.5 cm and the results are shown in Table 4.7. Figure  4.20  represents the effect of velocity at inlet temperatures of 153 ±3°C and 204.5 ±0.5°C, respectively.  Drying rate increases with velocity. As the figure shows, there is a 28%  and a 17% increase, respectively, in the maximum drying rate for runs at 153 ±3°C and 204.5 ±0.5°C for approximately a 31% increase in velocity. The higher value in the case  Chapter  2.0  4.  Results  •  • • i  and  i i  94  Discussion  i  I  i i  i I  I  1  1  1  I  1  1  1  1  1  1  1  I  T T  Run  1.8  °c  22 19 11&20 12  I  i  i  i I  221 205 151 126  i i  600 1200 1800 2 4 0 0 3000 3 6 0 0 4 2 0 0 4 8 0 0 e  (s)  Figure 4.17: Moisture Content versus Time at Different Temperatures  Chapter  4.  Results  0.0022  and  I  0 0020 to  *o °  0018  o £ 0 0016  I  95  Discussion  I  I  I  I  I  I  I  I  I  I  Run 22 19 11&20 12  I  I  I  I  T  I  I  I  I  I  I  I  I  I  I  I  I  I  I  in  °C 221 205 151 126  >>  £ 0 0014 0.0012 0  0.0010  ^0 a>  •  • 0. 0 tt  0 0.0000 0.0  i  i  i  I  i  t t  0.2 0.4 0.6 0.8 1.0 1.2 1.4 M (kg w a t e r / k g dry wood)  1.6  Figure 4.18: Drying Rates versus Moisture Content at Different Temperatures  Chapter  4.  Results  and  96  Discussion  0.0028  I  I  c/>  I 0.0024 o o 0.0020  I  I  p  111.7 k P a  Y  0.0204  v .i n  1.35  I  t  r  i  I  I  i  i  I  (d.b.)  m/s  0.0016 £ 0.0012 ^0.0008 60.0004 0.0000  i  20  60  100  i  i  140  i  180  i  t  I  220  T (°c) Figure 4.19: Maximum Drying Rates as a Function of Temperature  260  Chapter  4.  Results  and  97  Discussion  0.0022 Run  0.0020  •a o  —  l n  °C  8  1.84  204  19  1.39  205  4  1.77  156  11&20  1.35  151  0.0018  £ 0.0016 £  T  i n  m / s 7)  I  v  -  0.0014 0.0012  1  0  600  1  1  1  1  1  1  1  •  •  r-i-  -L i  i  i  I  i  i  1200 1800 2 4 0 0 3000 3600 4 2 0 0 4 8 0 0  0  (s)  Figure 4.20: Drying Rates versus Time at Different Mass Flow Rates  Chapter  4.  Results  98  and Discussion  Table 4.7: Summary of Runs at Different Velocities Run 11&20 4 3 19 8  m kg/hr 141.9 183.3 140.4 126.8 175.5  Tin  °C  150.9 155.7 241.3 204.8 204.0  v  in  m/s 1.35 1.77 1.57 1.39 1.84  Reo  ^max  xlO s1.07 1.37 1.81 1.25 1.46 3  10276 13163 8894 8471 11749  1  xlO s1.09 1.45 2.46 1.32 1.84 3  V  1  x 10 s3  8  UJ  1  Rmax Rfall  0.02 0.04 0.09 0.02 0.08  0.01 0.03 0.07 0.01 0.06  of the lower temperature runs might partially be due to the wider range of temperature difference between the two runs (11&20 and 4). To correct for temperature, Equation 4.13 is applied to Run 11&20. The result suggests that the temperature effect accounts for about a 3% rise in the maximum drying rate and 25% is attributed to the effects of mass flow rates. Therefore, on the average, there is a 21% increase in the maximum drying rate due to 31% increase in velocity.  This indicates that at both given temperatures  the maximum drying rate, governed by heat transfer, is related to the velocity to the power of approximately 0.71. Figure 4.21 shows both the relative effect of mass flow and temperature on velocity and hence on the rate of drying. As is shown in the figure, there is a 70% increase in the maximum drying rate for a 16% increase in velocity due to temperature rise. Therefore, it should be more precisely said, that the maximum drying rate is related to the mass flow rate to the power of 0.71. As both Figure 4.22 and Figure 4.23 indicate, the induction period is not affected by the changes in mass flow rate. Also, the change in the mass flow rate does not have an appreciable effect on the drying time for the runs taking place at 204 °C. The effect is much more pronounced for those at 153 °C, resulting in a 15% drop in the time to reach a moisture content of 0.3 kg water/kg dry wood for a 31% increase in velocity. As Figure 4.22 shows, the time is reduced by 30% for a 16% rise in velocity due to temperature  Chapter  4.  Results  and  99  Discussion  I ' ' ' I ' ' '  v  Run 3 4 11&20  in  m/s 1.57 1.77 1.35  l •l l• T  0  T,„  °C 241 156 151  — •  -  -  • • • • I I I !  600 1200 1800 2400 3000 3600 4200 4800  e  (s)  Figure 4.21: A Plot of Drying Rates versus Time at Various Velocities  Chapter  4. Results  and  100  Discussion  (Runs 3 versus 11&20). Plots of drying rate versus moisture content are shown in Figures 4.24 and 4.25. The first figure indicates that the critical moisture content slightly decreases with decreasing velocity. The slope of the curve during the initial stages of the falling rate period increases with velocity and the effect is much greater for velocity changes due to temperature. As expected the slope becomes relatively independent of changes in velocity due to mass flow rate ( Run 4 vs Run 11&20 ) at final stages. The drop in the drying rate for Run 3 at moisture contents below 0.3 kg water/kg dry wood can be explained by the receding plane model due to a more intense drying condition at the higher temperature. The second figure also represents a higher critical moisture content for drying under higher mass flow rates; however, the drying rate decreases with an increase in the mass flow rate at moisture contents below 0.6 kg water/kg dry wood. This might be due to a more non-uniform moisture content along the bed at a given average moisture content, which would result in a good portion of the heat supplied by the gas to be used to increase the internal energy of the drier wood in the lower part of the bed and hence a contact of a cooler gas with the wetter parts of the sample and a lower rate of drying.  4.7  4.7.1  T h e Nature of the D r y i n g M e d i u m  Flue Gas  The following is an approximation of the dry basis ultimate analysis of the wood fuel components (cellulose, hemicellulose and lignin) [41]:  Carbon  = 49.5%  Chapter  4.  Results  and  Discussion  101  2.0 1.8 TJ  1.6  | i i  1  Run  1  3  o o £ 1.4 ?->  u TJ  1.2  -  v  r -n T  m/s 1.57 1.77 1.35  4 11&20  T  in  in  °C  241 156 151  -  \  j  \w  • U ' Y\ \w 1.0 - \v\ ^  -  CD  •  0.8  V >  \A : \W :  l  \  j*>0.6  X  S 0.4  *  N  \  \  -  \  \\ \  0.2  • i1 6 0 0 1200 1800 2 4 0 0 3 0 0 0 3600 4 2 0 0 4 8 0 0 1  0.0 0  e  I  \~~\~T~£LL•  l  l  l  i  ( s )  Figure 4.22: Moisture Contents versus Time at Various Velocities  I  I  i  Chapter  4.  Results  2.0  1  and  I  1  Discussion  1  I  1  1  1  102  I  1  1  I  1  1  1  1  I  Run  1.8 h  o o  1  1  1  1  1  1  I  1  1  1  1  'in m  /  s  1.84 1.39  8  1.6  1  19  ° c  204 205  £ 1.4 -d 1.2 1.0 CD  "£ 0.8 ^0.6  S 0.4 0.2 •  0.0 0  •  1  1  1  1  1  1  •  1  1  1  I  •  •  • I  600 1200 1800 2400 3000 3 6 0 0 4 2 0 0 4 8 0 0 0 ( s )  Figure 4.23: Moisture Contents versus Time at Various flow rates  Chapter  4.  Results  0.0022  and  103  Discussion  i i I i i i I i i  i  I i  i  i  i i  1  i  i  i  i  I  i  I  i  i  i i  i  0.0020 ' 0.0018  o o  £ 0.0016 >>  £ 0.0014 b0  0.0012 CD  0.0010  £ 0.0008 -t-j rt  £ 0.0006 3 4 11&20  0.0004 0.0002 0.0000 0  //  °C  m/s  1.57 1.77 1.35  241 156 151  / i  i  i  •  M (kg  .  .  i  1.0  ,  .  w a t e r / k g dry  , i .  1.2  _1  I  wood)  Figure 4.24: Drying Rates versus Moisture Contents at Various Velocities  1_  1.6  Chapter  4.  Results  0.0022 0.0020  and  i  i i  I  Run  1 -  8 19  -  O O  v  in  m/s 1.84 1.39  -  00  ' 0.0018  104  Discussion  I  I  -  Tin  °c  -  204 205  -  -  £ 0.0016 £ 0.0014 0.0012 0.0010 CD  £ 0.0008 £ 0.0006 0.0004 tt  0.0002 0.0000 0.0  0.2  0.4  0.6  0.8  1.0  1.2  1.4  M (kg w a t e r / k g dry wood) Figure 4.25: Drying Rates versus Moisture Contents at Various Flow Rates  1.6  Chapter 4. Results and Discussion  105  Hydrogen =6% Oxygen  = 42%  Nitrogen = 1.0% Sulphur  < 0.1%  Ash  < 3%  Thus, the following equation would provide the composition of the stack gases for an stoichiometric combustion of wood material: {C H 0 ) s  12  B  + 8.5n0 + Z2nN —• SnC0 + QnH 0 + Z2nN  n  2  2  2  2  2  Wood fired boilers mainly operate based on an average value of 50% excess air [31, 81]. Combustion of natural gas under stoichiometric conditions is expressed by the following relationship: CH + 20 + 7.5iV —> C0 4  2  2  2  + 2H 0 + 7.5N . 2  2  The Eclipse natural gas burner operated at 400% excess air for the runs with hot air. The composition of the combustion gases are summarized in Table 4.8. A comparison between the two different types of flue gases indicates that their compositions differ mainly with respect to moisture and C0  2  content. The effect of humidity of the drying medium on  the rate of drying will be separately investigated.  C0  2  was added to the heated air  leaving the Eclipse natural gas burner to simulate the composition of wood fired boiler flue gases. The results are shown in Table 4.9. A plot of drying rate versus time is shown in Figure Runs 34 and 36 indicates that the C0  2  4.26.  A comparison between  content of the gas has virtually no effect on  the rate of drying. However, the induction period is longer, the drying process is more  Chapter  4.  Results  and  106  Discussion  Table 4.8: Composition of Combustion Gases for Wood Material and Natural gas Volumetric Concentration (%) Stoichiometric Wood N.G. Wood N.G. 50% Excess 400% Excess 17 10 12 2 13 19 9 4 70 71 72.5 77 0 0 6.5 16  Component C0 H0 2  2  N  2  o  2  Table 4.9: Summary of Runs with Varying C0  Content  2  Run 34 36 11&20  m  kg/hr 145.8 144.1 141.9  T-  - - in 1  °C  146.2 148.2 150.9  v  in  m/s 1.25 1.32 1.35  Rev  10643 10500 10276  Y  d.b. 0.0130 0.0114 0.0142  co  2  vol% 11.7 6.1 1.0  •^max  xlO s1.23 1.25 1.07 3  1  LO X  10  3  s1.01 1.11 1.09 1  x 10  3  8  V  s"  1  Rmax Rfall  0.02 0.02 0.02  0.01 0.01 0.01  Chapter  4. Results  and  Discussion  107  gradual and the maximum drying rate is lower in case of R u n 11&20. T h e differences cannot be attributed to the effect of CO2  content on radiation heat transfer.  Under  operating conditions used for Runs 34 and 36 and for a relatively small temperature gradient between gas and solid the total heat flux increases only by 0.26% and 0.39% for, respectively, a 6-fold and a 12-fold increase in C0  2  4-17, Page  volumetric concentration (see  Table  177 ). T h e difference in the Reynolds numbers accounts only for 1.5% and  2.5% for, respectively, a 6-fold and a 12-fold rise in C0  2  concentration.  One possibility for lower induction periods in case Runs 34 and 36 might be the higher initial temperature of the sample.  As was mentioned previously, the hog fuel samples  were stored in a cold room to prevent the wood from rotting in a damp and warm environment.  Care was taken to remove the samples from the cold area just before  addition to the column after the steady conditions have reached.  However, due to the  limited supply of CO2 and to ensure its availability during the length of the run, the samples were brought to the room temperature relatively earlier and remained in the room for a longer period of time for steady conditions to prevail.  This would result in  a higher initial temperature for the hog fuel sample and hence a lower induction period, a deeper desorption zone and a smaller degree of condensation of evaporated moisture on the upper section of bed.  This behaviour would promote a shorter heat transfer  region and a higher critical moisture content as is shown in the plot of drying rate versus moisture content, Figure  4.7.2  4.27.  Superheated Steam  The drying process was also studied at various temperatures with superheated steam at 215 k P a absolute pressure. Due to limitations in the steam supply, the experiments were  Chapter  4.  Results  and  108  Discussion  0.0022  i • •  0.0020  Run  1  34 36 11&20  CO  I 0.0018  O  £ 0.0016 -  i  1  1  '  C0 vol% 11.7 6.1 1.0 2  >>  £ 0.0014 c m  0.0012 ft  0  600 1200 1800 2400 3000 3600 4200 4800 ^  ( s )  Figure 4.26: Drying Rates versus Time for Various CQ Concentrations 2  Chapter  4.  Results  0.0022  and Discussion  T T  'I  1  1 1  I  109  I  GO  £  0.0016  £  0.0014 0.0012  I  Ii  I  I  I  I ' ' ' I  I  C0  2  vol%  34  11.7  36  6.1  11&20  1.0  0.0018  TJ O O  I I  Run  0.0020  '  I I I I  ft  £  0.0010  CD  £  0.0008  4->  cd  £  w  0.0006  0.0004  tt  0.0002  0.0000 0 .0  i  0.2  0.4  i  i  1 i  0.6  i  t  I  0.8  i  i  t  1 i  1.0  * i  1.2  1.4  1.6  M (kg w a t e r / k g dry wood) Figure 4.27: Drying Rates versus Moisture Content for Various CO2 Concentrations  Chapter  4. Results  110  and Discussion  Table 4.10: Summary of Superheated Steam Drying Runs Run 39 42 45 46 45&46 41 44 41&44 43 38  W  kg 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 1.50  T  in  °C 170.9 189.5 206.9 204.7 205.8 220.5 221.3 220.9 245.7 250.8  v  M  in  m/s 0.79 0.81 0.82 0.82 0.82 0.80 0.81 0.81 0.82 0.86  LU  cr  Rmax  d.b. 0.82 1.19 1.01 1.11 1.06 1.08 1.11 1.10 1.08 1.00  x l O s0.930 0.996 1.370 1.410 1.390 1.560 1.650 1.610 1.730 2.420 3  1  x l O s1.50 0.85 1.35 1.42 1.39 1.57 1.37 1.47 1.71 2.81 3  8  P  1  x 10 s-  Rmax  3  1  Rfall  0.04 0.10 0.05 0.09 0.07 0.10 0.10 0.10 0.06 0.20  0.04 0.04 0.03 0.04 0.04 0.05 0.04 0.05 0.04 0.13  done at an average inlet velocity of 0.82 m/s. The results are summarized in Table 4.10. Repeated runs were made at both 221 °C and 206 "C to insure the reproducibility of the data (see Table  ).  A plot of rates versus time, Figure 4.28, shows that the  maximum drying rate increases with temperature. The inverse relationship between the temperature and both the induction and the heat transfer controlled periods is noted in the plot of change in moisture content versus time shown in Figure 4.29.  The effect  of temperature on typical drying rate curves (R vs M) is shown in Figure 4.30. With the exception of Run 39 the slope of the curves during the falling rate period increases with respect to temperature.  The temperature rise has a much more pronounced effect  on maximum drying rates at higher drying temperatures (above 190 °C), while at lower temperatures it is more effective in reducing the duration of the induction period. Critical moisture content increases with temperature for T; < 190°C and remains approximately n  independent of temperature for T; > 190° C. These relationships are indicative of a n  change in the drying behaviour at 171 < T; < 190°C which will be discussed in detail. n  Chapter  4.  Results  0  and  111  Discussion  600  1200  1800 2 4 0 0 3 0 0 0 3600 4 2 0 0  e  4800  (s)  Figure 4.28: Superheated Steam Drying Rate versus Time at Various Temperatures  Chapter  4.  Results  a.nd  112  Discussion  2.0  I  _ 1.8 ' -  Run  43 41&44 45&46  O  o  \.  £ 1.4 \  4  2  39  vv  i| .  I.  |  T °C  in  246 221 206 190 171  -  -  73 1.2 • \ \ \ \ X 1.0 - \ v  -  : \\\  CJ  -  -  \\\  v  :  0.8 • 1  *>0.6  \\\ v  S 0.4  -  \\\ v  \\\  v  \W  :  _  V.  -  \\\ v  \\\  X  \\\ \  -  0.2 0.0 0  600 1200 1 8 0 0 2 4 0 0 3 0 0 0 3 6 0 0 4 2 0 0 4 8 0 0  0  ( s )  Figure 4.29: Moisture Content versus Time for Superheated Steam Drying  Chapter  4.  Results  0,0022  and  i  0.0020 CtO  ' 0.0018  O O  £ 0.0016  i i  113  Discussion  i  I  i  i  i  i i  Run 43 41&44 45&46 42 39  i  i  r  i  [  i  I  i  I  i  f  i i i i i [  i  r  i  °c  246 221 206 190 171  £ox 0.0014 0.0012 rt  0.0010  £ 0.0008 rt £ 0.0006 0.0004 0.0002 0.0000 0 .0  I  0.2 0.4 0.6 0.8  1.0  I  I  I  1.2 1.4  M (kg w a t e r / k g dry wood)  1.6  Figure 4.30: Drying Rate versus Moisture Content for Superheated Steam Drying  Chapter  4. Results  and  114  Discussion  Within the range investigated, the experimental data were related to the temperature using the following quadratic expression: Rno* = -0.35 x 10~ + 0.35 x 10" T - 0.56 x 1 0 ~ r 2  where T is in °C and R x ma  4  7  (4.14)  2  is in s~ . Figure 4.31 is a plot of maximum drying rate versus x  temperature at velocity of 0.82 m/s with the solid line representing the fitted relationship. It is believed that degradation of wood occurs much faster and is more severe in the moist heat than in the dry heat [82, 83, 84]. However, it is observed that the hog fuel particles shrink less and seem to be more structurally intact. This is in agreement with the experimental results of Meyer [25] (see Page 7). In addition, the absence of fire hazard makes superheated steam drying a particularly attractive alternative when burning is not an objective.  4.7.3  Humidified A i r  The effect of gas humidity on the drying process was investigated and the results are summarized in Table 4.11. A plot of the drying rate curves versus time, shown in Figure 4.32, indicates that generally the drying rate increases with increasing humidity. However, there is some discrepancy in case of Run 23 and Run 29 which could be due to the scatter of data resulting in a less reliable fit in case of the latter. This can be seen by comparing Figures 4.33 and 4.34 containing the experimental data in addition to the fitted curves.  To check the credibility of the trend, the maximum drying rate data for Runs 45 and 46, and for Run 26 were corrected (see Appendix  A)  for, respectively, velocity (Rm  ax  oc V  -0-71  )  and for both temperature and bed height using Equations 4.13 and 4.12. The results  Chapter  4.  Results  0.0028  and  T  Discussion  I  1  1  115  1  1  I I  1  I  1  T—r  C7)  I  0.0024  O O  P V  = 215 kPa i n  = 0.82 m / s  0.0020 0.0016 •2 0.0012 CO  ^ 0.0008 gO.0004 tt  0.0000 80,  1  120.  •  160.  200. 240. T (°C)  1  •  280.  1  1  320,  Figure 4.31: Maximum Drying Rate versus Temperature for Superheated Steam Drying  Chapter  4.  Results  0.0022  i  0.0020  0.0000  and  i  116  Discussion  i I i i i I  -  I  0  600  I  I  I  I  Run  Y,„ d.b.  30  0.2856  23  0.1422  29  0.1347  19  0.0210  I  I  •  !  I  I  I  1 , 1 ,  1200 1800 2400 3000 3600 4200 4800  0  (s)  Figure 4.32: Drying Rate versus Time at Different Air Humidities  Chapter  4.  Results  and  Discussion  117  0.0028  i  Experimental Fitted  O 0.0024 I •d o o  0.0020  Run  23  Ti„  196.5°C  V L M dp  1.32m/s 26.8cm 1.41d.b. 6.3 m m 1.5 vol% 0.1422d.b.  ln  £  0  0.0016  u  co  M  Y  0.0012  \  i i  2  ln  -  —  •  —  -  d rt  >  0.0008  U  0)  +J rt  0.0004  PH  O.OOOO<  -0.0004  J  0  I  1_  400  1  800  1200  0  1  I  1  1600  (a)  Figure 4.33: Drying Rate versus Time for Run 23  I  I  2000  I  I  2400  Chapter  4.  Results  and Discussion  ng  0.0028  i  O  0.0024  i  Experimental Fitted  CO  I  r  Run  1  •a  V L M dp C0  0.0020  O  l n  O  £ >> Ft TJ  0  0.0016  o  6> o  o  Yin  0.0012  •  rt  > CD  29 202.2°C 1.36m/s 25.0cm 1.41d.b. 6.3 m m 1.5 vol% 0.1347d.b.  -  -  —  -  rP  °  0.0008  2  I I  °  CO +J rt  o  °  0.0004 w  tt  0.0000  -0.0004  I  0  400  I I  800  I  1200 e (s)  1600  Figure 4.34: Drying Rate versus Time for Run 29  I  I  1  2000  '  1  2400  Chapter  4. Results  Run  3  and  119  Discussion  Table 4.11: Effect of Gas Humidity Y-i Tv w x 10 Rmax - in skg/kg °c m/s xlO s47.6 205. 1.39 1.32 1.25 22.2 202. 1.35 1.32 7.03 197. 1.32 1.41 1.09 7.42 202. 1.36 1.25 0.99 202. 1.39 3.50 1.66 1.77 0.00 206. 1.35 2.01  3  Y  in  1  19 26A 23 29 30 45A&46A a  d.b. .0210 .0450 .1422 .1347 .2856 oo  3  1  1  S x 10 s3  1  p  Rmax  Rfall  0.02  0.01  0.05 0.14 0.21  0.05 0.11 0.15  A = adjusted data  shown in Table 4.11 indicate the consistency of the trend.  Figure 4.35 is a plot of  maximum drying rate versus inverse humidity. The solid hne is a fit of experimental data excluding the scatter (Run 29) while the broken line represents a fit of all the data to an exponential function. As the figure shows, Run 29 does not have an appreciable effect even on the form of the fitted curve. Therefore, this run can be discarded since it is neither reliable nor trend determining and hence the following relationship for the solid line can be used:  iCox  = 0.741 x ' l 0 ~ e - ° 3  2 1 / y  + 0.128 x 10~  2  (4.15)  Figure 4.36 shows that the induction period is the shortest for the relatively dry medium (Run 19), goes toward a maximum at mid-humidity values and tends to decrease at high humidities. The inverse of the above mentioned trend exists with respect to the critical moisture content as is shown in Figure 4.37.  As expected, the humidity has no significant  effect on the slopes of the curves during the falling rate period for M < 0.3.  Chapter  4.  Results  0.0024  and  Discussion  I  I  I  O  o  I  T  I  0.0022  120  I  II  1  I  1  1  -  i  i  i  i  i  r  = 202  i n  = 1.35  i n  m/s  R u n 29 excluded  0020^  R u n 29  included  0018 CD  0.0016  ^ 0 0014 0 0012 0.0010  _i  0  i  i_  •  1  1  _i  i  i  i  i_  10 20 30 40 l / Y (kg d r y a i r / k g  i i i ii  50 60 water)  Figure 4.35: Maximum Drying Rate versus Inverse of Absolute Humidity  Chapter  4.  Results  2.0  1  1  1  and  1 1  121  Discussion  1  1  Run  1.8 h-  30 23 19  -  T3  1*6  o o  -  Y d.b. 0.2856 0.1422 0.0210 in  -  £ 1.4 -  >>  •a 1.2 \\1 :  —  <aj)  :  1.0 CD  rt 0.8  -:  V 1  \  \\  -  \  \  -  4  V  \  Sf0.6  S 0.4  V  0.2  <\ \\  '. . . i . . .  0.0 0  \  X  i  i  i  1 i i i  1  600 1200 1800 2400 3000 360042004800  e  ( s )  Figure 4.36: Moisture Content versus Time at Different Air Humidities  Chapter  4.  Results  arid  122  Discussion  0.0022 0.0020  -  ' 0.0018 O O £ 0.0016 £ox 0 . 0 0 1 4  rt  >  0.0012  -  0.0010  -  CD £ 0.0008 £ 0.0006  -  ax  0.0004  -  0.0002  -  tt  0.0000 0.0  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  M (kg w a t e r / k g dry wood) Figure 4.37: Drying Rate versus Moisture Content at Different Air Humidities  Chapter  4.7.4  4.  Results  and  123  Discussion  A Comparison —Different Types of Drying Media  Under the conditions investigated, the C0  2  content of the drying gas does not have any  appreciable effect on the drying kinetics. Thus in different drying media - hot air, flue gas etc, the water would be the main component having an appreciable impact on the drying rate. As was seen in Figure 4.35, under the conditions investigated, an increase in the humidity has a positive effect on the maximum drying rate. The experimental results of Yoshida and Hyodo [85] indicated that the rate of evaporation of water is higher into superheated steam than into dry air. This behaviour was experimentally confirmed by Nomura and Hyodo [86] and the effect of gas mass flow rate was investigated. To see whether the same trend prevails and also to compare the effect of temperature on superheated steam drying with air drying, the results of runs shown in both Figures 4.19 and 4.31 are corrected for velocity (see Appendix  A  ) and shown  in Figure 4.38 for mass velocity of 142 kg/hr (4383 kg/m hr). As the plot shows, the 2  maximum drying rate is much higher with superheated steam than with relatively dry air at temperatures above approximately 180°C while the relationship is reversed below this point. This is good in agreement with the reported results of Yoshida and Hyodo [85] on evaporation of water from a wetted-wall column into air, humid air and superheated steam. The above authors noted that, at a given mass velocity, there is a temperature (inversion point), at which the evaporation rate is independent of the humidity of the drying gas. They also found that at temperatures lower than the inversion point the rate of evaporation decreases with increasing humidity while at temperatures above this point the reverse relationship prevails. The values of 170°C and 176°C were respectively reported for mass flow rates of 18200 and 9100 kg/m hr and it was suggested, 2  "further  investigation of the inversion point is necessary to make clear theoretically the reasons  Chapter  4.  Results  and  124  Discussion  for its existence". The following discussion is an attempt to explain the above experimental findings. Since the drying process is accompanied by humidification of the drying gas, the evaporation process is first studied to investigate the effect of humidity on the rate of drying. Consider the contact of a flow of gas at some temperature T vapour p  db  db  and some partial pressure of water  with a fully wetted surface of a wood particle at temperature T . Equation aa  4.16 governs the maximum possible rate of evaporation of water into humid air and to facilitate the calculations, the wet bulb temperature is replaced by the adiabatic saturation temperature as they are almost the same for air-water mixtures. Since the evaporation of water into humid air would take place at wet bulb temperatures, any increase in air humidity would result in reduction of the thermal gradient (T — T ) in db  aa  addition to a drop in concentration gradient (Y — Y ) and hence, it is believed, to lower aa  db  the rate of evaporation at a given temperature.  Qeva  = m (H  P  a  P t  H  where  =  c (T Pa  as  - H)  = m Cs(T a  db  1+ Y  ~l  + Y  db  ~  - T ) + Y[X Tef  Tef  + c (T Pvap  - T ) aa  ( 4  - T )} ref  Qevap  = heat flow for evaporation (W)  m  = mass flow of dry air (kg/s)  A  = latent heat of vaporization (J/kg)  A  = molal latent heat of vaporization (J/kmol)  H  = enthalpy of the gas mixture per unit dry gas (J/kg)  c  = specific heat (J/kg.K)  a  p  (4.16) -  i 7 j  (4.18)  Chapter  4.  Results and  Discussion  0.0032  1  •  >  •  125  |  i  i  | ii  i  Mass velocity = 142 kg/hr  0.0028  A Air at 111.7 kPa &Y = 0.0204 d.b. .  to  i 0.0024 - O Steam at 215 kPa o o ^0.0020 —  —  0/  '.  0.0016 h+->  [or <  SU)  0.0012 h  1  -  1  -  0.0008  — *  S  1  I  V  •  -  £  1  S  0.0004 h  —  /  S  ^ •  -  •  -  / / /  /  1  S  0.0000 20  60  100  140 T (°C)  180  220  Figure 4.38: Maximum Drying Rate versus Temperature in Air and Steam  260  Chapter  4.  Results  and  126  Discussion  c  = specific heat of mixture per unit mixture (J/kg.K)  Cs  = specific heat of mixture per unit dry air (J/kg.K)  Y  — humidity (kg water/kg dry air)  Y'  = humidity (kg water/kg mixture)  T  = temperature (K)  vap, a  = representing vapour and dry air respectively  as,db  = denote properties at adia. sat. & dry bulb temperatures  ref  = represent properties at reference temperatures  Pt  As it appears in Equation 4.17, the heat capacity of the gas mixture also increases with humidity to the extent represented by the following relationship:  <fK= u^r  for 0 < Y <  °°  '  (4 19)  or ( | | )  T  p  = ^ - ^  ^  0<Y'<1  (4.20)  Therefore, an increase in humidity would result in two competing processes: the rise in specific heat is counter balanced by the rise in adiabatic saturation temperature and reduction of thermal gradient. To see the effect of humidity on adiabatic saturation temperature at a given dry bulb temperature, the following set of equations should be solved simultaneously: Cs{T -T ) db  a8  = {Y -Y )\ , a3  db  a  (4.21)  Chapter  4.  Results  and  127  Discussion  h IV. =  -4986.667 7p + 24.9  (4.23)  as  Ks = c  Pvap  where  (T  - T ) + \  as  ref  - C (T  r e f  L  -T  as  (4.24)  )  ref  Y  = dry basis gas humidity (kg water/kg mixture)  T  = temperature (K)  A  = latent heat of vaporization (J/kg)  \f  = latent heat of vaporization at T f = 0°C (J/kg)  p  = total pressure (Pa)  p  = vapour pressure (Pa)  CL  = specific heat of vapour component (H 0) in the liquid state (Pa)  db,as  = represent properties at dry bulb & adia. sat. temp.  re  re  t  v  2  Equation 4.21 represents [47] an adiabatic saturation curve on the psychrometric chart. The intersection of this curve with the curve representing 100% saturation on the chart provides T  as  at which the partial pressure of water vapour in the mixture equals the  vapour pressure of the pure water at that temperature. Therefore, Equation 4.22 defines the saturation absolute humidity (kg H 0/kg 2  dry gas) at T . Assuming vt <C v , for an aa  g  ideal gas the slope of the vapour pressure curve is related to the latent heat of evaporation [56] through: dT  ~  RT  2  g  Integration of Equation 4.25 over a short temperature range, where A can be considered constant [47], yields lnp„ as a linear function of ^:  P*  ln  =- ^ f +  B  (- ) 4  26  Chapter  4. Results  and  128  Discussion  Equation 4.23 is obtained by substituting the numerical values of the vapour pressure of the water at two extremes of a given temperature range (20°C - 100°C). Substitution of p  Vaa  from Equation 4.23 into Equation 4.22 represents the equation of 100% saturation  curve on the psychrometric chart. The latent heat of evaporation at adiabatic saturation temperature, \  a g  , is formulated as a function of T  at  and given by Equation 4.24. There-  fore, simultaneous solution of Equations 4.21 to 4.24 provides T  as  T  db  and Y  db  for 20°C < T  a8  as a function of both  < 100°C.  The results are plotted in Figure 4.39, as adiabatic saturation temperature versus humidity for various inlet temperatures. As is shown, the saturation temperature rises asymptotically with humidity; therefore, indicating that at a given temperature and high inlet humidities the magnitude of thermal gradient will be less affected by the rise in humidity. The asymptotic value is approached at much lower humidity values with increasing inlet temperatures.  For instance, the saturation temperature of 60 °C is expected for inlet  humidity and temperature of,respectively , 0.154 kg water/kg mixture and 20 °C. The same adiabatic saturation temperature exists for a 260 °C gas with an inlet humidity of 0.058 kg water/kg mixture. Figure 4.40 shows an increase in the maximum available enthalpy change in the gas with respect to temperature at a given humidity. The plot is indicative of the drop in heat capacity with humidity for a humidified gas compared to superheated steam below a certain temperature. The relationship is reversed above this temperature (inversion  temperature)  which itself decreases with increasing humidity.  The above investigations, therefore, show that there exists a temperature where the evaporation of water is as fast in superheated steam as it is in humidified air. However, it does not provide us with a common inversion temperature at which evaporation is independent of humidity. To find the locus of the inversion point for different humidities,  Chapter  4.  Results  0.0  and  129  Discussion  0.2  0.4  0.6  Y ' (kg w a t e r / k g  0.8  1.0  mixture)  Fi gure 4.39: Adiabatic Saturation Temperature as a Function of Humidity at Various temperatures  Chapter  4.  Results  20  a.nd  Discussion  60  100  130  140  180  220  T ( °C) Figure 4.40: Maximum Change in Gas Enthalpy versus Temperaure at Different Humidities  Chapter  4. Results  and  131  Discussion  the following equation which is based on the assumption of a fully saturated outcoming either air or superheated steam at a constant mass flow rate should be solved: c (T-T ) Ptt  where  b  = c (T-T ) Pt  as  T  = boiling point of water at system pressure (°C or K)  c  = specific heat at mean inlet and outlet temperatures (J/kg.K)  b  p  (4.27)  t, st = respectively representing gas mixture and steam properties  The above equation is solved simultaneously with Equations 4.21 to 4.24 to get the inlet temperature where the evaporation rates are equal (inversion point) in superheated steam and air at a given air humidity. Figure 4.41 shows the locus of the inversion point as a function of air humidity at atmospheric pressure. The plot indicates a value of 164°C for completely dry air which decreases with humidity reaching a plateau at humidities above 0.1 kg water/kg total gas. As mentioned previously, the calculations have been carried out using the physical properties of both air and superheated steam at atmospheric pressure due to a lack of tabulated properties at other pressures. The locus of inversion points is expected to shift up when superheated steam at higher pressures is used. Using the above procedure, an inversion point temperature of 189°C is obtained for superheated steam at 215 kPa and humidified air at Y = 0.0204 kg water/kg dry air and atmospheric pressure. This value is in a very good agreement with the experimental results (Figure 4.38) considering that the calculations are carried out for an ideal case of a uniform and fully saturated surface. A plot of mean specific heat capacity of the mixture is also prepared as a function of humidity at different temperatures as is shown in Figure 4.42. The specific heat increases  Chapter  4.  Results  200  and  i  T  132  Discussion  r  i  i  r  T  \  i  r  P = 1 atm. Constant mass  180  velocity  - Locus of i n v e r s i o n  point  160 \  u  o  140  1  120  100  80 0.0  _1  I  L_  '  0.4 0.2 0.6 0.8 Y (kg w a t e r / k g m i x t u r e ) 7  Figure 4.41: Locus of Inversion Point versus Humidity  1  1  1.0  Chapter  4. Results  and  133  Discussion  linearly with humidity to an extent given by Equation 4.20 and, in comparison, it is very little affected by the inlet temperature. For ease of calculations, the gases are assumed to be ideal and the enthalpy only temperature dependent. However, the enthalpy of a real gas is a function of both temperature and pressure and the total change in that property is represented by the following expression:  d  "^wV ^V T+{  -  p  (4 28)  Using the following mathematical relationship which exists between the derivatives of a function  Z = f(X,Y): (^-)  ( —)  ( —)  --1  (4 29)  we can write :  where  ( OT H)  ("I)  P  is the specific heat at constant pressure and 8T  (4-32)  M = £-)  OP H  is defined as Joule-Thomson coefficient. Thus, Equation 4.28 becomes: dH  (4.33)  = CpdT — pcpdp  As is seen in Equation 4.32, p relates the change in temperature with respect to pressure. A positive value for p indicates that a drop in pressure has a cooling effect on the gas. For an ideal gas p = 0 while for almost all real gases- except H , Ne and He- at normal 2  pressures and temperatures p > 0 and changes sign at high temperatures, or pressures as it goes toward the liquid state. Therefore, in the evaporation of water into air which is  Chapter  4.  Results  and  Discussion  Figure 4.42: Mean Specific Heat of the Mixture versus Humidity  134  Chapter  4. Results  and  135  Discussion  considered to be taking place under adiabatic conditions, the Joule-Thomson coefficient can be used to relate the changes of temperature with respect to pressure. Equation 4.33 indicates that the less positive the Joule-Thomson coefficient is, the higher would be the heat capacity of the gas. Substituting (4.34)  P=Pvap+Pa  into Equation 4.32 and rearranging would result in:  ~u ~  ~dT~  H  ~dT 6  ( 4  '  3 5 )  or - = (-) /*  It is obvious that fi  vap  V- vap  +(-)  (4-36)  V- a  is higher at low partial pressures of vapour. Also at a given  temperature the Joule-Thomson coefficient is lower for water than for air; therefore, the higher the partial pressure of the water the less positive would be the \i and hence the higher would be the heating capacity of the mixture. In view of all which has been said above, it can be concluded that since the adiabatic saturation temperature of air at high dry bulb temperatures is not strongly affected by its water content and the specific heat of the air rises rapidly with the water content, the latter would be considered the controlling factor in the evaporation process. Therefore, thermodynamics indicates that at high temperatures, the higher the air humidity, the higher would be the potential for evaporation of water from a fully saturated surface. The increase in the rate of evaporation with humidity seems to be in contradiction with the theoretically and widely accepted mass transfer law stating that the rate of transfer  Chapter  4.  Results  and  136  Discussion  is supposed to decrease as either the concentration or the vapour pressure gradient decreases. However, contrary to what might seem apparent at first sight, the gradient for mass transfer also increases with humidity at high temperatures. The instantaneous mass transfer flux between the gas and the saturated surface is represented by the following relationship: N = k (Y -Y ) Y  where  a8  (4.37)  db  N  = flux of evaporation (kg/m -s)  ky  = humidity dependent mass transfer coefficient (kg/m -s)  2  2  Ydbi Y  as  = dry basis abs. humidity at dry bulb &; adia. sat. temp.  Substituting Equation  4.23 into Equation  4.22, shows that the adiabatic saturation  humidity is an exponential function of the saturation temperature. Therefore, for a very humid air with a high and relatively constant adiabatic saturation temperature, even a small increase in the saturation temperature would greatly increase the saturation humidity and hence the concentration gradient (Y  as  — Y ). Figure 4.43 shows that the db  concentration gradient increases with humidity at temperatures above 100 °C and the effect is much stronger at higher temperatures. These results and Equation 4.21, confirm the fact that at high temperatures the specific heat of the drying medium is the determining factor in the rate of the drying process. Also, contrary to what is believed, an increase in humidity of the gas is expected to increase the concentration gradient and hence the rate of evaporation of water and result in a higher drying rate.  Chapter  4.  Results  1.0  and  Discussion  137  i  i  i  i  i  i  i  P = 1 atm. 0.8  0.6  Inlet  Temperature:  100 °C C 180 C 220 C 260 C  0.4  0.2  0.0  -0.2  i  0.0  i  0.2 0.4 0.6 0.8 Ydb (kg w a t e r / k g mixture)  Figure 4.43: Concentration Gradient versus Humidity at Various Temperatures  1.0  Chapter  4.8  4. Results  and  138  Discussion  Characteristic D r y i n g Curves  The possibility of the existence of a unified characteristic drying curve (see Section 2.7) is also investigated. Keey [61, 48] has used a receding plane model for the drying process which assumes the depth of recession of the evaporating front to be a function of the extent of drying (characteristic moisture content,^), and derived the normalized drying rate (relative drying rate) as a function of the fractional depth of recession, %, for nonhygroscopic materials during the subsurface evaporation using the following equation: N /  =  S3  Nmax  where  K-K-{Y -Y ) KY -(f} (Y ag  3  ^U(T -T )X  db  as  db  — Y ) db  /  = relative drying rate  N  — flux of evaporation (kg/m -s)  N  h(T  3S  — T )  db  as  as  \  SB  2  = maximum flux of evaporation (kg/m -s) 2  max  Ky  = humidity independent mass transfer coefficient (kg/m -s)  4>  = humidity potential coefficient  Y  = dry basis absolute gas humidity  K,  = overall mass transfer coefficient (kg/m -s)  T  = temperature (K)  h  = convective heat transfer coefficient (W/m -K)  U  = overall heat transfer coefficient (W/m -K)  A  = latent heat of evaporation (kJ/kg)  ss  = represents properties at the subsurface temperatures  2  2  2  2  as, db = depict, respectively, the adia. sat. and dry bulb temperatures  Chapter  4. Results  and  Discussion  139  Incorporating heat and mass transfer Biot numbers: B i  B i  =  H  M  j-  =  =  =  Bi' ^ H  =  ^  X  =  5 * '  H  X#*'M  (4.39)  (  4  -  4  °)  and with the help of some manipulations, he has obtained:  /  where  =  ,  •  1 +  \  ;  JXBI'M  £  = depth of recession (m), £ = 0 at the surface  k„  = conductivity of the dried out solid (W/m-K)  8  = boundry layer thickness (m)  pry  = diffusive resistance coefficient  b  = total body thickness (m)  BI'H,  Bi'u  (4-41)  Biot numbers based on total body thickness  =  Bin, B I M  = Biot numbers based on depth of recession  X  = fractional depth of recession £/6  H,M  = denote heat and mass transfer properties, respectively  a  = hygrothermal ratio  a  =  7  = evaporative resistance coefficient (8 — a)/(l — a)  Bi /Bi H  M  a has a negative value and approaches a limiting value of zero as the wet bulb temperature approaches the boiling point of water; therefore, the evaporative resistance coefficient, 7, approaches 8 at high humidities. This would indicate that at high wet bulb temperatures, the relative drying rate is a function of Bin; where BI'H is constant, Bin will only be  Chapter  4.  Results  and  140  Discussion  x/b  x/b  Figure 4.44: Moisture Profile in Solid at Onset of Falling Rate Period  a function of solid material or in another words of fractional depth of recession (see Equation  4-39 ).  Keey and Suzuki [87] have further examined the applicability of Equation 4.41 and the availability of a common characteristic drying rate curve for a given material. Their theoretical findings are based on two different moisture content profiles within the solid body at the onset of the falling rate period as is shown in Figure 4.44. High intensity drying is said to occur when the drying front has not swept through the whole solid body thickness during the heat transfer regime (Figure 4.44(a)). In this regime, the relative drying rate is a function of drying intensity defined by: 7 = ^ ™ -  where  (4.42)  /  = relative intensity of drying  N°  — initial mass transfer flux (kg/m -s) 2  Chapter  4. Results  and  141  Discussion  p„  = density of dried solid material (kg/m )  M  = initial dry basis moisture content of solid  3  0  D  = apparent moisture diffusivity (m /s) 2  a  Therefore, no common characteristic curve is found for high intensity drying. However, the relative drying rate is independent of drying intensity for drying under low drying intensities ( 4.44(b)). Under this condition the moisture profile within the body is affected and the depth of penetration of evaporating front, r, is approached the body thickness during the heat transfer period. The criterion for a single characteristic curve to prevail is shown to be I < 2. Equation 4.42 is mainly used for continuous drying processes where the solids are subjected to the same initial drying flux with respect to time. While for transient batch drying processes, the local drying intensity at any given point along the height of the column is a function of corresponding number of transfer units and is determined through the following relationship: I = I exp(-K ) z  where  I  z  (4.43)  = local drying intensity at position z  z  Ii N  in  n  = drying intensity at the bed inlet  z  = number of transfer units at point z  An attempt is made to investigate the agreement between the experimental data and the relationships derived by Keey and Suzuki [87] despite the fact that they had assumed a  Chapter  4. Results  and  142  Discussion  body of non-hygroscopic nature for their theoretical examinations. Therefore, the values of dependent parameters affecting the relative drying rates are calculated for the drying experiments and summarized in Table 4.12. The parameters given in Table 4.12 are evaluated (see Appendix A ) at the average value of the fluid properties along the drying chamber during the heat transfer regime. The initial drying intensities are calculated using the experimentally found mass transfer coefficients which are based on the whole height of the solid in the column. Therefore, the average relative drying intensities along the column should also be determined through either the integration of Equation 4.43 with respect to bed height or the initial flux of drying in Equation 4.42 should be replaced by the average flux across the bed as defined by the following expression: -lave  l-in^Tp *a  (4.44)  TZ * in  where the term in the denominator represents the humidity gradient at the bed inlet and Yi  m  is the average logarithmic humidity difference along the bed height.  The relative drying rates, / , are plotted as a function of characteristic moisture content, $, as defined by Equations 2.23 and 2.25, respectively. As is expected and illustrated in Figure 4.45, no common characteristic curve is found for the runs with varying bed heights. As the bed gets shallower, the relative depth of recession uniformly increases along the bed and the relative rate of drying decreases at a given average moisture content. The corresponding values in Table 4.12 are also indicative of this fact as the drying intensities drop with the bed height while the products of evaporative resistance and mass-transfer Biot number remains virtually constant.  The effect of particle size on the characteristic drying curve is shown in Figure 4.46. Curves become flatter as the thickness of the particles decreases indicating a higher degree of surface evaporation. Both the intensities of drying and the fBi'M  would increase with  1.50  Run 1.25  1.00  <M  "i"" i  1  T — l — — l — l — l r  i  i  i  'i  T-T  1  L cm  10 12 - 9 16 - 11&20 25 -  13  33  0.75  0.50  0.25  0.00 0.00  j  0.25  0.50  0.75  1.00  1.25  1.50  I  L  JLJ.  1.75  Figure 4.45: Characteristic Drying Curves for Runs of various Bed Depths  2.00  er 4.  Results  and  Discussion  Table 4.12: Summary of Parameters Affecting the Relative Drying Rates Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36  a  -0.316 -0.096 -0.050 -0.065 -0.055 -0.086 -0.073 -0.098 -0.090 -0.071 -0.081 -0.095 -0.077 -0.085 -0.081 -0.059 -0.093 -0.055 -0.034 -0.047 -0.035 -0.019 -0.075 -0.072 -0.099 -0.103  /3 0.016 0.017 0.018 0.017 0.017 0.017 0.017 0.017 0.016 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.018 0.018 0.018 0.018 0.018 0.016 0.016 0.017 0.017  7 0.25 0.10 0.06 0.08 0.07 0.09 0.08 0.10 0.10 0.08 0.09 0.10 0.09 0.09 0.09 0.07 0.10 0.07 0.05 0.06 0.05 0.04 0.08 0.08 0.10 0.11  Bi  M  61.2 37.2 22.0 31.1 18.9 28.2 32.9 31.0 38.4 27.9 16.5 48.6 27.1 8.4 44.9 18.2 24.3 19.0 25.7 22.6 17.4 36.9 33.4 33.6 42.2 43.1  jBi  ^ave  M  15.4 3.9 1.4 2.4 1.3 2.7 2.8 3.2 3.8 2.3 1.5 5.0 2.4 0.8 4.1 1.3 2.4 1.3 1.3 1.4 0.9 1.3 2.8 2.7 4.4 4.7  4.8 9.5 8.8 6.7 6.0 6.1 7.4 6.2 6.1 6.1 3.4 10.2 5.7 1.7 9.6 5.8 5.2 6.7 8.7 9.7 6.1 15.1 5.2 5.3 8.3 8.6  1.7 5.3 5.0 3.8 4.1 3.8 4.9 3.2 2.7 2.6 1.8 6.8 3.3 0.7 5.6 3.5 3.0 3.9 4.0 6.7 3.6 4.8 2.8 2.7 3.5 3.7  Chapter  4.  Results  and  Discussion  145  particle size, confirming the agreement between theoretical and experimental results. Previous investigations by Toei, et al. [88] indicated that the movement of water in wood is facilitated at higher humidities, and the constant rate period lasts longer in steam and humid air than in dry air. Therefore, a higher degree of surface evaporation and hence a natter characteristic drying curve is expected as the humidity increases. Comparison of Run 23 with Run 19 in Figure 4.47 indicates that evaporation takes place more at the surface at medium humidity values while it tends to recede within the particle at higher humidities (Run 30). This can be attributed to high drying intensity (see Table 4-l%)>  m  case of Run 30, which causes the moisture profile in the center of the particle to remain intact before the critical moisture content is reached. The effect of drying intensities on the characteristic drying rate curves is intensified at high wet bulb temperatures as the evaporative resistance coefficient is relatively constant, Table 4.12, giving rise to a more %-dependent relative drying rate function (Equation 4.41). The relative drying rate curves for runs with steam as a drying medium collapsed on each other except for the ones with shallower depth, Run 38, and at lower temperature, Run 39, which indicated a lower degree of surface evaporation. The former is expected and the latter is very likely to be due to the mechanism of moisture removal. As selfdiffusion cannot constitute a driving force; therefore, the transport of moisture in drying with a superheated vapour is due to pressure gradient between the the solid surface and the bulk of gas resulting in bulk flow of moisture. The wet surface is heated by the superheated steam until its temperature exceeds the saturation temperature of water at the system pressure by several degrees which would provide enough pressure gradient to cause hydraulic movement of the evaporated moisture. Chu et al. [89] reported a few hundreths of a degree while Wenzel and White [90] reported 1.5 °C to be sufficient to  Chapter  4.  Results  and  Discussion  I  o  I  146  I  I  T-r  i  i  i  i  i  i  i  o o  Figure 4.47: Characteristic Drying Curves for Runs at Different Air Humidities  Chapter  4.  Results  and  148  Discussion  provide bulk movement of water vapour. Thus, at high drying temperatures, the surface temperature is rapidly raised causing the bulk flow to start at very early stages of drying. This mechanism of moisture transport in conjunction with a greater moisture mobility within the solid would cause a higher degree of surface evaporation and a flatter curve than in air. However, at lower temperatures, the surface is not heated fast enough to induce the bulk movement of the vapour; instead, evaporation takes place within the particle until sufficient pressure gradient is produced. This would result in a moisture profile which remains intact at the core of the particle leading to a more intense drying characteristic. The  drying rate curves collapsed on each other for the rest of the runs as is shown in  Figure 4.48. Therefore, an attempt was made to find a general expression representing the set of data which follows an asymptotic behaviour approaching the value of 1 as the critical moisture content is reached. It is evident from Table 4.12 that the evaporative resistance coefficient, 7, is virtually constant for the constant humidity runs. Therefore, for particles of the same size and beds of equal height the characteristic drying curve is a function of internal and external resistances to the moisture removal. The ratio of these resistances, B%M, is defined by Equation 4.40 which is a determining factor in the shape of the curve. As the internal resistance and so as the B%M decreases, the curve becomes flatter indicating the possibility of a higher degree of surface evaporation. The following relationship could express the general shape of the curve: / = 1 - exp(-z)  (4.45)  where i is a declining function of BIM • For a porous non-hygroscopic material, the Biot number is merely a function of depth of recession, £, throughout the drying period. The experimental data of Morgan and  Chapter  4.  Results  and  149  Discussion  Yerazunis [91], indicate that an exponential relationship of the following form: (4.46)  ^ = exp(-a $) 0  may exist between the relative depth of recession and the percentage saturation of the beds of glass beads. In hygroscopic materials, the diffusion resistance coefficient, /i£>, rises very rapidly with decreasing moisture content, particularly during the removal of hygroscopic moisture. Schauss [61] reported a 35 fold increase in the value of diffusion resistance coefficient for radial movement of moisture in wood in the hygroscopic region (as moisture content approaches 0.1 kg water/kg dry solid). Thus, considering an inverse relationship of the form: y-D oc |  (4.47)  and replacing the appropriate expressions for fir) and £ in Equation 4.45, would yield: / = l-exp(-a $e *) a2  1  where  (4.48)  and a are fitting parameters. 2  The fit of experimental data to such a function is represented by: / = 1 - ea;p(-0.96$e - *) 1  and  is shown with a solid hne in Figure 4.48.  21  (4.49)  The 95% joint confidence region for  parameters is approximated [75] through Equation 4.10. The result indicates that there is a 95% probability that the predicted values (Equation 4.49) are within ±0.04 of the experimental ones. Peck and Kauh [92] attributed the drop of the drying rate during the falling rate period to the reduction of total wetted surface area. To formulate their so called wetted surface model, they defined an equivalent wet length, L , and assumed that the wet surface eq  Chapter  4. Results  and  150  Discussion  and the wet volume vary, respectively, as the square and the cube of this length. Thus, considering: / oc L  (4.50)  2 eq  and $ oc L  (4.51)  3  eq  they concluded: / =$  2 / 3  (4.52)  or more generally: / =$  n  (4.53)  They reported n = 0.6 for balsawood af thickness 9.5 mm. For thicker materials, a thickness factor was incorporated as expressed by the bracketed term in the following equation:  /=  ((M" •—- M " •) J l ' V  (4.54)  e  where M ,M , a  e  and M are, respectively, the surface, the equilibrium and the average  moisture content of the particles. The dashed hne in Figure 4.48 is the fit of experimental data to Equation 4.54 ( with S = ±0.06, Equation 4.10 ) which provides us with a p  thickness factor of 0.95 indicating that 95% of the time the surface moisture is about 95% of the average moisture content at a given time. This model, however simplified and unrealistic for drying coarse and thick particles, could provide us with acceptable predictions particularly during the initial stages of the falling rate period.  1.50  i  0 1.25  1.00  i  i i  Run 30  •  Run31&32  +  0  Run 8 Run 11&20  Run 34 Run 36  0  Run 12  •  0  Run 19 Run 22  a  Run 42  I  •  A. <M  Run 3 Run 4  i  X  0  X  &  o  Run41&44 •  0.75 •  0.50 0  0.25  0.00 0.00  i  0.25  i  i  I  i  0.50  i  Equation  4.49  Equation  4.54  i  i  I  0.75  i  i  i  i  I  1.00  A  •  o O  °  •  • i  1.25  1.50  * Figure 4.48: Unified Characteristic Drying Curve  1.75  2.00  Chapter  4.9  4.  Results  and  Pressure D r o p  152  Discussion  Analysis  Pressure drops were measured along the drying chamber (Figure 3.5). Only for the purpose of comparison with available data on flow in packed beds, the modified friction factors, fmf, are calculated applying the average value, over the depth and the residence time of solid in the bed (see Appendix A), of pressure drop in the following correlation given by Leva [76]: 2/ G L(l - e) 2  Ap =  where  m /  3  —v* -^ 3  3  Ap  = pressure drop (Pa)  G  = superficial mass velocity (kg/m -s)  L  = bed height (m)  dp  = particle Sauter mean diameter (m)  p  = density (kg/m )  \P  = sphericity  e  = voidage  n  = an asymptotic function of Reynolds number  (  }  2  3  Therefore, f  mf  =  3  tiji  2-n  -Eu —  1 - eJ  h  (4.56)  where the interstitial or hydraulic Euler number, Ehh, and hydraulic diameter, dh, are denned by: Eu  h  =  Ap  pv / e 2  2  (4.57)  Chapter  4.  Results  and  153  Discussion  and, 2 e -..  Z  l  _ ^  d  (4-58)  v  For particles of regular geometry * is readily calculated; however, this is not the case for hog fuel (see Figures  3.9 to 3.13).  Brown [78] indicates that sphericity,  is a declining  function of voidage, e, in randomly packed beds. The study on voidage in packed beds [93] indicates that if the particles are poured into a column, the resulting voidage would be smaller than the one for randomly loose packings. It is clear that this method of bed deposition does not provide a dense packing. Therefore, the hne representing the normal packing on Figure 4.50 can be used to approximate the relationship between e and \I>. This results in $ = 0.43 for the the average bed voidage of 0.66. The following equation proposed by Ergun [77]: 50(1 - e VRed,,  1  1 Ap  + 0.583  Vd  p  3pv /e 2  2  L  e  1  d  h  nEu -- L 1- e = 2  (4.59)  h  is used to check the relative accuracy of this value and to obtain an average experimental value for sphericity, \P, of hog fuel-sized particles. Therefore, the slope, a , of a linear m  fit of hydraulic Euler number versus ^p^,  Figure 4.49, is related to the friction factor,  / / , by: a  m  =  (4.60)  Replacing jj with the bracketed term in Equation 4.59 and solving the resultant quadratic equation for * using the average values of Red  p  —  418 and e = 0.66, would provide us  with an average value of 0.39 for sphericity. This is in good agreement with the results of Brown [78]. The modified friction factors, f f , are determined using 9 = 0.4 as the average value of m  sphericity in conjunction with the experimental voidage and pressure drop data in Equation 4.56. The results are shown in Table 4.13 and plotted in Figure 4.51 as a function  Chapter  4. Results  and  154  Discussion  of Reynolds number. The hne designated as Ergun equation is drawn for sphericity and voidage of 0.40 and 0.66, respectively, through comparison between Equation 4.56 and Equation 4.59 which indicates that: 2-n  fmf - yff  1  (4.61)  For a turbulent flow, n approaches the asymptotic value of 2 and the left term of the bracket in Equation 4.59 vanishes; therefore, the following relationship holds for Reynolds numbers exceeding 10 : 3  fmf =  4.10  = 0-875  (4.62)  Heat Transfer During Constant D r y i n g Rate Period  In simultaneous heat and mass transfer processes, the mechanism of heat transfer is complicated by the cross flow of evaporated moisture. The solution to different systems of simultaneous heat and mass transfer processes based on conservation principles are described by Mikhailov and Ozisjk [94]. As the authors indicate, three different system of equations were proposed to desribe the combined heat and mass transfer processes in capillary porous materials. The first system was proposed by Luikov to whom the drying theory is attributed. The other two systems by Krischer and by de Vries were independently defined but were of Luikov's type. To predict the drying process mathematical models based on different drying theories (see Section  2.6  ) are being proposed. Recently, a mathematical drying model for non-  hygroscopic capillary porous material was proposed by Schadler and Kast [95]. The model is based on both the Krischer's theory of capillary liquid transportation and the Darcy's  Chapter  4.  Results  and  155  Discussion  Table 4.13: Summary of Pressure Drop Data Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 L  a  b  d  dh  P  mm 6.30 9.00 6.30 6.30 6.30 6.30 6.30 6.30 6.30 6.30 5.00 11.00 7.00 3.00 9.00 6.30 6.30 6.30 6.30 6.30 6.30 6.30 6.30 6.30 6.30 6.30  mm 1.94 3.59 3.43 3.44 3.34 3.12 3.23 3.30 3.34 3.09 2.89 5.16 3.40 2.04 4.68 3.37 3.66 3.19 3.72 3.27 3.41 3.57 2.87 3.13 3.28 3.43  = 10.16 cm L = 20.32 cm  L  cm 23.13 32.31 25.97 26.00 25.39 16.11 12.34 23.99 27.04 32.95 26.86 24.51 24.10 30.18 25.27 25.27 26.43 24.51 26.82 12.49 25.00 25.58 18.86 21.48 24.50 24.42  ^ave  Ap/L  Ap  Pa/m 0.536 3922.8° 4045.4 0.599 1152.3 1176.9 0.671 2010.5 1838.8 0.672 2402.7 2145.3 0.666 2893.1 2733.7 0.650 2010.5 2041.0 2422.4 0.658 2451.8 0.662 1274.9 1299.4 0.665 2255.6 2218.9 2660.2 0.647 2795.0 0.684 1544.6 1581.4 0.637 662.0 637.5 0.645 1078.8 1029.7 0.718 1618.2 1704.0 0.661 956.2 943.9 0.667 1078.8 1029.7 0.685 1103.3 1127.8 0.655 1127.8 1103.3 1483.3 0.689 1397.5 0.661 833.6 797.8 0.670 1103.3 1091.0 1005.2 1029.7 0.680 0.631 1495.6 1479.3 1189.1 0.650 1176.9 956.2 919.4 0.661 0.671 956.2 919.4  6  ave  Pa 921.5 376.3 499.8 591.2 714.3 326.3 300.7 308.8 605.0 898.7 419.8 159.2 254.1 501.3 240.1 266.4 294.8 273.4 386.3 101.9 274.3 260.3 280.5 254.1 229.8 257.5  Re*,  572 615 379 514 476 385 385 396 436 396 315 677 438 190 558 344 393 341 380 316 381 420 402 400 406 402  n  1.92 1.92 1.90 1.91 1.91 1.90 1.90 1.90 1.90 1.90 1.89 1.93 1.90 1.85 1.92 1.89 1.90 1.89 1.90 1.89 1.90 1.90 1.90 1.90 1.90 1.90  Eu  h  116.7 77.4 141.0 111.6 133.5 93.6 84.0 93.8 162.6 262.5 135.5 42.7 70.7 185.0 70.5 92.7 92.1 97.5 159.2 38.6 99.8 96.4 79.0 73.6 69.7 77.8  fmf  0.72 0.64 1.43 1.13 1.34 1.38 1.68 0.98 1.53 1.87 1.12 0.68 0.76 0.99 0.99 0.94 0.98 0.97 1.70 0.77 1.04 1.03 0.91 0.81 0.71 0.84  Cha.pt.er  4.  400.  Results  i  i  O  and  156  Discussion  r  i  i  1  •  Experimental Fitted  320.  240.  160.  80.  0.  0.  20.  40. (1  -  € )  60. L /  ( e  80,  100.  dp)  Figure 4.49: A Fit of the Experimental Hydraulic Euler Number to Ergun Equation  Chapter  4.  Results  and  Discussion  157  Porosity  Figure 4.50: Sphericity as a Function of Voidage for Randomly Packed Beds, Courtesy of Brown [77]  4. Results  Chapter  1 0 "p  arid  1—i—I  O  158  Discussion  I I III i  1—I—I  I I II I i  Experimental Aloxite fused MgO granules, etc.,  U O  — — A l u n d u m , clay, etc.,  o rt  I I I I I—I  1—I—I  by  by Leva  Leva  Celite, porcelain, glass, etc.,  by Leva  Ergun equation  10  -l  10  J  I  I I I I I 11  I I I I 111  10  Re d p  10  1  1  I  I  I  I  11  10  Figure 4.51: A Plot of Modified Friction Factor as a Function of Reynolds number  Chapter  4.  Results  and  Discussion  159  law during the constant rate period and the predictions are in good agreements with the experimental results. The mathematical model developed by Stanish et al [96] use Darcy's law for the movement of free water in a capillary porous material and is coupled with the equations of conservation of mass and heat transfer and thermodynamic phase equilibria. Hassan et al [97] have theoretically studied evaporation from a wet surface under laminar conditions. They indicate that the evaporation rate from a cocurrently moving wet surface is higher than that of stationary surface. Numerical methods are also being applied to determine the heat, mass and momentum transfers between a porous material and an external flow [99]. As indicated by Prat [99] the model demands a precise knowledge of the characteristics of the external flow. The mutual effect of the transfer processes has also been studied experimentally, as the solution to the system of differential equations is not possible under real conditions of turbulent flow. The experimental investigations include the liquid evaporation from a free surface or a surface of a capillary porous body. Due  to cross flow of moisture some hydrodynamic conditions prevail which disturb the  boundary layer and affect the rate of heat transfer. The disturbances are attributed [101] to either wave formation at a gas-liquid interface which increases the evaporation surface, or volumetric evaporation which is the separation and entrainment of sub-microscopic liquid particles and their subsequent evaporation in the boundary layer. The effect of the wavy structure of the gas-liquid interface on mass transfer in turbulent flow was first described by Telles and Dukler [102]. Brumfield et al. [103] proposed a mass transfer model which accounted for this effect, and yielded good agreement with  Chapter  4.  Results  and  160  Discussion  experimental values. Smolsky [104] experimentally investigated the effect of wave formation on mass transfer flux by placing a nylon mesh close to the evaporating surface. The results indicated a 7% drop in the mass transfer flux, in the absence of surface waves, which was considered to be due to both a decrease in the evaporation surface and a change in the hydrodynamics of the boundry layer. The entrainment of sub- microscopic liquid particles in the boundary layer induces small disturbances which, however small, are expected to alter the rate of heat transfer. As proposed by Luikov and Mel'nikova [105, 106], the volumetric evaporation of the dispersed particles was considered to occur at the adiabatic saturation temperature irrespective of the surface temperature. The effect of the volumetric evaporation was incorporated into equation of energy transfer by considering a heat sink which is utilizing energy at a rate represented by: E  v  where  E p  (4.63)  == p\  = energy used for volumetric evaporation (W/m ) 3  v  = volumetric power, mass of sub-microscopic particles per unit volume abstracted per unit time (kg/m .s) 3  A  = latent heat of evaporation (J/kg)  Considering that the heat used for volumetric evaporation is supplied through conduction by the gas-vapour mixture, it can be written: ^(T -T ) db  aa  = pXl  (4.64)  Chapter  4.  Results  and  161  Discussion  and hence the thermodynamic state of the drying medium is represented by [107]:  pXl  2  Gu = — — = bfl-db  where  T - T db  aa  J-db  kf  = heat conductivity of the gas-mixture (W/m.K)  I  = characteristic length (m)  Tdb> T  aa  Gu  (4.65)  = dry bulb and asymptotic temperatures (K) = Gukhman number, the ratio of thermal potential of mass transfer to that of heat transfer  The effect of the mass transfer flow, due to entrainment and dispersion of sub-microscopic particles on the heat transfer process depends on the mass transfer rate. At high mass transfer rates, this process would reduce the rate of heat transfer due to thickening of the boundary layer. This was experimentally examined [108] through injection of a gas into a boundary layer. The results indicated that at a low mass transfer rate, which occurs during normal evaporation, the entrainment would not result in thickening of a boundary layer; therefore, the mass transfer process is expected to intensify the heat transfer process. The effect of surface structure, during evaporation from a free water surface as opposed to the surface of a water-saturated capillary porous body, on the heat transfer process was studied by Katto and Aoki [108]. Wire patterns of different cell sizes covered with a water film were used to simulate a capillary porous body. Within the range of investigations ( 30-175 °C, 3-40 m/s ), their experimental results indicated that the critical gas velocity for the onset of entrainment was approximately 5 m/s for evaporation from a free water surface. Under otherwise identical conditions, there was a 3-fold increase in the critical  Chapter  4. Results  and  162  Discussion  velocity for the patterns (irrespective of the size of the mesh).  The critical velocity  decreased with increases in the gas temperature. The convective heat transfer process is altered in the presence of liquid evaporation as some energy is consumed by sensible heating of the evaporated moisture. This effect was taken into account by Colburn and Drew [109] through an energy balance within the boundary layer and by introducing the dimensionless group X defined by: X = Nc Jh Vva  (4.66)  d  The heat transfer coefficient in the presence of mass transfer was then formulated by: h = iph  (4.67)  d  where h is heat transfer coefficient of a dry body and d  exp[X\ — 1  The change in value of ip is very gradual for low X values ( < 0.1 ) which are usually encountered in heat transfer processes from a gas to a liquid surface. Therefore, tp, which is also known as Ackermann coefficient, is close to unity for practical purposes. The effect of mass transfer on heat transfer was taken into account by Kast [98] by replacing X in Equation 4.68 with Nc Cl/h Pmix  d  where fi is given for both turbulent  and laminar boundry layers using empirical results for the former and a combination of extended laminar boundry layer equations and experimental values for the latter. He also indicates that the effect on laminar boundry layers are more extensive than on turbulent one. More recently, Loo and Mujumdar [100] had incorporated such an effect in superheated steam drying by using a relationship of the form shown in Equation 4.67 and substituting  Chapter  4. Results  ln(l + XX)jXX  and  163  Discussion  for ip where XX is defined by the following relationship: XX =c (T -T )/\ Pat  gt  (4.69)  b  Under the experimental conditions ecountered in this study and under the highest mass transfer rates, the coefficient taking into account the effect of mass transfer process on heat transfer coefficient of the dry body would be 0.95 for superheated steam drying and not less than 0.98 for the first two methods described above. Smolsky and Sergeyev [104] have experimentally examined the simultaneous heat and mass transfer process from a free water surface and the surface of a capillary porous body. Their experimental data indicated that the heat transfer from a free water surface was intensified due to the cross flow of mass transfer. Equations 4.70 and 4.71 represent their data within ±15% scatter for the range tested (3-15 m/s, T  dh  Nu = OM%Re Pr Gu os  ozz  0  <150°C, RH<80%).  2  Sh = OmARe°- Sc°- Gu 8  33  0 2  (4.70) (4.71)  A comparison between Equation 4.70 and heat heat transfer from a dry surface, Nu : d  Nu = 0M7 Re Pr 0S  0  (4.72)  33  d  results in the following relationship: N  u  Nu  =2.32Gu ' 0  (4.73)  2  Their experiments on capillary porous bodies, under otherwise identical conditions, are represented within ±7% scatter by the following empirical equations: Nu = 0.08QRe Pr Gu 2/3  1/3  01  (4.74)  Chapter  4. Results  and  164  Discussion  Sh = 0.11Re ^Sc Gu 2  1/3  •  ou  (4.75)  Therefore, they concluded that within the range investigated the rate of heat transfer with evaporation increases with intensity of evaporation, the main flow velocity and temperature; and it decreases with the relative humidity of the gas mixture. Vasilieva [110] has studied the liquid evaporation from a water saturated evaporation front within capillary porous bodies of different porosity. The experimental data were indicative of a lower temperature gradient within the solid with increasing porosity values. He also deduced that as drying proceeds and thickness of the dry sublayer and the hydraulic resistance to the movement of moisture grows, the temperature profile within the particle becomes steeper. Evaporation from a capillar}- porous body of 16% porosity and pore size of 0.8 mm in diameter was investigated by Zakharov and Krylov [111]. The results indicated an increase in the rate of mass transfer with increases in main flow velocity. However, the effect was less pronounced as the evaporation surface receded within the particle. Their correlated experimental data is expressed by: Nu  (4.76)  = ARe 0  7  where A depends on the location of the evaporating surface and decreases with increases in the depth of recession. The difference becomes smaller at lower main flow temperatures. The effect of mass transfer on Nu/Re  07  was taken into account through introduc-  tion of a Kutateladze number (Ku): Nv  —S3  = f(Ku) « Ku  02  (4.77)  A study of simultaneous heat and mass transfer in relatively shallow beds (2.5 - 6.4 cm) of granular solids was carried out by Gamson [112]. The results indicated that where  165  Chapter 4. Results and Discussion  the total solid surface is available for both heat and mass transfer, the heat and mass transfer J-factors are related by: J  H  = 1.064#  edp  -°-  41  = 1.076J  for Re^ > 350  M  (4.78)  and J = IS.lRe^  = 1.076J  1  H  for Re^ < 40  M  (4.79)  Parti [113] examined the applicability of the analogy between heat and mass transfer in deeper beds of solids. The correlated results were: J  H  = 1.1 J  M  = OJSe^Re^- ^  for  0  70 < Re^ < 900  (4.80)  which indicated the existence of the analogy and the absence of any relationship between the bed thickness and the transfer coefficients. The following is an attempt to examine the simultaneous heat and mass transfer processes in hog fuel drying experiments. Physical properties of the drying gas are obtained at the average film temperature (Tj) and are summarized in Table 4.14. The average heat and mass transfer coefficients along the bed height are calculated via Equations 4.81 and 4.82: Qc  (4.81)  •A Ti p  m  anc .  Rmax l^ds  =  ,  / . \ nn  (4.82)  v  with T  lm  = LMTD  T- — T = , in . out °  Y  lm  = LMYD  =  iri  (4.83)  u t  T  and  ^°  ut Y  l  in  (4.84)  Chapter  4. Results  and  166  Discussion  h  = convective heat transfer coefficient (W/m .K)  Qc  = convective rate of heat flow supplied by the gas (W)  ky  = mass transfer coefficient (kg/m .s)  2  2  Rmax= max rate of dring (kg H 0/kg 2  dry wood.s)  Ap  = total interfacial surface area in the column (ni )  w  = weight of the dried solid in the column (kg)  2  d8  Tim  = Logarithmic Mean Temperature Difference, LMTD, (°C) = Logarithmic Mean Humidity Difference, LMYD, (kg H 0/kg 2  dry gas)  The tabulated data for the heat transfer coefficient and dimensionless groups are reported in Table 4.15. The corresponding values for the mass transfer process are summarized in Table 4.16.  Contrary to what is expected, the analogy between the two transfer  processes seems not to be evident as the heat and mass transfer J-factors differ from each other.  This would require more thorough examination.  The mechanism of the  movement of moisture in drying with superheated steam (see Page 145) is responsible for this behaviour during Runs 38 to 46 (Tables 4.15 and 4.16). The following discussion elaborates on the type of process involved, during the rest of the runs, through the study of the adiabatic humidification of a gas across the column. In batch drying of solids a combination of the three processes of moisture evaporation, heat conduction to the solid and condensation of evaporated moisture are present (see Section 2.8). Figure 4.52 is a schematic diagram of the processes involved. Gas enthalpy and mass balances for an adiabatic condition are respectively represented by Equations 4.85 and 4.86.  Chapter  4.  Results  and  167  Discussion  H ut 0  A  cond Hevap  A  H  in  Figure 4.52: Adiabatic Humidification of a Gas  TTlaHin  TftevapHevap  —  mH i a  ou  -\-  TTl id.Hcond COT  Qsink  (4.85) (4.86)  where  H  = enthalpy of gas per unit dry gas (J/kg)  H  = enthalpy of gas per unit gas (J/kg)  m  = mass flow rate (kg/s)  Qaink  = t e of conductive heat transfer to the solid (W)  Y  = gas humidity (kg H 0 / kg dry air)  in, out  = respectively represent the inlet and outlet properties  a  = represents air  evap, cond  = respectively depict the evaporated and the condensed moisture  r a  2  Chapter  4. Results  and  168  Discussion  Substituting Equation 4.86 into Equation 4.85 and replacing Y  cond  tively = w and  and Y  evap  for respec-  yields: Hin  ~\~ Y pH p eva  — Hout ~\~ Y li  eva  cond  m  Upon replacement of the following equations: H  = Cs T  Hout  = Cs  in  in  (4.87)  -\-  cond  a  (4.88)  + YX  in  in  0  (4.89)  out T-out + Y X out  Y pCp T  H  eva  evap  H ond  A«  cond  mv  = A -  a  0  (4.90)  ae  Y \cp T  —  C  t  0  T (cp as  at  (4.91)  - c )  (4.92)  X \  as  t  Pwv  and expansion of the humid heat, Cs, Equation 4.93 representing the total rate of heat flow in adiabatic humidification of a gas travelling along the column will be obtained. Qevap  Cs (T ave  where  c  in  Qt  -  T ) out  ,  =AYc (T Pwv  ave  *  Q sens  -T  a s  )  s Qvap + AYX as  +Q  aink  (4.93)  = specific heat (kJ/kg.K)  p  Cs  = specific heat of mixture per unit dry gas (kJ/kg.K)  Qvap  —  Qsens  —  Q  = total rate of heat flow (W)  t  ra  te of heat flow for vaporization of the moisture (W)  rate of heat flow for sensible heating of the evaporated moisture (W)  Ao,A „ = latent heat of vaporization (kJ/kg) a  ave  = represent properties at average inlet and outlet temperature  wv,£  = represent properties for water vapour and liquid  Chapter  4.  Results  and  Discussion  Table 4.14: Summary of Physical Properties at Film Temperature Run T) x 10 kf x 10 c D xl0 Tf P kg/m °C kg/m-s J/kg-K W/m-K m /s 0 33.1 1.30 1.85 978 25.8 2.12 1 72.9 1.15 2.00 1013 28.6 2.68 3 103.3 1.04 2.08 1049 30.7 3.14 4 77.7 1.09 1.98 1033 29.0 2.84 8 91.9 1.07 2.05 1034 30.0 3.00 9 76.6 1.10 2.01 1018 28.9 2.82 10 83.5 1.07 2.03 1026 29.4 2.93 11 69.9 1.12 1.98 1015 28.4 2.71 12 65.3 1.13 1.94 1022 28.1 2.64 13 75.7 1.10 1.98 1030 28.8 2.79 14 1.11 72.5 1.98 1022 28.6 2.75 15 77.3 1.10 2.02 1014 28.9 2.83 16 75.4 1.10 1024 1.99 28.8 2.80 17 71.1 1.11 1.97 1022 28.5 2.73 18 76.5 1.08 2.00 1023 28.9 2.86 19 1.02 90.9 2.05 1034 29.9 3.13 20 73.5 1.10 1.99 1015 28.6 2.80 22 1.02 96.5 2.07 1039 30.4 3.17 23 100.5 1.00 1141 1.90 30.5 3.06 26 111.9 1.00 2.10 31.4 1065 3.31 102.2 29 1.00 1.93 1134 30.8 3.11 30 108.8 0.93 1.78 1244 31.1 3.18 31 73.9 1.17 1021 1.98 28.6 2.61 32 75.0 1.13 1.98 1026 28.8 2.72 34 1.14 70.6 1.98 1017 28.5 2.67 1.12 36 70.3 1.98 1016 28.5 2.71 38 162.0 1.03 1.37 1986 36.9 2.30 39 133.6 1.15 1.28 1978 34.3 1.95 41 1.14 146.9 1.33 1982 35.7 2.00 42 138.5 1.13 1.29 1979 34.8 1.99 43 1.34 152.6 1.09 36.2 1983 2.12 44 146.4 1.11 1.32 1982 35.5 2.06 1.12 45 142.8 35.2 1.31 1980 2.03 142.2 1.12 46 1.31 1980 35.1 2.03 5  3  p  3  a  Values denote Dww for Runs 38 to 46.  a  W G  2  5  Chapter  4.  Results  170  and Discussion  Table 4.15: Heat Transfer Coefficients and Dimensionless Groups Run  h  0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  W / m -K 55.4 43.0 62.8 55.0 63.9 45.8 37.7 40.1 43.5 39.7 40.2 37.5 43.6 41.1 46.0 46.3 46.9 43.5 38.4 56.8 63.7 41.1 41.4 40.4 51.3 60.7 50.9 60.9 50.9 53.6 46.5 50.1 52.9 53.6  Nu  Gu  13.5 13.5 12.9 12.0 13.4 10.0 8.1 8.9 9.8 8.7 7.0 14.3 10.6 4.3 14.3 9.7 10.3 9.0 7.9 11.4 13.0 8.3 9.1 8.8 11.3 13.4 8.7 11.2 9.0 9.7 8.1 8.9 9.5 9.6  xlO 30.7 82.4 124.8 80.3 107.1 88.0 99.8 74.8 59.3 78.9 74.9 93.2 80.6 73.0 85.6 109.1 82.4 118.3 85.5 135.3 90.6 81.3 75.8 77.3 77.1 77.9 93.8 27.2 55.5 38.7 70.5 56.7 48.5 47.2  2  572 616 380 514 476 386 386 397 436 396 316 678 439 190 559 345 393 341 380 316 381 420 402 400 407 402 338 414 373 398 347 368 386 390  Bi  H  Pr  Pe  H  3  1.00 0.99 0.99 0.99 0.99 0.99 0.98 0.99 0.99 0.99 0.99 0.98 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.98 0.99 0.98 0.99 0.99 0.99 0.99 0.98 0.99 0.99 0.99 0.98 0.98 0.99 0.99  1.4 1.5 1.5 1.3 1.5 1.1 0.9 0.9 1.0 0.9 0.8 1.6 1.1 0.5 1.6 1.1 1.1 1.0 0.9 1.3 1.5 1.0 0.9 0.9 1.2 1.4 1.2 1.4 1.2 1.3 1.1 1.2 1.3 1.3  0.70 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.74 0.74 0.74 0.74 0.74 0.74 0.74 0.74  403 435 270 364 337 273 273 280 308 280 223 479 310 134 395 244 278 242 271 225 271 300 284 283 287 284 249 305 274 293 255 271 284 287  st xlO  H 3  33.6 31.1 47.8 32.9 39.8 36.6 29.6 31.7 31.7 30.9 31.5 29.8 34.2 32.2 36.3 39.9 37.2 37.3 29.3 50.6 48.2 27.8 32.0 31.3 39.4 47.2 34.9 36.7 32.7 33.2 31.7 32.8 33.3 33.5  JH  xlO 26.6 24.7 38.0 26.1 31.7 29.1 23.5 25.1 25.2 24.6 25.0 23.6 27.1 25.6 28.8 31.7 29.5 29.6 23.3 40.3 38.4 22.2 25.4 24.8 31.3 37.4 28.5 30.0 26.7 27.0 25.9 26.8 27.2 27.3  3  Chapter  4.  Results  and  Discussion  Table 4.16: Mass Transfer Coefficients Run Red,, k x 10 Bi Sh kg/ m -s 572 0 41.9 9.49 61.2 1 616 20.0 5.76 37.2 3 380 18.3 3.40 22.0 4 514 4.82 31.1 24.3 8 476 15.3 2.93 18.9 9 386 21.9 4.37 28.2 10 386 26.0 5.09 32.9 11 397 23.6 4.80 31.0 12 436 28.9 5.94 38.4 13 396 21.6 4.32 27.9 14 316 15.9 2.55 16.5 15 678 21.7 7.53 48.6 16 439 18.9 4.20 27.1 17 13.4 190 8.4 1.30 18 559 24.4 6.96 44.9 19 345 14.7 2.82 18.2 20 393 . 18.7 3.77 24.3 22 341 2.94 19.0 15.5 23 380 21.3 3.99 25.7 19.2 26 316 3.51 22.6 14.4 29 381 2.70 17.4 30 420 5.72 36.9 31.1 402 31 25.7 5.17 33.4 32 400 5.21 33.6 26.0 34 407 32.2 6.54 42.2 36 402 32.9 6.68 43.1 38 338 3.9 1.06 6.9 414 39 8.0 2.59 16.7 41 373 7.5 2.37 15.3 42 398 6.5 2.06 13.3 43 347 7.4 2.19 14.2 44 368 8.1 2.48 16.0 45 386 7.6 2.35 15.2 46 390 7.9 2.47 15.9 3  a  Y  M  and Dimensionless Groups Sc  Pe  M  2  3  JM  M  xlO 24.7 14.4 14.1 ' 14.6 9.6 17.5 20.5 18.6 21.0 16.9 12.5 17.1 14.8 10.5 19.2 12.7 14.8 13.4 16.9 17.5 11.4 22.6 19.9 20.1 24.7 25.5 5.4 11.0 11.0 9.0 10.9 11.7 10.6 11.0  3  0.67 0.65 0.63 0.64 0.64 0.65 0.64 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.64 0.65 0.64 0.62 0.63 0.62 0.60 0.65 0.65 0.65 0.65 0.58 0.57 0.58 0.57 0.58 0.58 0.57 0.57  "Values represent kc (kg / m -s-(mol/m ) )for Runs 38 to 46. 2  St  384 400 241 331 305 250 249 258 283 256 205 440 284 123 361 221 255 219 235 200 237 253 260 259 265 262 196 236 216 228 201 212 222 224  xlO 18.9 10.8 10.4 10.9 7.1 13.1 15.3 14.0 15.7 12.6 9.3 12.8 11.1 7.9 14.4 9.5 11.1 10.0 12.3 12.9 8.3 16.1 14.8 15.1 18.6 19.2 3.8 7.5 7.6 6.2 7.6 8.1 7.3 7.6  3  Chapter  4.  Results  and  172  Discussion  The inequality of the rate of heat flow supplied by the gas, Q , and that consumed for t  evaporation of moisture,  Q  e v a p  ,  is indicative of a degree of heat conduction to the solid  which is present during the constant rate period ( Table 4.17 ). This is better illustrated in terms of the number of transfer units ( Equations 4.96 and 4.94 ) as in air-water systems the equality of these numbers is required should the analogy between the two transfer processes exist. As Figure 2.10 depicts, various zones are formed upon drying in relatively deep beds of solids. The height of the desorption zone is operating-condition dependent and where it becomes shorter than the bed height the discrepancy between the number of transfer units results. Therefore, all the relationships, which are based on the assumption of uniformity of solid surface temperature at the wet bulb temperature of the gas across the bed height, would provide better predictions as the height of the desorption zone approaches the bed height. This condition usually occurs as either the bed gets shallower or, for a given bed height, as the rate of mass transfer reduces, where the process is not thermodynamically limited. This is evident in the drying runs as, generally, the number of transfer units for mass and heat transfer approach each other with decreases in bed height, inlet gas temperature and velocity and with increases in particle size, initial fuel moisture content and inlet gas humidity. Figures 4.53(a) and 4.53(b) illustrate the process that a drying gas might undergo where the equality of the number of transfer units and also of other parameters, which are based on the analogy between the heat and mass transfer processes across the bed height, does not hold. In an ideal case, where the uniformity of temperature across the bed cross section exists, the adiabatic evaporation of water into the air ceases at position Z along e  the bed height as the vapour pressure of water at the solid surface becomes smaller than  Chapter  4.  Results  and  Discussion  173  the partial pressure of water vapour in the air-water mixture ( Figure 4.53(a) ) or the mixture becomes saturated at the adiabatic saturation temperature of the incoming gas ( Figure 4.53(b) ). Isobaric (with respect to partial pressure of water vapour) cooling of gas will take place for the former ( case A ) while condensation of a fraction of the evaporated moisture follows for the latter ( case B ) as the gas proceeds toward the column exit. Therefore, no mass transfer process is present within the distance Z and Z that e  t  the gas travels before exiting the column. The humidity of the gas will remain constant at Yz if the gas exiting the column is unsaturated. Figure 4 . 5 4 ilustrates the state of a c  drying gas, relative to the evaporating surface, as it travels along the column for case A. As Table 4 . 1 8 shows, generally, the exit gas is unsaturated for intense drying conditions; the reverse relationship exists for milder conditions. The results of a comparison between the asymptotic temperature of the inlet gas and the dew point temperature of the gas at point Z are indicative of the likelihood of the occurance of case A for more intense e  drying experiments and case B for milder conditions.  The cases discussed above would  provide us with a local number of mass transfer units for position Z : t  *M  =  Y  °V  Y  I  N  which actually correspondts to height Z up to which the number of heat, e  (4.94)  and mass,  K M , transfer units ( Table 4 . 1 9 ) are supposed to have the same value if the analogy exists. Therefore, in an air water system and for a not very thick packing, to insure absence of case B or more generally the absence of a saturated outcoming gas, the relationship between Z and Z can be obtained through Equation 4 . 9 5 : e  t  z  -  = f  where the number of heat transfer units,  = £  <*">  is calculated using the measured exit gas  Chapter  4.  Results  and  Discussion  174  Figure 4.53: Drying in Relatively Deep Beds of Solids: (a) Humidity-Temperature Relationships in the Gas Phase (case A); (b) Humidity-Temperature Relationships in the Gas Phase (case B); (c) Number of Transfer Units versus Bed Height  Chapter  4.  Results  and  175  Discussion  Z = Z  2  (Column  •  P  •  S t a t e of the gas travelling along the column  v  at  T  outlet)  s  Z = Z  Z = Zj  ( Column  inlet )  Figure 4.54: State of Drying Gas Traveling Along the Column (case A)  Chapter  4.  Results  and  176  Discussion  temperature via the following expression: H  H  =  T i n  ~  (4.96)  T o u t  The sohd hne in Figure 4.53(c) represents the number of heat transfer units as a function of bed height which coincides with the number of mass transfer units between Z = 0 and Z = Z for case A. Even though the section between inlet and Z constitutes the E  E  mass transfer zone, the mass transfer coefficients, ky, in Table 4.16 are evaluated over the whole bed height Z . This would indicate that the Kjvf follows the dashed hne in T  Figure 4.53(c) and hence results in a contradiction of the analogy between the heat and mass transfer processes across the bed height. Therefore, we do come up with a value for JH/JM which greatly deviates from unity. The inequality of the number of transfer units indicates that the total sohd area in the bed does not contribute toward evaporation of water and under specific conditions (case A) the ratio corresponds to relative area for heat and mass transfer and it is operating condition dependent. For an ideal case, where uniformity of temperature across the column diameter prevails, this ratio would provide us with the thickness of the desorption zone. However, in this study due to non-uniformity of particle size and hence temperature, the ratio only corresponds to the surface area of the fraction of the particles having surface temperature of T . Despite this fact, the height of desorption zone is calculated as  and tabulated in Table 4.19. Tz is determined through equality of Q and Q e  t  evap  in  Equation 4.93. A comparison between Tz and the recorded temperature profile along e  the bed height during the constant rate period (Table 4.18) indicates that the calculated height of the desorption zone (Table 4.19) is in a good agreement with the experimental results.  Chapter  4.  Results  177  and Discussion  Table 4.17: Rates of Heat Flow at Different Heat Transfer Modes ( W ) Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  Qc  Qr  2083 4356 7258 5165 7247 > 3704 3106 4114 3496 4366 4157 3269 3853 4131 3746 5294 4096 5749 4904 5664 5148 5098 4350 4347 3955 17 4073 10 4250 274 2692 125 4749 325 3417 197 5589 406 4769 297 4273 253 4207 239  Qt  2083 4356 7258 5165 7247 3704 3106 4114 3496 4366 4157 3269 3853 4131 3746 5294 4096 5749 4904 5664 5148 5098 4350 4347 3973 4083 4524 2816 5074 3614 5995 5066 4525 4446  Qvap  1942 3437 5314 4037 4295 2720 2595 3242 3024 3833 3119 2493 2904 3512 2968 3690 3104 4161 4077 3509 3609 4751 3290 3460 3663 3705 3233 2465 4105 2638 4704 4377 3631 3721  Qsens  29 160 415 187 278 137 152 136 99 173 132 133 134 145 146 242 145 301 219 306 207 251 142 153 159 162 244 50 179 78 263 193 136 135  Qevap  Qet  1971 3598 5729 4224 4573 2857 2747 3378 3123 4006 3252 2626 3038 3656 3114 3933 3249 4462 4296 3814 3816 5002 3432 3614 3822 3867 3477 2516 4284 2716 4967 4570 3767 3856  0.95 0.83 0.79 0.82 0.63 0.77 0.88 0.82 0.89 0.92 0.78 0.80 0.79 0.89 0.83 0.74 0.79 0.78 0.88 0.67 0.74 0.98 0.79 0.83 0.96 0.95 0.77 0.89 0.84 0.75 0.83 0.90 0.83 0.87  Chapter  4. Results  and  Discussion  178  Table 4.18: Summary of Temperature and Humidity Data Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  T,„ "C 62.3 151.8 241J 155.7 204.0 154.8 158.1 147.8 126.3 158.4 150.7 151.2 152.0 148.4 153.9 204.8 154.0 . 220.7 196.4 246.8 202.1 201.7 154.4 . 156.2 146.2 148.1 250.8 170.9 220.5 188.9 245.7 221.3 206.9 204.7  T, °C a  meu. 22.7 51.0 59.2 56.0 58.0 60.0 80.0 43.3 44.4 48.0 46.0 68.6 55.0 44.0 59.0 56.5 50.0 59.8 68.5 81.1 70.3 78.0 46.0 47.6 48.0 46.0 155.0 118.5 120.0 120.0 119.6 119.0 119.0 119.0  calc. 25.3 70.3 102.4 75.9 112.9 82.8 90.4 63.9 54.7 60.2 70.4 85.9 76.9 58.5 76.6 97.2 73.1 99.4 88.1 137.3 106.6 85.4 70.6 68.1 54.6 54.4 179.8 124.1 137.3 137.5 144.8 131.4 135.0 131.6 c  23.7 44.4 56.3 49.5 52.8 45.8 47.9 44.2 45.2 48.2 46.6 44.6 47.3 46.0 46.6 51.2 44.9 52.8 68.6 59.8 68.2 77.8 47.6 48.1 44.1 43.6 121.2 122.6 123.6 122.6 122.6 122.6 122.6 122.6  Tf °C  33.1 72.9 103.3 77.7 91.9 76.6 83.5 69.9 65.3 75.7 72.5 77.3 75.4 71.1 76.5 90.9 73.5 96.5 100.5 111.9 102.2 108.8 73.9 75.0 70.6 70.3 162.0 133.6 146.9 138.5 152.6 146.4 142.8 142.2  rp x  dew  °c  a  22.1 40.1 52.6 46.1 45.8 40.1 42.0 41.1 43.8 46.9 43.3 37.7 43.3 44.4 42.5 46.4 40.6 48.2 68.5 53.8 66.7 78.6 44.5 45.6 42.5 41.9 120.9 122.2 123.2 122.2 122.2 122.2 122.2 122.2  Y (d..b.) b  in  0.0021 0.0114 0.0263 0.0306 0.0246 0.0168 0.0233 0.0139 0.0261 0.0239 0.0212 0.0139 0.0233 0.0201 0.0211 0.0210 0.0145 0.0205 0.1422 0.0450 0.1347 0.2856 0.0195 0.0226 0.0130 0.0114 0.0474 0.0583 0.0541 0.0560 0.0499 0.0523 0.0539 0.0542  out  0.0168 0.0449 0.0854 0.0649 0.0626 0.0465 0.0516 0.0487 0.0567 0.0659 0.0550 0.0406 0.0549 0.0582 0.0535 0.0660 0.0479 0.0713 0.2004 0.0925 0.1848 0.3638 0.0546 0.0600 0.0512 0.0504 0.0580 0.0661 0.0679 0.0658 0.0659 0.0660 0.0660 0.0660  RH,  HHout  % 1.72 0.40 0.12 0.92 0.23 0.53 0.66 0.53 1.85 0.68 0.74 0.48 0.78 0.75 0.66 0.19 0.46 0.13 1.39 0.18 1.16 2.08 0.65 0.69 0.53 0.43 4.35 25.10 8.38 16.18 4.97 7.98 10.80 11.34  % 96.91 58.66 73.74 62.52 56.27 38.70 18.25 89.57 96.98 94.98 87.57 23.39 56.89 102.15 45.62 61.85 62.91 58.35 99.83 30.91 85.74 102.49 92.83 90.54 76.42 81.68 36.54 112.75 110.84 107.40 108.80' 110.93 110.93 110.93  n  as  0.0180 0.0573 0.1085 0.0779 0.0914 0.0639 0.0716 0.0584 0.0617 0.0723 0.0666 0.0597 0.0692 0.0647 0.0679 0.0883 0.0615 0.0941 0.2116 0.1312 0.2066 0.3679 0.0660 0.0700 0.0568 0.0561 0.0635 0.0662 0.0681 0.0662 0.0662 0.0662 0.0662 0.0662  "Dew point of the outcoming gas. ^Corresponds to molar concentration (mol/m ) for Runs 38 to 46. T h e outlet temperature should the analogy between the transfer processes exist. 3  c  RH  avt  % 31.33 14.17 8.56 18.50 9.96 13.19 11.74 17.31 27.40 19.25 18.68 11.13 16.95 20.32 15.27 9.96 14.69 8.68 24.94 7.60 21.99 29.74 18.26 18.68 17.58 16.88 30.27 70.17 49.16 60.66 40.62 48.37 53.60 54.49  Chapter  4. Results  and Discussion  179  Table 4.19: Summary of data Determining the Analogy between the Transfer Processes Run Re Rmax x 10 Re^ z JHI JM KM scm 3  D  e  1  0  18460  572  0.48  1.41  3.31°  2.57  1  13897  616  0.74  2.29  2.79  1.31  0.47  15.1  3.65  4.16  1.27  0.31  7.9  3  12252  380  1.81  4  16593  514  1.37  2.40  2.79  1.29  0.46  12.0  8  15356  476  1.46  4.43  3.37  0.84  0.25  6.3  9  12434  386  1.37  2.22  2.04  0.99  0.49  7.9  10  12443  386  1.75  1.54  1.23  0.88  0.72  8.8  11  12800  397  1.09  1.80  2.50  A  1.52  12  14069  436  1.02  1.60  2.80  A  13  12788  396  0.97  1.95  3.59  A  2.03  14  12840  316  1.05  2.68  3.30  A  1.36  15  12515  678  0.84  1.84  1.49  0.87  0.59  14.4  16  12740  439  0.98  2.45  2.61  1.17  0.45  10.8  17  12885  190  1.18  3.24  5.52  1.92  18  12617  559  1.00  2.00  2.16  1.18  0.55  13.8  A  19  11122  345  1.25  3.35  3.37  1.10  0.33  8.3  20  12684  393  1.05  2.66  3.06  1.24  0.40  10.7  22  11010  341  1.41  2.97  3.18  1.17  0.37  9.1  23  12271  380  1.41  1.90  2.57°  1.83  26  10201  316  2.40  3.12  2.17  0.80  0.37  4.6  29  12290  381  1.25  4.62  4.16  1.19  0.29  7.2  30  13555  420  1.66  1.38  2.53  31  12980  402  1.34  1.71  2.15°  1.41  32  12909  400  1.41  1.65  2.32  1.55  34  13118  407  1.23  1.68  3.27  2.07  0.63  15.5  36  12973  402  1.25  1.95  3.77  2.06  0.55  13.3  38  10896  338  2.43  7.55  1.34  39  13359  414  0.93  3.98  2.56  41  12023  373  1.56  3.50  2.87°  42  12839  398  1.00  4.34  2.71°  43  11185  347  1.78  3.41  2.66  44  11858  368  1.65  3.31  2.57°  45  12453  386  1.37  3.71  2.65  A  A  A  A  A  46 12578 390 1.41 3.59 2.59 Denotes infinitely long heat transfer section (see Appendix A ). A  a  1.96  2.99  Chapter  4.  Results  and  180  Discussion  The J-factors for the section where the bed height does not exceed the thickness of the desorption layer can be calculated by replacing Q  evap  for Q and Tz for T c  e  out  in Equation  4.81. However, it is more appropriate to use the experimental temperature data and the corresponding heat transfer coefficient, as it represents the whole bed height, to come up with an expression for Nusselt number as a function of Reynolds number. With the knowledge of the overall heat transfer coefficient, for a given operating condition, the total heat supplied by the gas can be calculated. Table 4.17 indicates that, conservatively, 80% of the calculated value is used for evaporation of moisture for intense drying conditions. Under less intense drying, approximately 90% of that value contributes toward moisture evaporation. With this information the maximum rate of drying can be approximated. Therefore, the Nusselt number is correlated with the flow properties and the hydrodynamics of the packed bed, tyRe^, and with the thermodynamic state, Gu, of the drying medium, and is represented by Equation 4.97. ^Nu = Q.094^Re ) - Pr°- Gu 0 812  333  0  0 9 5  dp  (4.97)  The results are also shown in Figure 4.55 in terms of the modified Nusselt number ( Equation 4.98 ) as a linear function of the Re^ on logarithmic coordinates. Nu N u  ™ = p o.333 o.o = 0-112fle° r  Git  95  812 p  (4.98)  The goodness of the fit for a 95% confidence limit was determined using Equation 4.10 and also Equation 4.9 for In Nu  m  as a function of In Re^. Both methods indicate that  95% of the time the predicted values approximate the experimental ones within ±14%. Equation 4.97 is in very good agreement with the empirical correlation of Smolsky and Sergeyev [104] as represented by Equation 4.74 for water evaporation from capillary porous bodies at Tdb < 150°C. The positive value of the exponent on the Gu number  Chapter  4.  Results  and  10  1—I  A  181  Discussion  I I I I  T  1  1—I  I I I  J  i  i  i i i  Experimental Fitted  2  CD C/3  ^  II  ^10  S S  '  <L>  A  a o  3 10  10  ' • '• 10  i  10  Re dp Figure 4.55: A Plot of Modified Nusselt Number as a Function of Reynolds number  Chapter  4. Results  and  182  Discussion  in Equation 4.97 seems to be contrary to the previous argument that the mass transfer is intensified with an increase in humidity at elevated temperatures.  However, the  contradiction is resolved considering the asymptotic behaviour of adiabatic saturation temperature at high humidities which would result in a humidity independent Gu increasing and approaching unity with increases in the gas dry bulb temperature.  4.11  Industrial  Implications  There are several factors which affect the design and sizing of both external dryers and hog fuel boilers; the extent and the importance of each parameter depends on the type of process under consideration. In general, as it is both maintenance and capital cost effective, there is an increasing tendency and need to reduce the size of the equipment under consideration. The feed through-put is increased as a measure to maintain the rate of production. This would reduce the residence time of the feed in the dryer or drying section of the hog fuel boiler and hence would increase the moisture content of the product. Therefore, an optimum should be obtained to make a process both economically and physically efficient. When burning is not the objective, a low moisture content and an intact structure of the material are the determining factors in the design of the equipment. However, in drying wood fuel not only is the product structure of no importance but also the complete removal of moisture is not necessary. Table 1.3 indicates that the typical thermal efficiency is about 60-65% for wood-fired boilers as opposed to the 70-75% for fossil-fuel boilers. A comparison with Figure 4.56 suggests that, a final moisture content of 0.3 < M < 0.67  Chapter  4.  Results  and  183  Discussion  kg water/kg dry wood (23% < M' < 40% wet basis ) is sufficient to guarantee an efficiency of 70-75% in a hog fuel boiler operating with an external dryer using stack gases. However, when drying takes place in a hog fuel boiler and the stack gases are discharged at relatively high temperatures, a smaller increase in in thermal efficiency occurs due to reduction in unburned particulate matter, fines and excess air. A more dry fuel, irrespective of the location where drying takes place, increases the boiler performance and capacity for steam production. Therefore, the required residence time for drying and hence the grate heat release rate of the hog fuel boiler (rate of energy delivered per unit surface area of the boiler hearth) should be determined to meet the plant requirements. The times to reach moisture contents of 0.3, 0.4, 0.5, 0.6 are listed in Table D.5. The data indicate that on the average it takes about 800 s to achieve an average moisture content of 0.6 kg H 0/kg 2  dry wood. Considering an average higher heating value of 20  GJ/mt of dry solid, a maximum grate heat release rate of 1080 kW/m is permitted to 2  insure a 70% efficiency for a hog fuel boiler which uses the waste energy of the stack gases. For a given cross sectional area, this corresponds to a bed depth of approximately 25 cm and it is in the range of the value ( 1100 kW/m  2  ) used in European sloping  grate hog fuel boilers as opposed to 2670 kW/m used for the North American ones. 2  Figures 4.57 and 4.58 show the effect of different factors on the time required to reach moisture contents of respectively 0.6 and 0.3 kg i? 0/kg dry wood. Even though a similar 2  trend exists between the drying time and the indicated parameters in both figures, the effects become more accentuated as the desired final moisture content decreases. The rise in temperature has a more intense effect when drying with superheated steam than with air. It should also be noted that there is a very sharp increase in the drying time for d > 9 mm. A comparison between the two figures indicates that the effect of particle p  Chapter  4.  Results  0  and  184  Discussion  20  40  60  80  100  P e r c e n t M o i s t u r e in W o o d , a s F i r e d (Wet B a s i s ) B a s i s ; Higher Heating V a l u e of 8 7 5 0 B tu / l b for Wood and B a r k . S t a c k T e m p e r a t u r e 2 6 0 ° C ( 5 0 0 ° F ) , % Excess A i r Equal to % Fuel M o i s t u r e . Figure 4.56: Effect of Wood Moisture Content on Boiler Efficiency (R.L. Stewart), [39]  Chapter 4.  Results and  Discussion  185  6.0  5.0  "| "T»T-T  -  X  Xref  L  10 cm 3 mm 100 ° C 100 ° C 0.1 d.b.  o A  dp  •  T ir a  o  4.0  Tsteam  Y,  •  CD  3.0  n  *  -  -  —  /  II  Z  CD  2.0  -  •  •  1.0  —  —  cr  •  0.0 h  -1.0  -  -  /  —  " •  _  /  •  ®<  ft  • A  Qret  ^~ -  —  -6. Q  -  A  600  s  1 , ,,  0.0  1.0  2.0  x/x  3.0  4.0  5.0  ref  Figure 4.57: The Effect of Various Parameters on the Normalized Drying Time to Reach M = 0.6  Chapter  4.  Results  and Discussion  7.0  I  I  I  I  I  186  I  I I  I  I  I  I  I  I  I  i  i  '  1  i  X 6.0  -  L  10  cm  dp  3  m m  Tair  100  °C  Tsteam  100  °C  Yin  0.1  d .b.  o A  • 5.0 •  A  /  CD 4 . 0 h CO  © II  CO  3.0 h -A.  x  2.0 h * - -  _  \ ^e \  1.0 h  0.0 0.0  •o  — A—  =  Bret  1  1  1  1  1  1.0  •  1  1  '  1  1  2.0  1  1  x/x  600  1  1  1  3.0  S  •  1  •  1  4.0  1  5.0  ref  Figure 4.58: The Effect of Various Parameters on the Normalized Drying Time to Reach M = 0.3  Chapter  4.  Results  and  187  Discussion  thickness on the drying time is much greater during the completely diffusion controlled region than during the initial stages of the falling rate period, this suggests that the drjnng process is accelerated for smaller particles more due to a shorter diffusional path than due to a greater transfer area. Therefore, for a final value of M =0.6, not very much is gained through reduction of the particle size beyond ~ 7 mm. There is a gradual increase in drying time with increasing bed height, which is representative of fuel through-put for a given cross sectional area. As Figure 4.57 indicates, to insure the final moisture content of 0.6 kg i7 0/kg dry wood, a 30% increase in the 2  bed height from a height of 25 cm would require an increase in the residence time which would only increase the grate heat release rate by 10% from 1100 kW/m . Extrapolating 2  the relationship between the drying time and the bed height (see Appendix  A, Page  252).  results in the following approximation: / %change in the \ _ / %change in the \ V grate heat release rate) ~ \ bed height )  204 1014L 4- 204  . ^  .  where L denotes the final bed height in m. Increases in humidity at Ti = 202° C would very gradually reduce the required residence n  time for the wood to get to a given moisture content, and it becomes less gradual as the desired moisture content decreases (Figures 4.57 and 4.58). This is due to a relatively longer induction period for humidified air drying which counter-balances the rapid increase in Rmax with increases in humidity. The induction period is shortened with increases in the inlet temperature and at higher inlet humidity. The combined effect of the rise in both the induction period and Rmax makes humidified air a good viable drying medium particularly at high temperatures, high inlet humidities and when a more dry product is required. The use of humidified air and superheated steam would also reduce the fire hazards and, as was determined visually, would not cause any shrinkage nor alter  Chapter  4.  Results  and  Discussion  188  the stuctural appearance of the material. Recirculation of boiler flue gases for the use in the external dryers is already common practice. This process has several advantages as it reduces the thermal losses from the boiler while it benefits from the positive effects of increasing both gas humidity and velocity on the drying process. Recycle of a portion of stack gases to the underfire air system may improve drying on the grate of hog fuel boilers particularly if compartmentalization of the undergrate air is viable. Under this condition, flue gases are fed under the inclined section of the grate which is usually used for the drying process. Hot air enters the boiler from the second compartment where it continues to dry the fuel on the grate and initiates burning. The waste energy from the unrecycled portion of the flue gas can contribute towards heating the air entering the second compartment.  Chapter 5  Concluding Remarks  Convective batch drying experiments in a packed column were carried out to examine the effect of operating conditions on the drying kinetics of Western Hemlock hog fuel particles. The instantaneous drying rates were determined and used for preparation of drying rate curves (R vs 6, R vs M and M vs 0) and for subsequent data analysis. The experimental data indicate that the drying process consists of three distinct regions of induction ( heat-up ), heat transfer, and falling rate periods. The drying behaviour during each period are operating-condition dependent. With the exception of a few cases, both the induction and the heat transfer controlled regions are short and generally last about 150 to 400 s. A typical drying rate curve (R vs M) indicates that, following the induction period, the drying process is represented by a maximum,  Rmax,  rather than a  sustained constant rate value. The transition from this heat transfer controlled period to the falling rate period usually takes place at 0.8 < M  cr  Generally, M  cr  < 1.1 kg water /kg dry sohd.  decreases as the intensity of the drying conditions decrease.  The falling rate period is generally represented by a linear relation of drying rate as a function of moisture content. The slope of this hne, ui, increases with increases in the drying intensity. With the exception of the few runs taking place under very mild drying conditions, the equilibrium moisture content, M , has a finite value. M , M ,u; and e  189  CT  e  5.  Chapter  Concluding  more specifically  Rmax  190  Remarks  have been used to quantify the drying process with respect to the  particle thickness (d ), the initial moisture content of the sample (M ) and the height of a  p  the bed (L), and to the inlet temperature (T^), velocity (V; ) and composition of the n  drying medium. As the particle thickness decreases and the transfer area increases, there is a higher degree of surface evaporation and the drying process becomes less dependent on the internal processes. Therefore, for the thinner fractions of 2-4mm and 4-6mm, the drying rate curve of R vs M becomes flatter and R has a finite value to essentially zero moisture content. For the thicker fractions, the drying rate approaches zero at M , and the critical e  moisture content increases resulting in a more distinct maximum value during the heat transfer controlled period. The maximum drying rate decreases linearly with increases  Under otherwise equal conditions, the drying rate curve of R vs M flattens with increasing bed height, L, or increasing the extent of surface evaporation due to increases in the initial moisture content, M . Neither of these parameters has any effect on the drying behaviour D  during the falling rate period and hence on u). There is a linear relationship between and L ~  2  R  m  a  x  over the range 12 cm < L < 33 cm.  Drying runs at inlet temperatures of both 153 and 205°C indicate that, on the average, there is a 21% rise in Rmax,  Rm  ax  for approximately a 31% rise in velocity. This suggests that  which is governed by heat transfer, is related to the mass flow of gas, and hence  to the Reynolds number, to a power of approximately 0.7. Drying is more affected by changes in temperature than in massflowrate. Under a given condition,  R  m  a  x  increases  by about 70% and 10% for a 16% rise in velocity due to, respectively, an increase in temperature at constant mass flow rate and an increase in mass flow rate at constant  Chapter  5. Concluding  191  Remarks  temperature. Particularly at lower temperatures, the falling rate period remains relatively unaffected by the change in velocity due to mass flow rate. However, the effect of velocity on the falling rate is appreciable for velocity changes due to temperature or due to mass flow rate at higher inlet temperatures. Drying experiments with relatively dry air ( Y = 0.0204 kg water / kg dry air ) and at 126 °C < Ti < 221°C indicate that both R n  and u increase with increases in temper-  max  ature. Due to spontaneous ignition of wood there was no data collected at T; = 221°C n  for M < 0.4; however, the remaining runs are indicative of a linear relationship between u> and T  in  < 221°C for 0.3 < M < 0.6. A quadratic expression is used to predict the  effect of temperature on Rmax- The same type of relationship, although stronger, exists between Rmax and T; with superheated steam drying at 215 kPa absolute pressure n  and 171 < T; < 246°C. At a constant mass flow of the drying medium, evaporation n  takes place faster in air than in steam for temperatures below 180 °C ( the inversion point); however, the relationship is reversed above this point. The critical moisture content decreases with increasing temperature for air drying while it remains approximately constant for superheated steam drying at T; > 190°C. In air there are limitations on n  predrying due to fire hazards, particularly at temperatures above 200°C. Drying with superheated steam ehminates the possibility of fire hazard and seems to cause less shrinkage of the wood material. Therefore, it can particularly be considered as a good choice for processes where burning is not the final objective. Addition of CO2 to simulate flue gas at stoichiometric burning conditions, indicates that the drying kinetics are insensitive to the C(9 content of the drying gas. However, 2  humidity of the drying media has an appreciable impact on the drying rate. Drying runs at approximately 202 °C indicate that the induction period increases and also the  Chapter  5. Concluding  Remarks  192  evaporation becomes more of a surface phenomenon with increases in humidity. The slope of the drying rate curve remains relatively unaffected with changes in humidity. However, there is an exponential increase in Rmax with decreases in the inverse of absolute humidity. This relationship, however counter intuitive, is explained through humidification process which accompanies the drying process. As the maximum rate of evaporation of water is determined by the change in the enthalpy of the drying medium, any increase in air humidity would result in two competing processes of a rise in the specific heat which is counter-balanced by the reduction of the thermal gradient. It is shown that at high temperatures the latter is relatively insensitive to changes in humidity and thus, the former which is an increasing function of humidity would become the controlling factor in the evaporation process. Consequently, thermodynamics indicates that at temperatures above the inversion point, the higher the air humidity, the faster would be the evaporation of water from a fully saturated surface. Contrary to initial intuition, the gradient for mass transfer also increases with humidity at high temperatures. The locus of inversion points as a function of air humidity at atmospheric pressure was determined. Below this inversion temperature, increasing humidity inhibits the drying process, but above it increasing humidity promotes more rapid drying. This behaviour justifies the use of closed-loop dryers in which the drying temperature exceeds the inversion temperature. Also, recirculation of the furnace flue gases for use in either the external dryers or the drying section of sloping grate hog fuel boilers is advantageous particularly at high temperatures, as the effect of the induction period becomes less dominant. The structure of the sample seemed to remain more intact with increases in the humidity. This, therefore, makes the humidified air a good alternative where the process is not restricted by fire hazards.  Chapter  5. Concluding  193  Remarks  The residence time of the feed in the drying section to reach a prespecified final moisture content was also determined. For a given cross-sectional area, a maximum bed height of 25cm is obtained for a boiler-dryer system to provide a 70% efficiency (Mfi i na  = 0.6).  This value corresponds to a grate heat release rate of 1080 kW which is approximately equal to the one used in design of European sloping grate wood-fired boilers. The required residence time increases very rapidly with particle thickness as increasing size of the particle beyond 9 mm greatly hinders the drying process. The residence time is not greatly affected by size reduction if final moisture content of not lower than 0.6 kg water/kg dry wood is needed. Humidity has little effect on the residence time, while the time decreases moderately with increasing air and sharply with increasing steam temperature. Normalized drying rate, / , and the characteristic moisture content, $, were determined and the concept of a common characteristic drying curve was verified. All the runs, with the exception of those with different particle size, bed height and inlet humidity, followed an exponential unified curve of / as a function of $ (Equation 4.49). As a rough estimate, the slope of a linear fit of experimental values of hydraulic Euler number, Eu^, versus  ^~~f*  L  is used in conjunction with the Ergun equation to determine  the sphericity, \f, of hog fuel particles.  The resulting value of $ = 0.4 is in a good  agreement with the suggested values of Brown [78]. The modified friction factors, / , m  are calculated using the experimental pressure drop data and \? = 0.4 and are within reasonable agreement with the reported values of Leva[76]. The transfer coefficients and the dimensionless groups for the heat and mass transfer processes during the constant rate period were calculated. The results indicate that under high mass transfer rates and when the drying process is controlled by thermodynamics,  Chapter  5. Concluding  Remarks  194  the areas of transfer for the heat and mass transfer processes are not identical; and therefore, the analogy between the two transfer processes would not prevail. In general, it is indicated that under the conditions examined, the packing height of 7 to 14 cm corresponds to the area where both heat and mass transfer occur simultaneously. Considering the concept of volumetric evaporation, the Nusselt numbers were empirically correlated to particle Reynolds numbers as expressed by Equation 4.97. Within a 95% confidence limit, this correlation approximates the experimental values with ±14% accuracy. The results are in very good agreement with those reported by Smolsky and Sergeyev [104] for evaporation from a capillary porous body. A combination of Equations 4.97 and 4.49 provides sufficient quantitative information on the drying rate of hog fuel sized particles during the entire drying process.  Nomenclature  Symbol  Description  Units  Roman  a ,ai,a  constants in Equations 4.46 and 4.48  a'i,b'i,c'i  constants in Equations 4.1 and A. 114  A  constant in Equation 4.76  Aij  coefficient in Equation A. 15  A  p  A  s  0  2  m /m  3  specific surface area  m /m  3  solid surface area in the column  m  b  thickness of the slab  m  bi  average thickness of zth thickness fraction  m  B  constant in Equation 4.26  c  specific heat in the gaseous state  J/kg-K  c  specific heat in the gaseous state  J/kmol-K  C  molar concentration  kmol/m  Cf  molar concentration at film temperature  kmol/m  3  logarithmic mean concentration difference  kmol/m  3  CL  specific heat in the liquid state  J/kg-K  C  correction factor for radiation heat transfer  p  p  Cj  r  Cs  m  2  2  specific heat of gas mixture per unit dry air  195  2  J/kg-K  3  Nomenclature  Symbol  Description  Units  Cs  specific heat of gas mixture per unit dry air  J/kmol-K  Cw  molar concentration of water  kmol/m  dh  hydraulic diameter Equation 4.58  m  d  Sauter mean or arithmetic mean thickness  m  D  diameter of the column  m  a  apparent moisture diffusivity within wet material  m /s  v  apparent vapour diffusivity within dry material  m /s  DWG  water diffusivity within gas medium  m /s  Dww  water vapour self diffusivity  m /s  E  emissive power in radiation heat transfer  p  D D  3  2  2  2  2  energy used for volumetric evaporation  W/m  EWG  energy of molecular attraction  J/molecule  f  relative drying rate  ff  friction factor Equation 4.59  fmf  modified friction factor Equation 4.56  F  F-type mass transfer coefficient  kg/m -s  G  superficial total gas mass velocity  kg/m -s  E  V  G  b  3  2  2  Gibbs function  G'  superficial dry gas mass velocity  kg/m -s  h  convective heat transfer coefficient  W/m2-K  2  h  convective heat transfer coefficient with no mass transfer W/m -K  H  enthalpy per unit either dry gas or incoming steam  J/kg  H  enthalpy of gas per unit gas  J/kg  2  d  Nomenclature  Symbol  197  Description  Units  grate heat release rate  kW/m  higher heating value of dry sohd  kJ/kg  drying intensity  m  drying intensity at the bed inlet  m  lave  mean drying intensity along the column  m  k  Boltzmann's constant  J/molecule-K  k  humidity dependent mass transfer coefficient  kg/m -s-(mol/m )  k  conductivity of fluid  W/m-K  K  conductivity of solid  W/m-K  ky  humidity dependent mass transfer coefficient  kg/m -s  Ky  humidity independent mass transfer coefficient  kg/m -s  kc  humidity independent mass transfer coefficient  kg/m -s-(mol/m )  I  c  f  Ky  s  2  2  3  2  2  2  3  humidity independent mass transfer coefficient during surface evaporation  kg/m -s 2  humidity independent mass transfer coefficient  eq  771 /  m M  during sub-surface evaporation  kg/m -s  characteristic length  m  height of the column  m  equivalent wet length  m  radiating beam length  m  total mass flow rate  kg/hr or kg/s  dry gas mass flow rate  kg/hr or kg/s  dry basis wood moisture content  kg H 0/kg  2  2  dry sohd  198  Nomenclature  Symbol  Description  Units  M  initial dry basis wood moisture content  kg H 0/kg  dry solid  M„  critical dry basis wood moisture content  kg H 0/kg  dry solid  M  equilibrium dry basis wood moisture content  kg H 0/kg  dry solid  M,  dry basis wood moisture content at the surface  kg H 0/kg  dry solid  M'  weight percent wood moisture content  M  average dry basis wood moisture content  kg H 0/kg  dry solid  M„  average critical dry basis wood moisture content  kg H 0/kg  dry solid  M  molecular weight  kg/kmol  MG  molecular weight of dry gas  kg/kmol  Mw  molecular weight of water  kg/kmol  MWG  vW+A  (kmol/kg)-  n  exponent in Equation 4.56  n  number of points, Equation 4.10  rii  molecules of species i  rii  number of ith point, Equation 4.9  N  mass transfer flux  kg/m -s  N°  mass transfer flux at the inlet conditions  kg/m -s  Nmax  maximum mass transfer flux, corresponding to  Nw  mass transfer flux for water  kg/m -s  N  molal flux of mass transfer  kmol/m -s  N  number of transfer units  N#  number of heat transfer units  0  e  number of mass transfer units  2  2  2  2  2  2  kmol  2  2  Rmax  kg/m -s 2  2  2  Nomenclature  Symbol  Description  P  number of parameters  P  pressure  Pa  Pc  critical pressure  Pa  Pt  total pressure  Pa  Pv  vapour pressure  Pa  P  partial pressure  Pa  Pco  partial pressure of CO2  Pa  Pw  partial pressure of water  Pa  pp  0.5( + p)  Pa  p  volumetric power  kg/m -s  1  flux of heat transfer  W/m  Q  rate of heat transfer  W  Qc  rate of convective heat transfer  W  Qet  Q evap 1Q t  Q evap  rate of heat flow for evaporation  W  Qr  rate of radiative heat transfer  W  Qsens  rate of heat flow for sensible heating  W  Qt  total rate of heat transfer  w  Qvap  rate of heat flow for change of state  w  R  rate of drying per dry weight of sohd  s-  RE  experimental rate of drying per dry weight of sohd  s"  RP  fitted rate of drying per dry weight of sohd  s-  Rg  gas constant  J/kmol-K  2  Pt  Units  3  2  1  1  1  Nomenclature  200  Symbol  Description  Units  RG  molecular separation at collision for dry gas  nm  Rmax  maximum drying rate per dry weight of sohd  s-  Rw  molecular separation at collision for water  nm  RWG  molecular separation at collision for humid gas  nm  Rep  replicate  Rep  mean value of replicates  RH  relative humidity  RM  M /M  R'  3R/d6  R"  dR'/dd  S  cross sectional area of the column  m  SEE  residual sum of squares due to pure experimental error  s-  Si  defined by Equation A. 16  Sij  defined by Equation A. 17  Sji  defined by Equation A. 18  SL  residual sum of squares due to lack of fit  s"  SP  sum of squares of the predicted values  s-  SR  residual sum of squares of the fitted curve  s"  cross sectional area of the column  m  temperature  °C or K  adiabatic saturation temperature  °C or K  average temperature  °C or K  dew point temperature  °C  T T J-  T T  W  (p/p )  dew  v  G  as  ave  1  2  2  2  2  2  2  or K  Nomenclature  201  Symbol  Description  Units  T  film temperature  °C or K  T  inlet temperature  °C or K  Tim  logarithmic mean temperature difference  °C or K  T,  surface temperature  °C or K  T  gas temperature at point Z along the column  °C or K  U  overall heat transfer coefficient  W/m -K  Vb  volumetric bulk flow rate of solids  m /s  Vg  molar volume of gas  m /kmol  V  molar volume of liquid  m /kmol  volumetric flow rate of solids  m /s  V  velocity  m/s  v,  sohd volume  m  3  v  total volume  m  3  t  v  void volume  m  3  v  weight of dry sohd in the column  kg  weight of wet sohd in the column  kg  X  distance  m  Xi  the ith point of an independent quantity, Equation 4.9  f  - in 1  z  t  V  s  w w  ds  yy ws  2  3  3  3  3  X x  mean value of the independent quantities, Equation 4.9  X  mole fraction  Y  dry basis air humidity  Yi  the fitted value of the ith point, Equation 4.9  kg # 0/kg 2  202  Nomenclature  Symbol  Description  Units  Yim  logarithmic mean humidity difference  kg H 0/kg  wet gas  Y'  wet basis air humidity  kg H 0/kg  wet gas  Y'  mole fraction of water vapour  z  diffusion path in boundry layer  m  i  independent parameter in Equation 4.45  m  Z  distance along the column  m  Z  c  Z  e  r  2  critical compressibility factor position along the column up to which heat and mass transfer processes occur simultaneously  Z  2  m  Z /Z e  r  Greek a  hygrothermal ratio  a  fitting parameter Equation 4.60  m  (3  m  Bi /Bi H  M  7  evaporative resistance coefficient  8  thickness of the boundary layer  £  deviation within 95% confidence interval  s  _1  experimental errors within 95% confidence interval  s  _1  95% confidence interval  s  _1  relative experimental errors with 95% confidence limit  s  _1  8  ee  8  8  P  ee  m  standard deviation of the predicted value within  A  denotes a change  Ap  pressure drop  Pa  Nomenclature  203  Symbol  Description  Units  e  voidage in the bed  m /m 3  3  gas emittance £»  sohd emittance  C  depth of recession  m  V  viscosity  kg/m-s  6  time  s  K,  overall mass transfer coefficient  kg/m -s  X  latent heat of evaporation  J/kg  X  molal latent heat of evaporation  J/kmol  A  defined by Equation A.6  P  Joule-Thomson coefficient  PD  diffusive resistance coefficient  Pi  chemical potential of the ith component  t  tortuosity  p  density  kg/m  3  Ps  density of dry wood (with green volume)  kg/m  3  °~ee  standard deviation of pure experimental errors  1/s  O-n  sample standard deviation  1/s  sample estimate of the population standard deviation  1/s  standard deviation of the fitted value of the drying rate  1/s  standard deviation of the fit  1/s  0~R(8)  accuracy of the drying rates  1/s  0~R  accuracy of the maximum drying rates  1/s  o-  p  2  Nomenclature  204  Symbol  Description  Units  cr _x  relative population standard deviation  1/s  &R(8)  relative accuracy of the drying rates  1/s  VRmax  relative accuracy of the maximum drying rates  1/s  r  depth of penetration of the drying front  (f>  humidity potential coefficient  {fi^wt  weight fraction of i t h thickness fraction  4>ij  coefficient in Equation A.9  4>ji  coefficient in Equation A. 10  $  characteristic moisture content  <p  Ackerman coefficient, Equation 4.68  X  fractional depth of recession  tp  porosity of the wood  \P  sphericity  ui  slope during falling rate period  u'  du/de  n  m  kg/kg  m/m . m /m 3  s  - 1  s"  Subscripts  Description  Subscripts  Description  a  air  b  boiling  a  apparent  c  conduction  as  adiabatic saturation c  critical  ave  average  critical  cr  2  3  Nomenclature  205  Subscripts  Description  Subscripts  Description  d  dry  ma  mixed air  da  diluting air  max  maximum  db  dry bulb  mix  mixture  dg  dry gas  o  initial properties  ds  dry solid  out  properties at the bed outlet  e  equilibrium  V  predicted  e  experimental  p  predicted  E  experimental  R  residual  ee  experimental error  s  solid  EE  experimental error  s  surface  f  properties at the film temperature sam  sample  fall  denotes falling rate period  sat  saturation  9  dry gas  ss  sub-surface  9  grate  st  steam  G  dry gas  t  total  GW  gas-water  V  vapour  H  heat transfer  vap  vapour  h  hydraulic  w  water  h  heat transfer  w  water  i  interfacial  wb  wet bulb  in  properties at the bed inlet  ws  wet solid  L  lack of fit  wv  water vapour  t  liquid  X  cross sectional area  M  mass transfer  z  position along the column  Nomenclature  Dimensionless Groups  206  Definition  Biff  heat transfer Biot number  hl/k.  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[83] Mclean, J.,D., "Effect of Steaming on the Strength of Wood," American WoodPreservers Association, Vol. 49, 1953, pp. 88-112.  [84] Mclean, J.,D., "Effect of Heating in Water on the Strength Properties of Wood," American Wood-Pre servers Association, Vol. 50, 1954, pp. 253-281.  [85] Yoshida, T., and Hyodo, T., "Evaporation of Water in Air, Humid Air, and Superheated Steam," Ind. Eng. Chem., Process Design and Development, Vol. 9,  No. 2, 1970, pp. 207-214.  [86] Nomura, T., and Hyodo, T., "Behaviour of Inversion Point Temperature and New Applications of Superheated Steam Vapour Drying," in Drying'85, Editor: Toei, R., and Mujumdar, A., New York, Hemisphere Pubhshing Corporation, 1985, pp. 517-522.  [87] Keey, R.B., Suzuki, M., "On the Characteristic Drying Curve," International Journal of Heat and Mass Transfer, Vol. 17, No. 12, 1974, pp. 1455-1464.  References  218  [88] Toei, R., Okazaki, M., Kimura, M., and Kubota, K., "Drying Characteristics of a Porous Sohd in Super-heated Steam," Kagaku Kogaku, (abridged version), Vol. 5, No. 1, 1967, pp. 140-141.  [89] Chu, C.J., Lane, A.M., and Conklin, D., "Evaporation of Liquids into their Superheated Vapors," Ind. Eng. Chem., Vol. 45, No. 7, 1953, pp. 1586-1591.  [90] Wenzel, L., and White, R.R., "Drying Granular Solids in Superheated Steam," Ind. Eng. Chem., Vol. 43, No. 8, 1951, pp. 1829-1837.  [91] Morgan, R.P., and Yerazunis, "Heat and Mass Transfer during Liquid Evaporation from Porous Materials," Chem. Eng. Prog. Series, Vol. 63, No. 79, 1967, pp. 1-13.  [92] Peck, R.E., and Kauh, J.Y., "Prediction of Drying Schedules," A. I. Ch. E. J., Vol.15, 1969, pp. 85-88.  [93] Eastwood, J., Matzen, E.J.P., Young, M.J., and Epstein, N., "Random Loose Porosity of Packed Beds," British Chemical Engineering, Vol. 14, No. 11, 1969, pp. 1542-1545.  [94] Mikhailov, M.D. and Ozi§ik, M.N., United Analysis and Solutions of Heat and  Mass Diffusion, John Wiley & Sons, New York, 1984.  [95] Schadler, N. and Kast, W., "A Complete Model of Drying Curve for Porous Bodies-Experimental and Theoretical Studies," International Journal of Heat and Mass Transfer, Vol. 30, No. 10, 1987, pp. 2031-2044.  References  219  [96] Stanish, M.A., Schajer, G.S., and Kaihan, F., "Mathematical Modeling of Wood Drying from Heat and Mass Transfer Fundamentals," in Drying '85, Editors: Toei, R., and Mujumdar, A.S., New York, Hemisphere Publishing Corporation, 1985, pp. 360-367.  [97] Hassan, M., Mujumdar, A.S., and Al-Taleb, M., "Laminar Evaporation from Flat Surfaces into Unsaturated and Superheated Solvent Vapour," Drying '86, Editor: Mujumdar, A.S., New York, Hemisphere Publishing Corporation, 1986, pp. 604616.  [98] Kast, W., "Coefficients for the Combined Heat and Momentum Transfer in Laminar and Turbulent Boundry Layers," in Proceedings of the Heat Transfer Conference held in Munich, 1982, pp. 263-268.  [99] Prat, M., "Heat and Mass Transfer Predetermination between a Drying Material and an External Flow," Drying '86, Editor: Mujumdar, A.S., New York, Hemisphere Publishing Corporation, 1986, pp. 105-111.  [100] Loo, E., and Mujumdar A.S., "A Simulation Model for Combined Impingement and Through Drying Using Superheated Steam as the Drying Medium," Drying '84, Springer Verlag, New York, 1984.  [101] Smolsky, B.,M., "Heat and Mass Transfer with Liquid Evaporation," in Progress in Heat and Mass Transfer, Vol. 4, New York, Pergamon Press, 1971, pp. 97-107.  [102] Telles, A.S., and Duckler, A.E., "Statistical Characteristics  of Thin, Vertical,  Wavy, Liquid Films," Ind. Eng. Chem. Fundamentals, Vol. 9, 1970, pp. 412-421.  References  220  [103] Brumfield, L.K., Houze, R.N., and Theofanous, T.G., "Turbulent Mass Transfer at Free, Gas-liquid Interfaces, with Applications to Film Flows," International Journal of Heat and Mass Transfer, Vol. 18, Great Britain, Pergamon Press, 1962, pp. 1077-1081.  [104] Smolsky, B.,M., and Sergeve, G.,T., "Heat and Mass Transfer with Liquid Evaporation," International Journal of Heat and Mass Transfer, Vol. 5, Great Britain,  Pergamon Press, 1962, pp. 1011-1021.  [105] Luikov, A.V., and Mel'nikov, I.R., "Heat and Mass Transfer in Evaporation Processes (Teplo-imassoobmen v protsessakh ispareniya)," hid. Akad. Stroitel'stva i Arkhitektury SSSR, 1959.  [106] Luikov, A.V., Theoretical Fundumentals of Building Thermophysics (Teoretich-  eskiye Osnovy Stoitel'noi Teplofiziki), Izd. Akad. auk B.S.S.R., Minsk, 1961.  [107] Gukhman, A.A., "One of the Arguments for Criterial Equations of Heat and Mass Transfer in Evaporation and Drying Processes" (Ob odnom iz argumentov kriterial'nykh uravnenii teplo-i massoobmena v protsessakh ispareniya i sushki), Teploenergetika, No. 5, pp. 32-41, 1954.  [108] Katto, Y., and Aoki, H., "Pecularity of Evaporating Liquid-surface with Reference to turbulent Heat Transfer," Heat and Mass Transfer, Vol. 2, Izd. Nauka i Tekhnika, Minnsk, 1968, pp. 309-319.  [109] Colburn, A.P., and Drew, T.B., "The Condensation of Mixed Vapours," Trans. Am. Inst. Chem. Engrs., Vol. 33, 1937, p. 197-215.  References  221  [110] Vasilieva, G.V., "Study of Heat and Mass Transfer with Deepening of a Liquid Evaporation Surface in a Capillary-porous Body," Heat and Mass Transfer, Vol. 2, Izd. Nauka i Tekhnika, Minsk, 1968, pp. 336-345.  [Ill] Zakharov, V.M. and Krylov, B.S., "Heat and Mass Transfer with Deepening of an Evaporation Surface," Heat and Mass Transfer, Vol. 2, Izd. Nauka i Tekhnika, Minsk, 1968, pp. 346-350.  [112] Gamson, B.W., Thodos, G., Hougen, O.A., "Heat, Mass and Momentum Transfer in the Flow of Gases through Granular Solids," A. I. Ch. E., Trans., Vol. 36, 1942, pp. 1-35.  [113] Parti, M., "Heat and Mass Transfer in Packed Beds," in Drying' 80, Editor: Mujumdar, A.S., New York, Hemisphere Publication Corp. Vol. 2, 1980, pp. 219223.  [114] Perry, R.H. and Chilton, C.H., Chemical Engineers' Handbook, 6th Edition, New York, McGraw-Hill Book Company, pp. 3-128 to 3-134.  [115] Perry, R.H. and Chilton, C.H., Chemical Engineers' Handbook, 6th Edition, New York, McGraw-Hill Book Company, pp. 3-278 to 3-285.  [116] Wilke, C.R., and Lee, C.Y., "Estimation of Diffusion Coefficients for Gases and Vapours," Ind. Eng. Chem. , Vol. 47, 1955, pp. 1253-1257.  [117] Hirschfelder, J.O., Bird, R.B., and Spotz, E.L., "Viscosity and Other Physical Properties of Gases and Gas Mixtures," Trans, of ASME , Vol. 71, 1949, pp.  References  222  921-937.  [118] Treybal, R.E., Mass-Transfer Operations, 3rd Edition, New York, McGraw-Hill Book Company, 1980, pp. 31-34.  [119] Perry, R.H. and Chilton, C.H., Chemical Engineers' Handbook, 5th Edition, New York, McGraw-Hill Book Company, 1973, p. 3-206.  [120] Perry, R.H. and Chilton, C.H., Chemical Engineers' Handbook, 5th Edition, New York, McGraw-Hill Book Company, 1973, p. 3-241.  [121] Smith, J.H.G., Kozak, A., "Thickness, Moisture Content, and Specific Gravity of Inner and Outer Bark of Some Pacific Northwest Trees," Forest Products Journal, Vol. 21, No. 2, 1971, pp. 38-40.  [122] Keey, R.B., Drying: Principles and Practice, International Series of Monographs in Chemical Engineering, Vol. 13, Oxford, Pergamon Press, 1972, p. 127.  [123] Keey, R.B., Drying: Principles and Practice, International Series of Monographs in Chemical Engineering, Vol. 13, Oxford, Pergamon Press, 1972, p. 344.  [124] Kreith, F., Principles of Heat Transfer, Chapt. 5, 3rd Edition, Series in Mechanical Engineering, New York, Harper &; Row Publishers, 1973.  [125] Hottel, H.C., and Egbert, R.B., "Radiant Heat Transmision from Water Vapour," Am. Inst. Chem. Engrs., Vol. 38, 1942, pp. 531-565.  223  References  [126] Keey, R.B., Drying  Operations,  Oxford, Pergamon Press, 1978, p. 171.  [127] Perry, R.H. and Chilton, C.H., Chemical  Engineers'  York, McGraw-Hill Book Company, 1973, p. 5-52.  Handbook,  5th Edition, New-  Appendix A  Sample Calculations  Determination of Factors Affecting the Properties of the F l u i d  Density, p, of the drying medium is determined considering an ideal gas law through the following equation:  > = kr where  p  = pressure (Pa)  M  = molecular weight (kg/kmole)  R  — gas constant (J/kmole-K)  T  = Temperature (K).  g  <*•»>  Specific heat, c , of the components of the drying medium is calculated [114] p  using the equations given in Table 2. The heat capacity of the mixture is obtained through: C  p * mi  where  =~Y1  i Pi  U  C  ( - ) A  2  denotes the number of molecules of the ith component and n is the the  total number of molecules in mixture.  224  Appendix  A. Sample  225  Calculations  Table A.l: Heat Capacities of the Components of the Drying Medium Subst. C0 N  2  2  o  2  H0 2  State g g g g  c x 1(T (J/kmole-K) 43.294 + 0.00115T - 818558.5/T 34.626 + 0.00108T - 785899.9/T  Range of T  3  p  (K) 273-1200 300-5000 300-3000 300-2500  2  2  27.216 + 0.004187r  Uncertainty  2  34.417 + 0.00063T + 0.00000561T  2  % l\  3 3 -  3. Viscosity, 77, of pure substances is calculated [115] via Equations A.3 to A.7 for Nonpolar gases: 77A = 10- x (4.61T, 7  0  618  - 2.04e-  + 1.94 - -  a4497;  4  e  058T  ' + 0.1)  (A.3)  Polar gases, hydrogen-bonding, T < 2.0: r  77A = 10  x (0.755T - 0.055)Z ~  -7  (A.4)  5/4  P  C  polar gases, non-hydrogen-bonding, T < 2.5 : r  77A = 10~ x (1.97; - 0.29) Z 7  4/5  (A.5)  2/3  c  A =  6  C  (A.6)  T}' M- / pV r c l  2  0.371 - 0.0343  3  log Vc  (A.7)  The mixture viscosity is determined using the following expression: VTUIX  XiTji  ^ ^  (A.8)  i= l  where: [1 + (r; /nj) (Mj/Mi) ] 1/2  =  [8(1 + 4>ji  1/4  i  =  Mi/M^l  2  (A.9)  2  (•nihi){MilM )<t>i j  i  (A.10)  endix  A. Sample  and  226  Calculations  T  = temperature (K)  M  = molecular weight  Z  = compressibility factor  77  = viscosity (kg/m-s)  c,r = denote critical and reduced properties, respectively = mole fraction of the ith component.  Xi  Thermal conductivity of the fluid, kf, is obtained [115] via thermal conductivities of its constituents by averaging Eucken (Equation A.11) and a modified form of Eucken correlations (Equation A.12) as the former is underpredictive and the latter is overpredictive.  18715.9)-g-  k  =  (c„, +  k  =  (1.32c,, + 18715.9)-|r  (A.12)  =  0.5(k +k )  (A.13)  fil  fi2  k  h  fil  ft2  (A.ll)  Conductivity of mixture is determined using the following expression: h = where  t  (A.14) 3 .  l  kf= heat conductivity (W/m-K) c = specific volume (J/kmole) v  v = viscosity (P) M— molecular weight (kg/kmole) i = denotes properties of the ith component.  Appendix A. Sample Calculations  227  Aij can be estimated using Lindsay Bromley relation: Vi, J}3/4, M  {1 +  +  T  -I 1/2  i  S  •\2(T + Sjj * T + Si {  Si  S  =  i:i  =  9-  —  1.5T  (A.15)  }  (A.16)  bi  (A.17)  CiSiS^  2  (A.18)  where C = 1, T is temperature (K) and T is the boiling point temperature of the bi  ith component in degrees Kelvin.  5. Diffusivity of water vapor i n the d r y gas, DWG, is calculated using a modified form [116] of the Hirschfelder-Bird-Spotz method [117] which is recommended [118] for gas mixtures containing at least a non-polar gas: 1Q- (1.084 - 0 . 2 4 9 M ^ ) T ' M G (R ) f(kT/E ) 4  3  G  =  ,  2  M  2  PT  WG  (  A  WG  with:  where  T  = absolute temperature (K)  Mw, MQ  = molecular weights of water and dry gas (kg/kmole)  Pt  = absolute pressure (Pa)  RWG  = molecular separation at collission (nm) =  EWG  — energy of molecular attraction (J/molecule)  f(kT/EwG)  = collision function [118].  R w  ^  R q  A A  I 9  M )  Appendix  A. Sample  228  Calculations  6. Inlet temperature, T; , is the average value over the length of a run. n  7. Instantaneous mean temperature, T (6), m  is the average of inlet and outlet  temperatures at any given point in time.  8. Latent heat of evaporation, X, is reproduced by fitting the tabulated data [119] to a spline function.  9. Adiabatic saturation temperature, T , is determined by solving the following ag  Equations 4.21 to 4.24 simultaneously.  10. Vapor pressure, p , of the water is calculated via interpolation of Equation A.21 v  between 20 and 100°C as is shown in Equation A.22. inp„  =  -—^—+const  (A.21)  Kgl  \np  v  =  -4986.667  + 24.9  (A.22)  / A  x  where R , X and T denote the gas constant (J/kmole-K), the molal latent heat of g  evaporation (J/kmole) and the gas temperature in degrees Kelvin, respectively.  A.2  Determination of the Drying Rate and the Related Properties  1. Humidity, Y, is determined through the measurement of the dew point temperature, Tdew, of a diluted  sample,  mixture, and its subsequent substitution for T in  Appendix  A. Sample  229  Calculations  Equation A.22. Substitution of p in Equation A.23 would provide the humidity of v  the mixture: Y = . ^  M {p - ) G  t  K  (A.23)  Pv  where p is the total pressure (Pa) and Mw and MG, respectively, represent the t  molecular weight of water and that of dry gas. The humidity of undiluted sample taken at the inlet and outlet of the drying column (Yi , Y ) are obtained through n  out  humidity of the mixture as represented by: tam  Yimi m  x  m  .  • YfiaTTicla  x  CIA\  \A.Z4J  — T^mix  where m is the mass flow rate and subscripts mix and da, respectively, denote the properties of mixture and diluting air.  2. Mass flow rate of the dry gas, m', is determined using both the inlet total mass flow, m; , and the inlet humidity, Y{ , as is represented by: n  n  m' = m ( l + Y ) in  (A.25)  in  3. Instantaneous drying rate, R(9), is determined through Equation A.26 for superheated steam runs and through Equation A.27 for remainder of the runs. R(6)  =  ( m  ° ;~  R(6)  =  ^-(Y -Y )  u  out  m  in  ,  n  )  (A.26) (A.27)  The accuracy of the calculated drying rates are expressed by the standard deviations of Equations A.26 and A.27 through, respectively, Equations A.28 and A.29. cr ) R{6  =  0.04 x 10~  3  (A.28)  Appendix  A. Sample  230  Calculations  cr  For an average value of  =  m  Rmax  VQQIR  + 88 x 10- x 106  2  (A.29)  3  = 1.5 x 10 for superheated steam runs and -3  Rmax =  1.2 x 10 for rest of drying runs, the following approximation is obtained: -3  =  = 0-025  (A.30)  4. Instantaneous mean superficial mass flow velocity along the column, G (t9), is obtained through the following Equation: m  G {6)  = 0.5{m +m )/S  m  where  S  x  m  out  in  outl  (A.31)  x  = cross sectional area of the column (m) = m  in  +  W R(6) da  5. Inlet velocity, Vi , and Instantaneous mean velocity along the bed,V (0), n  m  are determined by, respectively, substituting T, and n  T (9) ave  in Equation A . l and  subsequent substitution of pi and p (d) in : n  m  V =^ Pin  (A.32)  in  or V (0) = ^  (A.33)  m  6. Average properties,  T , ave  p , ave  G  instantaneous properties (i.e. T (0), m  run.  a v e  and  p (9), m  V  ave  are determined by averaging the  G {Q) and m  V (0)) over the length of a m  Appendix  A.3  A. Sample  231  Calculations  Parameters Determining Solid Properties 1. Moisture content, M, represents the ratio of mass of water to that of dry sohd. Its initial value was determined using a microwave oven while the instantaneous value was obtained using: (A.34) Numerical values are included in Tables C.l to C.34.  2. Particle thickness in a thickness fraction, d , is the arithmetic mean thickPi  ness in fraction which was determined using a Wennberg classifier [70, 71].  3. Particle density, p , is taken as 506.5 kg dry bark/m green volume as is sug3  g  gested by Smith and Kozak [121].  4. Conductivity of the wood, k, is determined by averaging the two relationships y  [120] for respectively weight percent moisture contents of M' < 40% and M' > 40%. k  = p,(0.2006 + 0.0040M') x 10~ + 0.02379 3  tl  ^(0.2006 + 0.0055M') x 10  k k  3  =  0.5(k +k. ) tl  2  W/m-K  -3  + 0.02379  (A.35) (A.36) (A.37)  where p is in kg dry solid/m green volume. 3  s  5. Porosity of the solid, -0, is approximated using the Skarr's [46] analysis of moisture in wood suggesting that complete uptake of water by capillaries will increase  Appendix  A. Sample  232  Calculations  the dry weight by 50%. Bound water, up to fibre saturation point, accounts for approximately 30% of the dry weight of sohd and the remainder (120%) would occupy the pores.  Therefore, for 1000 kg dry wood occupying 2 m of space 3  (p„ ~500kg/m ), the pore volume would be: 3  =  = 1.2 x (1000kg water)/(1000kg/m ) = 1.2 m 3  PH 0  3  (A.38)  2  Thus the porosity becomes:  •tjj =  1 2 — = 0.6 m / m 3  (A.39)  3  6. Krischer's diffusion resistance coefficient in a porous body, po, is defined  by: p  D  = ^  (A.40)  where ip is the sohd porosity and £ is the tortuosity which represents the ratio of the actual path length to that of the apparent one. The following relationship is suggested [122] to approximate the diffusion resistance: PD =  ty- * 1  (A.41)  7. V a p o u r diffusivity through d r y out material, D , is calculated via: V  Dv =  ?m  PD  where DWG is the water vapour diffusivity in the dry gaseous phase.  (A .42)  Appendix  A. Sample  233  Calculations  8. Apparent moisture diffusivity through the wet material, D , is approxia  mated as 0.0015 x l O  A.4  - 6  m /s from the experimental data [123]. 2  Factors Affecting Hydrodynamics of a Packed Bed  1. Bed Volume , V , is measured prior to and just after each run via weighing a t  volume equivalent bucket of water.  2. Voidage , e, is determined by a comparison between the dry solid, V , and the a  bulk volumes, V . The former is calculated using a dry solid density of 506.5 kg dry t  wood/ m green wood. An average value of initial and final voidage is used for sub3  sequent evaluation of other parameters. In the absence of the measured final value, a 10.39% drop in the initial value is used to approximate the final voidage in the bed.  3. Average particle size, d , is expressed by the arithmetic mean thickness, d , p  Pi  of a thickness fraction for unmixed samples or by the Sauter mean thickness of a mixture as shown in Equation A.43. 1  (A.43)  d  Pi  where  (<f>i)  wt  is the weight fraction of the ith thickness fraction.  4. Specific solid surface, A , is calculated via: p  6(1-0 d  p  (A.44)  Appendix  A. Sample  234  Calculations  where e is voidage and d is particle size. p  5. B e d h e i g h t , L, is obtained through the following expression: L = 4s  (A.45)  4  where V and D are bed volume and diameter, respectively. t  6. P a c k i n g D e n s i t y  The following comments are made concerning the uniformity of the packing density: (a) The drying chamber is 20 cm in diameter and some particles have lengths reaching about one-half the column diameter. (b) The diameter of the chamber was the maximum that could be used from experimental point of view. The intention was to study actual (as received) hog fuel particles rather than smaller particles. (c) Because of the size distribution, serious bypassing would not be expected. However, it is possible that some gas bypassing has occured, but this was not verified experimentally. (d) Pressure drop data along the bed height are indicative of the packing uniformity in the axial direction. Data in Table 4.13 show local A p / L  values to be  essentially constant. (e) Based on particle sauter mean thickness the ^ was quite low; this ratio was ranging between 0.015 to 0.055 from thinnest to thickest thickness fractions. (f) The experiments were done with solids in a loose packed voidage in order to simulate the moving bed.  Appendix  A.5  A. Sample  235  Calculations  Determination of Heat and Mass Transfer Coefficients and Dimensionless groups during Constant Rate Period  1. Humid heat, Cs, is obtained through the following equation: = Y^-  C s  where • .  M  (A.46)  + ^M  w  '  v  G  = humidity (kg H 0/kg dry gas)  Y  2  c  — specific heats of water (J/kg-K)  Pw  Cp  = specific heats of dry gas (J/kg-K)  g  2. Outlet temperature, T  ouf  , is measured as the mean of the approximately constant  values of the outcoming temperature during the constant rate period. The outlet temperature is also calculated by Equation A.47 and A.48 for, respectively, air and steam drying runs. J-out(calc)  n  out  =  T J-out{calc)  — Yi )(CLTOB — X ) + Csi Ti ^  {Y  m  0  rn c T in  Pin  + Am(C T  in  L  n  . l - 'J A  4  - X) a  =  (A.48J out p  m  where  as  n  c  out  CL = specific heat of liquid (J/kg-K) A = latent heat of evaporation at 0°C 0  3. Average temperature,  T , ave  is represented by:  Tave = 0.5(Tin  + Tout)  (A.49)  4. Film temperature, Tj, during the constant rate period is obtained by: Tf  = 0.5(T  ave  + T) as  (A.50)  Appendix  A. Sample  where T  ag  236  Calculations  approximates the solid surface temperature.  5. Total rate of heat flow, <5t,.is determined through an enthalpy balance across the packed bed (Figure 4.52). Equation A.51 represents an enthalpy balance for humidification of a gas in an adiabatic process between points 1 and 2.  •Hi +  Hi = H  (A.51)  2  where Hi denotes the enthalpy of evaporated moisture. However, as it was described in Sections 2.8 and 4.10, drying during constant rate period might be accompanied by some degree of heat conduction to the solid or of condensation of evaporated moisture. This would result in the modified form of Equation A.51 as is shown by: -Hi + Hi = H + H 2  (A.52)  c  where c and Z, respectively, represent heat conduction to the solid and enthalpy of the net evaporated moisture. Substituting the corresponding values for H , H and 1  2  Hi from Table A.2 would result in the change enthalpy and hence the total rate of heat flow supplied by the incoming gas as are shown in Equation A.53 and A.54 for humid air and superheated steam, respectively.  Qt  =  m'Ca (T -T ) 1  l  2  (A.53) ^(Ti-ra) Qt = m Am[X Cs  x  where  m'  =  aa  + c (T ps  2  - T )] + a3  Cp^Fx + c,  = mass flow rate of dry air (kg/s)  mH l  c  (A.54) (A.55)  endix  A. Sample  237  Calculations  Table A.2: Enthalpy of various streams Parameter  Humid air (J/kg dry air)  #i  Cs T  1  +  XY  H  Cs T  2  +  XY  1  2  2  Hi  CL(Y  mi  2  —  0  0  Steam incoming steam)  (J/kg  c Ti  1  + A  pi  0  2  Yi)T ,  CL(m  2  -  mi)T  a8  a  — mass flow of total incoming steam (kg/s)  c, c , c Pa  Pw  Ps  = respectively denote specific heats of air, water and steam at film temperature (J/kmole.K)  Flux of radiative heat transfer, q , between a radiating gas and a surface is r  calculated [124] using emissive power of a real body through the Stefan-Boltzman law:  where  k  = Stefan-Boltzman's constant, 1.3805xlO  T  = Temperature (K)  -23  £ , e, — emittance of the radiating gas and that of the sohd surface. g  Both e and £, are temperature dependent. e is approximately constant at 0.85 g  g  while e at 1 atm total pressure is given [125] as a function of radiating gas partial g  endix  A. Sample  238  Calculations  pressure, p , temperature and radiating beam length, L . For radiation within the w  r  packed ped, L is determined by: r  Volume of eas L  '  =  =  3  \ r e a of bounding surface  ZA  W^7)  (  A  '  5  7  )  The beam length for radiation between the solid surface and the gas volume occupying the space above the packed layer is approximated by: L where  = 0.9D  r  (A.58)  e = voidage in the bed (m /m ) 3  d= p  3  particle size (m)  D = Column diameter (m).  Therefore, the total rate of radiative flow will be obtained through the following equation: Q  T  = q A Tl  s  + q S r2  (A.59)  x  where the first term indicates the flux and the heat transfer area for radiation within the bed and the second term represents the corresponding values for radiation in the gas volume above the packed layer. The gas emissivity increases as the total pressure increases; therefore, Equation A.56 is multiplied by a correction factor, C , to account for the effect of pressure. r  For superheated steam at 1 atm total pressure and at 250°C< T < 350°C, e is g  relatively constant at 0.08 for radiation within the packed layer; e increases to g  a constant value of 0.32 for the radiation in the space above the packed layer.  Appendix  A. Sample  239  Calculations  Table A.3: Ernissivities of CO2  (Pa) 0.06  (cm) 0.882  x 10~ N/m 0.499  0.06  18.281  0.97  0.048  0.12  0.832  0.998  0.015  0.12  18.29  21.95  0.063  p  pL  L  T  T  3  0.008  Although no data is available for pp = 0.5(p + p ) > 1.2 atm, the asymptotic w  t  shape of the correction factor curves indicate that C (pp atm) r  =2  =  l-lC ^ r  pp=12  atm)  can provide a good approximation for superheated steam runs. This would result in C =1.87 for the former and C = 1.6 for the later. r  r  Ernissivities of carbon dioxide at 1 atm total pressure between the surface and average gas temperature of, respectively, 40 and 120°C at required p~cOiL values are T  given in Table A.3. C is unity as air drying runs have taken place at approximately r  1 atm total pressure.  7. Rate of convective heat transfer, Q , is obtained through the following relac  tionship: Qc  (A.60)  = Qt~Qr.  8. Logarithmic mean temperature difference, T j , is determined using Equation m  Appendix  A.61  A. Sample  240  Calculations  for a heat transfer process with a phase change. T  = ^V" T \ ln(i" y ) T  lm  s  ^ out  9. Convective heat transfer coefficient,  (A.61)  U  " J u l  '  h, is calculated using the following ex-  pression: h  =  ( A 6 2  >  Equation A.62 cannot be used when the outcoming gas leaves the column saturated as the dryer behaves like an infinetly long heat exchanger. Figure A.1(a) and A.1(b) illustrate the schematic diagrams of the temperature profiles of the drying gas (sohd hne) and the evaporating surface (broken hne) between points 1 and 2 along the column. When the sohd surface is uniformly and fully saturated at T , Figure a s  A.1(a), the total rate of convective heat flow between 1 and 2, Q , is calculated for c  an infinetly long heat exchanger ( A —> oo) by: s  Q  c  where AT(i) = T — T . x  as  (A.63)  = hAT  {1)  If the dryer behaves as two opposing infinitely long heat  exchangers, Figure A. 1(b), and considering a uniform heat transfer coefficient along the column, Q is determined through the following summation: c  Q  c  where AT(2)  — T2 — T»  (2)  = h(AT  {1)  + AT ) {2)  (A.64)  ~ 0- Therefore, Equation A.63 represents the total rate  of convective heat flow if the drying gas leaves the column saturated resulting in:  Appendix  A. Sample  Calculations  _  241  (a)  T  1  Figure A.l: Schematic Diagrams of Gas Temperature along the Column with a Uniform (a) and a Non-uniform (b) Solid Temperature A sample of the temperature distribution of the drying gas along the bed is shown in Figure A.2. 10. T h e Ackerman coefficient, tp, is determined using the following relationship: In [X + 1] <P  where  X  X  =  N  = Flux of mass transfer (kg/m -s)  Pva  (A.66)  Nc„„„/h 2  =  c  P  specific heat of vapor (J/kg).  11. Mass transfer coefficients, (fey, kc), for humid air and steam drying runs during the constant rate period are evaluated through, respectively, Equations A.67 and  Appendix  A.  Sample  Calculations  180  1  1  242  I  1  1  1  I  1  I  I  I  A  A  I  I  Run 11 160  o o o o o o o o j  8  f  140 h  f  i  •  o  D  . |  o  o  D  °  °  •  120 h o  l  Therm,  100 h  No.  80  •  o o  60 h  o  1  A  2  •  3 4  o  40  20  _1  0  600  1200  L  1800 6  1  1  1  2400  1  1  J_l_  3000  (s)  Figure A.2: Plot of Temperature Distribution along the Bed  3600  243  Appendix A. Sample Calculations  A.68. k  Y  k  c  where N  max  =  (A.67)  = ^  (A.68)  represents maximum flux of mass transfer, Y/ and Ci m  m  respectively  denote the logarithmic mean humidity and concentration difference as defined by the following equations: Y  lm  = ?%~_ \  (A.69)  Y  C Ut  ~  0  C;  ln(,? '~ff" ) 3a  where C = p/R T g  denotes the molar concentration of superheated steam. As dis-  cussed for Ti , Equations A.69 and A.70 approach the limiting value of, respectively, Y t sa  —  m  Yin and C  aat  — Ci for a saturated outcoming gas. n  The F-type mass transfer coefficient for humid air is determined via: F = ^M  y  (A.71) 1  G  and its corresponding value for superheated steam is represented by: F = k Cf  (A. 72)  c  where Cf is molar concentration at the film temperature.  12. Reynolds number, Re, representing the ratio of inertial to viscous forces is evaluated both based on the column diameter, D, and on the particle size, d , for P32  both inlet and average film temperatures andflowrates through: Gl  Rei = — V  .  (A.73)  Appendix  A. Sample  244  Calculations  where I denotes the characteristic length, D or d . Pi2  13. Nusselt number, Nu, determines the relative effect of convective and conductive heat transfer processes and is calculated at film temperature via: N  u  Mm. */  =  (A.74)  14. Sherwood number, Sh, represents the relative effect of convective and conductive processes in mass transfer. Sh is evaluated at film temperature using the following equations for, respectively, air and superheated steam drying: k S  h  y  d  =  D  =  Sh  W  G  ^ .  C  }  M  (A.75) G  (A.76)  Dww  15. P r a n d t l number, Pr, representing the relative effect of momentum and heat diffusivities at film temperature is obtained via: Pr = ^  k  (A.77) f  16. Schmidt number, Sc, which defines the ratio of momentum to mass diffusivities, is evaluated at T = Tf using: Sc = -JL-  (A.78)  PJ->WG  and  Sc = - f -  (A.79)  17. Peclet number, Pe, at film temperature is determined for both heat (Equation A.80) and mass (Equation A.81) transfer. Pe  =  Re^Pr  (A.80)  Pe  =  Re^Sc  (AM)  H  M  Appendix  A. Sample  245  Calculations  18. Stanton number, St, is evaluated for both processes at film temperature. »  =  St  St  H^Fr  =  M  (A.82) (A.83)  rie bc dj)  19. J-factors are calculated at T — Tj using the following expressions: JH  =  St Pr  JM  =  St Sc  (A.84)  2/3  H  (A.85)  2/3  M  (A.86) 20. Biot number, Bi, defines the ratio of external to internal conductances; therefore, its value for heat transfer process is determined by: hi  where I represents characteristic length and 8 is the thickness of hydrodynamic boundary layer. Similarly, the mass transfer Biot number is calculated via:  " = iBk  Bi  '  (A 88)  Substitution of D , apparent vapour diffusivity, from Equation A.42 and replacing v  r K, =  C D —- —M  Tj  W  Y  G  g  G  would result in: Bi  M  =  liD-  8  where pu is the Krischer's diffusion resistance corfficient in a porous body.  (A.89)  Appendix  A. Sample  246  Calculations  21. Gukhman number, Gu, represents the ratio of thermal potential of mass transfer to that of heat transfer and is evaluated using: (A.90)  Gu = 1  f  where temperatures are in degrees Kelvin.  22. Number of transfer units, N, is the number of times the average driving force divides into maximum change either of temperature, for heat transfer, or of absolute humidity, or molar concentration for mass transfer, across the column. The corresponding values are respectively shown by Equations A.91 andA.92. T-L  —T  in  -£  Tim  hA L p  out  C G'  (A.91)  Sl  KyA h v  Yin  or Gout — Ci-i  23. Height of transfer units, H*, is determined via:  rr-  L  (A.92)  24. Height of desorption zone, Z , is determined, considering that the heat transe  fer process prolongs along the total height of packed bed, throught the following relationship: Z. = L$r)  (A-93)  Appendix  A.6  A. Sample  247  Calculations  Determination of the Factors Affecting Characteristic Drying Curve 1. Hygrothermal  ratio, a, is a function of wet bulb temperature, T . w0  A spline  function is used to reproduce its numerical value from its graphical representation [87].  2. Evaporation resistance coefficient, 7, is defined by: 7 =  (A.94)  1— a  where 3 represents the ratio of heat to mass transfer Biot numbers (i.e. k f / k p r j ) t  and a is the hygrothermal ratio.  3. Drying intensity, N, is evaluated through the following Equation: N d N = "7 ^ pMD  (A.95)  V i  a  0  K  }  a  where ' N  —  kY Y  lm  or kcCl  m  is the initial mass transfer flux along the column, and M  Q  and D  a  respectively  denote the initial wood moisture content and apparent diffusivity within the wet material.  4. Relative drying rate, / , defines the normalized value of the instantaneous drying rate and is expressed by: f  _ m Rmax  endix  A. Sample  248  Calculations  1+  (A.96)  jBi  M  where BIM is the mass transfer Biot number based on the depth of recession.  5. C h a r a c t e r i s t i c m o i s t u r e c o n t e n t , $, is denned by Equation 2.25 for a hygroscopic material.  .7  D e t e r m i n a t i o n of F r i c t i o n F a c t o r a n d t h e R e l a t e d  Properties  1. A v e r a g e p r e s s u r e d r o p , Ap, is determined via: T  m  ]=m  (A.97) n—1  L  where L is the height of the packed layer and n and m respectively denote the number of pressure taps along the column and the number of points that the data is recorded.  2. H y d r a u l i c E u l e r n u m b e r , Euh, is calculated using: EUH = -^  (A.98)  where e is the average voidage and p and V respectively represent density and velocity at the inlet conditions.  3. S p h e r i c i t y , 'if, is approximated through Equation 4.60 using the method described in Section 4.9. The calculated $=0.4 is used for subsequent calculation of modified friction factor denned by Leva [76]  Appendix  A. Sample  249  Calculations  4. Modified friction factor, / y , is determined using Equation 4.56. The exponent m  of the bracketed value, [yz^] , is a function of Reynolds number. A spline function 2_n  is used to repreduce the numerical value of n from its graphical representation [127].  A.8  Parameters Determining the Falling Rate Behavior  1. Time intervals, 6, for the sample to reach moisture contents of 0.3, 0.4, 0.5, and 0.6 are determined (see  ).  Table D.5  2. Slope of the drying rate curve, o>, for 0.3< M(6) <0.6 is calculated by differentiating: R  =  ®  (A.99)  ^ i= l  with respect to M ; therefore:  (if) _  dR _ dM  dM(6)  dM  de  d6  dM  2  2  (A.100)  Using Equation A.99 the following would yield: dR  ita^e-^-c'^  u> dM  Rlri  3. Standard deviation of the slope, *M = 0  2  0 " (  * H  0  1  w  ) ,  +  (A.101)  is evaluated through Equation A.102.  OSV,  (A.102)  Substituting the following expressions in the above equation: ,  , d M ,  * ( M ) = (afi) H o  , .  (A.103)  Appendix  A. Sample  250  Calculations  would yield: °- n = ( ^ ) w 2  The  2  (A.105)  v  bracketed parameter: du  du dd  .  m Tem  ,  k  (A106)  =  .  is calculated by differentiation of Equations A.101 and A.99 with respect to 6 and their subsequent replacement in Equation A. 106 ^=R>  as is shown in the folio wings:  = ^a[6 '.e-V[)-c[]  (A.107)  b  du  R\  R"  R'  / A  thus, 1 . R" R'J  du;  8R =  R  [  - R J  +  R  ]  where fl(dR\  R  "  =  86  =  ^  <  LI  dKe  LI  ~ ' ^i ~ <) ~ P C  6  2  (A-11  The tabulated data for ui and (f^) are presented in Tables D.4 and D.3 respectively. The  average standard deviation of the drying rate during the falling rate period is  obtained using the data given in Tables C . l to C.34 via the following Equation:  = £ 5>5*)  (- ) A  M  i— l  where n corresponds to the number of the points between 0.3< M <0.6.  The  results of the drying rates and standards deviations are presented in Table D.2.  Appendix  A. Sample  251  Calculations  Table A.4: Maximum Drying Rates at Various Temperatures at Mass Flow of 142 kg/hr Run 12 11&20 19 22 39 42 45&46 41&44 43  A.9  m  kg/hr 152.5 141.9 126.8 126.7 97.9 95.5 94.0 90.9 86.3  T- - in 1  °c 126.3 150.9 204.8 220.7 170.9 189.5 205.8 220.9 245.7  iCa* x 10 s" at 142 kg/hr 0.97 1.07 1.36 1.53 1.22 1.34 1.88 2.24 2.46 3  P*max  s1.02 1.07 1.25 1.41 0.93 1.00 1.39 1.61 1.730 1  1  Correction of the Maximum Drying Rate for Mass Flow of Gas  The maximum drying rate for a gas flow of 142 kg/hr was determined using the following relationship (see Page 93 ):  ^ocV^am 0  7  (A.112)  1  The results for air and steam drying runs at various temperatures are tabulated in Table A.4.  A.10  Correction of Run 26 for Both Temperature and Mass of Wet Solid  A flow of 117.8 kg/hr of a humidified (Y = 0.0450) gas at V = 1.35 m/s and T in  in  = 246  °C is used on a 1.5 kg batch of wet hog fuel in Run 26. An estimate of the maximum rate of drying at 202 °C on a 3.0 kg wet sample is obtained through the following procedures.  252  Appendix A. Sample Calculations  Based on the experimental data ( see Section  4-3 ), a relationship of the form:  = "'^L + - "  0 823X10 3  Rmax  (A.113)  ' ' 11! S  exists between the maximum drying rate and the weight of wet solid. This would yield to the corrected value of  Rmax  —  1-47 x 10  -3  s  _1  for Run 26.  To correct for temperature, Equation 4.13 is extrapolated and a value of 1.11 for the ratio of  Rmax  value of  A.11  at 247°C to the one at 202°C is determined. This would yield to a corrected R  m  a  = 1.32 m/s for both temperature and weight of the wet solid.  x  Effect of Bed Height on the Grate Heat Release Rate  The grate heat release rate (h~ ) is a function of both the bed height, L, and the residence g  time of the fuel on the grate hearth as expressed by: A  h = h— g  where  h~  s  =%,p.{l - e) -  = A— = A-  (A.114)  = heigher heating value of dry fuel (kJ/kg)  s  Vf,, v  = bulk and solid volumetric flow rate (m /s)  6  = residence time (s)  3  s  Thus, the effect of bed height on the grate heat release rate is determined through the following equation: dh^^dh^ dL dL  8^d6_ 86 dL  =  A _ ALd6_ 6 0* dL  f A 115^1 '  Appendix  A. Sample  Equation A. 115  253  Calculations  can be evaluated if the effect of bed height on the required residence  time for a given final moisture content is known. For a final moisture content of 0.6 kg water/kg dry solid (Figure 4.57), this relationship can be simplified and approximated by the following linear expression: 6 = 408 + 20281 Substitution of Equation A. 116  in Equation A. 115  (A.116) and subsequent integration would  yield: =  2  0  (A.117)  4  h L 204 + 1014Z, where subscripts 1 and 2 indicate, respectively, the initial and final conditions. x  x  2  v  ;  Appendix B  D r y i n g Rate Curves  The instantaneous drying rates and their predicted values, Equation 4.1, are plotted as a function of time and shown in Figures B to B.l. The fitting parameters in Equation 4.1 are tabulated in Table B.l. Table B.2 contains general statistical information to indicate the average accuracy of the predicted values. The information is obtained using the sum of square of the residuals, SR, and an approximate method represented by Equation 4.10. See Appendix C for a precise statistical analysis of each predicted value.  254  Appendix  B.  Drying  Rate  Curves  255  0.0028  0.0032 Experimental Pitted  0.0028 •O 0.0024 o o » 0.0020  O 0.0024 Run T , .  V,. L  K  M.  d» CO,  0.0016  Y „  1A 62.3 *C 1.40m/s 23.1 om 1.14 d.b. 0.0 mm O.OvolX 0.0021 d.b.  Experimental Pitted  0.0020 -  Run T,. v , »  L  U. d, CO, Y i .  1 101.8 *C 1.43 m/s 32.3om 1.14d.b. 6.3 mm l.OvolX 0.0114d.b.  S* 0.0012 o •  0.0008  -0.0004  800  -0.0004  1600 2400 3200 4000 4800 9600 0 (a)  0.0028 0.0024  _ i _ L  800  1600  2400  e (»)  3200  4000  4800  0.0028 Experimental Pitted  Run T „  V, L  D  Mo  d» CO, Y,„  3 E4i.3*C 1.57 m/a 29.8 om 1.41 d.b. 6.3 mm 1.7voIX 0.0263d.b.  0.0024  -  Experimental Pitted  I  •rt o 0.0020 o  v , „  L  •  -  u  TS  a « u  Run T„  M.  0.0016  <h  CO, Y „  0.0012 -  4 106.7 *C 1.77m/» 28.0 em 1.41 d.b. 6.3mm l.OvolX 0.0306 d.b.  0.0008  « «•  0.0004 0.00001  -0.0004  _l_ 400  - L  800  1200  1600  2000  2400  -0.0004  400  800  6 («)  Figure B . l : Drying Rates versus Time  1200 1600 9 (a)  _l_ 2000  2400  Appendix  B.  Drying  Rate  256  Curves  0.0028 0.0084 -  0.0028 Experimental Pitted Run T„ V, L D  Mo  d. CO, T„  1  I  1  O 0.0024 -  8 204.0*C 1.84 m/a 28.4 om 1.41d.b. 8.3 mm l.SvolX 0.0246d.b.  1  1  1  I  1  1  1  I  Experimental Pitted  0.0020  Run T„ V, L  0 154.8*C 1.34 m / a 16.1 om 1.41d.b. 8.3mm 1.0 vol* 0.0168d.b.  D  M.  a. CO. Y..  0.0004  K  o.oooo< • -0.0004  400  800  1200 1800 0 (e)  2000  -0.0004  2400  0.0020  1800  2400  3200  4000  4800  6 (a)  0.0028 0.0024  800  0.0028 Experimental Pitted Run T„ V,. L Mo  0.0016  d. CO. Y,.  0.0012  0.0024 -  10 lSB.l'C 1.36m/s 12.3 om 1.41d.b. 6.3 mm l.OvolX 0.0233 d.b.  o o  0.0020  Experimental Pitted Run T„ V, L D  M.  t o.ooie •a  o»  CO, Yi.  • 11 • 147.8 *C 1.33 m / a 24.0om 1.41d.b. 6.3mm l.OvolX 0.0139d.b.  0.0008 ) 0.0004 J.0000< ? -0.0004  800  1600  2400 3200 e (a)  4000  4800  -0.0004  _i_L  800  1600  Figure B.2: Drying Rates versus Time  2400  6 (a)  3200  4000  4800  Appendix  B.  Drying  Ra.te  257  Curves  0.0028  0.0028 0.0024 0.0020 u  0.0016  0.0012  Experimental Pitted Run T„ V, L M. dt. CO, Y,. D  O 0.0024  12 126.3 *C 1.37 m/a 27.0 om 1.41d.b. 6.3mm l.OvolX 0.0261 d.b.  Experimental Pitted  I  •a o 0.0020 o u  Run  v  to  L M. d. CO. Y«  0.0016  13 198.9 *C 1.39 m/a 32.0om 1.41 d.b. 6.3mm l.OvolX 0.0238 d.b.  •  *  •  0.0008 0.0004 Ot 0.00OOC >• -0.0004  800  1600  2400 3200 0 (a)  4000  -0.0004  4800  0.0028 0.0024 -  I  800  1600  800  1600  2400 3200 0 (a)  4000 4800  0.0028 Experimental Pitted Run  v,.  0.0020  L M. d. CO, Y,.  0.0016 0.0012  0.0024 -  14 100.7*C 1.39m/a 26.9 am 1.41d.b. 4 - 6mm l.OvolX 0.0212d.b.  I IB O  0.0020 -  U  0.0016 -  e •  0.0012 -  0.0008  0.0008 0.0004 0.0000  -0.0004  _uJ_  800  1600  2400 3200 0 (a)  _i_L  4000  4800  -0.0004  Figure B.3: Drying Rates versus Time  B  2400 3200 (a)  4000  4800  Appendix  B.  Drying  Rate  258  Curves  0.0028  0.0028 Experimental Pitted Run T„  0.0024 I  o o  v,»  0.0020  L M. dp CO. Y,.  »  u 0.0016 •0 0.0012  0.0024  16 102.0'C 1.33 m/s 24.1 om 1.41d.b. 6 - 8mm l.OvolX 0.0233d.b.  Experimental Pitted Run T„  v,„  0.0020  L M. dp CO.  17 148.8 "C 1.33 m/a 30.2 om 1.41 d.b. 2 - 4 mm l.OvolX 0.0201 d.b.  0.0008 0.0004  os o.oooo< • -0.0004  800  1600  2400 3200 0 (a)  4000  -0.0004  4800  0.0028  800  1200 « («)  1600  2000  2400  0.0028 Experimental Pitted Run T,. V, L  0.0024 0.0020  D  Mo  0.0016  d. CO. Y„  0.0012  0.0024  18 163.8'C 1.37m/e 29.3 om 1.41d.b. 8 - 10mm l.OvolX 0.0211 d.b.  I  D o 0.0020 o u  Experimental Pitted Run T,. V, L B  M.  0.0016  d. CO. Y„  0.0012  0.0008  19 204.8*C 1.39m/a 29.3 om 1.14d.b. 6.3mm l.OvolX 0.0210d.b.  0.0008  0.0004  •a  03 0.0000( •)  -0.0004  400  0.0004  06 O.OOOOC •  I  I  800  I  I  t  1600  2400 3200 6 (a)  4000  4800  -0.0004  400  800  Figure B.4: Drying Rates versus Time  0  1200 1600 (a)  2000  2400  Appendix  B.  Drying  Raie  259  Curves  0.0028 0.0024  0.0028 Experimental Fitted  I •O 0.0020 o e  * b  •o  0.0016  -0.0004  Run T,. V,. L Mo d. CO, Y„  20 1B4.0*C 1.37 m/s 26.4 cm 1.41 d.b. 6.3 mm l.OvolX 0.0149d.b.  I o 0.0020 o  2400  3200  4000  to  v„ L  U.  u 0.0016 •0  J.  1600  800  Experimental Pitted Run T  0.0024 -  -0.0004  4800  d. CO,  400  800  0.0024  I  1  '  1  I  1  1  1  2000  2400  0.0096  T  I  Experimental Pitted  1600  6 (a)  6 («) 0.0028  1200  22 220.7 *C 1.41 m/a 24 .Bom 1.41d.b. 6.3mm l.OvolX 0.0209d.b.  O Run T„  v,  D  L M. d. CO, T|.  0.0048  23 186.0'C 1.32 m/a 26.8 om 1.41 d.b. 6.3mm l.OvolX 0.1422d.b.  Experimental Pitted  I  •d o 0.0040 o » u 0.0032 •0 «*  M  V.  o.  0.0024  Run T„ V,. L M. dp CO, Y.»  26 246.8*C 1.39 m/a 12.3cm 1.41d.b. 6.3mm 2.0volX 0.0490d.b.  •  •  0.0016 0.0008 M  (X o.ooooc r -0.0004  400  800  1200 1600 0 (e)  2000  2400  -0.0008  _l_  400  800  Figure B.5: Drying Rates versus Time  1200 1600 0 (a)  2000  2400  Appendix  B.  Drying  Rate  260  Curves  0.0028 0.0024 0.0020  0.0028 Experimental Pitted Run T„ V, L D  Mo  0.0018 -  d. CO, T,  0.0012  B  0.0024  28 202.2 *C 1.38 m/a 2S.0om 1.41d.b. 6.3mm l.OvolX 0.1347d.b.  Experimental Pitted  •e o 0.0020 I  O  o  >  U.  u 0.0016  d. CO, Y„  TJ  t*  M  \  30 201.7 *C 1.39 m/a 20.6 om 1.41d.b. 6.3mm l.OvolX 0.2896 d.b.  Run T„ V,. L  0.0012  •  •  • •  It  0.0008  Li  e «  0.0004 0.00001 -0.0004  0.0008 0.0004  OS 0.00001  400  800  1200 « <•)  1600  2000  2400  -0.0004  2000  0.0028 Experimental Pitted Run T„ v,  D  L Mo  d> CO, T„  0.0024 -  31 194.3*C 1.30m/a 18.9om 1.92 d.b. 6.3 mm l.OvolX 0.0199d.b.  2400  T " - r  Experlmental Pitted Run Ti.  v L„  0.0020 -  M. <«-  CO, Y  „  32 196.2 'C 1.33 m/a 21.9cm 1.92 d.b. 6.3mm l.OvolX 0.0226d.b.  • *  •  •  0.0000( •  800  1600  2400 3200 0 (a)  4000  4800  -0.0004  800  1600  Figure B.6: Drying Rates versus Time  2400  6 (a)  3200  4000  4800  Appendix  B.  Drying  Rate  261  Curves  0.0028 Experiment*! Fitted Run  34 148.2'C 1.29m/s 24.0om 1.41 d.b. 8.3mm U.7volX 0.0130d.b.  T„  V L M. d. CO, Y, 1D  D  800  1000  2400 3200 6 (a)  4000  -0.0004  4800  1800  2400 3200 (a)  4000  4800  6  0.0096 0.0048  800  0.0028 Experimental Fitted Run T„  I o 0.0040 o  V, L M. d. Y„ B  ft h 0.0032  •e  0.0024  38 200.8 *C 0.86 m / a 12.lorn 1.41d.b. 6.3mm ~d.b.  I  •>3 C O  0.0020  ft U  0.0024  0.0016  Experimental Fitted Run T„ V L M. d. Y„ t o  39 170.0 «C 900.69 m / a 9029.1 om 1.41d.b. 6.3mm •d.b.  0.0012 m >'  e  0.0016  ft0.0004  0.0008  06 o.oooo( >• -0.0008  0.0008  06 0.0000( •  400  800  1200 0 (a)  1600  2000  2400  -0.0004  _1_  800  1600  Figure B.7: Drying Rates versus Time  2400 3200 0 (a)  4000  4800  Appendix  B.  Drying  Rate  262  Curves  0.0028  0.0028 0.0024 0.0020 0.0016  '  11  1 1  o  Experimental Pitted Run Ti. V,. L M. d. T„  1  1'  1  1  1  Experimental Pitted  0.0024  41 280.8 *C 0.80m/a 27.3cm 1.41 d.b. 6.3mm ••d.b.  ' '  I  •O o 0.0020 o  »  0.0016  •o of  M  1  1  1  1  1  • •  Run T„ V,« L M. d, Yla  42 180.8 *C 0.81 m / a 27.7 om 1.41d.b. 8.3mm -d.b.  • *  •  •  0.0012  V.  P.  o p  O  e  u 0.0008  • tt »  1  JO  ]  q  0.0004 •  OS 0.0000< V -0.0004  400  800  1200 B (a)  1600  2000  2400  O 800  1600 0  0.0028 0.0024  -0.0004  i  Experimental Pitted Run T„ v,» 1. M. d, T„  43 248.7 *C 0.82 m / a 22.0 om 1.41 d.b. 6.3 m m -d.b.  2400 3200 (a)  0.0028  I ' ' ' I  0.0024  Experimental • Pitted  1  1  4000  4800  ' I  Run Tim  v, h M. d>  B  44 221.3*C 0.81 m / a 23.8 om 1.41d.b. 6.3mm -d.b.  • *  •  •  0.0004  '<*>  OS 0.0000C • -0.0004  JL 400  800  1200 0 (a)  _1_ 1800  2000  2400  -0.0004  400  800  Figure B.8: Drying Rates versus Time  1200 0 (a)  JL  1800  -L  2000  2400  Appendix  B. Drying  0.0028 0.0024 -  Rate  I  1  1  0.0018 -  i |ii iI  ' I  O Experimental Fitted  0.0020 -  263  Curves  i  i  i  0.0028  I  11 1  I  1 1 1  I  T  Experimental - Fitted 1  Run T„ V,. L M. d.  0.0024  40 200.8 *C 0.82 m / » 24.8cm 1.41 d.b. 8.3mm ~d.b.  Run  4 0 2 0 4 . 7  0.0020  *C  m/a cm 1 . 4 1 d.b. 8.3mm -d.b.  v „  0 . 8 2  L  2 0 . 2  U.  <», T»  •  • •  •  0.0012 0.0008 0.0004 0.0000( • -0.0004  400  800  I • • • I 1200 1800 « («)  _1_  2000  2400  -0.0004  400  Figure B.9: Drying Rates versus Time  I I 1800 2000  I 1 I  800  1200 0  (a)  2400  Appendix  B.  Drying  Rate  264  Curves  Table B . l : Parameters in the Fit" of Drying Rate Curve Run  a'i s ~  b'i ]  0.13E-09 0.24E-O7 0.26E-10 0.21E-07 8 0.18E-05 9 0.32E-06 10 0.16E-06 11 0.28E-06 12 0.16E-06 13 0.17E-06 14 0.14E-O5 15 0.17E-04 1(5 0.82E-06 17 0.14E-05 18 0.56E-07 19 0.38E-06 20 0.42E-06 22 0.38E-10 23 0.26E-11 26 0.19E-04 29 0.12E-11 30 0.26E-10 31 0.11E-05 32 0.19E-07 34 0.88E-06 36 0.24E-O6 38 0.13E-04 39 0.78E-06 41 0.59E-06 42 0.68E-08 43 0.46E-05 44 0.43E-05 45 0.13E-06 46 0.36E-06 a E q u a t i o n 4.1 0 1 3 4  a  c'-i  s 0.93E-03 0.14E-02 0.81E-02 0.16E-02 0.80E-02 0.28E-02 0.24E-02 0.25E-02 0.21E-02 0.20E-O2 0.84E-02 0.42E-03 0.63E-02 0.80E-02 0.17E-02 0.28E-02 0.40E-02 0.99E-02 0.44E-02 0.32E-01 0.38E-02 0.37E-02 0.60E-02 0.17E-02 0.50E-02 0.25E-02 0.24E-01 0.77E-02 0.19E-01 0.24E-02 0.13E-01 0.22E-01 0.21E-O2 0.29E-O2 1  0.20E+01 0.15E+01 0.35E+01 0.15E+01 0.15E+01 0.15E+01 0.-15E+01 0.15E+01 0.15E+01 0.15E+01 0.15E+01 0.30E+00 0.15E+01 0.15E+01 0.15E+01 0.15E+01 0.15E+01 . 0.35E+01 0.35E+01 0.15E+01 0.35E+01 0.30E+01 0.15E+01 0.15E+01 0.15E+01 0.15E+01 0.15E+01 0.15E+01 0.20E+01 0.20E+01 0.15E+01 0.15E+01 0.15E + 01 0.15E+01  s " 0.65E-11 0.17E-07 3  0.16E-08 0.28B-07 O.21E-07 0.18E-06 0.14E-06 0.24E-07 0.15E-06 0.29E-06 0.10E-08 0.19E-24 0.72E-08 0.12E-08 0.20E-07 0.42E-07 0.58E-07 0.11E-10 0.51E-09 0.11E-06 0.21E-09 0.14E-16 0.84E-07 0.85E-07 0.79E-11 0.14E-06 0.18E-06 0.71E-10 0.11E-07 0.13E-09 0.22E-07 0.19E-07 0.84E-07 0.18E-06  '  s 0.28E-02 0.39E-02 O.21E-02 0.39E-02 0.88E-02 0.11E-01 0.80E-02 0.77E-02 0.13E-01 0.30E-01 0.16E-02 0.42E-02 0.24E-02 0.18E-02 0.41E-02 0.82E-02 0.96E-02 0.40E-02 0.25E-01 0.58E-02 0.21E-01 0.11E-01 0.16E-01 0.74E-02 0.29E-02 0.99E-02 0.69E-02 0.64E-03 0.10E-01 0.82E-02 0.37E-02 0.35E-02 0.67E-02 0.11E-01 1  0.30E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.75E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01 CI.32E+01 0.32E+01 0.20E+01 0.32E+01 0.60E+01 0.20E + 01 0.20E+01 0.30E+01 0.20E+01 0.20E+01 0.20E+01 0.25E+01 0.30E+01 0.20E+01 0.20E+01 0.20E+01 0.20E+01  a'3  s  -  0.38E-06 0.84E-09 0.39E-08 0.12E-08 0.72E-10 0.20E-07 0.12E-O7 0.95E-09 0.14E-09 0.35E-09 0.64E-10 0.48E-23 0.87E-08 0.67E-10 0.72E-09 0.27E-08 0.86E-11 0.37E-08 0.18E-09 0.47E-08 0.16E-09 0.18E-10 0.34E-10 0.43E-10 0.37E-06 0.22E-07 0.68E-09 0.47E-10 0.83E-10 0.18E-05 0.34E-09 0.26E-08 0.13E-07 0.30E-07  c', s 0.59E-02 0.27E-01 0.17E-01 0.14E-01 0.49E-02 0.49E-01 0.28E-01 0.17E-01 0.84E-02 0.10E-01 0.50E-02 0.89E-02 0.38E-01 0.48E-02 0.14E-01 0.25E-01 0.29E-02 0.22E-01 0.76E-02 0.18E-01 0.68E-02 0.24E-01 0.35E-02 0.39E-02 0.20E-01 0.42E-01 0.14E-01 0.42E-02 0.49E-02 0.10E-01 0.94E-02 0.14E-01 0.39E-01 0.49E-01 1  1  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  15E+01 30E+01. 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 80E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 30E+01 40E+01 30E+01 30E+01 20E+01 30E+01 30E+01 30E+01 30E+01 15E+01 30E+01 30E+01 30E+01 30E+01  Appendix  B. Drying  Rate  Curves  Table B.2: Summary of Data Representing the Goodness of the Fit Run  n  SR X 10 2  0 1 3 4. 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  113 99 30 48 34 76 132 75 96 70 85 99 68 61 82 62 86 27 43 36 42 41 48 88 134 113 25 67 44 49 58 43 45 31  6  s0.004 0.322 0.171 0.119 0.283 0.452 2.838 0.044 0.078 0.479 • 0.107 0.155 0.088 0.134 0.139 0.035 0.027 0.029 0.293 0.745 1.309 3.229 1.636 0.408 0.069 0.046 0.506 0.214 0.250 0.245 0.245 0.227 0.144 0.208  o v x 10 s" 0.0000 0.0035 0.0071 0.0028 0.0101 0.0065 0.0225 0.0006 0.0009 0.0075 0.0014 0.0017 0.0014 0.0024 0.0018 0.0006 0.0003 0.0014 0.0079 0.0248 0.0364 0.0923 0.0390 0.0050 0.0005 0.0004 0.0266 0.0035 0.0066 0.0057 0.0047 0.0061 0.0037 0.0067 2  2  6  10 s0.006 0.059 0.084 0.053 0.101 0.080 0.150 0.025 0.030 0.086 0.037 0.041 0.038 0.049 0.043 0.025 0.018 0.037 0.089 0.158 0.191 0.304 0.197 0.071 0.023 0.021 0.163 0.059 0.081 0.075 0.069 0.078 0.061 0.082  <T x  1  a' = 0.05; therefore, 9 5 % confidence region fit of drying rates versus time(see Equation 4-1 )•  a  6  S  3  T  x 10 s0.004 0.366 0.277 0.159 0.432 0.538 3.122 0.053 0.090 0.579 0.125 0.178 0.108 0.167 0.164 0.044 0.031 0.049 0.407 1.106 1.829 4.508 2.176 0.473 0.076 0.052 0.938 0.262 0.345 0.323 0.309 0.314 0.195 0.305  p  2  2.100 2.100 2.490 2.340 2.450 2.220 2.100 2.240 2.220 2.240 2.230 2.220 2.250 2.250 2.250 2.250 2.250 2.560 2.380 2.420 2.380 2.310 2.310 2.200 2.100 2.180 2.700 2.250 2.380 2.300 2.300 2.340 2.340 2.400  6  6/  x  10  s0.0000 0.0039 0.0116 0.0038 0.0154 0.0077 0.0248 0.0008 0.0010 0.0091 0.0016 0.0019 0.0017 0.0030 0.0022 0.0008 0.0004 0.0024 0.0110 0.0369 0.0508 0.1288 0.0518 0.0058 0.0006 0.0005 0.0494 0.0043 0.0091 0.0075 0.0060 0.0085 0.0050 0.0098 2  6  <5 x 10 s0.006 0.063 0.107 0.062 0.124 0.088 0.157 0.028 0.032 0.095 0.040 0.044 0.042 0.055 0.046 0.028 0.020 0.049 0.105 0.192 0.225 0.359 0.228 0.076 0.024 0.022 0.222 0.065 0.095 0.087 0.077 0.092 0.071 0.099 P  1  3  Appendix  C  Tabulated Instantaneous D r y i n g Rate D a t a  The Instantaneous experimental and predicted (Equation 4.1) drying rates, their residual and the standard deviation of the predicted values, obtained using the BMD P-series statistical programs, are reporded in Tables C.l to C.34. The tables also contain the instantaneous values of wood moisture contents, M , relative drying rates, / , and characteristic moisture contents, $, used for prepration of the drying rate curves.  266  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  267  Data  Table C.l: Summary of Data for Run 1A  6  s 0 50 95 134 173 212 251 336 375 414 453 492 531 570 655 694 733 772 811 850 895 974 1013 1052 1091 1130 1175 1215 1293 1332 1371 1410 1474  R  x 10 s0.001 0.122 0.230 0.284 0.342 0.381 0.406 0.425 0.437 0.443 0.450 0.452 0.455 0.470 0.473 0.466 0.472 0.467 0.481 0.475 0.484 0.481 0.481 0.476 0.475 0.437 0.467 0.464 0.455 0.447 0.437 0.423 0.418  3  E  1  R  x 10 s0.000 0.103 0.210 0.285 0:342 0.382 0.409 0.437 0.443 0.446 0.448 0.450 0.452 0.454 0.461 0.465 0.468 0.472 0.475 0.477 0.480 0.481 0.481 0.479 0.477 0.474 0.469 0.463 0.450 0.443 0.435 0.426 0.411  3  P  1  (R  E  -R )x P  s0.001 0.019 0.021 -0.001 0.001 -0.000 -0.002 -0.012 -0.006 -0.003 0.002 0.002 0.003 0.016 0.012 0.001 0.003 -0.005 0.006 -0.003 0.004 -0.001 -0.000 -0.003 -0.002 -0.037 -0.002 0.001 0.004 0.004 0.002 -0.003 0.007 1  10  3  cT  x 10 s0.000 0.001 0.001 0.002 0.002 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002  3  p  M  1  1.140 1.138 1.131 1.121 1.109 1.095 1.079 1.043 1.026 1.008 0.991 0.973 0.956 0.938 0.899 0.881 0.863 0.845 0.826 0.808 0.786 0.748 0.729 0.711 0.692 0.674 0.652 0.634 0.598 0.581 0.564 0.547 0.520  /  $  0.000 0.213 0.435 0.592 0.710 0.793 0.849 0.909 0.920 0.927 0.931 0.934 0.939 0.944 0.957 0.965 0.972 0.980 0.986 0.992 0.997 1.000 0.999 0.996 0.991 0.984 0.973 0.962 0.935 0.920 0.903 0.885 0.853  1.113 1.111 1.104 1.094 1.082 1.068 1.053 1.017 1.000 0.983 0.965 0.948 0.930 0.913 0.874 0.856 0.838 0.820 0.802 0.783 0.762 0.724 0.705 0.687 0.668 0.650 0.629 0.610 0.575 0.557 0.540 0.524 0.497  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  268  Data  Table C.l: Summary of Data for Run 1A -(Continued)  e s  1495 1534 1612 3454 3468 3482 3511 3525 3539 3582 3596 3611 3639 3653 3668 3696 3725 3753 3767 3782 3810 3825 3839 3882 3896 3910 3939 3953 3967 3996 4024 4053 4067  R  E  x 10 s-  3  1  0.409 0.401 0.377 0.079 0.077 0.076 0.076 0.076 0.074 0.071 0.071 0.070 0.069 0.068 0.067 0.065 0.065 0.063 0.063 0.063 0.062 0.060 0.060 0.059 0.058 0.058 0.056 0.056 0.056 0.055 0.054 0.053 0.053  R  P  x 10 s-  3  1  0.405 0.395 0.375 0.078 0.077 0.077 0.075 0.075 0.074 0.072 0.071 0.070 0.069 0.068 0.068 0.067 0.065 0.064 0.064 0.063 0.062 0.061 0.061 0.059 0.059 0.058 0.057 0.057 0.056 0.055 0.054 0.053 0.053  (R  E  - R ) x 10 s-  3  P  1  0.004 0.005 0.002 0.000 -0.001 -0.001 0.001 0.001 0.001 -0.001 -0.000 -0.000 -0.000 -0.000 -0.001 -0.001 -0.000 -0.001 -0.000 0.000 -0.000 -0.001 -0.001 0.000 -0.001 -0.000 -0.001 -0.001 -0.001 -0.000 -0.001 -0.001 -0.000  <7  p  X 10 s-  3  M  /  $  0.511 0.496 0.466 0.121 0.120 0.118 0.116 0.115 0.114 0.111 0.110 0.109 0.107 0.106 0.105 0.103 0.101 0.099 0.099 0.098 0.096 0.095 0.094 0.091 0.091 0.090 0.088 0.087 0.087 0.085 0.083 0.082 0.081  0.842 0.821 0.779 0.163 0.161 0.159 0.156 0.155 0.153 0.149 0.148 0.146 0.143 0.142 0.141 0.138 0.136 0.133 0.132 0.131 0.129 0.127 0.126 0.123 0.122 0.121 0.119 0.118 0.117 0.115 0.113 0.111 0.110  0.488 0.473 0.443 0.100 0.099 0.098 0.096 0.095 0.094 0.090 0.089 0.088 0.086 0.086 0.085 0.083 0.081 0.079 0.078 0.077 0.075 0.074 0.074 0.071 0.070 0.069 0.068 0.067 0.066 0.065 0.063 0.061 0.061  1  0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  269  Data  Table C.l: Summary of Data for Run 1A -(Continued)  6  s 4081 4110 4124 4138 4181 4195 4210 4238 4252 4267 4295 4324 4352 4367 4381 4395 4424 4438 4492 4531 4570 4615 4655 4694 4733 4812 4851 4890 4954 4975 5014 5053 5132  R  E  X  10  s0.051 0.051 0.050 0.050 0.049 0.048 0.048 0.047 0.047 0.047 0.047 0.045 0.045 0.044 0.044 0.044 0.044 0.043 0.042 0.040 0.041 0.039 0.039 0.038 0.036 0.036 0.034 0.034 0.034 0.034 0.033 0.032 0.032 1  3  R  x 10 s0.053 0.052 0.051 0.051 0.050 0.049 0.049 0.048 0.048 0.047 0.046 0.046 0.045 0.045 0.044 0.044 0.043 0.043 0.041 0.041 0.040 0.039 0.038 0.037 0.036 0.035 0.034 0.033 0.032 0.032 0.031 0.030 0.029  3  P  1  {R  - R P ) X 10 s-0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.000 0.000 0.000 -0.001 -0.000 -0.000 -0.001 -0.000 0.000 0.000 0.000 -0.001 0.001 0.001 0.001 0.001 0.000 0.002 0.001 0.001 0.002 0.002 0.002 0.002 0.003  3  E  1  cT  p  X  10  3  s0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001  M  1  0.080 0.079 0.078 0.077 0.075 0.075 0.074 0.072 0.072 0.071 0.070 0.068 0.067 0.067 0.066 0.065 0.064 0.063 0.061 0.060 0.058 0.056 0.055 0.053 0.052 0.049 0.048 0.046 0.044 0.044 0.042 0.041 0.039  /  $  0.109 0.107 0.106 0.106 0.103 0.102 0.101 0.100 0.099 0.098 0.096 0.095 0.093 0.092 0.092 0.091 0.090 0.089 0.086 0.084 0.082 0.080 0.079 0.077 0.075 0.072 0.070 0.069 0.066 0.066 0.064 0.063 0.060  0.060 0.058 0.058 0.057 0.055 0.054 0.053 0.052 0.051 0.051 0.049 0.048 0.047 0.046 0.046 0.045 0.044 0.043 0.041 0.039 0.038 0.036 0.034 0.033 0.032 0.029 0.028 0.026 0.024 0.023 0.022 0.021 0.019  Appendix  C. Tabulated  Instantaneous  Drying  Rate  270  Data  Table C.2: Summary of Data for Run 1  e  s 0 66 109 153 196 240 283 327 370 413 457 500 544 588 631 675 718 762 805 849 892 935 979 1022 1066 1109 1153 1196 1240 1284 1327 1371 1414  R  x 10 s0.001 0.095 0.258 0.198 0.566 0.272 0.572 0.630 0.695 0.710 0.727 0.719 0.746 0.703 0.719 0.680 0.675 0.676 0.636 0.631 0.597 0.555 0.468 0.471 0.475 0.467 0.433 0.443 0.404 0.392 0.361 0.353 0.335  3  E  1  R  P  x 10  3  s0.000 0.110 0.212 0.303 0.383 0.461 0.531 0.595 0.645 0,684 0.712 0.729 0.736 0.734 0.726 0.712 0.694 0.672 0.647 0.621 0.594 0.567 0.539 0.513 0.486 0.460 0.435 0.412 0.389 0.368 0.348 0.329 0.311 1  {R  - Rp)x 10  3  E  s0.001 -0.015 0.045 -0.105 0.183 -0.189 0.041 0.035 0.050 0.026 0.015 -0.010 0.011 -0.031 -0.007 -0.032 -0.018 0.005 -0.012 0.010 0.003 -0.012 -0.071 -0.042 -0.011 0.007 -0.003 0.031 0.015 0.024 0.013 0.024 0.024 1  x 10 s0.000 0.046 0.039 0.036 0.035 0.027 0.023 0.023 0.023 0.023 0.021 0.020 0.018 0.017 0.017 0.016 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.015 0.015 0.014 0.014 0.013 0.013 0.013 0.013 0.013 0.013  3  <7p  M  /  $  1.140 1.137 1.130 1.119 •1.104 1.086 1.064 1.039 1.013 0.984 0.953 0.922 0.890 0.858 0.826 0.795 0.764 0.734 0.706 0.678 0.652 0.627 0.603 0.580 0.558 0.538 0.518 0.500 0.482 0.466 0.450 0.435 0.421  0.000 0.149 0.289 0.411 0.520 0.626 0.722 0.808 0.877 0.930 0.968 0.990 1.000 0.998 0.987 0.967 0.943 0.913 0.880 0.844 0.808 0.771 0.733 0.696 0.660 0.625 0.592 0.560 0.529 0.500 0.473 0.447 0.423  1.383 1.379 1.371 1.357 1.339 1.316 1.289 1.259 1.226 1.190 1.152 1.114 1.074 1.034 0.995 0.956 0.919 0.882 0.847 0.812 0.780 0.749 0.719 0.691 0.664 0.639 0.615 0.592 0.571 0.550 0.531 0.513 0.496  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  271  Data  Table C.2: Summary of Data for Run 1 -(Continued)  e  s 1457 1501 1544 1588 1631 1675 1718 1762 1805 1849 1892 1936 1979 2022 2066 2110 2153 2197 2240 2284 2327 2371 2414 2458 2501 2545 2588 2631 2675 2718 2762 2806 2849  R  x 10 s" 0.337 0.311 0.308 0.183 0.581 0.049 0.111 0.325 0.215 0.186 0.179 0.168 0.139 0.132 0.098 0.126 0.121 0.108 0.101 0.086 0.091 0.0.90 0.067 0.082 0.066 0.066 0.066 0.065 0.053 0.057 0.049 0.053 0.058  3  E  1  R  x 10 s0.295 0.279 0.265 0.251 0.238 0.226 0.215 0.205 0.195 0.186 0.177 0.169 0.161 0.154 0.147 0.141 0.135 0.129 0.124 0.119 0.114 0.109 0.105 0.100 0.096 0.092 0.089 0.085 0.082 0.078 0.075 0.072 0.069  3  P  1  (R  E  - R) P  s0.043 0.032 0.043 -0.068 0.342 -0.177 -0.104 0.121 0.020 0.000 0.002 -0.001 -0.023 -0.022 -0.050 -0.015 -0.014 -0.022 -0.023 -0.033 -0.023 -0.019 -0.038 -0.018 -0.031 -0.026 -0.022 -0.020 -0.028 -0.021 -0.026 -0.019 -0.011 1  x 10  3  x 10 s0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.012 0.012 0.012 0.011 0.011 0.011 0.011 0.010 0.010 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.010  3  cTp  M  1  0.408 0.396 0.384 0.373 0.362 0.352 0.343 0.333 0.325 0.316 0.309 0.301 0.294 0.287 0.281 0.274 0.268 0.262 0.257 0.252 0.247 0.242 0.237 0.233 0.228 0.224 0.220 0.217 0.213 0.210 0.206 0.203 0.200  /  $  0.401 0.379 0.360 0.341 0.324 0.307 0.292 0.278 0.265 0.252 0.241 0.229 0.219 0.210 0.200 0.191 0.183 0.175 0.168 0.161 0.154 0.148 0.142 0.136 0.131 0.125 0.120 0.115 0.111 0.106 0.102 0.098 0.094  0.480 0.464 0.450 0.436 0.423 0.410 0.398 0.387 0.376 0.366 0.356 0.347 0.338 0.330 0.322 0.314 0.306 0.299 0.293 0.286 0.280 0.274 0.268 0.263 0.257 0.252 0.247 0.243 0.238 0.234 0.230 0.226 0.222  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  272  Data  Table C.2: Summary of Data for Run 1 -(Continued)  9  s 2893 2936 2980 3023 3067 3110 3154 3197 3241 3284 3328 3371 3415 3458 3502 3545 3589 3632 3676 3719 3763 3806 3850 3893 3937 3980 4024 4067 4111 4154 4198 4241 4285  R  E  X  10  s0.041 0.046 0.056 0.047 0.041 0.053 0.047 0.042 0.038 0.049 0.061 0.078 0.075 0.083 0.074 0.059 0.047 0.041 0.036 0.058 0.044 0.038 0.046 0.044 0.068 0.036 0.046 0.053 0.065 0.057 0.073 0.058 0.046 1  3  R  x 10 s0.066 0.064 0.061 0.059 0.056 0.054 0.052 0.049 0.047 0.045 0.044 0.042 0.040 0.038 0.037 0.035 0.034 0.032 0.031 0.029 0.028 0.027 0.026 0.025 0.024 0.023 0.022 0.021 0.020 0.019 0.018 0.017 0.016  3  P  1  (R  E  - R) P  s-0.025 -0.018 -0.005 -0.012 -0.015 -0.001 -0.005 -0.008 -0.009 0.004 0.017 0.037 0.035 0.045 0.038 0.024 0.013 0.009 0.005 0.028 0.015 0.011 0.020 0.019 0.045 0.013 0.024 0.033 0.045 0.039 0.055 0.041 0.030 1  x 10  3  cT  x 10 s0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.007 0.000  3  p  1  M  /  0.197 0.090 0.194 0.086 0.191 0.083 0.189 0.080 0.186 0.076 0.184 0.073 0.182 0.070 0.180 0.067 0.177 0.064 0.175 0.062 0.173 0.059 0.172 0.057 0.170 0.054 0.168 0.052 0.166 0.050 0.165 0.048 0.163 0.046 0.162 0.044 0.161 0.042 0.159 0.040 0.158 0.038 0.157 0.037 0.156 0.035 0.155 0.034 0.154 0.032 0.153 0.031 0.152 0.029 0.151 0.028 0.150 0.027 0.149 0.026 0.148 0.024 0.147 0.023 0.147 0.022  $  0.219 0.215 0.212 0.209 0.205 0.202 0.200 0.197 0.194 0.192 0.189 0.187 0.185 0.183 0.181 0.179 0.177 0.175 0.174 0.172 0.170 0.169 0.168 0.166 0.165 0.164 0.162 0.161 0.160 0.159 0.158 0.157 0.156  Appendix  C. Tabulated  Instantaneous  Drying  Rate  273  Data  Table C.3: Summary of Data for Run 3  e  s 0 65 109 152 196 239 283 326 370 413 457 500 544 587 631 675 718 761 805 848 892 935 979 1022 1066 1109 1152 1196 1239 1283 1326 1370  R  x 10  3  E  s0.001 0.153 1.130 1.420 1.599 1.862 1.781 1.787 1.697 1.666 1.587 1.467 1.385 1.308 1.178 1.129 0.988 0.619 0.525 0.636 0.580 0.478 0.504 0.460 0.418 0.362 0.322 0.292 0.271 0.235 0.219 0.180 1  R  x 10 s0.000 0.400 0.968 1.414 1.679 1.789 1.811 1.784 1.731 1.662 1.578 1.484 1.379 1.270 1.157 1.044 0.938 0.839 0.746 0.664 0.589 0.525 0.467 0.419 0.377 0.342 0.312 0.286 0.264 0.245 0.229 0.214  3  P  1  (R  E  - R) P  s" 0.001 -0.247 0.162 0.006 -0.080 0.073 -0.030 0.002 -0.034 0.004 0.009 -0.018 0.006 0.038 0.022 0.085 0.050 -0.221 -0.221 -0.027 -0.009 -0.047 0.037 0.041 0.040 0.020 0.010 0.006 0.007 -0.010 -0.010 -0.035 1  x 10  3  x 10 s0.042 0.058 0.050 0.048 0.048 0.044 0.041 0.041 0.041 0.039 0.036 0.034 0.035 0.036 0.037 0.037 0.036 0.034 0.033 0.033 0.034 0.034 0.033 0.032 0.030 0.029 0.029 0.031 0.036 0.043 0.053 0.000  3  <7p  1  M  /  1.410 0.000 1.402 0.221 1.372 0.535 1.320 0.781 1.251 .0.927 1.176 0.988 1.097 1.000 1.019 0.985 0.942 0.956 0.869 0.918 0.798 0.872 0.732 0.820 0.669 0.762 0.612 0.702 0.558 0.639 0.510 0.577 0.467 0.518 0.429 0.464 0.394 0.412 0.364 0.367 0.337 0.325 0.313 0.290 0.291 0.258 0.272 0.232 0.254 0.208 0.239 0.189 0.225 0.172 0.212 0.158 0.200 0.146 0.189 0.135 0.178 0.126 0.169 0.118  $  1.376 1.368 1.338 1.287 1.219 1.145 1.066 0.990 0.913 0.841 0.770 0.705 0.642 0.586 0.533 0.485 0.443 0.405 0.371 0.341 0.313 0.290 0.268 0.249 0.232 0.217 0.203 0.190 0.178 0.167 0.157 0.147  Appendix  C. Tabulated  Instantaneous  Drying  Rate  274  Data  Table C.4: Summary of Data for Run 4  6 s  0 51 124 160 226 263 335 365 431 467 533 569 635 672 744 774 840 876 942 978 1044 1074 1146 1176 1248 1278 1344 1380 1446 1482 1555 1585 1621  R  x 10  3  E  s-  1  0.001 0.107 0.714 1.022 1.217 1.273 1.362 1.429 1.324 1.316 1.214 1.166 1.203 1.080 1.042 0.946 0.953 0.879 0.826 0.831 0.672 0.623 0.536 0.499 0.481 0.484 0.455 0.494 0.361 0.309 0.198 0.218 0.256  R  x 10  3  P  s-  1  0.000 0.144 0.693 0.944 1.240 1.320 1.366 1.361 1.325 1.299 1.245 1.213 1.149 1.111 1.031 0.997 0.919 0.876 0.797 0.755 0.681 0.649 0.575 0.546 0.481 0.456 0.405 0.379 0.336 0.315 0.275 0.261 0.244  {R  E  - R) P  s-  x 10  1  0.001 -0.037 0.021 0.078 -0.023 -0.047 -0.004 0.069 -0.002 0.016 -0.031 -0.047 0.053 -0.030 0.011 -0.050 0.034 0.003 0.029 0.076 -0.010 -0.026 -0.039 -0.047 0.000 0.028 0.050 0.115 0.025 -0.005 -0.078 -0.043 0.012  3  cr  x 10  3  p  s-  M  /  $  0.000 0.106 0.507 0.691 0.907 0.966 1.000 0.996 0.970 0.951 0.912 0.888 0.841 0.813 0.755 0.730 0.672 0.641 0.584 0.553 0.499 0.475 0.421 0.400 0.352 0.334 0.296 0.277 0.246 0.230 0.201 0.191 0.179  1.418 1.416 1.386 1.355 1.281 1.232 1.133 1.091 1.000 0.952 0.866 0.821 0.742 0.699 0.620 0.589 0.525 0.492 0.436 0.407 0.359 0.338 0.293 0.276 0.239 0.224 0.195 0.181 0.157 0.145 0.123 0.115 0.105  1  0.025 0.030 0.027 0.026 0.024 0.023 0.021 0.020 0.019 0.019 0.018 0.018 0.017 0.017 0.016 0.016 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.014 0.014 0.015 0.016 0.018 0.023 0.026 0.000  1.410 1.408 1.378 1.348 1.275 1.227 1.130 1.089 1.000 0.953 0.869 0.825 0.747 0.705 0.628 0.598 0.534 0.502 0.447 0.419 0.371 0.352 0.308 0.291 0.254 0.240 0.211 0.197 0.174 0.162 0.140 0.132 0.123  Appendix  C. Tabulated  Instantaneous  Drying  Rate  275  Data  Table C.5: Summary of Data for Run 8  e  s 0 48 84 114 150 186 216 289 325 361 391 427 457 493 566 602 632 668 704 734 770 836 872 909 945 981 1011 1047 1113 1149  R  x 10 s0.001 0.684 0.589 1.118 1.195 1.334 1.460 1.510 1.391 1.410 1.311 1.198 1.289 1.327 1.086 0.987 0.937 1.024 1.070 0.999 0.803 0.817 0.803 0.798 0.721 0.639 0.576 0.471 0.378 0.368  3  E  1  R  x 10 s" 0.000 0.451 0.817 1.054 1.254 1.376 1.431 1.455 1.433 1,399 1.366 1.323 1.285 1.239 1.144 1.097 1.057 1.009 0.961 0.921 0.872 0.784 0.737 0.689 0.643 0.599 0.564 0.522 0.451 0.415  3  P  1  (R  E  - Rp)  s0.001 0.232 -0.228 0.064 -0.059 -0.043 0.028 0.055 -0.041 0.011 -0.055 -0.125 0.004 0.088 -0.058 -0.110 -0.121 0.015 0.109 0.079 -0.070 0.033 0.067 0.109 0.077 0.040 0.012 -0.052 -0.073 -0.047  x 10  3  1  *  x 10 s0.000 0.065 0.060 0.050 0.049 0.049 0.047 0.039 0.039 0.040 0.039 0.037 0.035 0.033 0.032 0.032 0.033 0.033 0.033 0.032 0.030 0.028 0.027 0.027 0.029 0.030 0.032 0.035 0.039 0.040  3  p  M  1  '  1.410 1.400 1.377 1.349 1.307 1.260 1.218 1.112 1.060 1.009 0.967 0.919 0.880 0.834 0.747 0.707 0.674 0.637 0.602 0.574 0.541 0.487 0.459 0.433 0.409 0.387 0.369 0.350 0.317 0.302  / 0.000 0.309 0.560 0.723 0.860 0.944 0.982 0.998 0.982 0.959 0.937 0.907 0.881 0.850 0.785 0.752 0.725 0.692 0.659 0.631 0.598 0.538 0.505 0.472 0.441 0.411 0.387 0.358 0.309 0.285  1.324 1.315 1.293 1.266 1.226 1.181 1.141 1.040 0.990 0.941 0.902 0.856 0.819 0.775 0.692 0.654 0.623 0.588 0.554 0.527 0.496 0.444 0.418 0.393 0.370 0.349 0.332 0.314 0.283 0.268  Appendix C. Tabulated Instantaneous Drying Rate Data  276  Table C.6: Summary of Data for Run 9  9  s 0 51 81 117 153 183 249 285 322 358 394 424 490 526 556 592 622 658 724 760 790 826 863 899 965 1001 1031 1067 1097 1133 1206 1243 1279  R  E  x 10 s" 0.001 0.556 0.947 1.075 1.141 1.360 1.295 1.371 1.392 1.333 1.242 1.253 1.088 1.029 1.013 0.899 1.017 0.845 0.771 0.760 0.669 0.845 0.869 0.745 0.862 0.753 0.656 0.649 0.621 0.507 0.525 0.484 0.381  3  1  R  P  x 10 s" 0.000 0.594 0.883 1.089 1.233 1.313 1.370 1.352 1.314 1.269 1.221 1.182 1.102 1.063 1.032 0.998 0.970 0.937 0.879 0.848 0.822 0.791 0.759 0.728 0.671 0.641 0.616 0.586 0.562 0.534 0.478 0.452 0.427  3  1  {R  - Rp) x 10  3  E  s0.001 -0.039 0.064 -0.015 -0.092 0.048 -0.075 0.019 0.077 0.064 0.021 0.071 -0.014 -0.034 -0.019 • -0.099 0.047 -0.092 -0.108 -0.088 -0.153 0.054 0.110 0.017 0.190 0.112 0.040 0.063 0.058 -0.026 0.047 0.033 -0.046 1  <T x 10 s" 0.000 0.075 0.059 0.056 0.043 0.043 0.035 0.032 0.032 0.032 0.031 0.029 0.025 0.023 0.022 0.022 0.022 0.022 0.022 0.022 0.021 0.021 0.020 0.019 0.017 0.017 0.016 0.016 0.015 0.015 0.015 0.015 0.015  3  P  M  /  $  1.410 1.397 1.375 1.339 1.297 1.259 1.170 1.120 1.071 1.025 0.980 0.944 0.868 0.829 0.798 0.761 0.732 0.698 0.638 0.607 0.581 0.552 0.524 0.497 0.451 0.427 0.408 0.387 0.370 0.350 0.313 0.296 0.280  0.000 0.434 0.644 0.795 0.900 0.958 1.000 0.987 0.959 0.926 0.891 0.863 0.805 0.776 0.754 0.728 0.708 0.684 0.642 0.619 0.600 0.577 0.554 0.531 0.490 0.468 0.450 0.428 0.410 0.390 0.349 0.330 0.311  1.275 1.264 1.243 1.210 1.172 1.137 1.055 1.010 0.964 0.922 0.880 0.847 0.778 0.743 0.714 0.680 0.653 0.622 0.567 0.538 0.515 0.488 0.462 0.438 0.395 0.374 0.356 0.336 0.321 0.303 0.269 0.253 0.238  1  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  277  Data  Table C.6: Summary of Data for Run 9 -(Continued)  e  s 1315 1345 1381 1447 1484 1520 1557 1593 1630 1703 1739 1775 1805 1841 1871 1943 1973 2009 2039 2075 2112 2184 2214 2250 2280 2316 2346 2419 2455 2491 2521 2557 2587  x 10 s" 0.460 0.378 0.330 0.417 0.280 0.283 0.304 0.248 0.184 0.175 0.176 0.128 0.153 0.093 0.039 0.130 0.092 0.159 0.129 0.182 0.137 0.035 0.024 -0.034 -0.087 -0.110 -0.102 -0.048 0.031 -0.016 -0.101 -0.088 -0.042  3  RE  1  R  P  x 10 s0.403 0.383 0.361 0.322 0.302 0.283 0.265 0.248 0.232 0.202 0.189 0.176 0.166 0.155 0.146 0.127 0.119 0.111 0.105 0.097 0.090 0.078 0.073 0.068 0.063 0.059 0.055 0.047 0.044 0.040 0.038 0.035 0.033  3  1  (R  - R ) x 10 s0.058 -0.005 -0.031 0.095 -0.022 -0.000 0.039 -0.000 -0.048 -0.028 -0.013 -0.049 -0.013 -0.062 -0.108 0.003 -0.028 0.048 0.024 0.085 0.047 -0.043 -0.049 -0.101 -0.150 -0.168 -0.158 -0.095 -0.012 -0.056 -0.139 -0.123 -0.075  3  E  P  1  <jp x 10 s0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.011 0.011 0.010 0.010 0.010 0.009 0.008 0.008 0.008 0.007 0.007 0.006 0.006 0.006 0.005 0.005 0.005  3  M  /  $  0.265 0.253 0.240 0.217 0.206 0.195 0.185 0.176 0.167 0.151 0.144 0.137 0.132 0.127 0.122 0.112 0.108 0.104 0.101 0.097 0.094 0.088 0.086 0.083 0.081 0.079 0.077 0.074 0.072 0.070 0.069 0.068 0.067  0.294 0.280 0.263 0.235 0.220 0.207 0.194 0.181 0.169 0.148 0.138 0.129 0.122 0.113 0.107 0.093 0.087 0.081 0.076 0.071 0.066 0.057 0.053 0.049 0.046 0.043 0.040 0.034 0.032 0.029 0.028 0.026 0.024  0.225 0.214 0.202 0.181 0.170 0.161 0.151 0.143 0.135 0.120 0.114 0.108 0.103 0.098 0.094 0.085 0.081 0.077 0.074 0.071 0.068 0.062 0.060 0.058 0.056 0.054 0.053 0.049 0.048 0.046 0.045 0.044 0.043  1  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  278  Data  Table C.7: Summary of Data for Run 10  6  s 0 55 100 144 189 233 278 322 367 411 456 500 545 589 634 678 723 767 811 856 900 945 989 1034 1078 1123 1167 1212 1256 1301 1345 1389 1434  R  x 10 s0.002 0.779 1.589 1.803 1.732 1.648 1.534 1.497 1.377 1.412 1.387 1.200 1.157 0.911 0.901 0.782 0.778 0.630 0.704 0.713 0.606 0.540 0.474 0.394 0.333 0.286 0.334 0.307 0.363 0.357 0.263 0.667 0.982  3  E  1  R  P  x 10 s0.000 0.760 1.475 1.727 1.748 1.702 1.638 1.563 1.474 1.378 1.275 1.175 1.077 0.989 0.908 0.837 0.772 0.717 0.667 0.622 0.583 0.546 0.513 0.483 0.455 0.428 0.404 0.380 0.358 0.337 0.317 0.298 0.280  3  1  {R  - Rp) x 10  3  E  s0.002 0.000 0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 -0.000 0.000 0.001  Op  x 10  3  M  /  $  1.410 1.407 1.395 1.372 1.343 1.308 1.271 1.231 1.192 1.154 1.116 1.077 1.041 1.005 0.971 0.935 0.902 0.870 0.839 0.810 0.780 0.752 0.726 0.701 0.675 0.652 0.630 0.608 0.587 0.568 0.549 0.531 0.513  0.000 0.182 0.434 0.677 0.842 0.938 0.985 1.000 0.997 0.986 0.971 0.953 0.934 0.914 0.892 0.867 0.841 0.814 0.786 0.757 0.727 0.698 0.670 0.642 0.614 0.589 0.564 0.541 0.518 0.497 0.477 0.459 0.441  1.230 1.227 1.217 1.197 1.170 1.140 1.107 1.071 1.037 1.003 0.970 0.936 0.904 0.872 0.841 0.810 0.781 0.752 0.725 0.699 0.672 0.648 0.625 0.602 0.580 0.559 0.540 0.521 0.502 0.485 0.468 0.452 0.436  1  0.000 0.083 0.076 0.072 0.065 0.056 0.056 0.053 0.047 0.043 0.042 0.042 0.041 0.039 0.037 0.034 0.032 0.031 0.031 0.031 0.031 0.031 0.030 0.030 0.029 0.028 0.026 0.025 0.024 0.023 0.022 0.022 0.022  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  279  Data  Table C.7: Summary of Data for Run 10 -(Continued)  e s  1478 1523 1567 1612 1656 1701 1745 1790 1834 1879 1923 1967 2012 2056 2101 2145 2190 2234 2279 2323 2368 2412 2457 2501 2546 2590 2635 2679 2724 2768 2813 2857 2902  R  E  10  3  x  s-  1  0.469 0.386 0.349 0.302 0.191 0.148 0.061 0.024 0.013 0.037 0.021 0.024 0.026 0.031 0.286 0.063 0.010 -0.016 -0.042 -0.024 -0.045 0.031 0.053 -0.061 -0.125 -0.148 -0.116 0.026 0.148 0.591 0.344 0.076 0.039  R  P  x 10  3  s-  1  0.263 0.246 0.231 0.216 0.202 0.188 0.176 0.164 0.153 0.142 0.132 0.123 0.114 0.106 0.098 0.091 0.084 0.078 0.072 0.067 0.062 0.057 0.053 0.049 0.045 0.041 0.038 0.035 0.032 0.030 0.027 0.025 0.023  [R  E  - Rp) x 10  3  s"  1  0.000 0.000 0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.001 0.000 0.000 0.000  (T  P  10  3  X  s-  M  /  $  0.496 0.480 0.464 0.449 0.434 0.420 0.407 0.394 0.381 0.369 0.357 0.345 0.334 0.323 0.312 0.302 0.292 0.282 0.273 0.264 0.255 0.246 0.238 0.230 0.222 0.215 0.207 0.200 0.193 0.187 0.180 0.174 0.168  0.424 0.409 0.394 0.381 0.367 0.355 0.343 0.332 0.321 0.311 0.302 0.293 0.284 0.275 0.267 0.259 0.252 0.244 0.237 0.230 0.224 0.217 0.210 0.204 0.198 0.192 0.186 0.181 0.175 0.170 0.165 0.160 0.155  0.421 0.407 0.393 0.380 0.367 0.354 0.342 0.331 0.319 0.308 0.298 0.288 0.278 0.268 0.259 0.250 0.241 0.232 0.224 0.216 0.208 0.200 0.193 0.186 0.179 0.172 0.166 0.159 0.153 0.147 0.142 0.136 0.131  1  0.021 0.021 0.021 0.021 0.022 0.022 0.022 0.022 0.022 0.021 0.021 0.021 0.020 0.020 0.020 0.019 0.019 0.018 0.017 0.017 0.016 0.016 0.015 0.014 0.014 0.013 0.012 0.012 0.011 0.011 0.010 0.010 0.009  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  280  Data  Table C.8: Summary of Data for Run 11  6  s 0 66 110 153 197 240 327 371 415 458 502 545 633 676 720 763 807 851 938 981 1025 1069 1112 1156 1243 1287 1330 1374 1418 1461 1549 1592 1636  R  x 10 s0.001 0.180 0.616 0.848 0.947 1.016 1.064 1.076 1.104 1.162 0.906 1.095 0.990 0.970 0.937 0.933 0.864 0.877 0.804 0.759 0.747 0.703 0.672 0.650 0.602 0.555 0.528 0.501 0.455 0.425 0.384 0.353 0.329  3  E  1  R  x 10 s0.000 0.281 0.574 0.805 0.957 1.038 1.090 1.091 1.085 1,076 1.064 1.049 1.010 0.987 0.960 0.933 0.903 0.871 0.805 0.772 0.738 0.703 0.670 0.636 0.571 0.539 0.509 0.479 0.451 0.424 0.372 0.349 0.326  3  P  1  (R  E  - R) P  x 10  s" 0.001 -0.101 0.042 0.043 -0.010 -0.022 -0.026 -0.015 0.018 0.086 -0.157 0.046 -0.020 -0.016 -0.024 0.001 -0.038 0.006 -0.001 -0.013 0.010 -0.000 0.002 0.014 0.031 0.016 0.019 0.022 0.005 0.001 0.012 0.004 0.002  3  1  x 10 s" 0.000 0.018 0.017 0.015 0.015 0.014 0.012 0.012 0.012 0.011 0.011 0.011 0.010 0.009 0.009 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005  3  Op  M  1  .  1.410 1,403 1.384 1.354 1.315 1.272 1.179 1.131 1.083 1.036 0.989 0.944 0.853 0.810 0.767 0.727 0.686 0.647 0.574 0.540 0.507 0.476 0.446 0.417 0.365 0.340 0.318 0.296 0.276 0.257 0.222 0.206 0.191  /  $  0.000 0.258 0.526 0.738 0.877 0.951 0.999 1.000 0.995 0.986 0.975 0.961 0.925 0.904 0.880 0.855 0.827 0.798 0.738 0.708 0.676 0.644 0.614 0.583 0.523 0.494 0.467 0.439 0.413 0.389 0.341 0.320 0.299  1.463 1.456 1.436 1.404 1.363 1.318 1.220 1.169 1.119 1.070 1.020 0.972 0.877 0.832 0.787 0.744 0.701 0.660 0.583 0.548 0.513 0.479 0.448 0.418 0.363 0.337 0.314 0.291 0.269 0.249 0.212 0.196 0.180  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  281  Data  Table C.8: Summary of Data for Run 11 -(Continued)  6  s 1679 1723 1767 1854 1897 1941 1985 2028 2072 2159 2202 2246 2290 2333 2377 2464 2508 2551 2595 2638 2682 2769 2813 2856 2900 2944 2987 3074 3118 3162 3205 3249 3292  R  x 10 s0.311 0.292 0.267 0.239 0.222 0.195 0.183 0.162 0.145 0.140 0.124 0.109 0.101 0.088 0.080 0.074 0.054 0.047 0.047 0.039 0.035 0.031 0.030 0.011 0.020 0.019 0.005 0.007 0.006 0.002 -0.003 -0.007 -0.033  3  E  1  R  x 10 s0.305 0.285 0.265 0.230 0.214 0.199 0.185 0.171 0.159 0.136 0.126 0.117 0.108 0.100 0.092 0.078 0.072 0.067 0.061 0.057 0.052 0.044 0.041 0.037 0.034 0.031 0.029 0.024 0.022 0.020 0.019 0.017 0.016  3  P  1  {R  E  -Rp)x  s0.006 0.008 0.002 0.009 0.008 -0.004 -0.001 -0.009 -0.013 0.003 -0.003 -0.008 -0.007 -0.012 -0.013 -0.005 -0.018 -0.020 -0.015 -0.017 -0.017 -0.014 -0.011 -0.026 -0.014 -0.012 -0.024 -0.017 -0.016 -0.019 -0.022 -0.024 -0.049 1  10  3  cT  x 10 s0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001  3  p  M  1  0.178 0.165 0.153 0.131 0.122 0.113 0.104 0.097 0.089 0.077 0.071 0.066 0.061 0.056 0.052 0.045 0.041 0.038 0.035 0.033 0.030 0.026 0.024 0.023 0.021 0.020 0.018 0.016 0.015 0.014 0.013 0.013 0.012  /  $  0.280 0.261 0.243 0.211 0.196 0.182 0.169 0.157 0.146 0.125 0.116 0.107 0.099 0.091 0.084 0.072 0.066 0.061 0.056 0.052 0.048 0.040 0.037 0.034 0.031 0.029 0.026 0.022 0.020 0.019 0.017 0.016 0.014  0.166 0.153 0.140 0.117 0.107 0.098 0.089 0.081 0.073 0.060 0.054 0.048 0.043 0.038 0.034 0.026 0.022 0.019 0.016 0.014 0.011 0.007 0.005 0.003 0.001 -0.000 -0.002 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009  Appendix  C. Tabulated  Instantaneous  Drying  Rate  282  Data  Table C.9: Summary of Data for Run 12  6  s 0 65 109 152 196 240 283 327 370 414 457 501 545 588 632 675 719 762 806 849 893 937 980 1024 1067 1111 1155 1198 1242 1285 1329 1373 1416  R  E  x 10 s0.001 0.278 0.691 0.906 0.937 0.962 1.011 1.030 0.987 0.979 0.979 0.929 0.962 0.888 0.846 0.877 0.797 0.774 0.786 0.711 0.686 0.688 0.656 0.603 0.605 0.574 0.563 0.525 0.488 0.513 0.447 0.457 0.456  3  1  R  P  x 10 s0.000 0.371 0.654 0.840 0.949 1.001 1.019 1.018 1.006 0.988 0.966 0.941 0.915 0.889 0.862 0.836 0.809 0.784 0.758 0.734 0.709 0.684 0.661 0.637 0.614 0.591 0.568 0.546 0.524 0.502 0.481 0.459 0.439  3  1  (R  E  - R ) x 10  3  P  s0.001 -0.093 0.036 0.066 -0.012 -0.039 -0.008 0.012 -0.019 -0.008 0.014 -0.012 0.047 -0.000 -0.016 0.041 -0.012 -0.009 0.028 -0.023 -0.023 0.003 -0.005 -0.035 -0.009 -0.017 -0.005 -0.021 -0.036 0.011 -0.033 -0.002 0.017 1  CT-p  x 10  3  s0.000 0.020 0.019 0.016 0.016 0.016 0.014 0.013 0.013 0.013 0.013 0.012 0.011 0.011 0.011 0.011 0.011 0.010 0.010 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.007 0.007 0.007  M  1  1.410 1.400 1.377 1.345 1.305 1.262 1.219 1.174 1.130 1.086 1.044 1.002 0.962 0.923 0.884 0.848 0.812 0.777 0.743 0.711 0.680 0.649 0.620 0.591 0.565 0.538 0.513 0.489 0.465 0.443 0.421 0.401 0.381  /  $  0.000 0.364 0.642 0.825 0.931 0.982 1.000 0.999 0.987 0.969 0.948 0.923 0.898 0.872 0.846 0.820 0.794 0.769 0.744 0.720 0.696 0.672 0.649 0.625 0.603 0.580 0.558 0.536 0.514 0.493 0.472 0.451 0.431  1.299 1.290 1.268 1.238 1.201 1.161 1.120 1.078 1.038 0.997 0.957 0.918 0.880 0.844 0.808 0.774 0.740 0.708 0.676 0.646 0.616 0.588 0.561 0.534 0.509 0.484 0.460 0.438 0.416 0.395 0.375 0.356 0.338  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  283  Data  Table C.9: Summary of Data for Run 12 -(Continued)  6  s 1460 1503 1547 1591 1634 1678 1721 1765 1809 1852 1896 1940 1983 2027 2070 2114 2158 2201 2245 2288 2332 2376 2419 2463 2506 2550 2593 2637 2681 2724 2768 2812 2855  R  E  x 10 s0.423 0.416 0.415 0.390 0.390 0.333 0.298 0.326 0.283 0.284 0.248 0.252 0.243 0.230 0.240 0.197 0.172 0.160 0.167 0.155 0.145 0.130 0.112 0.121 0.120 0.101 0.087 0.059 0.072 0.092 0.063 0.043 0.052  3  1  R  P  x 10 s" 0.419 0.399 0.380 0.361 0.343 0.326 0.309 0.293 0.277 0.262 0.248 0.234 0.221 0.208 0.196 0.185 0.174 0.164 0.154 0.145 0.136 0.127 0.119 0.112 0.105 0.098 0.092 0.086 0.081 0.075 0.070 0.066 0.062  3  1  (R  E  - Rp) x 10  3  s0.004 0.017 0.035 0.029 0.047 0.007 -0.011 0.033 0.006 0.021 0.000 0.018 0.023 0.022 0.044 0.012 -0.002 -0.004 0.013 0.010 0.009 0.003 -0.008 0.009 0.015 0.003 -0.005 -0.027 -0.008 0.017 -0.008 -0.023 -0.009 1  x 10 s0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004  3  o-p  M  /  $  0.363 0.345 0.328 0.312 0.296 0.282 0.268 0.255 0.242 0.231 0.219 0.209 0.199 0.190 0.181 0.173 0.165 0.157 0.150 0.144 0.138 0.132 0.127 0.122 0.117 0.112 0.108 0.104 0.101 0.097 0.094 0.091 0.089  0.411 0.392 0.373 0.355 0.337 0.320 0.303 0.287 0.272 0.257 0.243 0.230 0.217 0.204 0.193 0.181 0.171 0.161 0.151 0.142 0.133 0.125 0.117 0.110 0.103 0.097 0.090 0.085 0.079 0.074 0.069 0.065 0.060  0.320 0.304 0.288 0.272 0.258 0.245 0.232 0.219 0.208 0.197 0.186 0.176 0.167 0.158 0.150 0.143 0.135 0.128 0.122 0.116 0.110 0.105 0.100 0.095 0.091 0.086 0.083 0.079 0.076 0.072 0.069 0.067 0.064  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  284  Data  Table C.9: Summary of Data for Run 12 -(Continued)  6  s 2899 2942 2986 3029 3073 3117 3160 3204 3247 3291 3334 3378 3422 3465 3509 3552 3596 3640 3683 3727 3770 3814 3857 3901 3945 3988 4032 4075 4119 4163  R  x 10 s0.048 0.031 0.023 0.017 0.024 0.011 0.014 0.013 0.014 -0.002 -0.026 -0.020 0.010 0.015 -0.008 -0.018 -0.033 0.003 -0.052 -0.031 -0.019 -0.011 -0.016 -0.021 -0.035 -0.026 -0.035 -0.042 -0.026 -0.045  3  E  1  R  P  x 10 s0.057 0.054 0.050 0.047 0.044 0.041 0.038 0.035 0.033 0.031 0.029 0.027 0.025 0.023 0.021 0.020 0.018 0.017 0.016 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.009 0.008 0.008 0.007  3  1  (R  E  - Rp) x 10  3  s-0.009 -0.022 -0.027 -0.030 -0.019 -0.029 -0.024 -0.022 -0.018 -0.033 -0.054 -0.047 -0.015 -0.008 -0.029 -0.038 -0.051 -0.014 -0.068 -0.046 -0.033 -0.024 -0.028 -0.032 -0.045 -0.035 -0.043 -0.050 -0.033 -0.052 1  cT  x 10 s0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001  3  p  M  /  $  0.086 0.084 0.081 0.079 0.077 0.075 0.074 0.072 0.071 0.069 0.068 0.067 0.066 0.065 0.064 0.063 0.062 0.061 0.060 0.060 0.059 0.058 0.058 0.057 0.057 0.057 0.056 0.056 0.055 0.055  0.056 0.053 0.049 0.046 0.043 0.040 0.037 0.035 0.032 0.030 0.028 0.026 0.024 0.023 0.021 0.020 0.018 0.017 0.016 0.015 0.014 0.013 0.012 0.011 0.010 0.009 0.009 0.008 0.007 0.007  0.062 0.059 0.057 0.055 0.053 0.052 0.050 0.049 0.047 0.046 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 0.036 0.036 0.035 0.035 0.035 0.034 0.034 0.033 0.033 0.033  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  285  Data  Table C.10: Summary of Data for Run 13  6  s 0 66 109 153 196 240 283 327 414 458 502 545 589 632 676 720 807 850 894 937 981 1025 1068 1112 1199 1243 1286 1330 1374 1417 1461 1504 1592  R  x 10 s0.001 0.271 0.504 0.574 0.651 0.660 0.892 1.103 0.940 0.862 1.033 1.039 0.844 0.896 0.786 0.763 0.748 0.864 0.731 0.670 1.100 0.859 0.734 0.700 0.581 0.632 0.800 0.774 0.525 0.531 0.401 0.366 0.336  3  E  1  R  x 10 s0.000 0.307 0.436 0.566 0.696 0.810 0.890 0.940 0.968 0,960 0.945 0.927 0.908 0.889 0.870 0.851 0.815 0.798 0.779 0.760 0.741 0.720 0.700 0.678 0.635 0.612 0.590 0.567 0.544 0.522 0.500 0.478 0.436  3  P  1  {R  E  - R) P  s0.001 -0.037 0.068 0.007 -0.045 -0.149 0.002 0.163 -0.028 -0.098 0.088 0.112 -0.064 0.007 -0.083 -0.088 -0.067 0.066 -0.048 -0.090 0.359 0.139 0.035 0.022 -0.054 0.020 0.210 0.207 -0.019 0.009 -0.099 -0.113 -0.100 1  x 10  3  cT  x 10 s0.000 0.083 0.063 0.057 0.044 0.045 0.044 0.039 0.034 0.035 0.034 0.033 0.030 0.028 0.026 0.025 0.025 0.025 0.025 0.025 0.025 0.024 0.023 0.022 0.020 0.019 0.018 0.018 0.017 0.017 0.016 0.016 0.016  3  p  M  1  1.410 1.400 1.384 1.362 1.335 1.301 1.265 1.224 1.141 1.098 1.057 1.016 0.976 0.937 0.899 0.861 0.788 0.754 0.719 0.686 0.653 0.621 0.590 0.560 0.503 0.475 0.449 0.424 0.399 0.377 0.354 0.333 0.293  /  $  0.000 0.318 0.451 0.585 0.719 0.837 0.920 0.972 1.000 0.992 0.976 0.958 0.938 0.918 0.899 0.880 0.843 0.824 0.805 0.786 0.765 0.744 0.723 0.701 0.656 0.632 0.609 0.586 0.562 0.540 0.517 0.494 0.450  1.350 1.340 1.324 1.303 1.276 1.244 1.209 1.169 1.088 1.047 1.006 0.967 0.928 0.891 0.853 0.816 0.746 0.712 0.679 0.646 0.614 0.583 0.553 0.524 0.469 0.442 0.417 0.392 0.368 0.346 0.324 0.304 0.265  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  286  Data  Table C.10: Summary of Data for Run 13 -(Continued)  e  s 1635 1679 1722 1766 1810 1853 1897 1984 2028 2071 2115 2158 2202 2246 2289 2376 2420 2463 2507 2551 2594 2638 2681 2769 2812 2856 2900 2943 2987 3030 3074 3161 3205  x 10 s0.568 0.539 0.425 0.377 0.256 0.488 0.467 0.222 0.192 0.160 0.169 0.161 0.179 0.133 0.117 0.126 0.282 0.272 0.266 0.102 0.180 0.119 0.074 0.023 0.130 0.116 0.045 0.101 0.050 0.024 0.011 -0.040 -0.004  3  RE  1  R  P  x 10 s0.416 0.396 0.376 0.358 0.339 0.322 0.305 0.274 0.259 0.244 0.231 0.218 0.205 0.194 0.182 0.162 0.152 0.143 0.134 0.126 0.119 0.111 0.104 0.092 0.086 0.080 0.075 0.071 0.066 0.062 0.058 0.050 0.047  3  1  (R  - R ) x 10 s0.152 0.143 0.048 0.020 -0.083 0.166 0.162 -0.052 -0.066 -0.085 -0.061 -0.057 -0.027 -0.061 -0.065 -0.036 0.130 0.129 0.131 -0.024 0.062 0.008 -0.031 -0.068 0.044 0.035 -0.031 0.030 -0.016 -0.038 -0.047 -0.091 -0.051  3  E  P  1  x 10 s0.016 0.016 0.016 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.014 0.014 0.014 0.013 0.013 0.013 0.012 0.012 0.011 0.011 0.010 0.010 0.009 0.009 0.009 0.008 0.008 0.007  cT  3  p  M  /  •$  0.275 0.257 0.240 0.224 0.209 0.194 0.181 0.155 0.144 0.133 0.122 0.113 0.104 0.095 0.087 0.072 0.065 0.058 0.052 0.047 0.041 0.036 0.032 0.023 0.019 0.016 0.012 0.009 0.006 0.003 0.001 -0.004 -0.006  0.429 0.409 0.389 0.370 0.351 0.333 0.315 0.283 0.267 0.253 0.238 0.225 0.212 0.200 0.189 0.167 0.157 0.148 0.139 0.130 0.123 0.115 0.108 0.095 0.089 0.083 0.078 0.073 0.068 0.064 0.060 0.052 0.049  0.247 0.230 0.214 0.198 0.183 0.169 0.156 0.132 0.120 0.110 0.100 0.090 0.081 0.073 0.065 0.050 0.044 0.037 0.031 0.026 0.021 0.016 0.011 0.003 -0.001 -0.004 -0.008 -0.011 -0.014 -0.016 -0.019 -0.023 -0.025  1  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  287  Data  Table C l l : Summary of Data for Run 14  6  s 0 51 81 117 147 183 220 256 293 329 366 402 438 468 504 534 570 606 636 672 702 738 774 804 840 877 913 943 979 1016 1052 1088 1118  R  x 10 s0.001 0.263 0.576 0.733 0.869 0.956 0.992 1.017 1.067 1.048 1.015 1.063 1.036 1.059 1.011 0.996 1.007 1.000 0.955 0.953 0.926 0.950 0.856 0.852 0.939 0.629 0.784 0.713 0.715 0.660 0.643 0.618 0.577  3  E  R  x 10  3  P  1  {R  E  - R) P  s0.001 -0.080 0.026 -0.006 0.020 0.018 -0.002 -0.008 0.024 -0.003 -0.038 0.012 -0.010 0.019 -0.020 -0.024 0.001 0.012 -0.016 0.004 -0.001 0.049 -0.016 0.004 0.122 -0.155 0.032 -0.013 0.021 -0.002 0.013 0.017 -0.000 1  0.000 0.344 0.550 0.739 0.849 0.938 0.994 1.025 1.042 1.050 1.052 1.051 1.046 1.040 1.031 1.020 1.005 0.988 0.971 0.948 0.928 0.901 0.872 0.847 0.817 0.784 0.752 0.726 0.694 0.661 0.631 0.601 0.577  x 10  3  x 10 s0.000 0.018 0.022 0.022 0.019 0.018 0.017 0.018 0.018 0.017 0.016 0.015 0.014 0.014 0.014 0.014 0.014 0.014 0.013 0.013 0.012 0.012 0.012 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011  3  <T  p  M  /  $  0.000 0.327 0.523 0.702 0.807 0.892 0.945 0.974 0.990 0.998 1.000 0.998 0.994 0.988 0.979 0.969 0.955 0.939 0.923 0.901 0.881 0.856 0.829 0.805 0.776 0.745 0.715 0.689 0.659 0.628 0.599 0.571 0.548  1.479 1.470 1.456 1.431 1.406 1.371 1.333 1.294 1.254 1.214 1.172 1.132 1.092 1.058 1.019 0.986 0.947 0.909 0.878 0.841 0.811 0.776 0.742 0.715 0.683 0.651 0.622 0.598 0.571 0.544 0.520 0.496 0.477  1  1.410 1.402 1.389 1.365 1.341 1.309 1.273 1.237 1.198 1.161 1.122 1.084 1.046 1.015 0.978 0.947 0.910 0.875 0.845 0.811 0.782 0.750 0.718 0.692 0.662 0.632 0.605 0.582 0.557 0.532 0.509 0.486 0.469  Continued  Appendix C. Tabulated Instantaneous Drying Rate Data  288  Table C l l : Summary of Data for Run 14 -(Continued)  6  s 1154 1184 1220 1256 1286 1322 1352 1388 1424 1454 1490 1520 1556 1586 1622 1658 1688 1724 1754 1790 1826 1856 1892 1922 1958 1995 2031 2067 2097 2133 2163 2199 2229  R  x 10 s0.551 0.506 0.512 0.475 0.455 0.414 0.419 0.378 0.345 0.382 0.552 0.265 0.300 0.344 0.321 0.300 0.296 0.289 0.284 0.272 0.235 0.236 0.215 0.208 0.198 0.201 0.149 0.138 0.145 0.168 0.197 0.151 0.158  3  E  1  R  x 10 s0.549 0.527 0.501 0.477 0.457 0.435 0.418 0.398 0.380 0.365 0.349 0.336 0.321 0.309 0.297 0.284 0.275 0.264 0.255 0.246 0.237 0.229 0.221 0.215 0.207 0.200 0.193 0.187 0.182 0.176 0.171 0.166 0.161  3  P  1  (R  - Rp) x 10  3  E  s0.002 -0.021 0.011 -0.002 -0.002 -0.022 0.001 -0.020 -0.034 0.016 0.203 -0.071 -0.021 0.034 0.025 0.016 0.021 0.025 0.028 0.027 -0.001 0.007 -0.006 -0.007 -0.010 0.001 -0.044 -0.049 -0.036 -0.008 0.026 -0.015 -0.003 1  cy, x 10  M  /  $  s0.011 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008  0.448 0.432 0.414 0.396 0.382 0.366 0.353 0.339 0.325 0.313 0.301 0.290 0.279 0.269 0.258 0.248 0.239 0.230 0.222 0.213 0.204 0.197 0.189 0.183 0.175 0.167 0.160 0.153 0.148 0.142 0.136 0.130 0.125  0.522 0.501 0.476 0.453 0.435 0.414 0.397 0.378 0.361 0.347 0.331 0.319 0.305 0.294 0.282 0.270 0.261 0.251 0.243 0.233 0.225 0.218 0.210 0.204 0.197 0.190 0.184 0.178 0.173 0.167 0.163 0.157 0.153  0.456 0.439 0.419 0.400 0.385 0.368 0.355 0.339 0.324 0.312 0.299 0.288 0.275 0.265 0.253 0.242 0.233 0.223 0.215 0.205 0.196 0.188 0.180 0.173 0.165 0.157 0.149 0.142 0.136 0.129 0.124 0.117 0.112  3  1  Continued  Appendix C. Tabulated Instantaneous Drying Rate Data  289  Table C l l : Summary of Data for Run 14 -(Continued)  e  s 2265 2302 2338 2375 2411 2447 2477 2513 2543 2579 2615 2645 2681 2711 2747 2777 2813 2850 2886 2922 2952 2988 3018 3054 3084 3120 3156 3186 3222 3252  R  x 10 s0.137 0.116 0.155 0.197 0.209 0.269 0.289 0.305 0.326 0.284 0.217 0.236 0.202 0.156 0.123 0.145 0.081 0.092 0.146 0.212 0.178 0.144 0.071 0.064 0.053 0.031 0.029 0.031 0.043 0.025  3  E  1  R  x 10 s0.156 0.151 0.147 0.142 0.137 0.133 0.130 0.126 0.122 0.118 0.115 0.112 0.108 0.105 0.102 0.099 0.096 0.093 0.090 0.087 0.084 0.082 0.079 0.077 0.075 0.072 0.070 0.068 0.065 0.063  3  P  1  (R  E  - Rp) x 10  3  s-0.020 -0.035 0.009 0.055 0.071 0.136 0.160 0.180 0.204 0.166 0.102 0.124 0.094 0.051 0.021 0.045 -0.015 -0.000 0.056 0.125 0.093 0.062 -0.009 -0.013 -0.022 -0.041 -0.041 -0.037 -0.023 -0.039 1  (T x 10 s0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.011 0.010 0.010 0.010 0.010  3  P  M  /  $  0.120 0.114 0.109 0.103 0.098 0.093 0.089 0.085 0.081 0.077 0.073 0.069 0.065 0.062 0.058 0.055 0.052 0.048 0.045 0.042 0.039 0.036 0.034 0.031 0.029 0.026 0.024 0.021 0.019 0.017  0.148 0.144 0.139 0.135 0.131 0.126 0.123 0.119 0.116 0.113 0.109 0.106 0.103 0.100 0.097 0.094 0.091 0.088 0.085 0.083 0.080 0.078 0.075 0.073 0.071 0.069 0.066 0.064 0.062 0.060  0.106 0.100 0.094 0.089 0.083 0.078 0.074 0.069 0.065 0.060 0.056 0.052 0.048 0.045 0.041 0.038 0.034 0.030 0.027 0.023 0.020 0.017 0.015 0.012 0.009 0.006 0.004 0.002 -0.001 -0.003  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  290  Data  Table C.12: Summary of Data for Run 15  e s 0 65 109 152 196 239 283 326 370 413 457 501 544 588 631 675 719 762 806 893 936 980 1024 1067 1111 1154 1198 1241 1285 1329 1372 1416 1459  R x 10 s0.001 0.102 0.124 0.125 0.133 0.136 0.145 0.149 0.147 0.140 0.145 0.146 0.362 0.598 0.542 0.571 0.719 0.835 0.831 0.730 0.691 0.615 0.627 0.827 0.946 0.779 0.680 0.631 0.562 0.511 0.497 0.537 0.574  3  E  1  R  x 10 s" 0.001 0.071 0.080 0.086 0.091 0.098 0.110 0.130 0.160 0.202 0.257 0.323 0.395 0.473 0.549 0.623 0.689 0.743 0.787 0.834 0.839 0.834 0.819 0.798 0.770 0.740 0.706 0.673 0.639 0.606 0.575 0.546 0.519  3  P  1  (R -R )x 10 s-0.000 0.031 0.044 0.040 0.042 0.038 0.034 0.019 -0.013 -0.062 -0.113 -0.177 -0.034 0.125 -0.007 -0.052 0.030 0.091 0.045 -0.104 -0.149 -0.219 -0.193 0.030 0.175 0.039 -0.027 -0.041 -0.077 -0.095 -0.078 -0.008 0.055  3  E  P  1  x 10 s0.000 0.012 0.013 0.013. 0.014 0.014 0.014 0.013 0.012 0.011 0.011 0.011 0.012 0.013 0.014 0.015 0.015 0.015 0.016 0.016 0.016 0.016 0.017 0.017 0.016 0.016 0.015 0.014 0.013 0.012 0.011 0.011 0.011  3  Op  M  /  $  1.410 1.406 1.403 1.399 1.395 1.391 1.387 1.382 1.375 1.368 1.358 1.345 1.329 1.310 1.288 1.263 1.234 1.203 1.169 1.098 1.062 1.025 0.989 0.954 0.920 0.887 0.855 0.826 0.797 0.769 0.744 0.719 0.697  0.001 0.085 0.095 0.102 0.108 0.117 0.131 0.155 0.191 0.241 0.306 0.385 0.471 0.563 0.654 0.742 0.821 0.885 0.937 0.994 1.000 0.994 0.976 0.950 0.918 0.881 0.841 0.802 0.761 0.722 0.685 0.650 0.619  1.479 1.475 1.471 1.467 1.463 1.459 1.454 1.449 1.442 1.434 1.423 1.409 1.393 1.373 1.349 1.322 1.291 1.258 1.222 1.147 1.109 1.070 1.031 0.994 0.957 0.923 0.889 0.857 0.826 0.797 0.770 0.744 0.720  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  291  Data  Table C.12: Summary of Data for Run 15 -(Continued)  9  s 1503 1547 1590 1634 1677 1764 1808 1851 1895 1939 1982 2026 2069 2113 2156 2200 2244 2287 2331 2374 2418 2461 2505 2549 2636 2679 2723 2766 2810 2853 2897 2941 2984  R  E  x 10 s0.542 0.544 0.528 0.504 0.452 0.364 0.309 0.316 0.342 0.331 0.328 0.320 0.303 0.282 0.284 0.269 0.264 0.257 0.292 0.259 0.262 0.229 0.206 0.176 0.161 0.163 0.162 0.149 0.149 0.139 0.136 0.132 0.122  3  1  R  P  x 10 s0.495 0.472 0.452 0.434 0.417 0.388 0.375 0.363 0.351 0.340 0.329 0.318 0.308 0.298 0.288 0.278 0.268 0.258 0.248 0.238 0.229 0.220 0.210 0.201 0.184 0.175 0.167 0.160 0.152 0.145 0.138 0.131 0.125  3  1  (R — Rp) x 10  3  E  s" 0.048 0.072 0.076 0.071 0.035 -0.024 -0.066 -0.047 -0.009 -0.009 -0.001 0.001 -0.005 -0.016 -0.004 -0.009 -0.003 -0.001 0.044 0.020 0.033 0.009 -0.005 -0.025 -0.022 -0.012 -0.005 -0.010 -0.003 -0.006 -0.002 0.001 -0.003 1  x 10 s0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.010 0.010 0.010 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.008 0.008 0.008 0.008 0.008 0.007  3  <7  p  M  /  $  0.674 0.653 0.633 0.614 0.595 0.560 0.544 0.528 0.512 0.497 0.482 0.468 0.455 0.441 0.429 0.416 0.404 0.393 0.382 0.371 0.361 0.352 0.342 0.333 0.316 0.309 0.301 0.294 0.287 0.281 0.275 0.269 0.263  0.589 0.562 0.539 0.517 0.497 0.462 0.447 0.432 0.418 0.405 0.392 0.379 0.367 0.355 0.343 0.331 0.319 0.307 0.296 0.284 0.273 0.262 0.250 0.240 0.219 0.209 0.199 0.190 0.181 0.173 0.164 0.156 0.149  0.696 0.673 0.652 0.632 0.612 0.575 0.557 0.540 0.523 0.507 0.492 0.477 0.462 0.448 0.435 0.422 0.409 0.397 0.385 0.374 0.363 0.353 0.343 0.333 0.315 0.307 0.299 0.291 0.284 0.277 0.271 0.264 0,259  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  292  Data  Table C.12: Summary of Data for Run 15 -(Continued)  6  s 3028 3072 3115 3159 3202 3246 3289 3333 3377 3420 3507 3551 3594 3638 3682 3725 3769 3812 3856 3900 3943 3987 4030 4074 4117 4161 4205 4248 4292 4379 4423 4466 4510  R  E  x 10 s0.125 0.133 0.121 0.111 0.100 0.104 0.092 0.084 0.075 0.074 0.076 0.084 0.067 0.072 0.063 0.067 0.059 0.057 0.048 0.066 0.062 0.063 0.056 0.054 0.043 0.038 0.013 0.018 0.033 0.035 0.042 0.017 0.019  3  1  R  P  x 10 s0.119 0.113 0.108 0.103 0.098 0.093 0.089 0.085 0.081 0.077 0.071 0.068 0.065 0.063 0.060 0.058 0.056 0.054 0.052 0.050 0.048 0.047 0.045 0.044 0.043 0.041 0.040 0.039 0.038 0.036 0.035 0.035 0.034  3  1  {R  - Rp) x 10  3  E  s0.006 0.020 0.013 0.008 0.002 0.011 0.003 -0.001 -0.006 -0.004 0.005 0.016 0.001 0.010 0.003 0.009 0.003 0.003 -0.004 0.016 0.014 0.016 0.011 0.010 0.001 -0.004 -0.027 -0.022 -0.005 -0.001 0.006 -0.018 -0.014 1  <T x 10 s0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009  3  P  M  /  $  0.258 0.253 0.248 0.243 0.239 0.235 0.231 0.227 0.223 0.220 0.214 0.210 0.208 0.205 0.202 0.200 0.197 0.195 0.192 0.190 0.188 0.186 0.184 0.182 0.180 0.178 0.176 0.175 0.173 0.170 0.168 0.167 0.165  0.142 0.135 0.128 0.122 0.117 0.111 0.106 0.101 0.097 0.092 0.085 0.081 0.078 0.075 0.072 0.069 0.066 0.064 0.062 0.060 0.058 0.056 0.054 0.052 0.051 0.049 0.048 0.047 0.045 0.043 0.042 0.041 0.040  0.253 0.247 0.242 0.238 0.233 0.228 0.224 0.220 0.216 0.213 0.206 0.203 0.200 0.197 0.194 0.191 0.188 0.186 0.183 0.181 0.179 0.177 0.174 0.172 0.170 0.168 0.166 0.165 0.163 0.159 0.158 0.156 0.155  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  293  Data  Table C.13: Summary of Data for Run 16  e s  0 66 110 153 197 240 284 327 371 458 502 545 589 632 676 720 763 807 894 937 981 1025 1068 1112 1155 1199 1242 1330 1373 1417 1460 1504 1548  R  x 10  3  E  s-  1  0.001 0.529 0.727 0.795 0.871 0.999 0.903 0.980 0.979 0.920 0.964 0.915 0.958 0.867 0.876 0.828 0.843 0.815 0.772 0.721 0.694 0.656 0.628 0.668 0.615 0.733 0.753 0.603 0.500 0.496 0.479 0.499 0.618  R  x 10  3  P  s-  1  0.000 0.526 0.726 0.810 0.873 0.924 0.960 0.977 0.981 0.960 0.943 0.924 0.903 0.883 0.862 0.841 0.821 0.800 0.759 0.739 0.717 0.695 0.674 0.651 0.629 0.606 0.584 0.538 0.515 0.493 0.471 0.449 0.427  (R  E  -  Rp) x 10  3  s-  1  0.001 0.003 0.001 -0.014 -0.003 0.074 -0.057 0.003 -0.001 -0.040 0.021 -0.009 0.055 -0.016 0.014 -0.013 0.022 0.014 0.013 -0.018 -0.023 -0.039 -0.045 0.016 -0.014 0.127 0.169 0.065 -0.015 0.003 0.008 0.050 0.190  Op  x 10  3  s-  M  /  $  1.410 1.395 1.366 1.333 1.296 1.257 1.216 1.174 1.131 1.046 1.004 0.964 0.924 0.886 0.847 0.810 0.774 0.739 0.671 0.638 0.606 0.575 0.546 0.517 0.489 0.462 0.436 0.387 0.365 0.342 0.322 0.301 0.282  0.000 0.536 0.740 0.826 0.891 0.943 0.979 0.997 1.000 0.979 0.961 0.942 0.921 0.900 0.879 0.858 0.837 0.816 0.774 0.753 0.731 0.709 0.687 0.664 0.642 0.618 0.595 0.548 0.526 0.503 0.480 0.458 0.436  1.376 1.361 1.333 1.300 1.263 1.225 1.184 1.143 1.100 1.016 0.975 0.935 0.895 0.857 0.819 0.782 0.747 0.711 0.644 0.612 0.581 0.550 0.521 0.492 0.465 0.438 0.412 0.364 0.341 0.319 0.299 0.279 0.259  1  0.000 0.036 0.028 0.025 0.020 0.020 0.019 0.016 0.014 0.014 0.014 0.014 0.013 0.012 0.011 0.011 0.010 0.010 0.010 0.011 0.011 0.011 0.011 0.011 0.010 0.010 0.010 0.009 0.009 0.008 0.008 0.008 0.008  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  294  Data  Table C.13: Summary of Data for Run 16 -(Continued)  6  s 1591 1635 1678 1765 1809 1852 1896 1940 1983 2027 2070 2114 2201 2245 2288 2332 2375 2419 2463 2506 2550 2637 2680 2724 2767 2811 2855 2898 2942 2985 3073 3116 3160  R  x 10 s0.317 0.341 0.359 0.323 0.366 0.308 0.325 0.292 0.310 0.246 0.184 0.180 0.141 0.192 0.246 0.195 0.174 0.160 0.255 0.157 0.088 0.096 0.074 0.066 0.028 0.069 0.046 0.011 0.002 0.017 0.011 -0.024 -0.008  3  E  1  R  x 10 s0.407 0.386 0.367 0.329 0.311 0.294 0.277 0.261 0.246 0,231 0.217 0.204 0.179 0.168 0.157 0.147 0.138 0.128 0.120 0.112 0.104 0.091 0.084 0.078 0.073 0.068 0.063 0.058 0.054 0.050 0.043 0.040 0.037  3  P  1  (R  E  - Rp)  s-0.089 -0.045 -0.008 -0.006 0.055 0.014 0.048 0.031 0.064 0.015 -0.033 -0.024 -0.039 0.024 0.088 0.048 0.036 0.031 0.136 0.046 -0.017 0.006 -0.010 -0.013 -0.045 0.001 -0.017 -0.047 -0.053 -0.033 -0.032 -0.064 -0.045 1  x 10  3  <T x 10 s0.008 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.003 0.003 0.003  3  P  M  1  0.264 0.247 0.231 0.200 0.186 0.173 0.161 0.149 0.138 0.127 0.118 0.109 0.092 0.084 0.077 0.071 0.064 0.059 0.053 0.048 0.043 0.035 0.031 0.028 0.024 0.021 0.018 0.016 0.013 0.011 0.007 0.005 0.003  /  $  0.415 0.394 0.374 0.335 0.317 0.299 0.282 0.266 0.251 0.236 0.222 0.208 0.183 0.171 0.160 0.150 0.140 0.131 0.122 0.114 0.106 0.092 0.086 0.080 0.074 0.069 0.064 0.060 0.055 0.051 0.044 0.041 0.038  0.242 0.224 0.208 0.179 0.165 0.152 0.139 0.128 0.117 0.106 0.097 0.088 0.071 0.064 0.057 0.050 0.044 0.038 0.033 0.028 0.023 0.015 0.011 0.008 0.004 0.001 -0.002 -0.004 -0.007 -0.009 -0.013 -0.015 -0.016  Appendix  C. Tabulated  Instantaneous  Drying  Rate  295  Data  Table C.14: Summary of Data for Run 17  6  s 0 54 84 120 157 193 229 259 295 332 368 398 434 470 500 536 566 602 638 668 704 741 777 813 843 879 909 945 975 1011 1047 1077 1113  R  E  x 10 s0.001 0.158 0.554 0.918 0.991 1.063 1.103 1.170 1.133 1.146 1.170 1.183 1.155 1.174 1.158 1.104 1.136 1.109 1.115 1.138 1.119 1.061 1.010 0.999 1.008 0.910 0.872 0.817 0.733 0.758 0.725 0.667 0.622  3  1  R  x 10 s0.000 0.381 0.597 0.799 0.945 1.040 1.101 1.134 1.160 1.175 1.183 1.185 1.184 1.179 1.172 1.161 1.149 1.130 1.109 1.088 1.061 1.030 0.997 0.963 0.933 0.896 0.865 0.827 0.796 0.758 0.721 0.690 0.655  3  P  1  {R  - RP) x 10 s0.001 -0.222 -0.043 0.119 0.046 0.023 0.002 0.035 -0.027 -0.030 -0.012 -0.002 -0.029 -0.006 -0.015 -0.057 -0.013 -0.022 0.006 0.049 0.058 0.031 0.012 0.036 0.075 0.014 0.007 -0.010 -0.063 -0.000 0.004 -0.024 -0.033  3  E  1  cT  x 10 s0.022 0.026 0.025 0.022 0.020 0.020 0.020 0.020 0.019 0.018 0.017 0.016 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.014 0.013 0.013 0.013 0.012  3  p  M  1  1.410 1.401 1.386 1.361 1.328 1.292 1.254 1.220 1.179 1.136 1.093 1.058 1.015 0.972 0.937 0.895 0.860 0.819 0.779 0.746 0.707 0.669 0.632 0.597 0.569 0.536 0.509 0.479 0.454 0.426 0.400 0.379 0.354  /  $  0.000 0.321 0.504 0.675 0.798 0.878 0.930 0.958 0.979 0.992 0.999 1.001 1.000 0.996 0.990 0.980 0.970 0.955 0.936 0.919 0.896 0.870 0.842 0.813 0.788 0.757 0.730 0.699 0.672 0.640 0.609 0.583 0.553  1.695 1.684 1.666 1.635 1.595 1.552 1.505 1.464 1.413 1.361 1.309 1.265 1.213 1.162 1.118 1.067 1.025 0.975 0.926 0.886 0.838 0.791 0.747 0.704 0.669 0.629 0.597 0.559 0.530 0.496 0.463 0.437 0.408  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  296  Data  Table C.14: Summary of Data for Run 17 -(Continued)  e s 1143 1179 1216 1252 1288 1318 1354 1384 1420 1457 1493 1529 1559 1595 1625 1661 1691 1727 1763 1793 1829 1859 1895 1931 1961 1997 2027 2063 2099 2129 2165 2195  R  x 10 s" 0.624 0.562 0.512 0.522 0.435 0.461 0.397 0.382 0.447 0.402 0.346 0.361 0.398 0.396 0.332 0.262 0.270 0.293 0.335 0.408 0.318 0.226 0.218 0.212 0.194 0.158 0.149 0.131 0.125 0.117 0.098 0.136  3  E  1  R  P  x 10 s" 0.626 0.592 0.559 0.528 0.499 0.476 0.449 0.428 0.404 0.381 0.360 0.340 0.325 0.307 0.293 0.278 0.265 0.252 0.239 0.229 0.217 0.208 0.198 0.189 0.181 0.173 0.166 0.159 0.151 0.146 0.139 0.134  3  1  (R  E  - Rp) x 10  3  s" -0.002 -0.031 -0.047 -0.006 -0.065 -0.015 -0.052 -0.047 0.042 0.021 -0.014 0.021 0.074 0.089 0.039 -0.016 0.005 0.042 0.096 0.179 0.101 0.017 0.020 0.023 0.013 -0.014 -0.017 -0.028 -0.027 -0.029 -0.041 0.001 1  x 10 s0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.013 0.014 0.015 0.015 0.017 0.018 0.019 0.020 0.021 0.000  3  (Tp  M  /  $  0.335 0.313 0.292 0.272 0.254 0.239 0.223 0.210 0.195 0.180 0.167 0.154 0.144 0.133 0.124 0.113 0.105 0.096 0.087 0.080 0.072 0.066 0.058 0.052 0.046 0.040 0.035 0.029 0.023 0.019 0.014 0.009  0.528 0.500 0.472 0.446 0.421 0.402 0.379 0.362 0.341 0.322 0.304 0.287 0.274 0.259 0.248 0.234 0.224 0.212 0.202 0.193 0.183 0.176 0.167 0.159 0.153 0.146 0.140 0.134 0.128 0.123 0.118 0.113  0.384 0.358 0.332 0.308 0.285 0.267 0.247 0.231 0.213 0.195 0.179 0.164 0.151 0.138 0.127 0.114 0.104 0.093 0.082 0.073 0.064 0.056 0.047 0.038 0.032 0.024 0.018 0.011 0.004 -0.002 -0.008 -0.013  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  297  Data  Table C.15: Summary of Data for Run 18  6  s 0 66 109 196 240 284 371 414 458 545 588 632 719 763 806 894 937 981 1068 1111 1155 1242 1286 1329 1417 1460 1504 1591 1634 1678 1765 1809 1852  R  x 10 s0.001 0.051 0.393 0.850 0.815 0.933 0.994 0.968 1.101 0.966 0.996 0.946 0.854 0.869 0.841 0.655 0.655 0.639 0.639 0.577 0.586 0.496 0.473 0.414 0.396 0.410 0.378 0.349 0.294 0.284 0.231 0.219 0.243  3  E  1  R  x 10 s0.000 0.174 0.401 0.783 0.892 0.955 1.000 1.001 0.996 0.970 0.951 0.928 0.874 0.843 0.812 0.744 0.710 0.676 0.611 0.581 0.550 0.494 0.468 0.444 0.398 0.377 0.357 0.321 0.305 0.289 0.260 0.247 0.235  3  P  1  (R  E  - Rp)  s0.001 -0.122 -0.008 0.067 -0.077 -0.021 -0.006 -0.033 0.105 -0.004 0.045 0.018 -0.020 0.026 0.030 -0.089 -0.056 -0.038 0.028 -0.004 0.035 0.001 0.005 -0.030 -0.002 0.033 0.021 0.028 -0.011 -0.005 -0.029 -0.028 0.008 1  x 10  3  x 10 s" 0.016 0.024 0.025 0.021 0.021 0.021 0.018 0.018 0.018 0.017 0.016 0.015 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.011 0.011 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.009 0.009 0.009  <r  3  p  M  /  1.410 1.406 1.394 1.341 1.304 1.263 1.177 1.134 1.090 1.005 0.963 0.922 0.844 0.806 0.770 0.702 0.670 0.640 0.584 0.558 0.533 0.488 0.467 0.447 0.410 0.394 0.378 0.348 0.335 0.322 0.298 0.287 0.276  0.000 0.173 0.400 0.782 0.891 0.953 0.998 1.000 0.994 0.968 0.950 0.927 0.873 0.842 0.810 0.743 0.709 0.675 0.610 0.580 0.550 0.494 0.467 0.443 0.397 0.376 0.357 0.321 0.304 0.289 0.260 0.247 0.235  1  1.390 1.386 1.374 1.321 1.284 1.243 1.157 1.114 1.070 0.985 0.943 0.902 0.824 0.786 0.750 0.682 0.650 0.620 0.564 0.538 0.513 0.468 0.447 0.427 0.390 0.374 0.358 0.328 0.315 0.302 0.278 0.267 0.256  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  298  Data  Table C.15: Summary of Data for Run 18 -(Continued)  6  s 1939 1983 2026 2113 2157 2201 2288 2331 2375 2462 2506 2549 2636 2680 2723 2811 2854 2898 2985 3029 3072 3159 3203 3246 3334 3377 3421 3508 3551 3595  R  x 10 s" 0.203 0.247 0.259 0.150 0.146 0.122 0.129 0.110 0.149 0.107 0.084 0.065 0.057 0.035 0.024 0.030 0.021 0.069 0.116 0.064 0.087 0.110 0.093 0.067 0.032 0.078 0.114 0.048 0.092 0.112  3  E  1  R  x 10 s0.212 0.202 0.192 0.173 0.165 0.157 0.142 0.135 0.128 0.116 0.110 0.105 0.095 0.090 0.086 0.077 0.073 0.070 0.063 0.059 0.056 0.051 0.048 0.046 0.041 0.039 0.037 0.033 0.031 0.030  3  P  1  (R  - R)  E  P  .  s-0.009 0.045 0.067 -0.023 -0.019 -0.035 -0.013 -0.025 0.021 -0.009 -0.027 -0.040 -0.038 -0.055 -0.061 -0.047 -0.052 -0.000 0.053 0.005 0.030 0.059 0.045 0.022 -0.009 0.039 0.077 0.015 0.061 0.082 1  x 10  3  x 10 s0.009 0.008 0.008 0.008 0.008 0.008 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.000  3  Op  M  1  0.257 0.248 0.239 0.223 0.216 0.209 0.196 0.190 0.184 0.173 0.169 0.164 0.155 0.151 0.147 0.140 0.137 0.134 0.128 0.125 0.123 0.118 0.116 0.114 0.110 0.109 0.107 0.104 0.102 0.101  / 0.212 0.201 0.191 0.173 0.165 0.156 0.142 0.135 0.128 0.116 0.110 0.105 0.095 0.090 0.085 0.077 0.073 0.069 0.063 0.059 0.056 0.051 0.048 0.046 0.041 0.039 0.037 0.033 0.031 0.030  0.237 0.228 0.219 0.203 0.196 0.189 0.176 0.170 0.164 0.153 0.149 0.144 0.135 0.131 0.127 0.120 0.117 0.114 0.108 0.105 0.103 0.098 0.096 0.094 0.090 0.089 0.087 0.084 0.082 0.081  Appendix C. Tabulated Instantaneous Drying Rate Data  299  Table C.16: Summary of Data for Run 19  6 s  0 48 84 120 150 186 222 252 288 325 361 391 427 463 493 529 566 602 638 668 704 734 770 806 836 872 908 938 974 1004 1040 1070 1106  R  E  x 10  3  s-  1  0.001 0.206 0.592 0.834 0.910 1.040 1.126 1.146 1.166 1.246 1.285 1.179 1.246 1.264 1.215 1.182 1.188 1.142 1.068 1.159 1.051 1.027 1.020 0.946 0.876 0.878 0.878 0.774 0.766 0.741 0.696 0.726 0.669  R  P  x 10  3  s"  1  0.000 0.264 0.569 0.804 0.936 1.042 1.115 1.159 1.199 1.228 1.245 1.251 1.250 1.241 1.228 1.208 1.182 1.154 1.122 1.094 1.059 1.029 0.991 0.953 0.922 0.883 0.845 0.813 0.776 0.745 0.709 0.679 0.644  (R  - R ) x 10  3  E  P  s"  1  0.001 -0.058 0.023 0.030 -0.026 -0.003 0.012 -0.013 -0.033 0.018 0.040 -0.072 -0.004 0.023 -0.013 -0.026 0.006 -0.011 -0.054 0.065 -0.008 -0.001 0.029 -0.007 -0.046 -0.005 0.033 -0.039 -0.010 -0.004 -0.013 0.047 0.025  <7  p  x 10  3  s-  M  /  $  1.410 1.405 1.390 1.365 1.339 1.303 1.264 1.230 1.188 1.143 1.098 1.061 1.016 0.971 0.934 0.890 0.846 0.804 0.763 0.729 0.691 0.659 0.623 0.588 0.560 0.527 0.496 0.471 0.443 0.420 0.394 0.373 0.349  0.000 0.211 0.455 0.643 0.748 0.833 0.891 0.927 0.959 0.982 0.995 1.000 0.999 0.992 0.982 0.966 0.945 0.922 0.897 0.875 0.846 0.822 0.792 0.762 0.737 0.706 0.676 0.650 0.620 0.596 0.567 0.543 0.515  1.598 1.592 1.575 1.546 1.516 1.475 1.430 1.391 1.342 1.291 1.239 1.196 1.144 1.093 1.050 1.000 0.949 0.901 0.854 0.815 0.771 0.735 0.693 0.653 0.621 0.583 0.547 0.519 0.486 0.460 0.430 0.406 0.378  1  0.015 0.018 0.015 0.015 0.014 0.012 0.012 0.012 0.012 0.011 0.010 0.010 0.010 0.009 0.009 0.009 0.008 0.008 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.006  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  300  Data  Table C.16: Summary of Data for Run 19 -(Continued)  9  s 1142 1172 1208 1244 1274 1310 1347 1383 1419 1449 1485 1515 1551 1588 1624 1660 1690 1726 1763 1799 1835 1865 1901 1938 1974 2010 2040 2076 2113 2149  R  x 10 s0.592 0.603 0.605 0.509 0.505 0.478 0.404 0.405 0.408 0.350 0.343 0.337 0.299 0.274 0.285 0.270 0.232 0.219 0.189  3  E  1  0.177  0.174 0.182 0.138 0.139 0.137 0.104 0.104 0.112 0.101 0.091  R  P  x 10 s0.611 0.583 0.551 0.521 0.496 0.467 0.439 0.413 0.388 0.368 0.345 0.327 0.307 0.286 0.268 0.250 0.236 0.221 0.205 0.192 0.178 0.168 0.156 0.145 0.135 0.126 0.118 0.110 0.101 0.094  3  1  (R  E  -RP)X  s-0.018 0.019 0.054 -0.012 0.009 0.011 -0.035 -0.008 0.020 -0.018 -0.002 0.010 -0.008 -0.012 0.017 0.020 -0.004 -0.002 -0.017 -0.015 -0.005 0.013 -0.018 -0.006 0.002 -0.022 -0.014 0.003 -0.000 -0.003 1  10  3  x 10 s0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.000  3  <7p  M  1  0.327 0.309 0.288 0.269 0.254 0.236 0.220 0.204 0.190 0.178 0.166 0.156 0.144 0.133 0.123 0.114 0.107 0.098 0.090 0.083 0.077 0.071 0.066 0.060 0.055 0.050 0.047 0.043 0.039 0.035  /  $  0.488 0.466 0.441 0.416 0.396 0.374 0.351 0.330 0.310 0.294 0.276 0.262 0.245 0.229 0.214 0.200 0.189 0.176 0.164 0.153 0.143 0.134 0.125 0.116 0.108 0.100 0.094 0.088 0.081 0.075  0.352 0.332 0.308 0.286 0.269 0.249 0.229 0.212 0.195 0.182 0.167 0.156 0.143 0.130 0.119 0.108 0.100 0.090 0.081 0.073 0.065 0.059 0.052 0.046 0.040 0.035 0.031 0.026 0.021 0.017  Appendix  C. Tabulated  Instantaneous  Drying  Rate  301  Data  Table C.17: Summary of Data for Run 20  e  s 0 66 109 196 240 283 370 414 457 544 588 632 719 762 806 893 936 980 1067 1111 1154 1241 1285 1328 1416 1459 1503 1590 1633 1677 1764 1807 1851  R  x 10 s0.001 0.210 0.579 0.923 0.960 1.025 1.019 1.025 1.009 0.981 0.959 0.927 0.880 0.871 0.810 0.749 0.739 0.714 0.660 0.612 0.600 0.545 0.541 0.490 0.452 0.455 0.422 0.378 0.361 0.346 0.317 0.304 0.267  3  E  1  R  x 10 s0.000 0.306 0.554 0.893 0.980 1.026 1.045 1.034 1.017 0.972 0.947 0.922 0.871 0.846 0.821 0.769 0.744 0.718 0.666 0.639 0.614 0.563 0.537 0.513 0.464 0.441 0.418 0.375 0.355 0.334 0.297 0.279 0.262  3  P  1  (R  E  - R )x P  s0.001 -0.096 0.025 0.030 -0.020 -0.001 -0.027 -0.009 -0.008 0.009 0.012 0.005 0.009 0.024 -0.011 -0.021 -0.005 -0.003 -0.005 -0.027 -0.014 -0.017 0.004 -0.023 -0.012 0.014 0.003 0.003 0.006 0.012 0.020 0.024 0.004 1  10  3  cT  x 10 s" 0.011 0.011 0.010 0.009 0.008 0.008 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004  3  p  M  /  $  1.410 1.402 1.383 •1.318 1.277 1.234 1.143 1.097 1.053 0.967 0.924 0.883 0.805 0.768 0.732 0.662 0.630 0.598 0.538 0.509 0.482 0.431 0.407 0.384 0.341 0.322 0.303 0.268 0.253 0.237 0.210 0.198 0.186  0.000 0.293 0.530 0.854 0.938 0.982 1.000 0.989 0.973 0.929 0.906 0.882 0.834 0.810 0.785 0.736 0.712 0.686 0.637 0.611 0.587 0.538 0.514 0.490 0.444 0.422 0.400 0.359 0.339 0.320 0.284 0.267 0.251  1.376 1.368 1.349 1.285 1.244 1.202 1.112 1.067 1.023 0.937 0.895 0.855 0.777 0.741 0.705 0.636 0.604 0.572 0.512 0.484 0.457 0.407 0.383 0.360 0.318 0.299 0.280 0.246 0.230 0.215 0.188 0.176 0.164  1  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  302  Data  Table C.17: Summary of Data for Run 20 -(Continued)  6  s 1938 1981 2025 2112 2156 2199 2286 2330 2373 2460 2504 2548 2635 2678 2722 2809 2852 2896 2983 3027 3070 3157 3201 3244 3331 3375 3418 3505 3549 3593 3680 3723  R  x 10 s0.245 0.222 0.203 0.186 0.174 0.132 0.119 0.116 0.116 0.096 0.096 0.081 0.082 0.069 0.063 0.043 0.039 0.023 0.017 0.040 0.019 0.022 0.014 0.026 0.012 -0.004 0.003 0.002 0.002 -0.003 -0.012 -0.005  3  E  1  R  P  x 10 s0.231 0.216 0.202 0.176 0.164 0.153 0.132 0.123 0.114 0.098 0.091 0.084 0.072 0.066 0.061 0.052 0.048 0.044 0.037 0.034 0.031 0.026 0.024 0.022 0^019 0.017 0.016 0.013 0.012 0.011 0.009 0.008  3  1  {R  E  - Rp) x 10  3  s0.014 0.006 0.001 0.010 0.010 -0.021 -0.014 -0.007 0.002 -0.003 0.005 -0.003 0.010 0.003 0.002 -0.009 -0.009 -0.021 -0.020 0.006 -0.012 -0.004 -0.011 0.003 -0.007 -0.021 -0.012 -0.011 -0.009 -0.014 -0.021 -0.013 1  x 10 s0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.000 0.000  3  o-  p  M  /  0.164 0.155 0.145 0.129 0.121 0.115 0.102 0.097 0.092 0.082 0.078 0.074 0.068 0.065 0.062 0.057 0.055 0.053 0.049 0.048 0.046 0.044 0.043 0.042 0.040 0.039 0.038 0.037 0.036 0.036 0.035 0.035  0.221 0.207 0.193 0.168 0.157 0.146 0.127 0.118 0.109 0.094 0.087 0.080 0.069 0.064 0.059 0.050 0.046 0.042 0.036 0.033 0.030 0.025 0.023 0.021 0.018 0.016 0.015 0.012 0.011 0.010 0.009 0.008  1  0.143 0.133 0.124 0.108 0.100 0.094 0.081 0.076 0.071 0.062 0.058 0.054 0.047 0.044 0.041 0.036 0.034 0.032 0.029 0.027 0.026 0.023 0.022 0.021 0.020 0.019 0.018 0.017 0.016 0.016 0.015 0.015  Appendix  C. Tabulated  Instantaneous  Drying  Rate  303  Data  Table C.18: Summary of Data for Run 22  6  s 0 51 87 117 153 190 226 262 292 328 364 394 430 460 496 533 569 605 635 671708 744 780 810 846 883 919 955  x 10 s0.001 0.155 0.453 0.692 0.912 1.036 1.074 0.949 1.313 1.351 1.448 1.430 1.388 1.363 1.387 1.317 1.272 1.330 1.287 1.169 . 1.082 1.114 1.060 1.011 0.965 0.987 0.899 0.861  R  3  E  1  R  x 10 s0.000 0.182 0.466 0.681 0.878 1.027 1.141 1.234 1.298 1.356 1.394 1.410 1.413 1.403 1.379 1.346 1.307 1.265 1.228 1.185 1.140 1.098 1.056 1.023 0.983 0.944 0.906 0.869  3  P  1  (R  E  - R) P  s" 0.001 -0.027 -0.013 0.011 0.034 0.009 -0.067 -0.285 0.016 -0.005 0.053 0.019 -0.025 -0.040 0.008 -0.029 -0.034 0.066 0.058 -0.016 -0.058 0.017 0.003 -0.012 -0.019 0.043 -0.007 -0.008 1  x 10  3  (T x 10 s0.018 0.025 0.021 0.021 0.022 0.021 0.020 0.020 0.019 0.017 0.016 0.015 0.015 0.016 0.015 0.015 0.014 0.014 0.014 0.015 0.015 0.015 0.014 0.014 0.015 0.019 0.026 0.000  3  P  M  1  1.410 1.407 1.396 1.378 1.350 1.315 1.276 1.233 1.195 1.147 1.097 1.055 1.004 0.962 0.912 0.862 0.814 0.767 0.730 0.687 0.644 0.603 0.565 0.533 0.497 0.462 0.428 0.396  /  $  0.000 0.129 0.330 0.482 0.621 0.727 0.807 0.873 0.919 0.960 0.987 0.998 1.000 0.993 0.976 0.952 0.925 0.895 0.869 0.838 0.807 0.777 0.748 0.724 0.696 0.668 0.642 0.615  1.511 1.508 1.495 1.476 1.446 1.407 1.365 1.318 1.277 1.225 1.171 1.125 1.070 1.024 0.970 0.915 0.863 0.812 0.772 0.725 0.678 0.634 0.592 0.558 0.519 0.480 0.444 0.409  Appendix C. Tabulated Instantaneous Drying Rate Data  304  Table C.19: Summary of Data for Run 23  e s 0 45 75 136 166 197 257 287 318 378 408 438 499 529 560 620 650 681 741 772 802 862 893 923 983 1014 1044 1104 1135 1165 1226 1256 1286  R  E  x 10 s0.001 0.061 0.134 0.266 0.404 0.594 0.712 0.720 1.021 1.073 1.098 1.118 1.315 1.485 1.358 1.418 1.366 1.512 1.489 1.449 1.331 1.252 1.265 0.989 1.145 1.182 1.048 1.086 0.978 0.937 0.718 0.885 0.596  3  1  R  P  x 10 s0.000 0.045 0.126 0.314 0.406 0.505 0.706 0.807 0.908 1.081 1.154 1.218 1.316 1.351 1.377 1.404 1.407 1.404 1.380 1.361 1.338 1.282 1.249 1.215 1.140 1.100 1.060 0.978 0.935 0.894 0.811 0.772 0.733  3  1  (R  E  -R )x P  s0.001 0.016 0.008 -0.048 -0.002 0.089 0.005 -0.087 0.113 -0.008 -0.056 -0.099 -0.001 0.135 -0.019 0.014 -0.041 0.108 0.108 0.088 -0.007 -0.031 0.016 -0.226 0.005 0.082 -0.011 0.108 0.043 0.044 -0.093 0.114 -0.137 1  10  3  x 10 s0.053 0.046 0.047 0.041 0.037 0.037 0.037 0.035 0.033 0.030 0.031 0.031 0.031 0.030 0.028 0.026 0.026 0.026 0.027 0.028 0.028 0.027 0.026 0.025 0.024 0.025 0.026 0.031 0.035 0.038 0.000 0.000 0.000  3  <r  p  M  1  1.410 1.409 1.407 1.393 1.383 1.369 1.332 1.310 1.283 1.223 1.190 1.154 1.077 1.037 0.994 0.911 0.868 0.825 0.741 0.699 0.658 0.580 0.540 0.503 0.433 0.398 0.366 0.304 0.275 0.247 0.195 0.172 0.149  /  $  0.000 0.032 0.090 0.223 0.289 0.359 0.502 0.574 0.645 0.768 0.820 0.865 0.936 0.960 0.979 0.998 1.000 0.998 0.981 0.967 0.951 0.911 0.888 0.863 0.810 0.782 0.753 0.695 0.665 0.635 0.577 0.548 0.521  2.317 2.316 2.312 2.289 2.271 2.248 2.187 2.149 2.105 2.005 1.949 1.890 1.761 1.694 1.624 1.484 1.414 1.341 1.202 1.131 1.064 0.933 0.867 0.806 0.688 0.630 0.576 0.474 0.425 0.379 0.292 0.253 0.215  Appendix  C. Tabulated  Instantaneous  Drying  Rate  305  Data  Table C.20: Summary of Data for Run 26  6  s 0 35 58 81 104 127 150 196 219 242 266 289 312 335 381 404 427 450 473 496 519 565 588 611 634 658 681 704 750 773 796 819  R  E  x 10 s" 0.002 1.382 2.103 1.933 2.155 2.034 2.375 2.349 2.334 2.402 2.100 2.238 2.286 2.130 2.076 1.595 1.727 1.785 1.576 1.673 1.682 1.303 1.350 1.033 1.035 0.999 0.744 0.784 0.718 1.043 0.887 0.423  3  1  R  P  x 10 s0.000 1.494 1.883 2.041 2.143 2.236 2.316 2.400 2.396 2.367 2.316 2.252 2.180 2.102 1.941 1.859 1.777 1.696 1.616 1.537 1.458 1.306 1.232 1.160 1.089 1.019 0.953 0.890 0.772 0.718 0.666 0.616  3  1  (R  E  - Rp) x 10  3  s0.002 -0.113 0.220 -0.108 0.012 -0.202 0.058 -0.051 -0.062 0.035 -0.216 -0.014 0.106 0.028 0.135 -0.263 -0.050 0.089 -0.040 0.136 0.224 -0.003 0.118 -0.126 -0.055 -0.019 -0.209 -0.106 -0.054 0.325 0.221 -0.194 1  x 10 s0.000 0.142 0.099 0.101 0.088 0.079 0.080 0.071 0.066 0.065 0.065 0.065 0.062 0.057 0.052 0.051 0.052 0.053 0.053 0.052 0.050 0.045 0.043 0.042 0.042 0.043 0.045 0.048 0.054 0.056 0.059 0.060  3  <7  p  M  /  1.410 1.382 1.343 1.297 1.249 1.199 1.146 1.037 0.982 0.927 0.871 0.819 0.768 0.718 0.625 0.582 0.540 0.500 0.462 0.426 0.391 0.328 0.298 0.271 0.245 0.220 0.197 0.176 0.138 0.121 0.105 0.090  0.000 0.623 0.785 0.850 0.893 0.932 0.965 1.000 0.999 0.986 0.965 0.938 0.908 0.876 0.809 0.775 0.741 0.707 0.673 0.640 0.608 0.544 0.513 0.483 0.454 0.424 0.397 0.371 0.322 0.299 0.277 0.257  1  1.580 1.548 1.503 1.451 1.397 1.339 1.280 1.156 1.093 1.031 0.967 0.908 0.850 0.794 0.688 0.638 0.591 0.545 0.502 0.461 0.422 0.350 0.316 0.285 0.256 0.227 0.201 0.177 0.134 0.114 0.096 0.079  Appendix  C. Tabulated  Instantaneous  Drying  Rate  306  Data  Table C.21: Summary of Data for Run 29  9  s 0 57 94 169 207 244 320 357 395 470 508 545 621 658 696 771 808 846 921 959 996 1072 1109 1147 1222 1260 1297 1373 1410 1448 1523 1561  x 10 s0.001 -0.236 0.278 0.558 0.464 0.566 0.860 1.052 0.806 0.961 1.320 1.394 1.007 1.270 1.088 1.137 ' 0.867 1.462 1.187 0.782 1.207 1.266 0.934 0.986 0.844 0.996 0.602 0.486 0.828 0.361 0.402 0.586  R  3  E  1  R  P  x 10 s0.000 0.047 0.135 0.363 0.485 0.604 0.832 0.929 1.015 1.141 1.185 1.215 1.244 1.245 1.239 1.211 1.190 1.165 1.108 1.076 1.043 0.972 0.936 0.898 0.824 0.786 0.750 0.677 0.642 0.607 0.541 0.509  3  1  {R  E  - Rp) x 10  3  s0.001 -0.284 0.142 0.195 -0.021 -0.038 0.028 0.123 -0.209 -0.181 0.135 0.179 -0.237 0.025 -0.152 -0.074 -0.323 0.297 0.079 -0.294 0.164 0.294 -0.002 0.087 0.019 0.210 -0.148 -0.191 0.186 -0.246 -0.139 0.077 1  cr x 10 s0.125 0.111 0.101 0.098 0.086 0.082 0.083 0.079 0.073 0.067 0.067 0.069 0.067 0.064 0.061 0.057 0.057 0.057 0.059 0.060 0.059 0.056 0.054 0.052 0.051 0.053 0.057 0.067 0.073 0.079 0.000 0.000  3  p  M  1  1.410 1.409 1.406 1.387 1.371 1.351 1.296 1.264 1.227 1.146 1.101 1.057 0.963 0.917 0.870 0.778 0.734 0.689 0.603 0.562 0.523 0.446 0.411 0.376 0.311 0.281 0.252 0.198 0.174 0.150 0.107 0.087  /  $  0.000 0.038 0.109 0.292 0.390 0.485 0.668 0.746 0.815 0.917 0.951 0.975 0.999 1.000 0.995 0.972 0.956 0.936 0.890 0.864 0.838 0.780 0.752 0.722 0.662 0.632 0.602 0.543 0.516 0.487 0.434 0.409  1.805 1.804 1.800 1.776 1.755 1.729 1.658 1.615 1.567 1.462 1.404 1.347 1.225 1.165 1.104 0.984 0.927 0.869 0.758 0.704 0.653 0.553 0.508 0.462 0.378 0.339 0.302 0.231 0.200 0.169 0.113 0.087  Appendix  C. Tabulated  Instantaneous  Drying  Rate  307  Data  Table C.22: Summary of Data for Run 30'  e  R x 10  R x 10  s 0 46 76 106 137 167 197 227 258 288 318 349 379 409 440 470 500 531 561 591 622 652 682 713 743 773 804 834 864 894 925 955 986  s" 0.001 -0.088 0.306 0.182 -1.516 -0.673 -0.561 -0.183 0.725 0.855 0.612 1.080 0.758 1.350 0.649 -0.235 9.729 9.239 2.841 2.724 1.823 1.806 1.978 1.286 1.504 1.048 1.562 0.850 1.571 0.748 1.437 0.656 1.328  s" 0.000 0.029 0.110 0.214 0.313 0.391 0.458 0.529 0.617 0.720 0.841 0.976 1.111 1.240 1.362 1.462 1.543 1.604 1.640 1.656 1.653 1.633 1.600 1.554 1.501 1.442 1.378 1.313 1.248 1.183 1.118 1.057 0.997  3  E  1  3  P  1  {R  E  -  Rp) x 10  3  s0.001 -0.118 0.196 -0.032 -1.829 -1.064 -1.019 -0.712 0.108 0.134 -0.228 0.103 -0.352 0.109 -0.713 -1.698 8.186 7.635 1.200 1.068 0.170 0.173 0.378 -0.268 0.003 -0.395 0.184 -0.463 0.324 -0.435 0.319 -0.401 0.331 1  x 10 s0.000 0.060 0.185 0.289 0.323 0.305 0.271 0.238 0.202 0.163 0.132 0.125 0.141 0.163 0.181 0.188 0.187 0.178 0.164 0.147 0.131 0.116 0.106 0.098 0.094 0.092 0.090 0.088 0.086 0.083 0.080 0.076 0.073  3  <r  p  M  /  $  1.410 1.410 1.408 1.403 1.395 1.384 1.371 1.356 1.339 1.319 1.295 1.267 1.236 1.201 1.160 1.118 1.073 1.024 0.975 0.926 0.874 0.825 0.777 0.728 0.682 0.638 0.594 0.554 0.515 0.479 0.443 0.410 0.379  0.000 0.018 0.066 0.129 0.189 0.236 0.277 0.319 0.372 0.435 0.508 0.589 0.671 0.749 0.822 0.883 0.932 0.968 0.990 1.000 0.998 0.986 0.966 0.938 0.906 0.871 0.832 0.793 0.7530.714 0.675 0.638 0.602  1.675 1.674 1.672 1.666 1.656 1.643 1.628 1.610 1.589 1.565 1.537 1.503 1.465 1.422 1.374 1.323 1.268 1.210 1.151 1.091 1.029 0.970 0.911 0.853 0.797 0.744 0.691 0.643 0.597 0.553 0.510 0.470 0.432  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  308  Data  Table C.22: Summary of Data for Run 30 -(Continued)  e  s 1016 1046 1077 1107 1137 1168 1198 1228 1259 1289 1319 1350 1380 1410 1441 1471 1501 1532 1562 1592 1623  R  x 10 s0.943 0.897 0.794 0.978 0.982 0.614 0.635 0.699 0.985 0.405 1.068 0.140 0.753 0.334 2.091 -0.224 0.890 0.333 0.674 -0.260 0.486  3  E  1  R  x 10 s0.941 0.889 0.837 0.791 0.747 0.705 0.666 0.630 0.595 0.563 0.533 0.503 0.477 0.451 0.426 0.403 0.381 0.360 0.340 0.321 0.303  3  P  1  (R  E  -Rp)x  s0.002 0.009 -0.043 0.188 0.234 -0.091 -0.031 0.069 0.390 -0.158 0.536 -0.364 0.276 -0.117 1.665 -0.627 0.509 -0.027 0.334 -0.582 0.183 1  10  3  x 10 s0.070 0.068 0.066 0.066 0.067 0.068 0.070 0.071 0.073 0.075 0.076 0.077 0.077 0.078 0.077 0.077 0.076 0.075 0.074 0.072 0.070  3  cTp  M  /  $  0.350 0.322 0.295 0.271 0.248 0.225 0.205 0.185 0.166 0.149 0.133 0.117 0.102 0.088 0.074 0.062 0.050 0.039 0.028 0.018 0.009  0.568 0.537 0.506 0.478 0.451 0.426 0.402 0.381 0.359 0.340 0.322 0.304 0.288 0.272 0.257 0.243 0.230 0.217 0.205 0.194 0.183  0.397 0.364 0.332 0.302 0.275 0.247 0.223 0.199 0.176 0.155 0.136 0.116 0.099 0.082 0.065 0.050 0.036 0.022 0.010 -0.002 -0.014  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  309  Data  Table C.23: Summary of Data for Run 31  6  s 0 67 112 157 202 246 291 336 381 426 471 516 560 605 650 695 740 785 830 875 920 964 1009 1054 1099 1144 1189 1234 1278 1323 1368 1413 1458  R  E  x 10  3  R  P  x 10 s0.000 0.525 0.849 1.056 1.178 1.246 1.286 1.309 1.323 1.331 1.336 1.338 1.336 1.332 1.324 1.312 1.296 1.276 1.252 1.223 1.191 1.157 1.118 1.077 1.033 0.988 0.942 0.895 0.849 0.802 0.755 0.709 0.664  3  1  0.001 0.403 0.903 1.163 2.062 1.150 2.337 1.226 2.320 1.264 1.560 1.393 1.715 1.367 1.718 0.801 1.307 1.160 1.195 1.094 1.043 1.258 0.794 1.447 0.621 1.108 1.128 1.232 1.153 1.214 0.290 0.774 0.675  (R  E  - Rp) x 10  3  s0.001 -0.122 0.054 0.107 0.884 -0.096 1.051 -0.083 0.997 -0.067 0.224 0.055 0.379 0.035 0.394 -0.511 0.011 -0.116 -0.057 -0.129 -0.148 0.101 -0.324 0.371 -0.412 0.119 0.186 0.337 0.305 0.412 -0.465 0.065 0.011 1  x 10 s0.165 0.130 0.142 0.148 0.139 0.130 0.123 0.114 0.103 0.095 0.093 0.094 0.094 0.093 0.088 0.082 0.075 0.069 0.064 0.061 0.059 0.059 0.058 0.058 0.057 0.056 0.054 0.053 0.052 0.050 0.050 0.049 0.049  3  <T  p  M  1  1.920 1.904 1.873 1.830 1.779 1.726 1.669 1.610 1.551 1.491 1.431 1.371 1.312 1.252 1.192 1.133 1.074 1.016 0.960 0.904 0.849 0.798 0.747 0.697 0.650 0.604 0.561 0.519 0.481 0.444 0.409 0.376 0.345  /  $  0.000 0.393 0.635 0.790 0.881 0.932 0.962 0.979 0.989 0.995 0.999 1.000 0.999 0.996 0.990 0.981 0.969 0.954 0.936 0.915 0.891 0.865 0.836 0.805 0.773 0.739 0.704 0.669 0.635 0.599 0.565 0.530 0.497  1.810 1.795 1.765 1.723 1.675 1.624 1.570 1.514 1.458 1.401 1.344 1.287 1.231 1.173 1.117 1.060 1.004 0.949 0.895 0.842 0.790 0.741 0.692 0.645 0.600 0.556 0.515 0.476 0.439 0.404 0.370 0.339 0.310  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  310  Data  Table C.23: Summary of Data for Run 31 -(Continued)  6  s 1503 1548 1593 1638 1683 1727 1772 1817 1862 1907 1952 1997 2042 2086 2131 2176 2221 2266 2311 2356 2401 2446 2490 2535 2580 2625 2670 2715 2760  R  x 10 s0.623 0.336 0.700 1.412 0.251 1.396 0.195 0.766 0.228 0.971 0.087 0.649 0.054 0.288 0.254 0.427 0.639 0.125 0.899 0.070 0.021 0.102 0.164 0.205 0.108 1.064 0.233 0.199 0.067  3  E  1  R  x 10 s0.621 0.579 0.538 0.500 0.463 0.429 0.395 0.364 0.335 0.307 0.282 0.258 0.235 0.215 0.196 0.178 0.162 0.147 0.133 0.121 0.109 0.099 0.089 0.081 0.073 0.065 0.059 0.053 0.047  3  P  1  (R  E  - Rp) x 10  3  s0.002 -0.243 0.161 0.913 -0.212 0.967 -0.201 0.402 -0.107 0.664 -0.195 0.392 -0.182 0.073 0.058 0.249 0.476 -0.022 0.766 -0.051 -0.088 0.003 0.074 0.125 0.035 0.999 0.174 0.146 0.020 1  (T x 10 s0.049 0.050 0.051 0.051 0.052 0.052 0.052 0.052 0.052 0.051 0.050 0.049 0.048 0.047 0.045 0.043 0.042 0.040 0.038 0.036 0.034 0.032 0.030 0.029 0.027 0.025 0.023 0.022 0.000  3  P  M  1  0.316 0.289 0.264 0.241 0.219 0.199 0.181 0.164 0.148 •0.134 0.120 0.108 0.097 0.087 0.078 0.070 0.062 0.055 0.049 0.043 0.038 0.033 0.029 0.025 0.022 0.019 0.016 0.013 0.011  /  $  0.464 0.282 0.433 0.256 0.403 0.232 0.374 0.210 0.346 0.190 0.320 0.171 0.296 0.153 0.272 0.137 0.250 0.122 0.230 0.108 0.210 0.096 0.193 0.084 0.176 0.074 0.161 0.064 0.147 0.055 0.133 0.047 0.121 0.040 0.110 0.033 0.100 0.027 0.090 0.022 0.082 0.017 0.074 0.013 0.067 0.009 0.060 0.005 0.054 0.002 0.049 -0.001 0.044 -0.004 0.039 -0.006 0.035 -0.008  Appendix  C. Tabulated  Instantaneous  Drying  Rate  311  Data  Table C.24: Summary of Data for Run 32  6  R  x 10  3  E  s  s"  0 46 76 106 136 167 197 227 258 288 318 349 379 409 439 470 500 530 560 591 621 651 682 712 742 773 803 833 863 894 924 954 985  0.001 0.165 0.372 0.568 0.638 0.723 0.904 1.046 1.172 1.266 1.314 1.378 1.431 1.484 1.489 1.433 .1.389 1.241 1.211 0.712 0.668 0.828 1.008 1.251 1.416 1.303 1.200 1.183 1.180 1.260 1.360 1.266 1.206  1  R  x 10  3  P  s-  1  0.000 0.138 0.307 0.490 0.667 0.830 0.966 1.077 1.170 1.241 1.295 1.336 1.365 1.385 1.398 1.405 1.408 1.406 1.401 1.393 1.382 1.369 1.353 1.336 1.316 1.294 1.270 1.245 1.218 1.189 1.160 1.129 1.096  (R  E  - R) P  x 10  s"  1  0.001 0.028 0.065 0.078 -0.029 -0.107 -0.061 -0.031 0.002 0.026 0.019 0.042 0.066 0.099 0.091 0.027 -0.019 -0.165 -0.190 -0.681 -0.715 -0.541 -0.345 -0.085 0.100 0.009 -0.070 -0.063 -0.039 0.071 0.200 0.137 0.1.10  3  o>  x 10  3  M  s"  /  $  0.000 0.098 0.218 0.348 0.474 0.590 0.686 0.765 0.831 0.881 0.920 0.949 0.970 0.984 0.993 0.998 1.000 0.999 .0.995 0.990 0.982 0.973 0.961 0.949 0.935 0.919 0.902 0.884 0.865 0.845 0.824 0.802 0.779  1.610 1.608 1.603 1.593 1.578 1.558 1.535 1.509 1.480 1.449 1.417 1.382 1.348 1.313 1.277 1.240 1.205 1.169 1.133 1.097 1.061 1.026 0.990 0.956 0.923 0.888 0.856 0.824 0.792 0.761 0.731 0.702 0.673  1  0.000 0.019 0.027 0.030 0.031 0.030 0.028 0.026 0.025 0.025 0.025 0.025 0.024 0.024 0.024 0.024 0.024 0.024 0.025 0.025 0.025 0.025 0.024 0.024 0.023 0.022 0.021 0.020 0.020 0.019 0.018 0.018 0.017  1.920 1.918 1.911 1.899 1.882 1.858 1.831 1.801 1.766 1.730 1.692 1.651 1.610 1.569 1.527 1.484 1.442 1.399 1.357 1.314 1.272 1.231 1.189 1.148 1.109 1.068 1.030 0.992 0.955 0.918 0.882 0.848 0.814  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  312  Data  Table C.24: Summary of Data for Run 32 -(Continued)  6  s 1015 1045 1075 1106 1136 1166 1197 1227 1257 1288 1318 1348 1378 1409 1439 1469 1500 1530 1560 1590 1621 1651 1681 1711 1742 1773 1803 1833 1863 1894 1924 1954 1984  R  E  x 10 s1.115 1.049 1.013 0.930 0.889 0.866 0.829 0.719 0.678 0.638 0.641 0.608 0.628 0.624 0.558 0.576 0.606 0.581 0.578 0.577 0.544 0.472 0.470 0.450 0.395 0.252 0.186 0.181 0.207 0.205 0.222 0.215 0.225  3  1  R  P  x 10 s1.064 1.030 0.997 0.961 0.927 0.893 0.858 0.824 0.790 0.756 0.723 0.691 0.660 0.629 0.599 0.570 0.541 0.514 0.489 0.464 0.439 0.416 0.394 0.373 0.352 0.332 0.314 0.296 0.280 0.263 0.249 0.234 0.221  3  1  (R  E  - Rp) x 10  3  s0.052 0.019 0.017 -0.032 -0.038 -0.027 -0.028 -0.104 -0.112 -0.118 -0.082 -0.083 -0.032 -0.005 -0.041 0.006 0.065 0.067 0.090 0.114 0.105 0.056 0.076 0.077 0.043 -0.080 -0.128 -0.115 -0.072 -0.058 -0.027 -0.019 0.004 1  cT  x 10 s0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.016 0.016 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.014 0.014 0.014 0.014 0.014 0.014  3  p  M  /  0.781 0.750 0.719 0.689 0.661 0.633 0.606 0.581 0.557 0.533 0.511 0.490 0.469 0.449 0.431 0.413 0.396 0.380 0.365 0.351 0.337 0.324 0.312 0.301 0.289 0.279 0.269 0.260 0.251 0.243 0.235 0.228 0.221  0.755 0.732 0.708 0.683 0.659 0.634 0.609 0.585 0.561 0.537 0.514 0.491 0.469 0.446 0.425 0.405 0.385 0.365 0.347 0.329 0.312 0.295 0.280 0.265 0.250 0.236 0.223 0.210 0.199 0.187 0.177 0.167 0.157  1  0.645 0.618 0.593 0.567 0.543 0.520 0.497 0.476 0.455 0.435 0.416 0.398 0.381 0.364 0.348 0.333 0.319 0.305 0.293 0.280 0.269 0.258 0.247 0.238 0.228 0.219 0.211 0.203 0.196 0.189 0.182 0.176 0.170  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  313  Data  Table C.24: Summary of Data for Run 32 -(Continued)  6  s 2015 2045 2075 2106 2136 2166 2196 2227 2257 2288 2318 2348 2378 2409 2439 2469 2500 2530 2560 2590 2621 2651 2681 2712 2742 2772  R  x 10 s0.247 0.246 0.244 0.160 0.160 0.182 0.173 0.150 0.151 0.135 0.128 0.118 0.122 0.093 0.082 0.040 0.030 0.023 0.043 0.059 0.060 0.080 0.103 0.055 0.045 0.046  3  E  1  R  x 10 s0.208 0.196 0.185 0.174 0.164 0.154 0.145 0.137 0.129 0.121 0.114 0.107 0.101 0.095 0.090 0.085 0.080 0.075 0.071 0.067 0.063 0.059 0.056 0.053 0.050 0.047  3  P  1  (R  E  - R) P  x 10  s0.039 0.050 0.060 -0.014 -0.004 0.028 0.028 0.013 0.022 0.014 0.013 0.010 0.020 -0.002 -0.008 -0.045 -0.049 -0.052 -0.028 -0.008 -0.003 0.020 0.047 0.002 -0.005 -0.002 1  3  <T  x 10 s0.014 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.014 0.014 0.014 0.015 0.015 0.016 0.016 0.017 0.017 0.018 0.018 0.019 0.019 0.020  3  p  M  1  0.214 0.208 0.203 0.197 0.192 0.187 0.183 0.178 0.174 0.171 0.167 0.164 0.161 0.158 0.155 0.152 0.150 0.147 0.145 0.143 0.141 0.139 0.137 0.136 0.134 0.133  /  $  0.148 0.139 0.131 0.123 0.116 0.110 0.103 0.097 0.091 0.086 0.081 0.076 0.072 0.068 0.064 0.060 0.057 0.053 0.050 0.048 0.045 0.042 0.040 0.038 0.036 0.034  0.165 0.160 0.155 0.150 0.146 0.142 0.138 0.134 0.131 0.128 0.125 0.122 0.119 0.117 0.114 0.112 0.110 0.108 0.106 0.104 0.103 0.101 0.100 0.098 0.097 0.096  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  314  Data  Table C.25: Summary of Data for Run 34  6  s 0 76 137 197 258 318 379 440 500 561 621 682 743 803 864 925 985 1046 1107 1167 1228 1289 1349 1410 1471 1531 1592 1653 1713 1774 1834 1895 1956  R  x 10 s0.001 0.885 1.203 1.191 1.229 1.150 1.109 1.146 1.062 0.985 0.922 0.889 0.822 0.737 0.708 0.697 0.616 0.599 0.561 0.497 0.513 0.444 0.451 0.397 0.402 0.372 0.345 0.317 0.302 0.263 0.250 0.247 0.216  3  E  1  R  x 10 s" 0.000 0.878 1.186 1.233 1.218 1.190 1.152 1.103 1.048 0.988 0.928 0.869 0.814 0.764 0.718 0.675 0.636 0.599 0.565 0.533 0.502 0.472 0.443 0.416 0.389 0.363 0.338 0.314 0.292 0.270 0.249 0.229 0.211  3  P  1  - Rp) x 10 s0.001 0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 0.000  3  {R  E  1  x 10 s0.014 0.012 0.012 0.010 0.009 0.009 0.008 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004  3  tT  p  M  1  1.410 1.399 1.378 1.348 1.313 1.277 1.240 1.203 1.165 1.128 1.093 1.056 1.021 0.987 0.952 0.920 0.888 0.856 0.826 0.796 0.768 0.740 0.713 0.688 0.662 0.638 0.615 0.591 0.569 0.548 0.527 0.507 0.488  /  $  0.000 0.434 0.712 0.878 0.962 0.993 1.000 0.996 0.988 0.977 0.965 0.950 0.934 0.916 0.895 0.873 0.850 0.825 0.801 0.777 0.753 0.728 0.705 0.683 0.660 0.640 0.620 0.600 0.582 0.565 0.547 0.531 0.516  1.264 1.254 1.234 1.207 1.175 1.142 1.109 1.075 1.041 1.008 0.975 0.942 0.910 0.879 0.848 0.818 0.789 0.760 0.732 0.706 0.680 0.654 0.630 0.607 0.584 0.562 0.541 0.519 0.500 0.480 0.461 0.443 0.425  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  315  Data  Table C.25: Summary of Data for Run 34 -(Continued)  e s 2016 2077 2138 2199 2259 2320 2380 2441 2502 2563 2623 2684 2745 2805 2866 2927 2987 3048 3109 3169 3230 3291 3351 3412 3473 3533 3594 3655 3716 3776 3837 3898 3958  R  E  x 10 s0.198 0.208 0.167 0.170 0.138 0.133 0.143 0.105 0.091 0.067 0.070 0.076 0.037 0.046 0.035 0.007 0.022 0.011 0.018 0.014 -0.002 -0.018 -0.005 -0.002 -0.013 0.008 -0.027 -0.020 0.002 -0.031 -0.009 -0.035 -0.015  3  1  R  x 10 s0.193 0.177 0.161 0.147 0.134 0.121 0.110 0.099 0.089 0,081 0.073 0.065 0.058 0.052 0.047 0.042 0.037 0.033 0.030 0.026 0.023 0.021 0.018 0.016 0.014 0.013 0.011 0.010 0.009 0.008 0.007 0.006 0.005  3  P  1  {R  - RP) x 10 s0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.000 -0.000 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000  3  E  1  x 10 s0.004 0.004 0.004 0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0,002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001  3  <T  p  M  1  0.468 0.450 0.432 0.415 0.398 0.382 0.365 0.350 0.335 0.320 0.307 0.293 0.279 0.267 0.255 0.242 0.231 0.220 0.209 0.198 0.188 0.178 0.169 0.160 0.152 0.143 0.135 0.128 0.120 0.113 0.106 0.100 0.093  /  $  0.500 0.486 0.472 0.458 0.445 0.432 0.419 0.407 0.395 0.383 0.371 0.360 0.348 0.337 0.326 0.315 0.305 0.295 0.284 0.275 0.265 0.255 0.246 0.237 0.228 0.219 0.210 0.202 0.194 0.186 0.178 0.171 0.164  0.408 0.391 0.375 0.359 0.344 0.329 0.314 0.300 0.287 0.273 0.260 0.248 0.236 0.224 0.213 0.202 0.192 0.182 0.171 0.162 0.153 0.144 0.136 0.127 0.120 0.112 0.105 0.098 0.091 0.084 0.078 0.072 0.067  Appendix  C. Tabulated  Instantaneous  Drying  Rate  316  Data  Table C.26: Summary of Data for Run 36  e  s 0 46 76 106 137 167 197 258 288 318 349 379 409 440 500 530 561 591 621 651 682 742 773 803 833 864 894 924 985 1015 1045 1076 1106  R  x 10  R  3  E  s0.001 0.559 0.886 1.045 1.091 1.170 1.206 1.252 1.232 1.195 1.171 1.118 1.127 1.099 1.071 0.972 0.976 0.999 0.947 0.906 0.917 0.805 0.857 0.758 0.787 0.738 0.722 0.693 0.626 0.665 0.650 0.545 0.565 1  x 10  3  P  s0.000 0.555 0.891 1.036 1.110 1.165 1.209 1.246 1.240 1.221 1.193 1.162 1.128 1.093 1.030 1.000 0.972 0.946 0.922 0.898 0.875 0.832 0.811 0.790 0.769 0.748 0.728 0.707 0.665 0.644 0.624 0.603 0.582 1  .  (R  E  - R) P  s0.001 0.004 -0.005 0.009 -0.019 0.006 -0.003 0.005 -0.007 -0.026 -0.022 -0.043 -0.001 0.006 0.041 -0.028 0.004 0.052 0.025 0.008 0.042 -0.027 0.046 -0.032 0.018 -0.010 -0.005 -0.014 -0.039 0.021 0.026 -0.058 -0.018 1  x 10  3  cT  x 10  3  p  s0.000 0.017 0.014 0.014 0.012 0.010 0.010 0.009 0.008 0.007 0.007 0.007 0.007 0.007 0.006 0.006 0.006 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.004 0.004 0.004 0.004 0.004  M  /  $  1.410 1.400 1.378 1.349 1.315 1.281 1.245 1.170 1.133 1.096 1.058 1.023 0.989 0.954 0.891 0.860 0.830 0.801 0,773 0.746 0.718 0.667 0.641 0.617 0.594 0.571 0.548 0.527 0.485 0.465 0.446 0.427 0.410  0.000 0.446 0.715 0.831 0.891 0.935 0.970 1.000 0.995 0.980 0.957 0.932 0.905 0.877 0.826 0.803 0.780 0.759 0.740 0.721 0.702 0.668 0.651 0.634 0.617 0.600 0.584 0.567 0.534 0.517 0.501 0.484 0.467  1.264 1.255 1.234 1.208 1.177 1.146 1.114 1.046 1.012 0.978 0.944 0.912 0.881 0.849 0.792 0.764 0.736 0.710 0.684 0.660 0.635 0.588 0.565 0.543 0.522 0.500 0.480 0.461 0.423 0.405 0.388 0.370 0.354  1  Continued  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  317  Data  Table C.26: Summary of Data for Run 36 -(Continued)  6  s 1136 1167 1227 1257 1288 1318 1348 1379 1409 1470 1500 1530 1561 1591 1621 1651 1712 1742 1772 1803 1833 1863 1894 1955 1985 2015 2046 2076 2106 2137 2197 2227 2258  R  E  x 10 s" 0.566 0.525 0.473 0.443 0.458 0.438 0.455 0.437 0.394 0.362 0.356 0.337 0.329 0.301 0.298 0.284 0.248 0.246 0.246 0.220 0.232 0.212 0.211 0.178 0.178 0.181 0.157 0.152 0.141 0.133 0.088 0.100 0.088  3  1  R  P  x 10 s0.562 0.542 0.503 0.484 0.465 0.446 0.429 0.411 0.394 0.361 0.345 0.330. 0.315 0.301 0.287 0.274 0.249 0.237 0.226 0.215 0.204 0.194 0.184 0.166 0.158 0.150 0.142 0.135 0.128 0.121 0.109 0.103 0.097  3  1  {R  - Rp) x 10  3  E  s0.004 -0.017 -0.030 -0.040 -0.007 -0.009 0.027 0.026 0.000 0.001 0.011 0.008 0.015 0.001 0.011 0.010 -0.000 0.009 0.020 0.006 0.028 0.018 0.027 0.012 0.021 0.031 0.015 0.017 0.013 0.012 -0.020 -0.003 -0.009 1  <r x 10  M  $  s0.004 0.004 0.004 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.002 0.002  f  0.392 0.375 0.344 0.329 0.314 0.301 0.288 0.275 0.263 0.240 0.229 0.219 0.209 0.200 0.191 0.182 0.166 0.159 0.152 0.145 0.139 0.133 0.127 0.117 0.112 0.107 0.103 0.099 0.095 0.091 0.084 0.081 0.078  0.451 0.435 0.404 0.388 0.373 0.358 0.344 0.329 0.316 0.289 0.277 0.265 0.253 0.241 0.230 0.220 0.200 0.190 0.181 0.172 0.164 0.156 0.148 0.133 0.127 0.120 0.114 0.108 0.103 0.097 0.087 0.083 0.078  0.339 0.323 0.294 0.281 0.268 0.255 0.243 0.231 0.221 0.200 0.190 0.181 0.172 0.163 0.155 0.148 0.133 0.127 0.120 0.114 0.108 0.103 0.098 0.088 0.083 0.079 0.075 0.071 0.068 0.064 0.058 0.055 0.052  3  p  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  318  Data  Table C.26: Summary of Data for Run 36 -(Continued)  6  s 2288 2318 2349 2379 2439 2470 2500 2531 2561 2591 2622 2682 2713 2743 2773 2804 2834 2864 2925 2955 2986 3016 3046 3077 3107 3168 3198 3228 3259 3289 3319 3349 3410  R  E  x 10 s0.075 0.077 0.084 0.078 0.057 0.071 0.057 0.059 0.054 0.058 0.061 0.051 0.031 0.028 0.026 0.039 0.028 0.022 0.022 0.010 0.014 0.009 -0.002 0.010 0.022 0.004 -0.010 -0.014 -0.026 -0.010 -0.011 -0.009 -0.017  3  1  R  P  x  10  s0.092 0.087 0.082 0.078 0.070 0.066 0.062 0.059 0.055 0.052 0.049 0.044 0.042 0.039 0.037 0.035 0.033 0.031 0.027 0.026 0.024 0.023 0.022 0.020 0.019 0.017 0.016 0.015 0.014 0.013 0.013 0.012 0.010 1  3  (R  - RP) x 10 s-0.017 -0.010 0.001 -0.000 -0.013 0.006 -0.005 0.001 -0.002 0.005 0.012 0.007 -0.010 -0.011 -0.011 0.004 -0.005 -0.008 -0.005 -0.015 -0.011 -0.014 -0.023 -0.011 0.003 -0.013 -0.026 -0.029 -0.040 -0.023 -0.024 -0.021 -0.027  3  E  1  <T  x 10 s0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001  3  P  M  1  0.075 0.072 0.069 0.067 0.063 0.060 0.059 0.057 0.055 0.053 0.052 0.049 0.048 0.046 0.045 0.044 0.043 0.042 0.040 0.040 0.039 0.038 0.037 0.037 0.036 0.035 0.035 0.034 0.034 0.033 0.033 0.033 0.032  /  $  0.074 0.070 0.066 0.063 0.056 0.053 0.050 0.047 0.045 0.042 0.040 0.035 0.033 0.031 0.030 0.028 0.026 0.025 0.022 0.021 0.020 0.018 0.017 0.016 0.015 0.014 0.013 0.012 0.011 0.011 0.010 0.009 0.008  0.050 0.047 0.045 0.043 0.039 0.037 0.035 0.033 0.032 0.030 0.029 0.026 0.025 0.024 0.023 0.022 0.021 0.020 0.019 0.018 0.017 0.016 0.016 0.015 0.015 0.014 0.013 0.013 0.012 0.012 0.012 0.011 0.011  Appendix  C. Tabulated  Instantaneous  Drying  Rate  319  Data  Table C.27: Summary of Data for Run 38  e s 0 78 130 181 233 285 337 389 441 493 544 596 648 700 752 804 856 907 959 1011 1063 1115 1167 1219 1271 1323 1375 1427 1478 1530 1582 1634  R  x 10 s0.002 2.119 2.368 2.429 2.270 2.484 2.201 2.050 1.938 1.337 1.035 0.850 0.970 0.961 0.696 0.691 0.312 0.238 0.201 -0.002 0.111 0.035 -0.037 0.125 -0.096 -0.125 -0.014 -0.093 0.016 -0.162 -0.024 0.034  3  E  1  R  x 10 s0.000 2.132 2.337 2.407 2.427 2.361 2.210 1.998 1.755 1.507 1.274 1.058 0.866 0.702 0.563 0.448 0.353 0.278 0.217 0.168 0.130 0.099 0.076 0.058 0.044 0.033 0.025 0.019 0.014 0.011 0.008 0.006  3  P  1  {R  E  - R) P  s" 0.002 -0.013 0.032 0.022 -0.157 0.123 -0.009 0.052 0.182 -0.170 -0.240 -0.208 0.104 0.259 0.133 0.243 -0.042 -0.041 -0.016 -0.170 -0.019 -0.064 -0.113 0.067 -0.140 -0.158 -0.039 -0.112 0.002 -0.173 -0.032 0.028 1  x 10  x 10 s0.139 0.127 0.096 0.096 0.081 0.079 0.077 0.069 0.064 0.064 0.063 0.059 0.054 0.050 0.048 0.048 0.048 0.047 0.045 0.042 0.038 0.034 0.030 0.025 0.021 0.018 0.015 0.012 0.010 0.008 0.006 0.000  3  3  CT  p  M  /  $  1.410 1.308 1.191 1.070 0.944 0.819 0.700 0.590 0.492 0.407 0.337 0.276 0.226 0.186 0.153 0.127 0.106 0.090 0.077 0.067 0.059 0.053 0.049 0.045 0.043 0.041 0.039 0.038 0.037 0.037 0.036 0.036  0.000 0.879 0.963 0.992 1.000 0.973 0.911 0.823 0.723 0.621 0.525 0.436 0.357 0.289 0.232 0.184 0.146 0.115 0.089 0.069 0.053 0.041 0.031 0.024 0.018 0.014 0.010 0.008 0.006 0.004 0.003 0.002  1.738 1.610 1.463 1.312 1.155 0.998 0.849 0.712 0.590 0.484 0.396 0.320 0.258 0.207 0.166 0.133 0.107 0.087 0.071 0.059 0.049 0.042 0.036 0.032 0.028 0.026 0.024 0.023 0.022 0.021 0.020 0.020  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  320  Data  Table C.28: Summary of Data for Run 39  6  s 0 78 130 182 234 338 390 442 494 546 650 701 753 805 857 961 1013 1065 1117 1169 1273 1325 1377 1429 1481 1585 1637 1689 1741 1793 1897 1949 2001  R  x 10 s0.001 0.317 0.542 0.560 0.666 0.896 0.811 0.974 0.799 0.991 1.019 0.859 0.876 0.934 0.793 0.701 0.827 0.664 0.717 0.434 -1.714 -0.620 -0.725 0.242 0.365 0.312 0.226 0.348 0.226 0.225 0.104 0.120 0.070  3  E  1  R  x 10 s0.000 0.313 0.489 0.608 0.691 0.802 0.843 0.878 0.904 0,923 0.931 0.921 0.902 0.876 0.843 0.764 0.720 0.675 0.629 0.584 0.497 0.457 0.419 0.384 0.351 0.294 0.270 0.248 0.228 0.210 0.181 0.169 0.159  3  P  1  (R  - RP) x 10 s0.001 0.004 0.054 -0.048 -0.025 0.094 -0.033 0.096 -0.105 0.069 0.089 -0:062 -0.027 0.058 -0.051 -0.064 0.107 -0.010 0.089 -0.150 -2.210 -1.077 -1.144 -0.142 0.014 0.017 -0.044 0.100 -0.002 0.014 -0.077 -0.050 ' -0.089  3  E  1  x 10 s0.034 0.035 0.030 0.027 0.027 0.025 0.023 0.022 0.021 0.021 0.021 0.020 0.020 0.019 0.019 0.020 0.021 0.021 0.022 0.022 0.022 0.021 0.020 0.020 0.018 0.016 0.015 0.014 0.014 0.013 0.013 0.013 0.013  3  Op  M  /  $  1.410 1.399 1.377 1.349 1.315 1.237 1.194 1.149 1.103 1.055 0.959 0.911 0.864 0.818 0.773 0.689 0.651 0.614 0.580 0.549 0.493 0.468 0.445 0.424 0.405 0.372 0.357 0.344 0.331 0.320 0.300 0.291 0.282  0.000 0.336 0.525 0.653 0.742 0.861 0.906 0.942 0.971 0.991 0.999 0.989 0.969 0.941 0.906 0.820 0.773 0.724 0.675 0.626 0.534 0.490 0.450 0.412 0.377 0.316 0.290 0.266 0.245 0.226 0.195 0.182 0.170  1.738 1.723 1.697 1.661 1.619 1.521 1.467 1.411 1.353 1.294 1.173 1.114 1.055 0.997 0.941 0.836 0.788 0.743 0.700 0.661 0.591 0.560 0.532 0.505 0.482 0.440 0.421 0.405 0.389 0.375 0.350 0.338 0.328  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  321  Data  Table C.28: Summary of Data for Run 39 -(Continued)  6  s 2053 2105 2209 2261 2313 2365 2417 2521 2573 2625 2677 2729 2833 2885 2937 2989 3042 3146 3198 3250 3302 3354 3458 3510 3562 3614 3666 3770 3822 3874 3926 3978 4082  R  x 10  3  E  s-  1  0.207 0.070 0.141 0.265 0.074 0.231 0.129 0.027 0.165 0.046 0.116 0.082 0.065 0.102 0.071 0.121 0.137 0.123 0.054 0.103 0.086 0.137 0.035 0.157 0.138 0.190 0.071 0.123 0.192 0.071 0.175 0.089 0.090  R  x 10 s0.150 0.142 0.129 0.124 0.120 0.116 0.113 0.108 0.106 0.104 0.103 0.102 0.100 0.099 0.099 0.098 0.098 0.097 0.096 0.096 0.096 0.095 0.094 0.094 0.093 0.093 0.092 0.091 0.091 0.090 0.089 0.089 0.087  3  P  1  (R  E  - R ) x 10 s0.058 -0.072 0.012 0.141 -0.046 0.115 0.016 -0.081 0.059 -0.059 0.013 -0.020 -0.035 0.003 -0.028 0.022 0.040 0.026 -0.043 0.007 -0.010 0.042 -0.060 0.064 0.045 0.097 -0.021 0.032 0.101 -0.019 0.086 0.000 0.003  3  P  1  cT  x 10 s0.013 0.013 0.013 0.013 0.013 0.013 0.013 0.012 0.012 0.012 0.012 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.012 0.012 0.013 0.013 0.015 0.015 0.016 0.017 0.018 0.019 0.020 0.021 0.022 0.022 0.000  3  p  M  1  0.274 0.266 0.252 0.246 0.239 0.233 0.227 0.216 0.210 0.205 0.200 0.194 0.184 0.178 0.173 0.168 0.163 0.153 0.148 0.143 0.138 0.133 0.123 0.118 0.113 0.109 0.104 0.094 0.089 0.085 0.080 0.075 0.066  /  $  0.161 0.152 0.139 0.133 0.128 0.125 0.121 0.116 0.114 0.112 0.111 0.109 0.108 0.107 0.106 0.105 0.105 0.104 0.103 0.103 0.103 0.102 0.101 0.101 0.100 0.100 0.099 0.098 0.097 0.097 0.096 0.095 0.094  0.317 0.308 0.290 0.282 0.274 0.267 0.259 0.245 0.238 0.231 0.224 0.218 0.205 0.198 0.192 0.185 0.179 0.166 0.160 0.154 0.147 0.141 0.129 0.123 0.117 0.111 0.105 0.093 0.087 0.081 0.075 0.069 0.058  Appendix  C.  Tabulated  Instantaneous  Drying  Rate  322  Data  Table C.29: Summary of Data for Run 41  6  s 0 67 156 201 290 335 425 469 559 603 693 738 827 872 961 1006 1096 1140 1230 1274 1364 1409 1498 1543 1632 1677 1766 1811 1901 1946 1991  R  x 10 s0.001 0.864 1.381 1.550 1.547 1.317 1.354 1.142 1.056 1.178 1.112 0.884 0.802 0.753 0.691 0.505 0.480 0.519 0.408 0.327 0.286 0.238 0.031 0.201 0.161 0.043 -0.017 0.104 0.096 -0.067 0.001  3  E  1  R  P  x 10 s0.000 0.971 1.559 1.553 1.438 1.382 1.286 1.243 1.154 1.108 1.005 0.949 0.835 0.776 0.661 0.605 0.499 0.451 0.363 0.325 0.256 0.226 0.175 0.153 0.117 0.102 0.077 0.066 0.049 0.042 0.036  3  1  {R  - Rp) x 10  3  E  s0.001 -0.108 -0.178 -0.002 0.109 -0.064 0.067 -0.102 -0.099 0.070 0.107 -0.065 -0.033 -0.024 0.030 -0.100 -0.019 0.067 0.045 0.002 0.030 0.012 -0.144 0.048 0.045 -0.058 -0.094 0.037 0.047 -0.109 -0.035 1  cT  x 10 s0.000 0.072 0.054 0.047 0.044 0.041 0.036 0.036 0.033 0.031 0.028 0.028 0.028 0.027 0.025 0.023 0.022 0.022 0.022 0.022 0.022 0.022 0.021 0.020 0.018 0.017 0.014 0.013 0.011 0.010 0.009  3  p  M  /  1.410 1.381 1.260 1.189 1.056 0.993 0.873 0.817 0.709 0.659 0.564 0.520 0.441 0.405 0.341 0.312 0.263 0.242 0.205 0.190 0.164 0.153 0.135 0.128 0.116 0.111 0.103 0.100 0.095 0.093 0.091  0.000 0.623 1.000 0.996 0.922 0.886 0.825 0.798 0.741 0.711 0.645 0.609 0.536 0.498 0.424 0.388 0.320 0.290 0.233 0.208 0.164 0.145 0.112 0.098 0.075 0.065 0.049 0.042 0.032 0.027 0.023  1  1.311 1.284 1.170 1.103 0.977 0.918 0.805 0.752 0.650 0.603 0.513 0.472 0.397 0.363 0.303 0.276 0.229 0.209 0.175 0.160 0.136 0.126 0.109 0.102 0.091 0.086 0.079 0.076 0.071 0.069 0.067  Appendix  C. Tabulated  Instantaneous  Drying  Rate  323  Data  Table C.30: Summary of Data for Run 42  9  s 0 78 130 182 234 286 338 390 442 494 546 598 650 702 754 806 858 910 961 1013 1065 1117 1169 1221 1273 1325 1377 1430 1482 1533 1585 1637 1689  R  x 10 s0.001 0.905 0.816 1.038 0.970 0.675 0.899 0.917 1.040 0.760 0.880 0.798 0.883 0.813 0.640 0.623 0.710 0.974 0.800 0.872 0.664 0.647 0.559 0.668 0.143 0.479 0.392 0.392 0.343 0.412 0.448 0.398 0.382  3  E  1  R  x 10 s0.000 0.603 0.851 0.962 0.997 0.993 0.972 0.945 0.917 0.889 0.863 0.839 0.817 0.795 0.775 0.754 0.734 0.713 0.692 0.671 0.648 0.625 0.601 0.577 0.553 0.528 0.503 0.478 0.453 0.430 0.406 0.383 0.360  3  P  1  (R  E  -Rp)x  s0.001 0.301 -0.035 0.076 -0.027 -0.318 -0.073 -0.028 0.123 -0.129 0.017 -0.042 0.066 0.018 -0.134 -0.132 -0.024 0.261 0.108 0.201 0.016 0.022 -0.042 0.091 -0.410 -0.049 -0.111 -0.086 -0.110 -0.018 0.042 0.015 0.021 1  10  3  cr x 10 s0.129 0.070 0.049 0.054 0.049 0.043 0.042 0.041 0.038 0.035 0.032 0.031 0.031 0.030 0.029 0.027 0.026 0.025 0.024 0.024 0.024 0.024 0.024 0.023 0.023 0.022 0.021 0.019 0.019 0.018 0.017 0.017 0.016  3  p  M  /  $  0.000 0.605 0.854 0.966 1.000 0.996 0.975 0.948 0.920 0.892 0.866 0.842 0.820 0.798 0.777 0.757 0.736 0.716 0.695 0.673 0.650 0.627 0.603 0.579 0.555 0.530 0.505 0.480 0.455 0.431 0.407 0.384 0.362  1.252 1.231 1.197 1.154 1.108 1.061 1.015 0.970 0.926 0.884 0.843 0.803 0.764 0.727 0.690 0.654 0.619 0.585 0.553 0.521 0.490 0.460 0.432 0.404 0.378 0.352 0.328 0.305 0.283 0.263 0.243 0.225 0.207  1  1.410 1.387 1.348 1.301 1.250 1.198 1.147 1.097 1.048 1.001 0.956 0.912 0.869 0.827 0.786 0.746 0.707 0.670 0.634 0.598 0.564 0.531 0.499 0.469 0.439 0.411 0.384 0.358 0.334 0.312 0.290 0.269 0.250  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  324  Data  Table C.30: Summary of Data for Run 42 -(Continued)  6  s 1741 1793 1845 1897 1949 2001 2053 2105 2157 2209 2261 2313 2365 2417 2469 2521 2573 2625 2677 2729 2781 2833  x 10 s0.362 0.363 0.312 0.310 0.225 0.277 0.175 0.244 0.092 0.231 0.126 0.283 0.096 0.147 0.116 0.032 0.151 -0.102 0.155 0.004 0.177 0.075  3  RE  1  R  x 10 s0.339 0.318 0.297 0.278 0.260 0.242 0.226 0.210 0.195 0.181 0.168 0.155 0.143 0.133 0.122 0.113 0.104 0.096 0.088 0.081 0.074 0.068  3  P  1  (R  E  - Rp)  x 10  s0.024 0.045 0.014 0.032 -0.035 0.035 • -0.050 0.034 -0.102 0.050 -0.041 0.128 -0.048 0.014 -0.007 -0.081 0.047 -0.198 0.067 -0.077 0.102 0.006 1  3  x 10 s0.016 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.015 0.015 0.015 0.014 0.014 0.013 0.012 0.000  <T  3  p  M  1  0.232 0.215 0.199 0.184 0.170 0.157 0.145 0.133 0.123 0.113 0.104 0.096 0.088 0.081 0.074 0.068 0.062 0.057 0.052 0.048 0.044 0.040  /  $  0.340 0.319 0.299 0.279 0.261 0.243 0.226 0.210 0.195 0.181 0.168 0.156 0.144 0.133 0.123 0.113 0.104 0.096 0.088 0.081 0.075 0.069  0.191 0.175 0.161 0.148 0.135 0.123 0.112 0.102 0.093 0.084 0.076 0.068 0.061 0.055 0.049 0.043 0.038 0.033 0.029 0.025 0.022 0.018  Appendix  C. Tabulated  Instantaneous  Drying  Rate  325  Data  Table C.31: Summary of Data for Run 43  6  s 0 45 75 106 136 166 197 227 257 287 318 348 378 408 438 468 499 529 559 589 620 651 681 712 742 773 803 834 864 894 925 955 986  x 10 s0.001 . 0.786 1.342 1.408 1.849 1.791 1.750 1.829 1.660 1.573 1.178 1.162 1.501 1.532 1.481 1.500 1.465 1.130 1.185 1.120 1.039 1.125 0.842 0.864 0.937 0.825 0.765 0.785 0.754 0.763 0.635 0.619 0.627  3  R  E  1  R  P  x 10 s0.000 0.825 1.278 1.562 1.705 1.766 1.777 1.760 1.727 1.686 1.638 1.589 1.538 1.485 1.430 1.375 1.318 1.263 1.207 1.153 1.098 1.044 0.993 0.942 0.894 0.846 0.802 0.758 0.717 0.677 0.638 0.602 0.567  3  1  (R  E  - Rp)  x 10  s" 0.001 -0.039 0.064 -0.153 0.144 0.025 -0.028 0.069 -0.067 -0.113 -0.461 -0.427 -0.036 0.047 0.050 0.124 0.147 -0.132 -0.023 -0.033 -0.059 0.081 -0.151 -0.078 0.044 -0.021 -0.037 0.027 0.037 0.086 -0.004 0.017 0.060 1  3  <T x 10 s0.046 0.042 0.035 0.035 0.034 0.032 0.031 0.032 0.033 0.034 0.033 0.031 0.028 0.026 0.024 0.024 0.023 0.023 0.023 0.022 0.021 0.020 0.020 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.019 0.018 0.018  3  P  M  1  1.410 1.393 1.361 1.316 1.267 1.215 1.160 1.107 1.054 1.003 0.952 0.903 0.856 0.811 0.767 0.725 0.683 0.645 0.608 0.572 0.537 0.504 0.474 0.444 0.416 0.389 0.364 0.340 0.318 0.297 0.277 0.258 0.240  / 0.000 0.464 0.719 0.879 0.960 0.994 1.000 0.990 0.972 0.949 0.922 0.894 0.865 0.835 0.805 0.774 0.742 0.710 0.679 0.649 0.618 0.587 0.559 0.530 0.503 0.476 0.451 0.426 0.403 0.381 0.359 0.339 0.319  1.311 1.295 1.265 1.223 1.176 1.127 1.075 1.025 0.976 0.927 0.879 0.833 0.789 0.746 0.705 0.665 0.626 0.589 0.554 0.521 0.488 0.457 0.428 0.400 0.374 0.348 0.325 0.302 0.281 0.262 0.242 0.225 0.208  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  326  Data  Table C.31: Summary of Data for Run 43 -(Continued)  6  s 1016 1047 1077 1108 1138 1169 1199 1230 1260 1291 1321 1352 1382 1413 1443 1473 1504 1534 1565 1595 1626 1656 1687 1718 1748 1779 1809  R  E  10  3  x  s0.499 0.503 0.491 0.431 0.455 0.362 0.382 0.355 0.299 0.334 0.287 0.131 0.284 0.193 0.217 0.253 0.079 0.180 0.156 0.159 0.165 0.088 0.130 0.087 0.026 0.158 0.065 1  R  P  10  3  x  s0.534 0.501 0.472 0.442 0.415 0.389 0.364 0.340 0.318 0.297 0.277 0.258 0.241 0.224 0.209 0.194 0.180 0.167 0.155 0.144 0.133 0.123 0.114 0.105 • 0.097 0.090 0.083 1  {R  - RP) x 10 s-0.035 0.001 0.019 -0.012 0.040 -0.026 0.018 0.015 -0.020 0.037 0.009 -0.127 0.043 -0.031 0.008 0.059 -0.101 0.012 0.001 0.015 0.032 -0.036 0.016 -0.019 -0.072 0.068 -0.018  3  E  1  <r x v  10  3  s" 0.017 0.016 0.016 0.015 0.015 0.015 0.014 0.014 0.015 0.015 0.015 0.015 0.015 0.015 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.015 0.015 0.015 0.014 0.014 0.000  M  1  0.224 0.208 0.193 0.179 0.166 0.153 0.142 0.131 0.121 0.112 0.103 0.095 0.087 0.080 0.074 0.068 0.062 0.057 0.052 0.047 0.043 0.039 0.035 0.032 0.029 0.026 0.023  /  $  0.300 0.282 0.265 0.249 0.234 0.219 0.205 0.191 0.179 0.167 0.156 0.145 0.136 0.126 0.117 0.109 0.101 0.094 0.087 0.081 0.075 0.069 0.064 0.059 0.055 0.051 0.047  0.192 0.177 0.163 0.150 0.138 0.126 0.115 0.105 0.096 0.087 0.079 0.071 0.064 0.057 0.051 0.045 0.040 0.035 0.030 0.026 0.022 0.018 0.015 0.011 0.008 0.006 0.003  Appendix  C. Tabulated  Instantaneous  Drying  Rate  327  Data  Table C.32: Summary of Data for Run 44  e  R x 10  R x 10  (R - Rp) x 10  s 0 67 156 201 290 336 425 470 559 604 693 738 827 872 961 1006 1096 1141 1230 1275 1364 1409 1498 1543 1633 1677 1767 1812 1902 1946 1991  s0.001 0.907 1.569 1.647 1.182 1.301 1.284 0.838 0.959 0.979 0.813 0.868 0.720 0.758 0.526 0.379 0.656 0.529 0.387 0.373 0.244' 0.314 0.292 0.251 0.096 0.153 0.160 0.076 0.013 0.133 -0.008  s0.000 0.900 1.550 1.653 1.546 1.421 1.193 1.103 0.975 0926 0.844 0.805 0.728 0.689 0.610 0.570 0.493 0.457 0.388 0.357 0.299 0.272 0.226 0.204 0.167 0.151 0.122 0.110 0.088 0.079 0.071  s0.001 0.007 0.019 -0.007 -0.364 -0.120 0.091 -0.265 -0.016 0.053 -0.031 0.062 -0.009 0.070 -0.084 -0.191 0.163 0.073 -0.001 0.016 -0.055 0.042 0.067 0.046 -0.071 0.002 0.037 -0.034 -0.076 0.054 -0.079  3  E  1  3  P  1  ;  3  E  1  cT  x 10 s" 0.000 0.077 0.052 0.050 0.047 0.043 0.041 0.037 0.029 0.028 0.027 0.027 0.024 0.022 0.020 0.019 0.018 0.019 0.019 0.019 0.019 0.019 0.018 0.017 0.016 0.016 0.014 0.013 0.012 0.011 0.010  3  p  M  /  $  1.410 1.379 1.266 1.193 1.048 0.980 0.864 0.813 0.721 0.678 0.599 0.562 0.494 0.462 0.404 0.378 0.330 0.308 0.271 0.254 0.225 0.212 0.190 0.180 0.164 0.157 0.144 0.139 0.130 0.127 0.123  0.000 0.544 0.937 1.000 0.935 0.860 0.721 0.667 0.590 0.560 0.511 0.487 0.441 0.417 0.369 0.345 0.298 0.276 0.235 0.216 0.181 0.165 0.136 0.124 0.101 0.091 0.074 0.067 0.053 0.048 0.043  1.275 1.247 1.143 1.076 0.944 0.881 0.775 0.727 0.643 0.604 0.531 0.497 0.435 0.405 0.352 0.328 0.284 0.265 0.230 0.215 0.188 0.176 0.156 0.147 0.132 0.125 0.114 0.109 0.101 0.098 0.095  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  328  Data  Table C.33: Summary of Data for Run 45  9  s 0 67 111 156 201 245 291 335 380 425 469 514 559 604 648 693 738 783 827 872 917 961 1006 1051 1096 1141 1186 1230 1275 1320 1365 1409 1454  R  x 10 s" 0.001 0.566 0.866 1.017 1.101 1.219 1.306 1.392 1.395 1.432 1.310 1.224 1.328 0.848 0.901 0.802 0.767 0.787 0.722 0.793 0.607 0.695 0.529 0.464 0.551 0.452 0.538 0.421 0.542 0.391 0.462 0.362 0.345  3  E  1  R  x 10 s0.000 0.585 0.838 1.002 1.154 1.272 1.347 1.372 1.360 1.319 1.262 1.194 1.121 1.048 0.979 0.912 0.850 0.792 0.741 0.694 0.651 0.613 0.577 0.544 0.514 0.486 0.460 0.436 0.413 0.391 0.371 0.352 0.333  3  P  1  (R  E  - Rp) x 10  3  s0.001 -0.018 0.028 0.015 -0.053 -0.053 -0.040 0.020 0.035 0.112 0.048 0.030 0.207 -0.200 -0.078 -0.110 -0.082 -0.005 -0.019 0.099 -0.044 0.082 -0.048 -0.081 0.037 -0.034 0.078 -0.015 0.129 -0.000 0.091 0.010 0.011 1  x 10 s0.058 0.046 0.040 0.031 0.032 0.030 0.026 0.024 0.024 0.025 0.026 0.026 0.025 0.023 0.021 0.020 0.018 0.018 0.017 0.017 0.017 0.017 0.017 0.017 0.016 0.016 0.015 0.015 0.014 0.014 0.014 0.013 0.014  3  Op  M  /  $  1.410 1.393 1.361 1.320 1.271 1.218 1.157 1.097 1.036 0.975 0.919 0.863 0.811 0.762 0.718 0.675 0.636 0.599 0.565 0.533 0.503 0.475 0.448 0.423 0.399 0.376 0.355 0.336 0.316 0.298 0.281 0.265 0.250  0.000 0.426 0.611 0.731 0.841 0.927 0.982 1.000 0.991 0.962 0.920 0.870 0.817 0.764 0.713 0.665 0.619 0.578 0.540 0.506 0.475 0.447 0.421 0.397 0.375 0.354 0.335 0.318 0.301 0.285 0.270 0.256 0.243  1.404 1.387 1.355 1.313 1.264 1.210 1.149 1.088 1.026 0.965 0.908 0.852 0.799 0.750 0.705 0.662 0.622 0.585 0.551 0.518 0.487 0.459 0.432 0.407 0.383 0.360 0.339 0.319 0.299 0.281 0.264 0.248 0.232  1  Continued  Appendix  C. Tabulated  Instantaneous  Drying  Rate  329  Data  Table C.33: Summary of Data for Run 45 -(Continued)  6  s 1499 1543 1588 1633 1678 1723 1767 1812 1857 1902 1946 1991 2036 2080 2125 2170 2215  R  E  x 10 s0.364 0.215 0.301 0.186 0.238 0.206 0.244 0.247 0.066 0.332 0.055 0.178 0.084 0.087 0.157 0.091 0.145  3  1  R  P  x 10 s0.316 0.299 0.283 0.267 0.253 0.239 0.225 0.213 0.200 0.189 0.178 0.167 0.157 0.148 0.139 0.130 0.122  3  1  (R  E  - Rp) x 10  3  s0.048 -0.084 0.018 -0.082 -0.015 -0.033 0.019 0.034 -0.134 0.143 -0.123 0.010 -0.074 -0.061 0.019 -0.039 0.023 1  x 10 s0.014 0.014 0.014 0.015 0.015 0.016 0.016 0.016 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.016 0.000  3  <T  p  M  /  $  0.235 0.222 0.209 0.196 0.185 0.174 0.163 0.153 0.144 0.135 0.127 0.120 0.112 0.106 0.099 0.093 0.087  0.230 0.218 0.206 0.195 0.184 0.174 0.164 0.155 0.146 0.137 0.130 0.122 0.114 0.108 0.101 0.095 0.089  0.217 0.204 0.191 0.178 0.166 0.155 0.145 0.135 0.125 0.117 0.108 0.101 0.093 0.086 0.080 0.074 0.068  1  Appendix  C. Tabulated  Instantaneous  Drying  Rate  Data  330  Table C.34: Summary of Data for Run 46  0  s 0 ' 68 112 201 246 291 380 425 470 559 604 648 738 782 827 916 961 1006 1096 1140 1185 1274 1319 1364 1453 1498 1542 1632 1676 1721 1811  R  E  x 10 s" 0.001 0.885 1.191 1.566 1.276 1.483 1.019 1.245 1.158 0.884 0.986 0.901 0.815 0.835 0.886 0.820 0.562 0.544 0.551 0.419 0.284 0.373 0.406 0.207 0.278 0.301 0.202 0.204 0.122 0.242 0.213 1  3  R  x 10 s0.000 0.895 1.142 1.381 1.406 1.380 1.268 1.205 1.145 1.039 0.990 0.944 0.854 0.811 0.768 0.683 0.641 0.601 0.523 0.487 0.452 0.388 0.358 0.330 0.279 0.256 0.235 0.196 0.180 0.164 0.136  3  P  1  {R  E  - Rp) x 10  s" 0.001 -0.010 0.049 0.184 -0.130 0.103 -0.249 0.040 0.013 -0.155 -0.004 -0.043 -0.040 0.024 0.119 0.137 -0.080 -0.057 0.028 -0.069 -0.169 -0.015 0.048 -0.123 -0.001 0.045 -0.033 0.008 -0.057 0.078 0.077 1  3  <r x 10 p  s" 0.000 0.082 0.076 0.053 . 0.044 0.040 0.043 0.040 0.036 0.030 0.029 0.029 0.028 0.027 0.025 0.022 0.021 0.020 0.020 0.020 0.021 0.021 0.022 0.022 0.022 0.021 0.021 0.020 0.019 0.019 0.017  3  M  /  1  1.410 0.000 1.381 0.637 1.335 0.812 1.221 0.983 1.159 1.000 1.096 0.982 0.978 0.902 0.922 0.857 0.869 0.815 0.772 0.739 0.726 0.704 0.684 0.672 0.603 0.608 0.566 0.577 0.531 0.546 0.466 0.486 0.436 0:456 0.408 0.427 0.358 0.372 0.336 0.347 0.315 0.322 0.277 0.276 0.260 -0.255 0.245 0.235 0.218 0.199 0.206 0.182 0.195 0.167 0.176 0.140 0.167 0.128 0.160 0.116 0.146 0.097  1.275 1.249 1.207 1.102 1.044 0.987 0.878 0.827 0.779 0.690 0.648 0.609 0.535 0.501 0.469 0.409 0.382 0.356 0.310 0.290 0.270 0.236 0.221 0.206 0.182 0.171 0.161 0.143 0.135 0.128 0.116  Appendix D  Tabulated Data on Maximum and Falling Drying Rates  The summary of data on the predicted values of the maximum drying rates and their relative standard deviations, a and 6 , are shown in Table D . l . The drying rate at fuel p  P  moisture contents of M = 0.3 to M = 0.6 and the average standard deviations within that period are included in Table D.2. Table D.3 contains the values obtained through Equation A.109 at four different moisture contents; their average value is incorporated into Equation 4.5 for determination of the standard deviation of the slope of the drying rate curve and the results are shown in Table D.4. The slope of the drying rate curves (R vs M) is also evaluated at four different moisture contents (Table D.4). Their average value is calculated and compared, to check the linearity of the curve, with the slope of the hne connecting  RM=O.Z  and RM=O.& as is reported in Table D.4; the mean values are used  within the text. The residence time required to obtain several final moisture contents are tabulated in Table D.5.  331  Appendix  D. Tabulated  Data  on Maximum  and Falling  Drying  Rates  Table D.l: Maximum Drying Rate Data and the Confidence Intervals Run  M„  Rmax X 10 s-  0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  1.03 0.83 1.03 1.00 1.07 1.11 1.12 0.97 1.09 1.05 0.96 0.96 1.03 0.84 0.97 0.89 1.03 0.94 0.62 0.90 0.79 0.85 1.07 1.20 1.12 1.12 0.82 0.82 1.08 1.10 1.08 1.11 1.01 1.11  1  0.481 0.736 1.811 1.366 1.458 1.370 1.753 1.091 1.019 0.968 1.052 0.839 0.981 1.184 1.001 1.251 1.045 1.413 1.407 2.400 1.245 1.656 1.338 1.408 1.233 1.246 2.427 0.931 1.559 0.997 1.777 1.653 1.372 1.406  a  p  x s -  10  3  1  0.002 0.020 0.044 0.020 0.043 0.037 0.061 0.012 0.014 0.033 0.015 0.016 0.014 0.016 0.018 0.011 0.008 0.016 0.028 0.071 0.069 0.109 0.099 0.024 0.010 0.008 0.100 0.022 0.048 0.050 0.033 0.050 0.027 0.046  S x p  s -  10  3  1  0.004 0.039 0.086 0.039 0.083 0.072 0.120 0.024 0.027 0.066 0.030 0.031 0.028 0.032 0.035 0.021 0.015 0.032 0.055 0.139 0.136 0.214 0.195 0.047 0.019 0.017 0.196 0.042 0.095 0.097 0.065 0.099 0.053 0.091  endix  D.  Tabulated  Data  on Maximum  and Falling  Drying  Rates  Table D.2: Summary of Data on Drying Rates During the Falling Rate Period Run M  0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  x 10 sM = 0.4 M = 0.5 0.324 0.398 0.287 0.412 0.756 1.019 0.730. 0.871 0.625 0.808 0.606 0.727 0.609 0.754 0.615 0.730 0.459 0.557 0.544 0.634 0.482 0.619 0.262 0.340 0.550 0.638 0.718 0.854 0.385 0.505 0.719 0.851 0.530 0.631 0.874 0.987 1.102 1.211 1.479 1.696 0.924 1.022 1.039 1.219 0.743 0.872 0.549 0.708 0.551 0.648 0.571 0.680 1.484 1.975 0.342 0.507 0.922 0.768 0.518 0.602 0.866 1.037 0.604 0.736 0.515 0.646 0.588 0.728 R  = 0.3 0.235 0.169 0.495 0.561 0.415 0.465 0.454 0.489 0.348 0.444 0.349 0.165 0.448 0.570 0.264 0.571 0.415 0.972 1.238 0.811 0.849 0.596 0.373 0.450 0.445 1.146 0.182 0.579 0.417 0.682 0.442 0.394 0.427  3  1  <r M  = 0.6 0.451 0.539 1.247 1.001 0.966 0.841 0.932 0.830 0.645 0.707 0.758 0.418 0.713 0.966 0.630 0.966 0.720 1.094 1.298 1.894 1.106 1.390 0.984 0.850 0.749 0.775 2.020 0.656 1.045 0.672 1.195 0.845 0.794 0.850  x 10  3  HR)  s0.002 0.013 0.035 0.015 0.032 0.017 0.031 0.007 0.007 0.017 0.010 0.009 0.009 0.013 0.010 0.006 0.005 0.017 0.027 0.050 0.057 0.078 0.052 0.015 0.005 0.004 0.067 0.018 0.027 0.022 0.020 0.022 0.017 0.022 1  S  x 10 s0.004 0.026 0.069 0.030 0.063 0.034 0.061 0.013 0.014 0.034 0.020 0.019 0.019 0.026 0.020 0.012 0.010 0.033 0.053 0.097 0.112 0.153 0.101 0.030 0.010 0.008 0.132 0.035 0.052 0.044 0.039 0.043 0.033 0.043  3  P{R)  1  Appendix  D. Tabulated  Data  on Maximum  and Falling  Drying  Rates  Table D.3: Summary of Data Affecting the Slope of the Falling Rate Curve Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  M = 0.3  M = 0.4  0.318 1.007 1.167 0.645 1.523 1.582 0.602 0.896 1.001 0.745 1.230 1.322 1.188 0.499 0.385 0.833 1.103  1.111 0.479 0.403 0.932 1.423 1.712 2.337 0.989 0.996 0.866 0.164 2.062 1.264 0.936 0.185 0.887 1.067 0.721 1.441 1.777 1.190 0.295 1.263 0.996 0.181 1.176 2.320 0.036 1.649 1.439 0.518 1.665 0.714 1.101  1.231 1.947 1.097 0.097 1.196 0.858 0.806 1.080 2.008 5.040 1.570 1.296 0.564 1.473 0.031 1.051  du/dR M = 0.5 M = 0.6 2.014 0.165 1.098 1.174 1.364 1.752 2.203 1.146 0.905 1.017 0.622 0.093 1.292 1.357 0.183 0.989 1.045 0.351 1.806 1.571 1.375 0.815 1.386 1.110 0.323 1.173 3.668 1.016 1.739 1.538 0.585 1.602 0.878 1.084  3.875 0.821 1.539 1.411 1.239 1.411 0.996 1.388 0.690 1.112 1.337 2.364 1.180 1.842 0.649 1.167 0.993 0.211 2.504 1.555 1.757 1.577 1.567 1.239 0.420 0.843 3.917 1.639 1.728 1.441 0.725 0.386 0.532 0.839  0.3 < M < 0.6 2.259 0.697 1.129 1.079 1.391 1.620 1.708 1.121 0.907 0.945 0.963 1.703 1.232 1.261 0.399 0.977 1.053 0.479 1.811 1.720 1.378 0.901 1.360 1.060 0.491 1.077 3.091 2.698 1.673 1.431 0.603 1.384 0.626 1.024  334  Appendix  D. Tabulated  Data  on Maximum  and Falling  Drying  335  Rates  Table D.4: Summary of Data on the Slope of the Falling Rate Curve Run 0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  ui x 10 s d  1  M = 0.3  M = 0.4  M = 0.5  M = 0.6  0.935 1.068 2.620 1.721 2.349 1.553 1.345 1.372 1.179 1.079 1.273 1.089 1.105 1.557 1.191 1.556 1.231  0.828 1.250 2.700 1.555 1.967 1.360 1.503 1.226 1.040 0.946 1.384 0.858 0.949 1.424 1.238 1.398 1.076 1.169 1.200 2.294 1.063 1.891 1.379 1.677 0.974 1.172 3.158 1.706 1.702 0.921 1.770 1.464 1.257 1.500  0.644 1.286 2.444 1.371 1.649 1.184 1.717 1.074 0.923 0.806 1.342 0.738 0.809 1.231 1.239 1.244 0.943 1.094 0.983 2.067 0.908 1.769 1.204 1.505 0.986 1.011 2.286 1.588 1.379 0.765 1.655 1.186 1.396 1.306  0.404 1.167 2.069 1.161 1.390 1.030 1.900 0.917 0.834 0.677 1.173 0.887 0.692 1.010 1.176 1.092 0.830 1.061 0.755 1.878 0.748 1.523 1.035 1.335 1.038 0.887 2.181 1.344 1.111 0.632 1.527 1.031 1.530 1.156  c  1.414 2.574 1.222 1.911 1.563 1.846 1.037 1.349 3.608 1.366 2.080 1.092 1.891 1.779 1.196 1.715  6  "average of the four values slope of the line connecting M = 0.3 and M = 0.6 Average values represent the region of 0.4 < M < 0.6 6  c  r  M  0.3 < M < 0.6 0.703 0.720 1.193 1.235 2.459 2.507 1.452 1.467 1.839 1.837 1.282 1.255 1.616 1.596 1.147 1.137 0.994 0.991 0.877 0.874 1.293 1.366 0.893 0.843 0.889 0.882 1.305 1.321 1.211 1.218 1.322 1.318 1.020 1.017 1.108 1.098 1.088 1.088 2.203 2.188 0.985 0.982 1.773 1.805 1.295 1.293 1.591 1.590 1.009 0.996 1.105 1.099 2.912 2.808 1.501 1.580 1.568 1.552 0.852 0.850 1.711 1.707 1.365 1.343 1.345 1.333 1.419 1.411 a  6  s 0.006 0.013 0.056 0.023 0.063 0.040 0.075 0.011 0.009 0.023 0.014 0.023 0.017 0.024 0.006 0.008 0.007 0.011 0.069 0.121 0.111 0.099 0.099 0.023 0.003 0.006 0.295 0.069 0.063 0.045 0.017 0.043 0.015 0.032 _ 1  x s1  0.013 0.025 0.110 0.046 0.123 0.078 0.147 0.021 0.018 0.045 0.027 0.045 0.032 0.047 0.012 0.016 0.015 0.022 0.135 0.236 0.218 0.195 0.195 0.045 0.007 0.012 0.577 0.135 0.124 0.089 0.033 0.084 0.029 0.062  Appendix  D. Tabulated  Data  on Maximum  and Falling  Drying  Rates  336  Table D.5: Particle Residence Time Required to Reach Various Final Moisture Contents Run  9. M  0 1 3 4 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 26 29 30 31 32 34 36 38 39 41 42 43 44 45 46  0.3 2160 1936 957 1160 1149 1225 1080 1360 1623 1574 1490 2729 1506 1204 1753 1186 1510 =  1108 586 1235 1070 1529 1711 1334 1320 574 1893 1027 1561 890 1159 1315 1219  M  0.4 1800 1479 800 1000 960 1043 870 1184 1373 1375 1248 2260 1306 1050 1442 1030 1298 950 1012 513 1121 964 1380 1492 1133 1123 498 1496 878 1346 760 968 1094 1021 =  M  0.5 1524 1196 685 880 818 900 737 1035 1177 1200 1066 1930 1138 920 1225 902 1125 843 926 450 1019 877 1256 1332 966 963 394 1260 760 1168 655 818 922 868 =  M  = 0.6 1288 979 596 770 700 768 620 906 1009 1054 906 1666 990 810 1043 794 976 747 846 394 924 798 1148 1204 822 825 384 1086 659 1010 566 692 782 742  Appendix E  Calibration Curves and Equations  The following two tables provide the calibrated values of flowmetering devices and thermocouples.  337  Appendix  E. Calibration  Curves  and  338  Equations  Table E.l: Calibration Equations for Flowmeters Flowmeter Ch.E. No Substance Fisher rotameter Fisher rotameter Matheson rotameter Brooks rotameter Keiso rotameter 3 inch orifice 2 inch orifice l | inch orifice 1 inch orifice Rosemount transducer^  3162 3227B 3227B  m kg/hr Air @ STP — 1.61994-E - 07 + 0.742X Air @ STP 1.232523 + 0.344086X Air @ STP c + X +cX +cX Water 32.5476 + 5.69366X Steam © 115 kPa -3.66793 + 8.6555X Air @ STP 1.7068^/Ap Air @ STP 1.745-/Sp Air © STP 0.325 A^ Air © STP 0.079 £p -1.62634 + 0.394172X  0  2  0  Cl  3  2  b  3  c  /  V  /  v  X denotesflowmeterreading. ^co = 2.0 x 10- , - 31.2 x 10-6, c = 4.7 x 10~ and c = -15.9 x 10~ Ap is in Pa. Ap= 337.603-178.195X +23.170X and X = -0.102765 + 0 .204591XX where XX is the computer input in mv; the shunt which is used has 5f2 resistance and XX = 20.0 for m = 0.0. a  3  6  C l  2  c  d  2  9  3  Appendix  E. Calibration  Curves and  Equations  Table E.2: Calibration Equations for ThermocoupL rp b Thermocouple No." -L calib °c 1 1.01067T . -0.979519 2 1.01094Tta6 - 1.127330 1.00546T - 1.069770 3 4 1.008007U - 1.080000 1.00916T - 1.094820 5 6 1.00900Tta6 - 0.855151 7 1.00303T - 0.628659 1.00832T - 1.092280 8 1.00747T - 0.881030 9 10 1.0074lT - 0.884514 11 1.00804T - 0.654781 12 1.00998T - 0.800983 1.01188T - 1.005180 13 14 1.00982Tta6 - 0.909653 15 1.009387*6 - 0.726555 16 1.009327^6 - 0.729694 17 1.00747^ + 0.745452 18 1.01025T + 0.923989 19 1.00864^ + 1.223050 20 1.007267*06 + 1.188360 21 1.01158T 6 + 1.249230 22 1.00747T o6 + 1.091800 23 1.004247*06 + 1.471470 24 1.01018Tto6 + 0.900685 25 0.99982T 6 + 2.767340 28 1.00189Tte6 + 1.926900 29 1.00663Tta6 + 1.874640 30 1.00243Tta6 + 2.023960 31 1.00244T + 1.815340 32 1.00842Tta6 + 1.892020 c  tafc  tab  ta6  ta6  tafe  tab  tao  tab  tao  ta6  ta6  ta  f  ta  tab  As is marked on the flow diagram. ^Calibrated temperature. Temperature calculated using tabulated linearized data.  a  c  Appendix F  Computer Programs  The following table contains the computer program which was used to determine the instantaneous humidities, mass flow rates and drying rate data. The rest of the computer programs can be obtained from either the author or the Chemical Engineering Department.  340  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates C C  RATE Program t o c a l c u l a t e  rate o l drying  _  c  C C  AP= i n t e r f a c i a l  C  AREBED= area of the bed ; m**2  C  AVEMAS=  C  DPAVE= ave. e f f e c t i v e  C  DEN= mean instantaneous  C  DENAVE= time averaged  C  DENIN= ave. i n l e t d e n s i t y  C  DENW0D= wood d e n s i t y  C  E= voidage  time  surface/total  average  bed v o l . ;m**2/m**3  GSAVE values particle  diam. ; m  density  ; kg/m**3  mean instantaneous  density  ; kg/m**3  ; v o l . s o l i d / v o l . bed  C  EPS=error t o l e r a n c e p r e s c r i b e d by the user  C  F= vapor press, of water a t dew p o i n t of o u t l e t  C  GMS1= i n l e t dry a i r ; kg/hr  C  GMAS1= i n l e t t o t a l  C C  ; kg/m**3  ; kg/m**3  a i r ; kg/hr  the mass through  gas ; itimHg  : i n the READ statement  3" o r i f i c e and i n the output  , i t is i t i s the  t o t a l mass throug the bed.  C  GS1,GS2= i n and out t o t a l  gas/cross  C  GSAVE= ave t o t . gas/cross  section.time 0.5*(GS1*GS2); kg/hr.m**2  C  HTBED= t o t a l height of bed ; m  C  K= no. of dew p o i n t temp readings  section.time  ; kg/hr.m**2  C  KS= l a s t no of reading before the contact of s o l i d ft gas s t a r t s  C  KSFLAG= i s "0" when read. no. KS+1 not considered  C  KB= no of reading a f t e r which the gas was by-passed  C  KJ= the l a s t KJ no of readings  C  axe averaged  mass flow f o r the steam runs  C  N= degree of the polynomial  C  NRUN= Run no.  i n e v a l . of Y l  t o get the incoming  ; chosen as 4 i n the program  i n RPDLY2 subroutine  C  PT= t o t a l p r e s s .  C  RATEIN= r a t e of d r y i n g  ; mmHg  C  RATE= r a t e of d r y i n g  C  RATEVP=rate  C  RATEX= r a t e of d r y i n g  C  SUPVEL= average  C  TDP2= o u t l e t  C  TDPAIR= dew p o i n t temp of the d i l u t i n g  C  TIME= time dew p o i n t temp, measured  C  TG1= i n l e t gas temp.  C  TG1KS= ave. i n l e t gas temp, when the bypass l i n e i s shut o f f ; oC  C  TG2= o u t l e t  C  TGAVE= ave. temp, of icoming  C  TGAVER= ave. of TGAVE values; oC  ; kg water/hr.m**2 of i n t e r f a c i a l  area  ; (kg water/kg dry wood)/sec  of evaporation  ; kg water/sec  ; kg water/hr.m**2 of cross  superficial  velocity  section  (mean of VEL values)  ; m/hr  gas dew p o i n t temp ; oC a i r ; oC  ; sec  ; oC  gas temp, (thermo. #4 i n steam runs;#7 f o r r e s t ) ; oC and outgoing  gas .5*(TG1+TG2); oC  Appendix  F. Computer  342  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C  VEL= mean instantaneous  C  VELAVE= ave. s u p e r f i c i a l  superficial  C  VELIN= ave. i n l e t  C  VOLBED= bed volume  C  WODDRY= mass of dry wood ; kg  velocity  superficial  velocity  of gas ; m/s  of gas ; m/s  velocity  of gas ; m/s  ; m**3  C  W0DMAS= mass of wet wood ; kg  C  Y1,Y2= i n l e t  C  Zl= i n i t i a l  and o u t l e t  gas humidity  wood moisture  content  , dry b a s i s  , dry b a s i s  C IMPLICIT REAL*8(A-H,0-Z) INTEGER LIST(1)/'*'/ DIMENSION  GS2(300),VEL(300),DEN(300)  DIMENSION  RATEIN(300),RATEX(300),RATEVP(300)  DIMENSION WEIT(300) DIMENSION  WT(300),GSAVE(300)  DIMENSION  XX(301),RATE(301),TIMCOR(300)  C0MM0N/BL0CKA/TIME(300),TG1,TG2(300),Y2(300),TGAVE(300) COMMON/BLOCKB/VALUE(300,40),ROT,PRESO,TDPAIR,GSAM,AIRP C0MM0N/BL0CKE/K,N32 (40)  ,NRUN,GMAS1,RSTEAM,PSTEAM,TSTEAM  C0MM0N/BL0CKG/RC02,PC02,C02,STEAM,TIN(300) COMMON/SET2/N C0MM0N/FUN1/A1 C0MM0N/FUN2/A2 C0MM0N/FUN3/A3 C0MM0N/FN1/YY1 C0MM0N/FN2/TTG1 EXTERNAL AUX EXTERNAL FUN EXTERNAL FN LOGICAL LZ DATA WEIT/300+1.D0/ C C  Input  data  C C  N=2  C  PT=760. NAREA=1  C C ******************************************************************** C *  Reading the data by loading two data f i l e s  C *  the f o l l o w i n g values and the second  C *  PC contains temperature  file  ;first  file  contains *  i s the one obtained by *  data.  C * C ********************************************************************  * *  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued) READ(5,LIST) READ(5,LIST)  NRUN,K,KB,KS,KSFLAG GMAS1,WODMAS,Zl,VOLBED,DP32,RSTEAM,PSTEAM  READ(5,LIST) ROT,PRESO,TDPAIR,AIRP,PBED,RC02,PC02 C C C ************************************************ C * Read input data from the f i l e created by PC * C.************************************************ C NK=K NKM=K-1 STFLAG=0. C  KJ=4 DBED=8.  C CALL READ C C C  IN STEAM RUNS Y2(I) IS MASS FLOW PASSING THROUGH THE 3" ORIFICE  C C C  CALCULATE MASS OF WOOD,BED HEIGHT AND INCOMING GAS PROPERTIES  C SUMY1=0. NKB=0 SUMT1=0. IF(KB.NE.O) GO TO 23 SUMY1=0. GO TO 26 23  DO 25 1=1,KB SUMY1=SUMY1+Y2(I) SUMT1=SUMT1+TIN(I) NKB=NKB+1  25 26  CONTINUE SUMYF=SUMYl KSP=KS+1 DO 80 I=KSP,K SUMT1=SUMT1+TIN(I)  80  CONTINUE TG1KS=SUMT1/( (K-KS)+KB) IF(KSFLAG*1) 32,31,32  31  IF(NKB.EQ.O) GO TO 33 Y1=SUMY1/NKB NKBSTM=NKB  343  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) GO TO 33 32  SUMY1=SUMY1+Y2(KSP) Y1=SUMY1/(NKB+1) NKBSTM=NKB+1  33  CONTINUE YW1=Y1/(1+Y1) IF(Yl.GT.l.) STFLAG=1.  C C  Determining  the i n l e t  flow f o r steam runs  C IF(STFLAG.NE.L)  GO TO 34  SUMYL=0. DO 38 1=1,4 KJ=K-(I-1) SUMYL=Y2(KJ)+SUMYL 38 C  CONTINUE Yl=(SUMYF+SUMYL)/(NKB+4) Yl=(SUMY1+SUMYL)/(NKBSTM+4) GMAS1=Y1  C 34  GMAS1=GMAS1+(GSAM*.4536*60.) PI=4.*ATAN(1.) AREBED=(PI*((DBED*0.0254)**2.))/4. GS1=GMAS1/AREBED  C WATM0L=YW1* GMAS1/18. C02M0L=C02/44. AIRM0L=(GMASl-YWl*GMASl-C02)/29. T0TM0L=AIRM0L+WATM0L+C02M0L C02FRC=C02M0L/T0TM0L AIRFRC=AIRM0L/T0TM0L WATFRC=WATM0L/T0TM0L DENC0R=(44.*C02FRC+18.*WATFRC+29.*AIRFRC)/29. C IF(STFLAG.EQ.1.) DENC0R=14.7*.667*376.32/.075/16.019/293./16.7 IF(STFLAG.EQ.1.)  GMAS1=Y1  DO 35 1=1,KS RATEX(I)=0. RATE(I)=0. RATEVP(I)=0. GS2(I)=GS1+RATEX(I) GSAVE(I)=(GSl+GS2(I))/2. DEN(I)=DENCOR*.075*16.019*293.*(14.7+PBED)/14.7/(TGAVE(I)+273.) VEL(I)=(GSAVE(I)/3600.)/DEN(I)  344  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued)  35  TIMCOR(I)=0. CONTINUE TSTART=TIME(KS)+DINT((TIME(KSP)-TIME(KS))II.) TZER0=0. EVPST=0. RATEST=0. RINST=0.  C DENIN=DENCOR*.075*16.019*293.*(14.7+PBED)/(14.7*(TG1+273.)) DENIKS=DENC0R*.075*16.019*293.*(14.7+PBED)/(14.7*(TG1KS+273.)) GMS1=GMAS1/(1.+Y1) IF(STFLAG.EQ.1.) GMS1=1.0 IF(STFLAG.EQ.1.) CALL VISTEM(TG1KS.VISCOS) IF(STFLAG.EQ.O.) CALL VISAIR(TG1KS,VISCOS) VELIN=GMAS1/(AREBED*DENIN*3600.) VELIKS=GMAS1/(AREBED*DENIKS*3600.) REBED=GMAS1*DBED*.0254/(AREBED*VISC0S*3600.) REPART=GMAS1*DP32/(AREBED*VISC0S*3600.) W0DDRY=W0DMAS/(1.+Z1) C C***Density of bark taken from the article published i n Dobie J. C***in 1965 C*** C*** density= oven dry weight /volume C*** =34 lb/cu. f t . = 544.65 kg/cu. m C*** C***Also another a r t i c l e by Smith and Kozak i n Feb. 1971 of Forest C***Products Journal C*** C*** density= oven dry weight /green volume C*** =506.5 kg/cu. m C DENW0D=506.5 V0LW0D=W0DDRY/DENW0D E=1.-(V0LW0D/V0LBED) HTBED=V0LBED/AREBED IF(STFLAG.EQ.1.) GO TO 65 YY1=Y1 TTG1=TG1 XL1=0.D0 XL2=99.D0 C CALL ZER01(XL1,XL2,FN,5.D-9,LZ) C  Appendix  F. Computer  Programs  Table F.l: Program to Calculate trie Instantaneous Drying Rates -(Continued) IF(.NOT.LZ) GO TO 310 PAS=(DEXP(((-4986.6670D0)/(XL1+273.0D0))+20.0D0)) TAS=XL1 YAS=( 18. *PAS) / (29. * (PT-PAS) ) C  C C 65 10 11 12  15 16 17  50  55 20  30 C C31 C 60  WRITE INITIAL CONDITIONS WRITE(6,10) FORMAT('1') IF(STFLAG.EQ.L) WRITE(6,11) F0RMAT(/,10X,'STEAM IS THE DRYING MEDIUM'/) WRITE(6,12)NRUN,GMAS1 FORMAT('RUN=',I3,/,'INLET TOTAL MASS FL0W= \F6.2,' kg/hr') IF(STFLAG.EQ.1.) GO TO 16 WRITE(6,15)GMS1,Y1 FORMAT('INLET DRY GAS= ',F6.2,' kg/hr',/, 1 'DRY BASIS GAS HUMIDITY=',F7.4) WRITE(6,17)TG1,VELIN FORMAT('AVE. INLET GAS TEMP= '.F6.2,' o C 1,/,'AVE. INLET SUPERFICIAL GAS VELOCITY= >,F4.2,' m/sec') WRITE(6,50)TG1KS,VELIKS,DENIKS FORMAT('AVE. INLET GAS TEMP WITH NO BYPASS FLOW= ',F6.2,' oC 1,/,'AVE. INLET SUPERFICIAL GAS VELOCITY WITH NO BYPASS FLOW= ', 1F4.2,' m/sec',/,'AVE. INLET DENSITY WITH NO BYPASS FLOW=' 1.F5.2,' kg/m**3') WRITE(6,55)REBED,REPART FORMAT('Re BASED ON BED DIAMETER=',F7.0,/,'Rep=',F5.0) WRITE(6,20)WODMAS,WODDRY,Z1,HTBED FORMAT('MASS OF WET WOOD=',F5.2,' kg',/, l'MASS OF DRY WOOD=',F5.2,' kg',/, 1'DRY BASIS INITIAL MOISTURE CONTENT=',F5.2,/, 1'HEIGHT OF THE BED=',F7.4,' m') WRITE(6,30)E FORMAT('VOIDAGE=',F6.3) WRITE(6,31) YAS.TAS FORMAT(2D15.6) CONTINUE  C  C C C  CALCULATE RATE (kg water/kg dry wood/sec) and RATEX (kg water/sq.m of cross sect./hr) SUMVEL=0. SUMMAS=0.  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) SUMTG=0. DO 70 1=1,K XX(I)=TIME(I) C 70 C  CONTINUE KSP2=KS+2 DO 72 I=KSP2,K RATEX(I)=(GMS1*(Y2(I)-Yl))/AREBED RATEVP(I)=(GMSl*(Y2(I)-Yl))/(3600.) RATE(I)=RATEVP(I)/WODDRY GS2(I)=GS1+RATEX(I) GSAVE(I)=(GSl+GS2(I))/2.  72 C  DEN(I)=DENCOR*.075*16.019*293.*(14.7+PBED)/14.7/(TGAVE(I)+273.) VEL(I)=(GSAVE(I)/3600.)/DEN(I) SUMMAS=SUMMAS+GSAVE(I) SUMVEL=SUMVEL+VEL(I) SUMTG=SUMTG+TGAVE(I) TIMC0R(I)=TIME(I)-TIME(KS)-DINT((TIME(KSP)-TIME(KS))/2.) CONTINUE AVEMAS=(SUMMAS/3600.)/(K-KSP) SUPVEL=SUMVEL/(K-KSP) TGAVER=SUMTG/(K-KSP) DENAVE=DENCOR*0.075*16.019*293.*(14.7+PBED)/(14.7*(TGAVER+273.)) VELAVE=AVEMAS/DENAVE  C C C 120  140 C C C  CALCULATE AVE PARTICLE DIAM .SPECIFIC SURFACE AND RATE (RATEIN) DPAVE=DP32 AP=(6.*(1.-E))/DPAVE DO 140 1=1,K RATEIN(I)=RATEX(I)/(AP*HTBED) CONTINUE WRITE DATA  WRITE(6,220) AVEMAS,SUPVEL FORMAT('AVE. SUPERFICIAL MASS VEL0CITY= \F4.2,' kg/sq.m/sec',/, 1'AVE. TOTAL SUPERFICIAL GAS VEL0CITY= '.F4.2,' m/sec') WRITE(6,222) DP32 222 FORMAT('SAUTER MEAN DIAM.=',F7.4,' m') WRITE(6,225) 225 FORMAT('1',/,'M = dry basis moisture content',/,  220  347  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) l'Rint = kg water/hr.m**2 ol i n t e r f a c i a l area',/, l'R = dM/dt (l/sec)') KF=0 KI=1 229 KF=KF+54 IF(K.LE.KF) KF=K IF(STFLAG.HE.1.) GO TO 400 WRITE(6,420) 420 FORMAT(' 1',/,' I TIME TG2 3" 0 TIME Revp ', • 1' R Rint ') WRITE(6,440) 440 F0RMATC sec oC kg/hr sec kg/sec l/sec', 1' kg/hr/sq.m',/) GO TO 450 400 230  235 450  236  252 254 258  470  232 234 238 260  WRITE(6,230) Revp FORMAT01',/,' I TIME TG2 Y2 TIME 1' R Rint ') WRITE(6,235) oC FORMAT(' sec kg/sec l/sec' 1' kg/hr/sq.m',/) IF(KS.LT.KI) GO TO 236 KFSAVE=KF KF=KS IF(STFLAG.NE.1.) GO TO 470 WRITE(6,258)(I,TIME(I),TG2(I),Y2(I).TIMCOR(I),RATEVP(I),RATE(I), 1RATEIN(I),I=KI,KF) IF(KF.NE.KS)GO TO 239 WRITE(6,252) TSTART,YI,TZERO,EVPST,RATEST,RINST WRITE(6,254) KSP.TIME(KSP),TG2(KSP),Y2(KSP) F0RMAT(4X,F7.0,8X,F8.2,F8.0,2F10.6,F9.3) F0RMAT(1X,I3,F7.0,F8.2,F8.2) FORMAT(1X,I3,F7.0,F8.2,F8.2,F8.0,2F10.6,F9.3) GO TO 260 WRITE(6,238)(I,TIME(I),TG2(I),Y2(I),TIMC0R(I),RATEVP(I),RATE(I), lRATEIN(I),I=KI,KF) IF(KF.NE.KS)GO TO 239 WRITE(6,232) TSTART,YI,TZERO,EVPST,RATEST,RINST WRITE(6,234) KSP,TIME(KSP),TG2(KSP),Y2(KSP) F0RMAT(4X,F7.0,8X,F8.4,F8.0,2F10.6,F9.3) F0RMAT(1X,I3,F7.0,F8.2,F8.4) F0RMAT(1X,I3,F7.0,F8.2,F8.4,F8.0,2F10.6,F9.3) KI=KSP2  348  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued)  239  240  241  242 C  KF=KFSAVE GO TO 236 IF(KF.GE.K)GO TO 240 KI=KF+1 GO TO 229 KC0R=K-KSP+1 NEVAP=0 TIMC0R(KSP)=l.D-06 RATE(KSP)=l.D-06 RATEVP(KSP)=l.D-06 WRITE(6,241) KCOR,KCOR,NRUN,Z1,WODDRY,NEVAP,NAREA FORMAT(' 1' , //,' TIME RATE 1' '//,3I5/,2F15.6,2I5) WRITE(6,242) (TIMCOR(I),RATE(I),WEIT(I),I=KSP,K) FORMAT(3F15.6)  NEVAP=1 WRITE(6,245) KCOR,KCOR,NRUN,Z1,WODDRY,NEVAP,NAREA 245 FORMAT (.'1',//,' TIME Revap 1' V/,3I5/,2F15.6,2I5) WRITE(6,247) (TIMCOR(I),RATEVP(I),WEIT(I),I=KSP,K) 247 F0RMAT(3F15.6) C GO TO 300 310 WRITE(6,320) 320 FORMAT(' ') WRITE(6,330) 330 FORMAT('ZEROl FAILS TO CALCULATE ADIABATIC TEMP.') 300 STOP END C C************************ C FUNCTION AUX * C************************ C DOUBLE PRECISION FUNCTION AUX(P,D,Z) IMPLICIT REAL*8(A-H,0-Z) COMMON M DIMENSION D(5),P(5) D(l)=1.0 D(2)=1.-DEXP(-P(3)*Z) D(3)=P(2)*Z*DEXP(-P(3)*Z) AUX=P(1)+P(2)*(1.-DEXP(-P(3)*Z)) RETURN  WT  WT  Appendix  F. Computer  350  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) END C C Subroutine READ * C*************************** C SUBROUTINE READ IMPLICIT REAL*8(A-H,0-Z) INTEGER LIST(l)/'*'/ C0MM0N/BL0CKA/TIME(300),TG1,TG2(300),YDSAM(300),TGAVE(300) COMMON/BLOCKB/P(300,40),ROT,PRESO,TDPAIR,GSAM,AIRP C0MM0N/BL0CKE/NR,NP(40),NRUN,GMAS1,RSTEAM,PSTEAM,TSTEAM C0MM0N/BL0CKG/RC02,PC02,C02,STEAM,TIN(300) DIMENSION TRANSP(300) DIMENSION YDMIX(300),YWMIX(300),GSTD(300),DENSAM(300),GWSAM(300) DIMENSION YWSAM(300),GWMIX(300),PDR0P(300),TDP2(300) DIMENSION FLOWCH(300),PCHECK(300),T0UT(300) C C C C C C C C 1 S 10  30 20 C  NR= no. of readings P(I,J)= no. of points TIME(I)= time at which the data was recorded R0T= rotameter readings PRES0= upstream o r i f i c e pressure TDPAIR= dew point temperature of diluting a i r FORMAT(' FORMAT(F8.2) F0RMAT(I3,F9.3) READ(5,1) DO 20 1=1,NR READ(5,1) READ(5,5) TIME(I) DO 30 J=l,32 READ(5,10) NP(J),P(I,J) CONTINUE CONTINUE SUMTG1=0. SGSAM=0. RNR=0. SUMTST=0. 1=0 DO 40 J=1,NR 1=1+1  ')  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued) C C********************* for Run# 23 C IF(NRUN.NE.23.0R.I.NE.4) GO TO 39 1=1+28 39 SUMTG1=SUMTG1+P(I,1) SUMTST=SUMTST+P(I,20) RNR=RNR+1. IF(I.EQ.NR) J=NR 40 CONTINUE TG1=SUMTG1/RNR TTG1=TG1 TSTEAM=SUMTST/RNR IF(RSTEAM.NE.0.) GO TO 42 STEAM=0. GO TO 43 42 DUMST=DSqRT(376.32*(PSTEAM+14.7)/(TSTEAM+273.)/16.7) STEAM=DUMST*(8.6555*RSTEAM-3.66793) IF(STEAM.LT.50.)G0 TO 43 C C In steam Runs YDSAM i s the mass flow through the 3" orifice C PREDUM=PRESO DO 46 1=1,NR TIN(I)=P(I,1) TG2(I)=P(I,4) TGAVE(I)=(TIN(I)+TG2(I))/2. IF(NRUN.Eq.38.AND.I.GE .13.AND I.LE.18) IF(NRUN.Eq.38.AND.I.GE .19.AND I.LE.20) IF(NRUN.Eq.38.AND.I.GE .28.AND I.LE.39) IF(NRUN.Eq.38. AND.I.GE .40.AND .I.LE.43) IF(NRUN.Eq.39. AND.I.GE .13.AND .I.LE.29) IF(NRUN.Eq.40. AND.I.GE .15.AND .I.LE.16) IF(NRUN.Eq, 40. AND.I.GE .17.AND .I.LE.17) IF(NRUN.Eq.41. AND.I.GE .13.AND •I.LE.19) IF(NRUN.Eq.43. AND.I.GE .17.AND .I.LE.23) IF (NRUN. Eq.44. AND.I.GE .14.AND •I.LE.14) IF(NRUN.Eq,45. AND,I.GE .15.AND .I.LE.17) IF(NRUN.Eq, 46. AND,I.GE .12.AND .I.LE.12) IF (NRUN. Eq,46.AND, I.GE .13.AND •I.LE.14) IF(NRUN.Eq, 46.AND, I.GE .15.AND .I.LE.15)  PRES0= 15.7 PRES0= 15.5 PRES0= 14.5 PRES0= 14.7 PRES0= 17.0 PRES0= 17.8 PRES0= 17. PRES0= 17.7 PRES0= 16.7 PRES0= 18. PRES0= 17. PRES0= 20. PRES0= 18. PRES0= 17.  /  Appendix F. Computer Programs  352  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C  TRANSP(I) i s the value recorded by P.C. using the f i t t e d curve of  C  the measured voltage by P.C. vs the panel readout  (Aug 86) ;  C IF(PDR0P(I).LT.O.) PDROP(I)=0. C C  t h e r e f o r e , the panel reading  C  recorded  value  . That  should i d e a l l y  was the reason  be equl t o the comp.  that panel reading was used  C  i n c a l i b . of the 1" o r i f i c e i n Aug 86 ;however the comp. recorded  C  values were used f o r c a l i b .  C  from the i d e a l  i n Aug 87 t o include any changes  situation.  C 90  TRANSP(I)=P(I,27) PDROP(I)=1.35529-0.715355*TRANSP(I)+0.0930134*(TRANSP(I)**2.) IF(PDR0P(I).LT.O.)  PDR0P(I)=0.  DENSAM(I)=.667*376.32*(PRES0+14.7)/16.7/(P(1,22)+273.) YDSAM(I)=DSQRT(DENSAM(I)*PDR0P(I) /1.65564D-03 )• PRES0=PREDUM 46  CONTINUE GSAM=0. GO TO 80  C 43  IF(RC02.NE.O.) GO TO 44 C02=0. GO TO 45  44  DUMC02=DSQRT((PC02+14.7)*44./14.7/29.)  C C********************  calib.  f o r small F i s h e r r o t . i n Aug 86  C C02=DUMC02*(0.0452867+0.0126428*RCD2)*60.*.4536 C C In the f o l l o w i n g GMAS1 i s the mass passing through  3 inch o r i f i c e  C 45  STM0LE=STEAM/18. C02M0L=C02/44. AIRM0L=(GMAS1-STEAM-C02)/29. T0TM0L=AIRM0L+STM0LE+C02M0L C02FRC=C02M0L/T0TM0L AIRFRC=AIRM0L/T0TM0L STFRAC=STM0LE/T0TM0L C0RFAC=(44.*C02FRC+18.+STFRAC+29.*AIRFRC)/29.  C DUMAIR=DEXP(((-4986.667D0)/(TDPAIR+273.DO))+20.DO) YDAIR=(18.*DUMAIR)/(29.*(760.-DUMAIR)) YWAIR=YDAIR/(1.+YDAIR)  Appendix  F. Computer  353  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued) C  52 C 49  IF(NRUN.NE.20)GO TO 49 DO 52 1=5,44 P(I,27)=10.15 CONTINUE DO 50 1=1,NR IF(NRUN.NE.2)GO TO 55 IF(I.LE.73.0R.I.GE.92) R0T=30. IF(I.LT.92.AND.I.GT.73) R0T=40. IF(NRUN.GT.24.)GO TO 56  55 C C******************** calib. f o r small Fisher rot. i n Aug 86 C GAIR=0.0452867+0.0126428+ROT GO TO 58 C 56 IF(NRUN.NE.33) GO TO 57 C C******************** for Run #33 C IF(I.LE.67.0R.I.GE.28) R0T=15.D0 IF(I.LT.28.AND.I.GT.67) R0T=20. C C******************** calib for large Fisher rot. i n Aug 30/87 C 57 GAIR=(-0.16199D-6+0.74200DO*ROT)/.4536/60. 58 GAIR=GAIR*(((14.7+AIRP)/14.7)**.5) IF(ROT.EQ.O.) GAIR=0. TIN(I)=P(I,1) TG2(I)=P(I,7) TDP2(I)=P(I,26) TRANSP(I)=P(I,27) DUMMIX=DEXP(((-4986.667D0)/(P(I,26)+273.DO))+20.DO) YDMIX(I)=(18.+DUMMIX)/ (29.*(760.-DUMMIX)) YWMIX(I)=YDMIX(I)/(1.+YDMIX(I)) T0UT(I)=P(I,22) PDROP(I)=1.35529-0. 715355*TRANSP(I)+0.0930134*(TRANSP(I)**2.) C C********************** Aug 26/1987 calibrations C C First point i s left out in calib. of the 1" orifice ( f i l e orlmet2) C C GSTD(I)=(0.397307D0+P(I,27)-0.166121D1)/60./.4536 3  Appendix  F. Computer  354  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C C  A l l the p o i n t s  used f o r the c a l i b .  of the 1" o r i f i c e  (file  orlmet)  C C**********************  used f o r a l l runs  C GSTD(I)=(0.394172D0*P(I,27)-0.162634D1)/60./.4536 C C************ Dec 21/87 c a l i b r a t i o n s t o check previos C  ones  they agree w e l l .  C C  First  point  is left  out i n c a l i b .  of the 1" o r i f i c e  (file  orl2)  (file  orll)  C C  GSTD(I)=(0.395075D0*P(I,27)-0.170554D1)/60./.4536  C C  A l l the p o i n t s  used f o r the c a l i b .  of the 1" o r i f i c e  C C  GSTD (I) = (0.390145D0*P (I,27)-0.164424D1) /60. /. 4536  C DENSAM(I)=C0RFAC*0.075*(1.+(PRES0/14.7))*293./(273.+P(I,19)) GWSAM(I)=GSTD(I)*((DENSAM(I)/0.075)**0.5) FL0WCH(I)=GWSAM(I)/(DENSAM(I)**0.5) PCHECK(I)=0.635775-12.0481*FL0WCH(I)+46.6921*(FL0WCH(I)**2.) GWMIX(I)=GWSAM(I)+GAIR YWSAM(I)=(YWMIX(I)*GWMIX(I)-YWAIR*GAIR)/GWSAM(I) YDSAM(I)=YWSAM(I)/(1.-YWSAM(I)) TGAVE(I)=(P(I,l)+P(I,7))/2. 50  CONTINUE NNR=0  11=1 IF(NRUN.Eq.l7)  11=3  1=0 DO 51 J=II,NR  1=1+1 C C*********************  f o r Run# 23  C IF(NRUN.NE.23.0R.I.LT.3) IF(I.GT.3)G0  TO 64  1=1+30 64 60  GWSAM(I)=GWSAM(I+30) SGSAM=SGSAM+GWSAM(I) NNR=NNR+1 IF(I.EQ.NR) GO TO 51  51  CONTINUE  GO TO 60  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) GSAM=SGSAM/NNR IF(NRUN.EQ.O.) C 80  GSAM=4./60./.4536  RETURN END  C c****************** C FUN * C****************** c DOUBLE PRECISION FUNCTION FUN(X) IMPLICIT REAL*8(A-H,0-Z) C0MMQN/FUN1/A C0MM0N/FUN2/B C0MM0N/FUN3/C INTEGER LIST(l)/'*'/ C FUN=A*(DABS(X)**2. )+B*X+C C RETURN END C C************************* C Function FN(X) * C************************* c DOUBLE PRECISION FUNCTION FN(X) IMPLICIT REAL*8(A-H,0-Z) C0MM0N/FN1/YY1 C0MM0N/FN2/TTG1 INTEGER LIST(l)/'*'/ CA=1884.D0 CB=1005.D0 CAL=4187.D0 CD=CA-CL CS1=CB+CA*YY1 PT=760.D0 TO=O.DO HTVAP=2502300.DO FN=((((18.D0*(DEXP(((-4986.667DO)/(X+273.DO))+2O.DO)))/(29.DO* 1(PT-(DEXP(((-4986.667D0)/(X+273.DO))+20.DO)))))-YY1)*(HTVAP+(X* 1CD)))-((TTG1-X)*CS1)  RETURN END  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued) c C function F(Z) * C********************* C DOUBLE PRECISION FUNCTION F(Z) C C Spline interpolation function. The interval found by bisection. C IMPLICIT REAL*8(A-H,0-Z) INTEGER LIST(1)/'*'/ C0MM0N/SPL1/X(301),Y(301),N,NM C0MM0N/SPL2/Q(300),R(301),S(300) 1=1 IF(Z.LT.X(1)) GO TO 30 IF(Z.GE.X(NM)) GO TO 20 J=NM 10 K=(I+J)/2 IF(Z.LT.X(K)) J=K IF(Z.GE.X(K)) I=K IF(J.EQ.I+1) GO TO 30 GO TO 10 20 I=NM 30 DX=Z-X(I) F=Y(I)+DX*(Q(I)+DX*(R(I)+DX*S(I))) RETURN END C C SUBROUTINE VISAIR * C*************************** c SUBROUTINE VISAIR(TGAVE,VISAVE) IMPLICIT REAL*8(A-H,0-Z) INTEGER LIST(1)/'*'/ DIMENSION TGF(30),VIS(30) C0MM0N/SPL1/X(301),Y(301),N,NM C0MM0N/SPL2/Q(300),R(301),S(300) DATA TGF/0.,32.,100. ,200.,300.,400.,500.,600.,700.,800.,900., 1 1000./ DATA VIS/1.11E-05,1.165E-05,1.285E-05,1.44E-05,1.610E-05, 1 1.75E-05,1.89E-05,2.E-05,2.14E-05,2.25E-05,2.36E-05,2.47E-05/ C N=12  356  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) NM=N-1 C  5  DO 5 1=1,N X(I)=TGF(I) Y(I)=VIS(I) CONTINUE  C CALL SPLINE C TG=(TGAVE*9./5.)+32. VISAVE=(F(TG))+1.488 C RETURN END C C*************************** C  SUBROUTINE VISTEM  *  C SUBROUTINE VISTEM(TGAVE.VISAVE) IMPLICIT REAL*8(A-H,0-Z) INTEGER LIST(l)/'*'/ DIMENSION TGF(30),VIS(30) C0MM0N/SPL1/X(301),Y(30l),N,NM COMM0N/SPL2/Q(30O),R(30l),S(300) DATA TGF/212.,300.,400.,500.,600.,700.,800.,900.,1000.,1200./ DATA VIS/.870E-05,1.000E-05,1.130E-05,1.265E-05,1.420E-05, 1 1.555E-05,1.700E-05,1.810E-05,1.920E-05,2.140E-05/ C N=10 NM=N-1 C  5  DO 5 1=1,N X(I)=TGF(I) Y(I)=VIS(I) CONTINUE  C CALL SPLINE C TG=(TGAVE*9./5.)+32. VISAVE=(F(TG))*1.488 C RETURN END  357  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued) c C SPLINE * C************************ c SUBROUTINE SPLINE C C C C C C C C C C  Interpolation using cubic splines with f i t t e d end points. Input:  X Y N NM  Array of independent x-values Array of dependent y-values Number of data points N-l  Output: Q,R,S Coefficients of cubic spline equations IMPLICIT REAL*8(A-H,0-Z) C0MM0N/SPL1/X(301),Y(301),N,NM C0MM0N/SPL2/q(300),R(30l),S(300) DIMENSION H(300),A(301),B(301),C(301),D(301),C0EFF(4,5)  C C C  Coefficient matrices for end point cubics  10  20 C C C  30  INTEGER FLAG DATA M/4/ IS=0 FLAG=0 MP=M+1 MM=M-1 DO 20 1=1,M II=I+IS C0EFF(I,MP)=Y(II) C0EFF(I,1)=1. DO 20 J=2,M C0EFF(I,J)=C0EFF(I,J-1)*X(II) Gauss elimination to find A4 and B4 DO 30 K=1,MM KP=K+1 DO 30 I=KP,M DO 30 J=KP,MP C0EFF(I,J)=C0EFF(I,J)-C0EFF(I,K)*C0EFF(K,J)/C0EFF(K,K) IF(FLAG.NE.O) GO TO 40  Appendix  F. Computer  Programs  Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued)  40 C C C 50 C C C  60  C C C  A4=C0EFF(M,MP)/COEFF(M,M) FLAG=1 IS=N-M GO TO 10 B4=C0EFF(M,MP)/C0EFF(M,M) Calculate H(I) DO 50 1=1,NM H(I)=X(I+1)-X(I) Coefficients  of tridiagonal  equations  A(1)=0. B(l)=-H(l) C(1)=H(1) D(l)=3.*H(l)*H(l)*A4 DO 60 1=2,NM IP=I+1 IM=I-1 A(I)=H(IM) B(I)=2.*(H(IM)+H(I)) C(I)=H(I) D(I)=3.*((Y(IP)-Y(I))/H(I)-(Y(I)-Y(IM))/H(IM)) A(N)=H(NM) B(H)=-E(HM) C(N)=0. D(N)=-3.*H(NM)*H(NM)*B4 C a l l Thomas algorithm to solve tridiagonal set CALL TDMA(A,B,C,D,R,N)  C C C  70  Determine Q(I) and S(I) DO 70 1=1,NM IP=I+1 Q(I)=(Y(IP)-Y(I))/H(I)-B(I)*(2.*R(I)+R(IP))/3. S(I)=(R(IP)-R(I))/(3.*H(I)) RETURN END  Appendix  F. Computer  Programs  Table F . l : Program to Calculate the Instantaneous Drying Rates -(Continued)  c c******************** C TDMA * C******************** c SUBROUTINE TDMA(A,B,C,D,X,N) C C Thomas algorithm C IMPLICIT REAL*8(A-H,0-Z) DIMENSION A(N),B(M),C(N),D(N),X(N),P(301),Q(301) NM=N-1 P(l)=-C(l)/B(l) Q(1)=D(1)/B(1) DO 10 1=2,N IM=I-1 DEN=A(I)*P(IM)+B(I) P(I)=-C(I)/DEN 10 Q(I)=(D(I)-A(I)*q(IM))/DEN X(N)=Q(N) DO 20 11=1,NM I=N-II 20 X(I)=P(I)*X(I+l)+q(I) RETURN END C  

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