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

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DRYING OF HOG FUEL FN A FIXED BED By ROYA SHEIKHOLESLAMI B.Sc, The University of Kansas M.A.Sc., The University of British Columbia A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E STUDIES C H E M I C A L E N G I N E E R I N G We accept this thesis as conforming to the required standard T H E UNIVERSITY O F BRITISH C O L U M B I A January 1990 © ROYA SHEIKHOLESLAMI, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of 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) Abstract Hog fuel is increasingly becoming an alternative to alleviate the energy problems associ-ated 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. The convective drying of wood-waste on the slow moving bed of hog fuel boilers was simulated in a packed bed. The 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. The 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 D ) on the drying process were investigated using a mixture of several thickness fractions having an average (sauter mean) particle thickness (dp) of 6.3 mm. 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 mois-ture content and bed depth. The effects of gas temperature, velocity and humidity have also been quantitatively established. The drying process was insensitive to CO2 content of the drying gas. The existence of an inversion temperature above which drying rates increase with hu-midity 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 ver-ified. Using a receding plane model, / was formulated as a function of $, for dp = 6.3 mm 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. The 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. The 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 Objectives of this Study 32 3 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 Drying Rate Measurements 45 3.3.1 Humidity Measurement 47 3.3.2 Mass Flow Measurement 49 3.4 Temperature and Flow Measurement • • • °0 3.5 Hog Fuel Sample Preparation : 52 3.6 Procedure for a Drying Run 58 4 Results and Discussion ' 61 4.1 General Procedures 61 4.2 Particle Size . . . 73 4.3 Bed Height : 79 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 4.7.4 A Comparison —Different Types of Drying Media 123 4.8 Characteristic Drying Curves . . 138 4.9 Pressure Drop Analysis 152 4.10 Heat Transfer During Constant Drying Rate Period 154 4.11 Industrial Implications 182 5 C o n c l u d i n g R e m a r k s 189 N o m e n c l a t u r e 195 References 207 A Sample Ca lcu la t ions 224 A.l Determination of Factors Affecting the Properties of the Fluid 224 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 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 B D r y i n g R a t e C u r v e s 254 v i 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] . 18 2.6 Movement of Free Water in Tangential Direction Due to Capillarity (Spolek 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 plate 46 3.7 Electric Diagram, of the Dew Point Sensor 48 V l l l 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 . . . . 95 4.19 Maximum Drying Rates as a Function of Temperature . 96 IX 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 . . . . 122 4.38 Maximum Drying Rate versus Temperature in Air and Steam 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 Hu-midities 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 . . 158 4.52 Adiabatic Humidification of a Gas 167 4.53 Drying in Relatively Deep Beds of Solids: (a) Humidity-Temperature Re-lationships in the Gas Phase (case A); (b) Humidity-Temperature Rela-tionships 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 The Effect of Various Parameters on the Normalized Drying Time to Reach M = 0.6 185 4.58 The Effect of Various Parameters on the Normalized Drying Time to Reach M = 0.3 186 A . l Schematic Diagrams of Gas Temperature along the Column with a Uni-form (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 Time 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 C02 239 A. 4 Maximum Drying Rates at Various Temperatures at Mass Flow of 142 kg/hr 251 B. l Parameters in the Fit of Drying Rate Curve 264 B. 2 Summary of Data Representing the Goodness of the fit 265 C. l to C.34 Summary of Data for Runs 1A to 46 267 to 330 D. l Maximum Drying Rate Data and the Confidence Intervals 332 D.2 Summary of Data on Drying Rates During the Falling Rate Period . . . 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 Program to Calculate the Instantaneous Drying Rates 341 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. x i v C h a p t e r 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 Energy % Petajoules Total Residential 1275 18.75 Commercial 850 12.5 Industrial 2210 32.5 Transportation 1700 25.0 Other 765 11.25 Total 6800 100.0 1 Chapter 1. Introduction 2 Table 1.2: End Use Industrial Energy Demand 'in Petajoules) in 1985 Pulp &; Paper Region Hog Fuel Other Total & Other Industrial Pulping Liquor Canada 402.2 344.8 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. Introduction 3 Table 1.3: Heat Contents and Typical Efficiencies of Fuels Type of Fuel Unit Heat Content Cost" Cost" Typical GJ/unit $/unit $/GJ Efficiency Heavy fuel oil (#6 Oil ) m 3 41.6 108.21 2.60 80% Light fuel oil (#2 Oil ) m 3 39.1 216.00 5.52 75% Natural gas m 3 0.037 0.10 ' 2.70 70% Steam coal mt6 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% Douglas fir bark mt dry 23.4 67% Western hemlock bark mt dry 22.7 10.00c 0.44c 66% Electricity kWh 0.0036 0.039 10.83 95% "Average reported [9] values for 1988. ^Metric tonne. cReported [11] value for 1985. 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. Introduction 4 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 comparatively-lower 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 $1701/m3 ($27/Barrel) in 1983 and also speculated 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 volume2 for hog fuel in B.C. coastal mills 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: 1 Prices are in Canadian dollars 2 200 ft3 of bulk volume = 2 m 3 of solid volume = 2 mt of wet wood based on 60% wet basis moisture content 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 experi-mental 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 Wood 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 Review 8 Induced Sustained Spontaneous ignition burning ignition 270 300 4 0 0 5 0 0 500 -D-LI6NIN (90%) •ignition (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 com-bustion 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 combus-tion 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 ad-dition 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 Chapter 2. Literature 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 Hog 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 in fluidization of 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 Review 13 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 Review 14 Fuel Drying Zone -Burn-out Arch and Burning Zone Ash Dumping Zone Ash Rake Final Burn-out Zone Figu re 2.3: A B a r e t u b e G r a t e Furnace w i t h a Reverse G r a t e , J a g e r l u n d [38] 2.3 Structure of the Wood W o o d is a hygroscopic , anisot ropic , porous bu t not very permeable m a t e r i a l w h i c h m a i n l y consists of cells made of cel lulose,hemicel lulose and l i g n i n w i t h a ho l low air space, l u m e n , ins ide t h e m (F igure 2.4). T h e cell w a l l contains microvoids h a v i n g less t h a n 2% of to t a l cell vo lume [44]. W h e n d r y w o o d is p l aced i n a s t ream of h u m i d air , water vapor molecules str ike the sol id surface, condense a n d release heat of adsorp t ion [45]. A t a relat ive vapor pressure (pa r t i a l pressure o f the water v a p o r / v a p o r pressure of the water at the d ry bu lb temperature) of 0.995 the mic rovo ids i n the cel l w a l l become comple te ly sa turated w i t h W a t e r exists as l i q u i d i n the microvoids due to format ion of hydrogen bonds between water [44]. Chapter 2. Literature Review 1 5 Gross structure of a typical hardwood. Plane T T is the cross section. R R is the radial surface, and T G is the tangential surface. The vessels or pores are indicated by P, and the elements are separated by scalariform perforation plates, S C . The fibers. F. have small caviiies and thick walls. Pits in the walls of the fibers and vessels. K. provide for the flow of liquid be-tween the cells. The wood rays are indicated at W R . A R indicates one annual ring. The early-wood (springwood) is designated S. while the latewood (summerwood) is S M . The true middle lamella is located at M L . (Courtesy of U . S . D . A . Forest Service.) Figure 2.4: Structure of a Typical Hardwood [49] 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 conden-sation 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 ef-fect. 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 Wood 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 non-hygroscopic and highly capillary porous (pore radius > l//m) materials, where moisture Chapter 2. Literature Review 18 Chapter 2. Literature Review 19 L f / / / / / / 7~r rl «W*W" G A S 4 i 7 — 7 — 7 7 , 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 cap-illaries 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 re-gion 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 pe-riod 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 Review 20 CD -t-o cn CD > CD rr R i\ / ' One-pore ! / / evapo ra t i on 1 / / i i ! j Two-pore evaporation • ! 0 A Superficial .0 moisture Relat ive fi l l ing of pores 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 Review 21 w O S z F i g u r e 2.8: Concen t r a t i on Grad ien t as a F u n c t i o n of the Dif fus ional P a t h cap i l la ry , diffusion or in t e rna l l i q u i d mass transfer. 2.5 Vapour Transport within a Drying Medium If a par t ic le of w o o d is being dr ied i n a gas, the vapour brought to the surface by dif fusional processes or evaporated at the surface w i l l diffuse th rough the mass transfer b o u n d a r y layer su r round ing the par t ic le 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 (F igu re 2.8). T h e f lux is descr ibed t h r o u g h F i c k ' s first l aw: dCw J w = -D WG' dz (2.1) where Jw = diffusional f lux ( k m o l / m 2 - s ) DWG = d iffusivi ty of water vapour t h r o u g h gas ( m 2 / s ) Cw = concentra t ion of water vapour ( k m o l / m 3 ) Chapter 2. Literature Review 22 = 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: Nw = Jw + ^ ( N W + NG) (2.2) or ^ w ~ — i — V-6' 1 _ kML 1 C where Nw = flux of mass transfer of water vapour (kmol/m 2-s) NG = flux of mass transfer of gas (kmol/m2-s) C = total molar concentration of gas stream (kmol/m 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: 1 c Substituting for Jw would yield: NW = Z ^ S L ^ L ( 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 = [£°™]]nf±zSl (2.6) 1 * J (1-Yi') V ' Chapter 2. Literature Review 23 and Nw = Mw CD WG (RM + Y1)  ln(RM + Y2) ( 2 - ? ) where 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/m2-s) Mw, MQ = molecular weights of water and gas, respectively (kg/kmol) RM = ratio of molecular weights (MW/MQ) 1,2 = represent properties at the start and end of diffusion path 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 + Y1)(Y1-Y2) yields: Nw = FMG RM RM + Yi (Yi - Y3) or KY 4, NwHFM^.Z^^-Y,) (Yi - Y2) (2.8) (2.9) therefore, Nw = KY4\Y1-Y2) (2.10) and ky = Ky-<f> (2.11) Chapter 2. Literature Review 24 where Y\ — Y2 = humidity potential 4> = humidity potential coefficient Ky = humidity independent mass transfer coefficient (kg/m2-s-( r^^™ a l e r)) ky = humidity dependent mass transfer coefficient (kg/m2-s-("^^"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: kY ~ F.MG (2.12) For more intense drying conditions, Equation 2.8 is used to express the flux of mass transfer. 2.6 D r y i n g 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. Literature Review 25 2.6.1 Diffusion Theory M a s s transfer takes place th rough molecu la r diffusion i n fluids w i t h no or very slow m o t i o n [47]. M o l e c u l a r diffusion occurs w i t h i n a phase or between phases of a sys tem where 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 reva i l . T h e d r i v i n g force for the diffusion process is the chemica l po ten t ia l , /x;, w h i c h is defined by the fo l lowing re la t ionship [56]: w = (§=r) (2-1 3) where Gj, = G i b b s func t ion (k J ) rii = kmoles of species i at any ins tant W i t h i n a phase however , the chemica l po ten t i a l gradient can be replaced b y the con-centra t ion gradient . In mul t iphase systems, concent ra t ion gradient can also be used as a measure of d r i v i n g force since i t is cus tomary to deal 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 assumed the diffusion of l i q -u i d mois tu re t h r o u g h a so l id porous m e d i u m to be a result of concent ra t ion gradient and predic ted uns teady concent ra t ion of water t h rough F i c k ' s second law of diffusion. The re was a good agreement between the exper imenta l da t a and theoret ical models b o t h when the effect of mois tu re content is incorpora ted i n the evaluat ion of diffusion coefficient, a n d at mois tu re contents be low the fibre sa tu ra t ion poin t . Chapter 2. Literature Review 26 2.6.2 Capillary Theory 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^ (2.14) where N = flux of mass transfer (kg/m 2-s) pa = density of dry wood (kg/m 3 ) Da = apparent moisture diffusivity through wet material (m 2 /s) M = moisture content (kg water/kg dry wood) x = mass transfer path (m) 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. The 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 Review 27 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: KY„ = F„MG = ^.MG (2.15) Dv = ^ (2.16) = ( | ) (2-17) where £ = diffusional path or depth of recession from surface (m) Dv = vapor diffusivity in the dried material (m 2 /s) ip = porosity of the solid ( m 3 / m 3 ) £ = tortuosity fiD = diffusion resistance coefficient ss = represent properties during subsurface evaporation By considering the additive property of mass transfer gradients within the dry pores and across the boundary layer: (Y„ - Ydb) = (Yt. - Y.) + (Y. - Ydb) (2.18) or K-<t>ss KYta.<t>as KYa.<t>. the following overall mass transfer coefficient is derived: N N N -,nins r f — (2.19) Chapter 2. Literature Review 28 where N = flux of evaporation (kg/m 2-s) Ky = humidity-independent mass transfer coefficient (kg/m2-s) 4> = humidity potential coefficient Y = dry basis absolute gas humidity K = overall mass transfer coefficient (kg/m 2-s) BIM = mass transfer Biot No., ratio of the internal resistance of dry solid 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. Literature Review 29 2.7 Characteristic Drying 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 con-densations 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 = KY.<l>.(Ytu-Ydb).f(C,Bi'M) (2.21) max KY.cf>.(Yaa-Ydb) (2.22) where N flux of evaporation (kg/m2-s) Chapter 2. Literature Review 30 Stage I Stage 2 Stage 3 Stage 4 Capillary flow Evaporation-condensation Vapour flow Drying »»-Figure 2.9: Moisture Transport in Drying a Porous Material, Keey [46] N 1 * max Ky f(C,Bi'M) c Bi' M = maximum flux of evaporation (kg/m2-s) = humidity independent mass transfer coefficient (kg/m2-s) = humidity potential coefficient = dry basis abs. humidity at adia. sat. & dry bulb temp. = relative drying rate, representing the effect of the material = relative depth of evaporative plane, where £=1 represents evaporation at the surface = mass transfer Biot No. based on solid thickness The comparison between the experimental data and Equations 2.21 and 2.22 also indi-cated that the evaporative plane remains close to the surface until 80% of the water is Chapter 2. Literature Review 31 removed [63]; therefore, suggesting that for a g iven mate r ia l , the no rma l i zed d r y i n g rate N R f = = (2.23) N iL„ 1 * max x Kjmax is a func t ion of the extent of d r y i n g or, i n other words , a character is t ic mois ture content , $ . T h i s parameter is denned for non-hygroscopic mater ia ls [64] as M $ = — (2.24) a n d , for hygroscopic bodies by : M - Me $ = T, TT 2 - 2 5 where M , MCT, and Me represent, respectively, the ins tantaneous, c r i t i ca l , a n d equ i l ib -r i u m average dry-basis mois ture content of the body . Therefore, for a ma te r i a l unchanged i n f o r m / = / ( $ ) . A plot of relat ive d r y i n g rate versus character is t ic mois ture content is ca l led the character is t ic d r y i n g curve. A s Schl i inder suggests [65], i n d u s t r i a l dryers are u s u a l l y designed based on the exper imenta l d a t a ob ta ined f rom labora tory-sca le b a t c h tests present ing the d r y i n g rate as a funct ion of mois ture content. Therefore, the design a n d s iz ing of large-scale dryers w i l l be faci l i ta ted i f a characteris t ic d r y i n g curve is ob-t a ined for a d r y i n g process. Howevever , for processes where the d r y i n g is not l i m i t e d by kinet ics and is rather e q u i l i b r i u m - l i m i t e d , such as d ry ing of disperse systems or systems w i t h very sma l l or very large mass transfer coefficients [66], this does not h o l d . 2.8 Batch Drying in a Packed Bed D u r i n g the ba tch d r y i n g process i n a packed bed , various d r y i n g zones are formed a long the b e d height (F igure 2.10(a)). T h e sol id tempera ture is increased as the d r y i n g gas travels a long the c o l u m n . T h e humid i f i ca t ion process follows as the sol id surface temper-ature, T s , approaches the wet bu lb temperature , Twb, of the d r y i n g gas. In re la t ive ly deep Chapter 2. Literature Review 32 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 < Ze, where T„ > Twb and of heating the solid or of condensation of evaporated moisture, Z > Ze, where Ts < Twb. The drying zone, Ze, passes through the column as drying proceeds (Figure 2.10(b)). 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 Ze is saturated at the prevailing temperature and pressure. However, for unsaturated drying gas at Ze, the heat conduction to the solid is taking place at the 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 under-standing 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 (dp) Chapter 2. Literature Review 33 ^ (a) z o n e o f d r y i n g u n b o u n d m o i s t u r e z o n e o f d r y i n g b o u n d m o i s t u r e h e a t c o n d u c t i o n t o t h e s o l i d Figure 2.10: Batch Drying of Thick Beds of Solids: (a) Drying Zone Resides within the Bed; (b) Drying Zone Passed through Drying Column Chapter 2. Literature Review 34 H o g fuel i n i t i a l mois ture content (M0) B e d dep th (L) D r y i n g temperature ( T ; n ) G a s ve loc i ty (Vin) G a s h u m i d i t y (Yin) CO2 content of the d r y i n g gas on the kinet ics of the d r y i n g process d u r i n g the constant and the fa l l ing rate per iods; 2. to s tudy heat a n d mass transfer processes du r ing the constant rate per iod ; 3. to examine the concept of the invers ion poin t tempera ture b o t h theore t ica l ly a n d exper imenta l ly ; 4. to invest igate the pos s ib i l i t y of the existence of b o t h a uni f ied character is t ic d r y i n g rate curve a n d a m a t h e m a t i c a l expression for / as a funct ion of $ us ing a receding p lane mode l ; 5. to evaluate for hog fuel the app l i cab i l i t y of some design equations for pressure drop i n packed beds; 6. to invest igate the effect of the above ment ioned factors on par t ic le residence t ime required for d r y i n g , a n d o n the grate heat release rate i n hog fuel boi lers . Chapter 3 Methods and Materials 3.1 Overview The 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)- The changes which occur simultane-ously in both moisture content and temperature of the wood during this process depend on the drying condition and the nature of the material. The apparatus shown in Figure 3.1 was designed to investigate the effect of different factors on the kinetics of drying process. The 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. The 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. The main items of 35 Chapter 3. Methods and Materials 36 Figure 3.1: Photograph of the Apparatus Chapter 3. Methods and Materials 37 2 <r> CO N (O m v ro w r- h- H H H H H t u a A M — M irrfjtiO -*> — — — CM I cn c o o o <D X Chapter 3. Methods and Materials 38 equipment1 are: • 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 Apparatus 3.2.1 The Burner 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 m3/hr of heated air and operates at higher than 200% excess air. Pressure taps across the nozzle provide a means for flow mea-surement. 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 Materials 40 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% C02 by volume. Therefore, it can either approximate hot air or simulate stack gases from wood-fired boilers through addition oiC02. 3.2.2 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 2 , is made of a 2 in (I.D. = 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, manufac-tured 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 Materials 42 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 ) flanged to 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 2 0 drop in pressure under the flow conditions 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 Materials 44 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. When 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. The 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. C02 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. The 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 Materials 47 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 fol-lowing 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 = ^G'{Yout-Yin) (3.2) w here -y- YmixTnmix Ydanida . out — * sam — V"""/ 3.3.1 Humidity Measurement A recent review [67] summarizes the different parameters such as Tm0, TdeW) 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 Materials 49 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 1-Octadecene (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 Materials 50 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 constan-tan (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. A l l 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 mea-surements are logged on an A T & T I B M AT compatible computer. Data acquisition takes place through 2 EXP-16 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. Methods and Materials 52 3.5 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 basis2 (1.41 kg 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)wt, of the different thicknesses, 6;, of the accepts is shown below: 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, re-spectively, of the 4mm-6mm, 6mm-8mm and 8mm-10mm particles was chosen for the majority of the runs. Using the following relationship: 1 .(*) (3.4) (kg water/kg wet wood) x 100 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 54 Figure 3.10: A Photograph of 4 - 6 mm Thick Particles 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 Drying Run 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 de-pending 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 for 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 deter-mine 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 Discussion Table 4.1: Summary of Drying Experiments* 62 WOOD DRYING MEDIUM RATE HATER RUI RUH MASS M.C. SIZE HEIGHT VOID VOID FLOW TEMP HUMID C02 Vin Vave Re Rep DEN. MAX. TIME RATIO kg d.b. ran cm in f i n l kg/hr oC d.b. '/, m/s m/s kg/cu.m 1/s s fit/me as PRE 3. 54 1. 14 23.13 .565 195.0 82.3 .0021 0.0 1.40 1. 38 18845 522 1.19 0.49 6240 PRE 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 f i r e 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 fi r e 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 fi r e 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 f i r e 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 for the legends Chapter 4. Results and Discussion 63 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{ n is the time average superficial velocity of the inlet gas. 11. V a v e is the time average superficial velocity at the mean inlet and outlet gas temperature. 12. Re and R e p are the inlet gas Reynolds numbers based on the diameter 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. Chapter 4. Results and Discussion 64 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 Range Studied Type of species Western Hemlock Bed depth" (cm) 25b (12-33) Initial wet bed weight (kg) . 3 (1.5-4.0) Particle thickness (mm) 6.3C (2-4 to 10-12) Hog fuel initial moisture content (d.b.d) 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 2 content (%Vol.) 1 (0-11.7) Inlet gas humidity6 0.02 (O-002-oo) Degrees of superheat of steam (°C) (50-125) "Measured by weight of wet sample. *Corrsponds to 3 kg of wet hog fuel. cDenotes a 40, 35 and 25 wt% mixture of, respectively, 4-6, 6-8 and 8-10 mm thick particles. dkg H20/kg dry solid. ekg H 2 0/kg dry air. 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, for 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(Ma — M)/d8) is fitted to the following expression. The fitting 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. R=dM^M}^±a^.> (4.!) 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 e) moisture contents which respectively represent the end of the constant and the falling rate periods are operating-condition dependent. MCT 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. Me is the solid moisture content when in equilibrium with the drying gas which is essentially zero for the runs; however, an approximate value of 0.02 kg Chapter 4. Results and Discussion 66 7) I O o (-1 d > O) 4-> 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 rX 0.0000CB--- 0 . 0 0 0 4 T—r T—P o E x p e r i m e n t a l F i t t e d R u n 11 -1 4 7 . 8 ° C -v,» 1 . 3 3 m / s -L 2 4 . 0 c m • M 0 1.41d.b. -dp 6.3 m m — c o 2 1.0 v o l % -0 . 0 1 3 9 d . b . -1 1 ' • • • _L 0 8 0 0 1 6 0 0 2 4 0 0 3 2 0 0 0 ( s ) 4 0 0 0 4 8 0 0 Figure 4.1: A Plot of Drying Rate versus Time Chapter 4. Results and Discussion 67 0.0022 0.0020 h 7) ' 0.0018 O O £ 0.0016 £ 0.0014 0.0012 0.0010 h OS £ 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 water/kg dry wood) Figure 4.2: A Plot of Rate versus Moisture Content Chapter 4. Results and Discussion 68 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, Rmax] thus, showing that 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 H20/kg 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 ( Fig-ure 4.2 ) is calculated at four different moisture content values ranging from 0.3 to 0.6 with an increment of 0.1 kg H20/kg 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. Results and Discussion 69 0 600 1200 1800 2400 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 Discussion 70 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) and abscissa is the characteristic moisture content, $ = (M - Me)/(Mcr - Me). 7. The modified friction factor, f m f , proposed by Leva [76] and represented by Equa-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 voidage-sphericity relationship of Brown [78]. = Vmle>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 possi-bility 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% accurate (see Appendix A, Page 229 for more details). 10. A check of the reproducability of the data has been made through several replicate runs. The sample, an, and the sample estimate of the population, crn_1, standard 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, See, and the corresponding relative deviations, See, are determined using the "Student's er 4. Results and Discussion 72 t test". The results indicate that the average value of, 6ee, is within ±7% for the 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, crp, are included in 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 j N2 2 , / 9 u J 2 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 AP(U) = 1A(TP(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 (6P). The same procedure is used to determine the deviations on the rate, within a 95% confidence band, during the falling rate period. According to Equation 4.6, p^(w) = l-4<^ p(fl) would, with 95% confidence, determine the error on the slope. The sum of square of residuals, SR = ^ (RE ~ Rp)2, shown in Table B.2, represents pure experimental error, SEE, p l u s the error associated with the lack of fit, SL, [75] Chapter 4. Results and Discussion 73 as shown by: SR = SEE + SL (4.7) The mean square of pure experimental errors, o" 2 e e , can be approximated from a number of genuine replicate runs. A comparison between <r2ee and mean square of residuals, o~2r, can be used to approximate the lack of fit [75]. 12. In a linear fit of the form: Yi = a + b(Xi - x) ' (4.8) the variance of predicted (fitted) value, crp2, is calculated [74] through mean square of the residuals, crr2 via Equation 4.9: 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 = SR l + —^Fa,(p,n-p) n — p (4.10) where Fai(p,n — p) is the significance point of F-distribution with p and n — p degrees of freedom. 4.2 Particle Size The 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 Repl ReP2 Rep 0~n-l 8ee% 11&20 1.09 1.04 1.07- 0.03 0.04 0.04 0.08 7 •^"max 31&32 1.34 1.46 1.40 0.06 0.08 0.06 0.15 11 xlO 3 41&44 1.56 1.65 1.61 0.05 0.06 0.04 0.12 7 is'1) 45&46 1.37 1.41 1.39 0.02 0.03 0.02 0.06 4 Average 0.04 0.05 0.04 10 7 11&20 1.15 1.02 1.09 0.07 0.09 0.08 0.18 15 31&32 1.30 1.36 1.33 0.03 0.04 0.03 0.08 6 xlO 3 41&44 1.57 1.41 1.49 0.08 0.11 0.07 0.21 14 45&46 1.35 1.42 1.38 0.03 0.05 0.04 0.10 7 Average 0.05 0.07 0.06 0.14 11 Table 4.3: Summary of Runs with Varying Partic Run La T-•*- in v in dp •^max Sp x 103 s"1 cm °C m/s mm xlO 3 s-1 xlO 3 s-1 Rmax Rfall 15 24.5 151.2 1.34 10-12 0.84 0.89 0.03 0.02 18 25.3 153.9 1.37 8-10 1.00 1.21 0.03 0.02 16 24.1 152.0 1.35 6-8 0.98 0.89 0.03 0.02 14 26.9 150.7 1.35 4-6 1.05 1.29 0.03 0.02 17 30.2 148.5 1.33 2-4 1.18 1.31 0.03 0.03 Size "Weight of wet hog fuel = 3 kg. Chapter 4. Results and Discussion 75 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 - 3 s _ 1 to 1.18 xl0~ 3 s _ 1 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 10~2 - 0.1976 x l O " 3 ^ 0 4 8 (4.11) where dp is the particle size in mm and Rmax is the maximum drying rate in s _ 1. 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 Discussion 76 0 . 0 0 2 2 0 . 0 0 2 0 I 0 . 0 0 1 8 o % 0 . 0 0 1 6 £ 0 . 0 0 1 4 X 0 . 0 0 1 2 d l> 0 . 0 0 1 0 0 . 0 0 0 8 0 . 0 0 0 6 N — ' 0 . 0 0 0 4 0 . 0 0 0 2 0 . 0 0 0 0 0 6 0 0 1 2 0 0 1 8 0 0 2 4 0 0 3 0 0 0 3 6 0 0 4 2 0 0 4 8 0 0 e ( s ) Figure 4.5: Drying Rates versus Time for Various Particle Sizes Chapter 4. Results a,nd Discussion 77 0.0014 I O O 0 . 0 0 1 3 0 . 0 0 1 2 T3 0 . 0 0 1 1 CD 0 . 0 0 1 0 £ 0.0009 0.0008 0.0007 0.0006 T - T 0 I I I T i n = 1 5 1 ° C T — T I I I I I" i n 1 . 3 5 m / s O o o ' 1 4 6 8 dp (mm) 1 0 1 2 Figure 4.6: Maximum Drying Rate versus Particle Thickness Chapter 4. Results and Discussion 78 O O \ CD 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1 1 1-1 • 1 . • R u n dp : m m - — — — 17 14 2 - 4 4 - 6 - — 16 6 - 8 Y — • — 18 8 - 1 0 " • V 15 1 0 - 1 2 : \ V * \\\\ - Vs. W \ x\ -\ ; \ \ --0 600 1200 1800 2400 3000 3600 4 2 0 0 4 8 0 0 6 ( s ) Figure 4.7: Moisture Content versus Time for Various Particle Sizes Chapter 4. Results and Discussion 79 Due 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 Discussion 80 0.0022 0.0020 en ' 0.0018 O O £ 0.0016 £ 0.0014 Cut) > 0.0012 0.0010 £ 0.0008 £ 0.0006 GO 0.0004 0.0002 0.0000 I I I I I I I I ' ' ' i i i I i i i Run d p m m 17 2 - 4 14 4 - 6 16 6 - 8 18 8 - 10 15 10 - 12 I I I I I 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M (kg water/kg dry wood) 1.6 Figure 4.8: Drying Rates versus Moisture Content for Various particle sizes Cha.pter 4. Results and Discussion 81 0 . 0 0 2 2 0 . 0 0 2 0 i i i i i i i j i i 1 J i l i | I l i i l l I l l i Run 1 0 9 1 1 & 2 0 1 3 0 . 0 0 0 0 L c m 12 16 2 5 3 3 1 1 1 1 1 0 6 0 0 1 2 0 0 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 4.9: Drying Rate versus Time for Various Bed Depths Chapter 4. Results and Discussion 82 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 1.75x10~3 s - 1 to 0.97x10~3 s _ 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 = + 0.85 x IO"3 (4.12) where Rmax is in s _ 1 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 Discussion 83 0.0022 0.0020 ' 0.0018 O O £ 0.0016 £ 0.0014 0.0012 o . o o i o > £ 0.0008 rt £ 0.0006 CK) 0.0004 0.0002 0.0000 Run 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 M (kg water/kg dry wood) Figure 4.10: Drying Rate versus Moisture Content for Various Bed Depths Chapter 4. Results and Discussion 84 2.0 1.8 o o £ 1.4 1.2 1.0 X CD "£ 0.8 S 0.4 0.2 0.0 R u n L ' ' ' ' . • c m 10 12 9 16 -11&20 25 k — 13 33 -\> \ » \ \ - \\ \\ \ --S J = J r.i . l 1 , , , " 0 600 1200 1800 2400 3000 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 and Discussion 85 Table 4.4: Summary of Runs with Varying Bed Height Run W L dp T-J- in vin Rmax Sp x 103 s"1 kg cm mm °C m/s xlO 3 s-1 xlO 3 s-1 Rfall 10 1.50 12.3 6.3 158.1 1.36 1.75 1.62 0.12 0.06 9 2.00 16.1 6.3 154.8 1.34 1.37 1.28 0.07 0.03 ll&20 a 3.00 25.2 6.3 150.9 1.35 1.07 1.09 0.02 0.01 13 4.00 33.0 6.3 158.5 1.35 0.97 0.88 0.07 0.03 18 3.00 25.3 8-10 153.9 1.37 1.00 1.21 0.03 0.02 1 4.18 32.3 8-10 151.8 1.37 0.74 1.19 0.04 0.03 38 1.50 12.1 6.3 250.8 0.86 2.42 2.81 0.20 0.13 43 3.00 22.9 6.3 245.7 0.82 1.76 1.71 0.06 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 Discussion 86 0 .0022 ^ 0 .0020 O £ 0 .0018 T3 0 .0016 > 0 . 0 0 1 4 M 0) £ 0 .0012 Qi) 0.0010 (3 0.0008 0 .0006 1 1 i i i i i i i i i i i T i n = 156 ° C V i n = 1.35 m / s i i | i i i . . . i i i i j . • • 1 10 14 18 22 26 30 34 L ( c m ) Figure 4.12: Maximum Drying Rate versus the Bed Depth Chapter 4. Results and Discussion 87 Table 4.5: Summary of Runs with Varying Hog Fuel Initial Moisture Content Run W *' ws wda L T- M0 UJ x 103 Sp x 103 s-1 kg kg cm °C m/s d.b. xlO 3 s-1 s"1 Rmax Rfall 31&32 3.00 1.03 20.17 155.3 1.32 1.92 1.38 1.44 0.12 0.07 11&20 3.00 1.24 25.21 150.9 1.35 1.41 1.07 1.09 0.02 0.01 11A&20A0 2.48 1.03 20.17 155.0 1.32 1.41 1.18 9 2.00 0.83 16.11 154.8 1.34 1.41 1.37 1.17 0.07 0.03 a A = adjusted data. 4.4 Hog 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 and Discussion 88 0.0022 0.0020 cn 1 0.0018 TJ O O £ 0.0016 >> f-i TJ 0.0014 0.0012 ft 0.0010 CD <D 0.0008 «S 0.0006 0.0004 tt 0.0002 0.0000 1 1 1 I i i i j i r i j i i i i • ' • i 1 • • i i i r R u n Mo wW 8 L d.b. kg cm 31&32 1.92 3.0 20 9 1.41 2.0 16 11&20 1.41 3.0 25 T 1 r T -L • 1 1 1 1 • 1 0 600 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 R u n — 31&32 9 11&20 i i i i i i i I i i i Mo W w a L d.b. kg cm 1.92 3.0 20 1.41 2.0 16 1.41 3.0 25 _I_J_ 0 600 1200 1800 2400 3000 360042004800 6 ( s ) Figure 4.14: Moisture Contents versus Time for Various Initial Moisture Contents Chapter 4. Results and Discussion 90 Table 4.6: Summary of Runs with Varying Temperature Run T-in vin y. 1 in Rmax LO 8P x 103 s-1 °C m/s dry basis xlO 3 s-1 xlO 3 s-1 •^max Rfall 22a 220.7 1.41 .0205 1.41 0.03 0.03 19 204.8 1.39 .0210 1.25 1.32 0.02 0.01 11&20 150.9 1.35 .0142 1.07 1.09 0.02 0.01 12 126.3 1.37 .0261 1.02 0.99 0.03 0.01 "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 Drying 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 and Discussion 91 I T J 0 O o * 0 !>> u 0 em ft * 0 (> 0.0022 0.0020 .0018 .0016 .0014 .0012 .0010 0 fn 0.0008 £ 0.0006 0.0004 Ph 0.0002 0.0000 i i i i • • • i • • • I ' 1 1 I i i i i i i i i i i i i i i R u n Mo wW8 L d . b . k g c m 31&32 1.92 3.0 20 9 1.41 2.0 16 11&20 1.41 3.0 25 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 M (kg water/kg dry wood) Figure 4.15: Drying Rates versus Moisture Content for Various Initial Moisture Contents Chapter 4. Results and Discussion 92 0 . 0 0 2 2 0 6 0 0 1 2 0 0 1 8 0 0 2 4 0 0 3 0 0 0 3 6 0 0 4 2 0 0 4 8 0 0 e ( s ) Figure 4.16: Drying Rates versus Time at Different Temperatures Chapter 4. Results and Discussion 93 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: Rmax = -0.314 x 10~3 + 0.135 x 10~4T - 0.272 x 10"7T2 (4.13) where T is in °C and R m a x is in s - 1. 4.6 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 4. Results and Discussion 94 2.0 1.8 • • • i i i i I i i i I I 1 1 1 I 1 1 1 1 1 1 1 I T T R u n 22 19 11&20 12 I i i i I i i ° c 221 205 151 126 600 1200 1800 2400 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 and Discussion 95 0.0022 0 to *° o o £ 0 >> £ 0 0020 0018 0016 0014 0 0.0012 0.0010 ^ 0 a> • • 0. I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I tt 0 0 0.0000 Run 22 19 11&20 12 T i n °C 221 205 151 126 i i i I i t t 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M (kg water/kg dry wood) 1.6 Figure 4.18: Drying Rates versus Moisture Content at Different Temperatures Chapter 4. Results and Discussion 96 0.0028 c/> I 0.0024 o o 0.0020 0.0016 £ 0.0012 ^ 0 . 0 0 0 8 60.0004 0.0000 I I I I I p Y v. i n 111.7 k P a 0.0204 (d.b.) 1.35 m / s t i r I I I i i i i i t I i i 20 60 100 140 180 220 260 T (°c) Figure 4.19: Maximum Drying Rates as a Function of Temperature Chapter 4. Results and Discussion 97 0 . 0 0 2 2 0 . 0 0 2 0 7) I 0 . 0 0 1 8 •a o £ 0 . 0 0 1 6 £ 0 . 0 0 1 4 0 . 0 0 1 2 R u n v i n T l n — m / s °C 8 1 .84 2 0 4 19 1 .39 2 0 5 -4 1 .77 1 5 6 -1 1 & 2 0 1 .35 151 -1 1 1 1 1 1 1 1 • • r - i - -L i i i I i i 0 6 0 0 1 2 0 0 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 4.20: Drying Rates versus Time at Different Mass Flow Rates Chapter 4. Results and Discussion 98 Table 4.7: Summary of Runs at Different Velocities Run m T-in vin Reo ^max UJ 8V x 103 s-1 kg/hr °C m/s xlO 3 s-1 xlO 3 s-1 Rmax Rfall 11&20 141.9 150.9 1.35 10276 1.07 1.09 0.02 0.01 4 183.3 155.7 1.77 13163 1.37 1.45 0.04 0.03 3 140.4 241.3 1.57 8894 1.81 2.46 0.09 0.07 19 126.8 204.8 1.39 8471 1.25 1.32 0.02 0.01 8 175.5 204.0 1.84 11749 1.46 1.84 0.08 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 Discussion 99 I ' ' ' I ' ' ' Run vin T,„ — m / s °C • 3 1.57 241 4 1.77 156 -11&20 1.35 151 -• • T l l l • • • • I I I ! 0 600 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 Discussion 100 (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 The Nature of the Drying Medium 4.7.1 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 T J 1.6 o o £ 1.4 ?-> u TJ 1.2 1.0 CD 0.8 j*>0.6 S 0.4 0.2 0.0 1 R u n | i i r T - n v i n m / s T i n °C 1 3 1.57 241 -4 1.77 156 -11&20 1.35 151 -\ - \w ' Y\ j • U \w - v\ -\ ^ • V > X : \lA \ * N : \W \ \ \ \ \ \ --1 I \~~\~T~£LL • l • i- l l i 1 I I i 0 600 1200 1800 2400 3000 3600 4 2 0 0 4 8 0 0 e ( s ) Figure 4.22: Moisture Contents versus Time at Various Velocities Chapter 4. Results and Discussion 102 2.0 1.8 h 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 1 1 1 1 I 1 1 1 1.6 o o £ 1.4 -d 1.2 1.0 CD "£ 0.8 ^ 0 . 6 S 0.4 0.2 0.0 Run 8 19 ' i n m / s 1.84 1.39 ° c 204 205 • • 1 1 1 1 1 1 • 1 1 1 I • • • I 0 600 1200 1800 2400 3000 360042004800 0 ( s ) Figure 4.23: Moisture Contents versus Time at Various flow rates Chapter 4. Results and Discussion 103 0.0022 0.0020 ' 0.0018 o o £ 0.0016 >> £ 0.0014 b0 CD 0.0012 0.0010 £ 0.0008 - t- j rt £ 0.0006 0.0004 0.0002 0.0000 0 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 3 4 // 11&20 / i i i • m / s °C 1.57 241 1.77 156 1.35 . . i , 151 . , i . 1.0 1.2 _1 I 1_ 1.6 M (kg water/kg dry wood) Figure 4.24: Drying Rates versus Moisture Contents at Various Velocities Chapter 4. Results and Discussion 104 0.0022 0.0020 00 ' 0.0018 O O £ 0.0016 £ 0.0014 1 Run vin Tin -- m / s °c -- 8 1.84 204 -- 19 1.39 205 -CD 0.0012 0.0010 £ 0.0008 £ 0.0006 0.0004 tt 0.0002 0.0000 i i i I I I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M (kg water/kg dry wood) 1.6 Figure 4.25: Drying Rates versus Moisture Contents at Various Flow Rates 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: {CsH120B)n + 8.5n02 + Z2nN2 —• SnC02 + QnH20 + Z2nN2 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: CH4 + 20 2 + 7.5iV2 —> C02 + 2H20 + 7.5N2. 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 C02 content. The effect of humidity of the drying medium on the rate of drying will be separately investigated. C02 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 4.26. A comparison between Runs 34 and 36 indicates that the C02 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 Discussion 106 Table 4.8: Composition of Combustion Gases for Wood Material and Natural gas Volumetric Concentration (%) Component Stoichiometric Wood N.G. Wood N.G. 50% Excess 400% Excess C02 17 10 12 2 H20 13 19 9 4 N2 70 71 72.5 77 o2 0 0 6.5 16 Table 4.9: Summary of Runs with Varying C02 Content Run m T--1- in vin Rev Y co2 •^max LO X 103 8V x 103 s" 1 kg/hr °C m/s d.b. vol% xlO 3 s-1 s-1 Rmax Rfall 34 145.8 146.2 1.25 10643 0.0130 11.7 1.23 1.01 0.02 0.01 36 144.1 148.2 1.32 10500 0.0114 6.1 1.25 1.11 0.02 0.01 11&20 141.9 150.9 1.35 10276 0.0142 1.0 1.07 1.09 0.02 0.01 Chapter 4. Results and Discussion 107 gradual and the maximum drying rate is lower in case of Run 11&20. The 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 C02 volumetric concentration (see Table 4-17, Page 177 ). The difference in the Reynolds numbers accounts only for 1.5% and 2.5% for, respectively, a 6-fold and a 12-fold rise in C02 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 4.27. 4.7.2 Superheated Steam The drying process was also studied at various temperatures with superheated steam at 215 kPa absolute pressure. Due to limitations in the steam supply, the experiments were Chapter 4. Results and Discussion 108 0.0022 0.0020 CO I 0.0018 O £ 0.0016 ->> £ 0.0014 c m 0.0012 i • • 1 i 1 1 ' Run 34 36 11&20 ft C0 2 vol% 11.7 6.1 1.0 0 600 1200 1800 2400 3000 3600 4200 4800 ^ ( s ) Figure 4.26: Drying Rates versus Time for Various CQ2 Concentrations Chapter 4. Results and Discussion 109 0 . 0 0 2 2 0 . 0 0 2 0 GO T T 'I 1 1 1 I I I I I I I I I I i I I I I I ' ' ' I ' 0 . 0 0 1 8 TJ O O £ 0 . 0 0 1 6 £ 0 . 0 0 1 4 0 . 0 0 1 2 ft £ 0 . 0 0 1 0 CD £ 0 . 0 0 0 8 4-> cd £ 0 . 0 0 0 6 w tt 0 . 0 0 0 4 0 . 0 0 0 2 0 . 0 0 0 0 0 Run 3 4 3 6 1 1 & 2 0 C02 vol% 11 .7 6.1 1.0 i i i 1 i i t I i i t 1 i * i .0 0 .2 0 .4 0 .6 0 . 8 1.0 1.2 1.4 M (kg water/kg dry wood) 1.6 Figure 4.27: Drying Rates versus Moisture Content for Various CO2 Concentrations Chapter 4. Results and Discussion 110 Table 4.10: Summary of Superheated Steam Drying Runs Run W Tin vin Mcr Rmax LU 8P x 103 s- 1 kg °C m/s d.b. x l O 3 s- 1 x l O 3 s-1 Rmax Rfall 39 3.00 170.9 0.79 0.82 0.930 1.50 0.04 0.04 42 3.00 189.5 0.81 1.19 0.996 0.85 0.10 0.04 45 3.00 206.9 0.82 1.01 1.370 1.35 0.05 0.03 46 3.00 204.7 0.82 1.11 1.410 1.42 0.09 0.04 45&46 3.00 205.8 0.82 1.06 1.390 1.39 0.07 0.04 41 3.00 220.5 0.80 1.08 1.560 1.57 0.10 0.05 44 3.00 221.3 0.81 1.11 1.650 1.37 0.10 0.04 41&44 3.00 220.9 0.81 1.10 1.610 1.47 0.10 0.05 43 3.00 245.7 0.82 1.08 1.730 1.71 0.06 0.04 38 1.50 250.8 0.86 1.00 2.420 2.81 0.20 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; n < 190°C and remains approximately independent of temperature for T; n > 190° C. These relationships are indicative of a change in the drying behaviour at 171 < T; n < 190°C which will be discussed in detail. Chapter 4. Results and Discussion 111 0 6 0 0 1 2 0 0 1 8 0 0 2 4 0 0 3 0 0 0 3 6 0 0 4 2 0 0 4 8 0 0 e (s ) Figure 4.28: Superheated Steam Drying Rate versus Time at Various Temperatures Chapter 4. Results a.nd Discussion 112 2.0 1.8 O o £ 1.4 73 1.2 1.0 X CJ 0.8 *>0.6 S 0.4 0.2 0.0 '_ R u n I i | . I . | T i n - °C -43 246 -41&44 221 -45&46 206 -\. 4 2 190 -\ 39 171 -vv -• \ \ \ \ - \ v -: \\\ \\\v -: \\\ v _ • \\\ v -1 \\\ v\ W V. : \ \ \ v \\\ X -\ \ \ \ -0 600 1200 180024003000360042004800 0 ( s ) Figure 4.29: Moisture Content versus Time for Superheated Steam Drying Chapter 4. Results and Discussion 113 0,0022 0.0020 CtO ' 0.0018 O O £ 0.0016 £ 0.0014 ox rt 0.0012 0.0010 £ 0.0008 rt £ 0.0006 0.0004 0.0002 0.0000 0 i i i i I i i i i i i i r i [ i I i I i f i i i i i [ i r i R u n °c 43 246 41&44 221 45&46 206 42 190 39 171 I I I I .0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M (kg water/kg dry wood) 1.6 Figure 4.30: Drying Rate versus Moisture Content for Superheated Steam Drying Chapter 4. Results and Discussion 114 Within the range investigated, the experimental data were related to the temperature using the following quadratic expression: Rno* = -0.35 x 10~2 + 0.35 x 10"4T - 0.56 x 10~ 7r 2 (4.14) where T is in °C and Rmax is in s~x. Figure 4.31 is a plot of maximum drying rate versus 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 Air 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 (Rmax oc V-0-71) and for both temperature and bed height using Equations 4.13 and 4.12. The results Chapter 4. Results and Discussion 115 0.0028 C7) I O O 0.0024 0.0020 0.0016 •2 0.0012 CO ^ 0.0008 gO.0004 tt 0.0000 T I 1 1 1 1 I I P = 215 kPa V i n = 0.82 m/s 1 I 1 T—r 1 • 1 • 1 1 80, 120. 160. 200. 240. T ( °C) 280. 320, Figure 4.31: Maximum Drying Rate versus Temperature for Superheated Steam Drying Chapter 4. Results and Discussion 116 0 . 0 0 2 2 i i i I i i i I 0 . 0 0 2 0 - Run 3 0 2 3 2 9 19 Y,„ d.b. 0 . 2 8 5 6 0 . 1 4 2 2 0 . 1 3 4 7 0 . 0 2 1 0 0 . 0 0 0 0 I I I I I I I • ! I I I 1 , 1 , 0 6 0 0 1 2 0 0 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 4.32: Drying Rate versus Time at Different Air Humidities Chapter 4. Results and Discussion 117 I • d o o £ u M \ d rt > U 0) +J rt 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 PH O.OOOO< -0.0004 i i i O Experimental Fitted Run 23 -Ti„ 196.5°C -V l n 1.32m/s — L 26.8cm • M 0 1.41d.b. -dp 6.3 mm — co2 1.5 vol% -Y l n 0.1422d.b. -J I 1_ 1 1 1 I I I I I 0 400 800 1200 1600 0 (a) 2000 2400 Figure 4.33: Drying Rate versus Time for Run 23 Chapter 4. Results and Discussion n g 0.0028 0.0024 CO 1 •a O 0.0020 O £ >> Ft 0.0016 T J • 0.0012 rt > CD 0.0008 CO +J rt 0.0004 w tt 0.0000 -0.0004 i i r I I I O Experimental Fitted o 6 > o o ° rP ° o ° Run 29 -202.2°C -V l n 1.36m/s -L 25.0cm -M 0 1.41d.b. -dp 6.3 mm — C0 2 1.5 vol% -Y i n 0.1347d.b. -I I I I I I 1 ' 1 0 400 800 1200 1600 2000 2400 e (s) Figure 4.34: Drying Rate versus Time for Run 29 Chapter 4. Results and Discussion 119 Table 4.11: Effect of Gas Humidity Run3 Y Y-i T-- 1 in vin Rmax w x 103 Sp x 103 s-1 d.b. kg/kg °c m/s xlO 3 s-1 s-1 Rmax Rfall 19 .0210 47.6 205. 1.39 1.25 1.32 0.02 0.01 26A .0450 22.2 202. 1.35 1.32 23 .1422 7.03 197. 1.32 1.41 1.09 0.05 0.05 29 .1347 7.42 202. 1.36 1.25 0.99 0.14 0.11 30 .2856 3.50 202. 1.39 1.66 1.77 0.21 0.15 45A&46A oo 0.00 206. 1.35 2.01 a 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: i C o x = 0.741 x ' l 0 ~ 3 e - ° - 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 and Discussion 120 0.0024 I O o 0.0022 0020^ 0018 CD 0.0016 ^ 0 0 0014 0012 0.0010 I I I I I I I I 1 1 1 - i i i i i r T i n = 202 i n = 1.35 m / s Run 29 excluded Run 29 included _ i i i _ • 1 1 _ i i i i i _ i i i i i 0 10 20 30 40 50 60 l / Y (kg d r y a i r / k g water) Figure 4.35: Maximum Drying Rate versus Inverse of Absolute Humidity Chapter 4. Results and Discussion 121 2.0 1.8 h T3 1*6 o o £ 1.4 >> •a 1.2 <aj) 1.0 CD rt 0.8 Sf0.6 S 0.4 0.2 0.0 1 1 1 1 1 1 1 Run Y i n - d.b. -- 30 0.2856 -- 23 0.1422 -- 19 0.0210 -: \\ — V \ -1 1 : \\ - \ -: \ -4 V \ V ' . . . i . . . <\ \ \ \ X i i i 1 i i i 1 0 600 1200 1800 2400 3000 360042004800 e ( s ) Figure 4.36: Moisture Content versus Time at Different Air Humidities Chapter 4. Results arid Discussion 122 0 .0022 0 .0020 -' 0 .0018 O O £ 0 .0016 £ 0 .0014 ox rt > CD 0 .0012 -0 .0010 -£ 0 .0008 £ 0 .0006 -ax tt 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 water/kg dry wood) Figure 4.37: Drying Rate versus Moisture Content at Different Air Humidities Chapter 4. Results and Discussion 123 4.7.4 A Comparison —Different Types of Drying Media Under the conditions investigated, the C02 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 evapo-ration 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 2hr). As the plot shows, the 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 2hr and it was suggested, "further investigation of the inversion point is necessary to make clear theoretically the reasons Chapter 4. Results and Discussion 124 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 Tdb and some partial pressure of water vapour pdb with a fully wetted surface of a wood particle at temperature Taa. Equation 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 (Tdb — Taa) in addition to a drop in concentration gradient (Yaa — Ydb) and hence, it is believed, to lower the rate of evaporation at a given temperature. QevaP = ma(Has - Hdb) = maCs(Tdb - Taa) (4.16) P t ~ 1 + Y ~ l + Y ( 4 - i 7 j H = cPa(T - TTef) + Y[XTef + cPvap(T - Tref)} (4.18) where Qevap = heat flow for evaporation (W) ma = 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) cp = specific heat (J/kg.K) Chapter 4. Results and Discussion 125 0.0032 0.0028 to i 0.0024 o o ^0.0020 +-> SU) 0.0016 h 0.0012 h 0.0008 0.0004 h 0.0000 1 • > • | i i i | i i Mass velocity = 142 kg/hr A Air at 111.7 kPa & Y = 0.0204 d.b. . - O Steam at 215 kPa — — 0/ '. -- [or < - 1 - 1 S 1 ^ £ -— S / * I — -• S 1 -• / • / V / S / 1 20 60 100 140 180 T (°C) 220 260 Figure 4.38: Maximum Drying Rate versus Temperature in Air and Steam Chapter 4. Results and Discussion 126 cPt = 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 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: < f K = u ^ r f o r 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{Tdb-Ta8) = {Ya3-Ydb)\a, (4.21) Chapter 4. Results and Discussion 127 -4986.667 h IV. = 7p + 24.9 (4.23) as Ks = cPvap (Tas - Tref) + \ r e f - CL(Tas - Tref) (4.24) where Y = dry basis gas humidity (kg water/kg mixture) T = temperature (K) A = latent heat of vaporization (J/kg) \ref = latent heat of vaporization at Tref = 0°C (J/kg) pt = total pressure (Pa) pv = vapour pressure (Pa) CL = specific heat of vapour component (H20) in the liquid state (Pa) db,as = represent properties at dry bulb & adia. sat. temp. 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 Tas 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 H20/kg dry gas) at Taa. Assuming vt <C vg, for an ideal gas the slope of the vapour pressure curve is related to the latent heat of evaporation [56] through: dT ~ RgT2 Integration of Equation 4.25 over a short temperature range, where A can be considered constant [47], yields lnp„ as a linear function of ^: lnP* = - ^ f + B (4-26) Chapter 4. Results and Discussion 128 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 pVaa 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 Tat and given by Equation 4.24. There-fore, simultaneous solution of Equations 4.21 to 4.24 provides Tas as a function of both Tdb and Ydb for 20°C < Ta8 < 100°C. The results are plotted in Figure 4.39, as adiabatic saturation temperature versus humid-ity for various inlet temperatures. As is shown, the saturation temperature rises asymp-totically 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 and Discussion 129 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1.0 Y ' (kg w a t e r / k g m i x t u r e ) Fi gure 4.39: Adiabatic Saturation Temperature as a Function of Humidity at Various temperatures Chapter 4. Results a.nd Discussion 1 3 0 20 60 100 140 180 2 2 0 T ( °C) Figure 4.40: Maximum Change in Gas Enthalpy versus Temperaure at Different Humidi-ties Chapter 4. Results and Discussion 131 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: cPtt(T-Tb) = cPt(T-Tas) (4.27) where Tb = boiling point of water at system pressure (°C or K) cp = specific heat at mean inlet and outlet temperatures (J/kg.K) 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 and Discussion 132 200 T i r i i r T \ i r 180 P = 1 atm. Constant mass velocity - Locus of invers ion point 160 \ u o 140 120 1 100 80 _1 I L_ ' 1 1 0.0 0.2 0.4 0.6 0.8 Y 7 (kg w a t e r / k g m i x t u r e ) 1.0 Figure 4.41: Locus of Inversion Point versus Humidity Chapter 4. Results and Discussion 133 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"^wVT+{^Vp (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 P is the specific heat at constant pressure and (H) ("I) 8T M = £ - ) (4-32) OP H is defined as Joule-Thomson coefficient. Thus, Equation 4.28 becomes: dH = CpdT — pcpdp (4.33) 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 H2, Ne and He- at normal 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 134 Figure 4.42: Mean Specific Heat of the Mixture versus Humidity Chapter 4. Results and Discussion 135 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 P=Pvap+Pa (4.34) into Equation 4.32 and rearranging would result in: ~u ~ ~dT~ H ~dT 6 ( 4 ' 3 5 ) or - = (-) +(-) (4-36) /* V- vap V- a It is obvious that fivap 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 Discussion 136 is supposed to decrease as either the concentration or the vapour pressure gradient de-creases. 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 rep-resented by the following relationship: N = kY(Ya8-Ydb) (4.37) where N = flux of evaporation (kg/m2-s) ky = humidity dependent mass transfer coefficient (kg/m2-s) Ydbi Yas = 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 (Yas — Ydb). Figure 4.43 shows that the 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 and Discussion 137 1.0 0.8 0.6 0 . 4 0.2 0.0 -0.2 i i i i i P = 1 atm. Inlet Temperature: 100 °C 180 220 260 C C C C i i i i 0.0 0.2 0.4 0.6 0.8 1.0 Ydb (kg w a t e r / k g m i x t u r e ) Figure 4.43: Concentration Gradient versus Humidity at Various Temperatures Chapter 4. Results and Discussion 138 4.8 Characteristic Drying 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 non-hygroscopic materials during the subsurface evaporation using the following equation: / = N K-K-{YS3-Ydb) ^U(Tdb-T3S)Xas Nmax KYag-(f}3(Yas — Ydb) h(Tdb — Tas) \SB where / = relative drying rate N — flux of evaporation (kg/m2-s) Nmax = maximum flux of evaporation (kg/m2-s) Ky = humidity independent mass transfer coefficient (kg/m2-s) 4> = humidity potential coefficient Y = dry basis absolute gas humidity K, = overall mass transfer coefficient (kg/m2-s) T = temperature (K) h = convective heat transfer coefficient (W/m2-K) U = overall heat transfer coefficient (W/m2-K) A = latent heat of evaporation (kJ/kg) ss = represents properties at the subsurface temperatures as, db = depict, respectively, the adia. sat. and dry bulb temperatures Chapter 4. Results and Discussion 1 3 9 Incorporating heat and mass transfer Biot numbers: B i H = j- = Bi'H^ = X 5 * ' H ( 4 . 3 9 ) B i M = ^ = = X # * ' M ( 4 - 4 ° ) and with the help of some manipulations, he has obtained: / = , • \ ; ( 4 - 4 1 ) 1 + JXBI'M where £ = 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 = 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 = BiH/BiM 7 = evaporative resistance coefficient (8 — a)/(l — a) 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 Discussion 140 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 = ^ ™ - (4.42) where / = relative intensity of drying N° — initial mass transfer flux (kg/m2-s) Chapter 4. Results and Discussion 141 p„ = density of dried solid material (kg/m3) M0 = initial dry basis moisture content of solid Da = apparent moisture diffusivity (m2/s) 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 sub-jected 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: Iz = Iinexp(-Kz) (4.43) where Iz = local drying intensity at position z Iin = drying intensity at the bed inlet Nz = 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 Discussion 142 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 TZ (4.44) * a * in where the term in the denominator represents the humidity gradient at the bed inlet and Yim 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 1.25 1.00 <M 0.75 0.50 0.25 0.00 T — l — — l — l — l r 1 Run L cm - 10 12 - 9 16 - 11&20 25 - 13 33 "i"" i i i i ' i 1 T - T j I L JLJ. 0.00 0.25 0.50 0.75 1.00 1.25 1.50 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 a /3 7 BiM jBiM ^ave 0 -0.316 0.016 0.25 61.2 15.4 4.8 1.7 1 -0.096 0.017 0.10 37.2 3.9 9.5 5.3 3 -0.050 0.018 0.06 22.0 1.4 8.8 5.0 4 -0.065 0.017 0.08 31.1 2.4 6.7 3.8 8 -0.055 0.017 0.07 18.9 1.3 6.0 4.1 9 -0.086 0.017 0.09 28.2 2.7 6.1 3.8 10 -0.073 0.017 0.08 32.9 2.8 7.4 4.9 11 -0.098 0.017 0.10 31.0 3.2 6.2 3.2 12 -0.090 0.016 0.10 38.4 3.8 6.1 2.7 13 -0.071 0.017 0.08 27.9 2.3 6.1 2.6 14 -0.081 0.017 0.09 16.5 1.5 3.4 1.8 15 -0.095 0.017 0.10 48.6 5.0 10.2 6.8 16 -0.077 0.017 0.09 27.1 2.4 5.7 3.3 17 -0.085 0.017 0.09 8.4 0.8 1.7 0.7 18 -0.081 0.017 0.09 44.9 4.1 9.6 5.6 19 -0.059 0.017 0.07 18.2 1.3 5.8 3.5 20 -0.093 0.017 0.10 24.3 2.4 5.2 3.0 22 -0.055 0.018 0.07 19.0 1.3 6.7 3.9 23 -0.034 0.018 0.05 25.7 1.3 8.7 4.0 26 -0.047 0.018 0.06 22.6 1.4 9.7 6.7 29 -0.035 0.018 0.05 17.4 0.9 6.1 3.6 30 -0.019 0.018 0.04 36.9 1.3 15.1 4.8 31 -0.075 0.016 0.08 33.4 2.8 5.2 2.8 32 -0.072 0.016 0.08 33.6 2.7 5.3 2.7 34 -0.099 0.017 0.10 42.2 4.4 8.3 3.5 36 -0.103 0.017 0.11 43.1 4.7 8.6 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 self-diffusion 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 146 I I I I T - r i i i i i i i o o o Figure 4.47: Characteristic Drying Curves for Runs at Different Air Humidities Chapter 4. Results and Discussion 148 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 Discussion 149 Yerazunis [91], indicate that an exponential relationship of the following form: ^ = exp(-a0$) (4.46) 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 1 $e a 2 *) (4.48) where and a2 are fitting parameters. The fit of experimental data to such a function is represented by: / = 1 - ea;p(-0.96$e1-21*) (4.49) and is shown with a solid hne in Figure 4.48. 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, Leq, and assumed that the wet surface Chapter 4. Results and Discussion 150 and the wet volume vary, respectively, as the square and the cube of this length. Thus, considering: / oc Leq2 (4.50) and $ oc Leq3 (4.51) 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: / = ("•-"•Jl 'V (4.54) (M — Me) where Ma,Me, 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 Sp = ±0.06, Equation 4.10 ) which provides us with a 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 1.25 1.00 <M 0.75 0.50 0.25 0.00 i i I i i i 0 Run 3 X Run 4 0 a Run 8 0 Run 11&20 0 Run 12 0 Run 19 A. Run 22 Run 42 Equation 4.49 Equation 4.54 i i i I i i i i I i i i i I i • Run 30 • Run31&32 + Run 34 X Run 36 • Run41&44 & o • • 0 A • O ° • • o 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 * Figure 4.48: Unified Characteristic Drying Curve Chapter 4. Results and Discussion 152 4.9 Pressure D r o p 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 / m / G 2 L ( l - e ) 3 -A p = — v * 3 - ^ 3 ( } where Ap = pressure drop (Pa) G = superficial mass velocity (kg/m2-s) L = bed height (m) dp = particle Sauter mean diameter (m) p = density (kg/m3) \P = sphericity e = voidage n = an asymptotic function of Reynolds number Therefore, 3 tiji fmf = -Euh— 1 - eJ 2 - n (4.56) where the interstitial or hydraulic Euler number, Ehh, and hydraulic diameter, dh, are denned by: Euh = Ap pv2 / e2 (4.57) Chapter 4. Results and Discussion 153 and, 2 e -.. Z l _ ^ d v (4-58) 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 1 + 0.583 VRed,, 1 Ap Vdp e 1 dh = nEuh-- (4.59) 3pv2/e2 L 1 - e 2 L 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 m , of a linear 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 Redp — 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 m f , are determined using 9 = 0.4 as the average value of sphericity in conjunction with the experimental voidage and pressure drop data in Equa-tion 4.56. The results are shown in Table 4.13 and plotted in Figure 4.51 as a function Chapter 4. Results and Discussion 154 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: fmf - yff 1 2 - n (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 103: fmf = = 0-875 (4.62) 4.10 Heat Transfer During Constant Drying 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 Discussion 155 Table 4.13: Summary of Pressure Drop Data Run dP dh L ^ave Ap/L Apave Re*, n Euh fmf mm mm cm Pa/m Pa 0 6.30 1.94 23.13 0.536 3922.8° 4045.46 921.5 572 1.92 116.7 0.72 1 9.00 3.59 32.31 0.599 1152.3 1176.9 376.3 615 1.92 77.4 0.64 3 6.30 3.43 25.97 0.671 2010.5 1838.8 499.8 379 1.90 141.0 1.43 4 6.30 3.44 26.00 0.672 2402.7 2145.3 591.2 514 1.91 111.6 1.13 8 6.30 3.34 25.39 0.666 2893.1 2733.7 714.3 476 1.91 133.5 1.34 9 6.30 3.12 16.11 0.650 2010.5 2041.0 326.3 385 1.90 93.6 1.38 10 6.30 3.23 12.34 0.658 2451.8 2422.4 300.7 385 1.90 84.0 1.68 11 6.30 3.30 23.99 0.662 1274.9 1299.4 308.8 396 1.90 93.8 0.98 12 6.30 3.34 27.04 0.665 2255.6 2218.9 605.0 436 1.90 162.6 1.53 13 6.30 3.09 32.95 0.647 2795.0 2660.2 898.7 396 1.90 262.5 1.87 14 5.00 2.89 26.86 0.684 1544.6 1581.4 419.8 315 1.89 135.5 1.12 15 11.00 5.16 24.51 0.637 662.0 637.5 159.2 677 1.93 42.7 0.68 16 7.00 3.40 24.10 0.645 1078.8 1029.7 254.1 438 1.90 70.7 0.76 17 3.00 2.04 30.18 0.718 1618.2 1704.0 501.3 190 1.85 185.0 0.99 18 9.00 4.68 25.27 0.661 956.2 943.9 240.1 558 1.92 70.5 0.99 19 6.30 3.37 25.27 0.667 1078.8 1029.7 266.4 344 1.89 92.7 0.94 20 6.30 3.66 26.43 0.685 1103.3 1127.8 294.8 393 1.90 92.1 0.98 22 6.30 3.19 24.51 0.655 1127.8 1103.3 273.4 341 1.89 97.5 0.97 23 6.30 3.72 26.82 0.689 1397.5 1483.3 386.3 380 1.90 159.2 1.70 26 6.30 3.27 12.49 0.661 833.6 797.8 101.9 316 1.89 38.6 0.77 29 6.30 3.41 25.00 0.670 1103.3 1091.0 274.3 381 1.90 99.8 1.04 30 6.30 3.57 25.58 0.680 1005.2 1029.7 260.3 420 1.90 96.4 1.03 31 6.30 2.87 18.86 0.631 1495.6 1479.3 280.5 402 1.90 79.0 0.91 32 6.30 3.13 21.48 0.650 1176.9 1189.1 254.1 400 1.90 73.6 0.81 34 6.30 3.28 24.50 0.661 956.2 919.4 229.8 406 1.90 69.7 0.71 36 6.30 3.43 24.42 0.671 956.2 919.4 257.5 402 1.90 77.8 0.84 aL = 10.16 cm b L = 20.32 cm Cha.pt.er 4. Results and Discussion 156 4 0 0 . 3 2 0 . 2 4 0 . 1 6 0 . 8 0 . 0 . i i r O Experimental Fitted 0 . i i 1 • 2 0 . 4 0 . 6 0 . (1 - € ) L / ( e d p ) 8 0 , 1 0 0 . 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] Chapter 4. Results arid Discussion 158 U O o rt 10 "p 1 — i — I I I I I I i 1—I— I I I I I I i 1 — I — I I III I—I O Experimental Aloxite fused MgO granules, etc., by Leva — — Alundum, clay, etc., by Leva Celite, porcelain, glass, etc., by Leva Ergun equation 10 - l 10 J I I I I I 111 10 I I I I I 11 10 1 1 I I I I 1 1 10 Re dp 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 sur-face 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 Discussion 160 experimental values. Smolsky [104] experimentally investigated the effect of wave forma-tion 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: Ev == p\ (4.63) where Ev = energy used for volumetric evaporation (W/m3) p = volumetric power, mass of sub-microscopic particles per unit volume abstracted per unit time (kg/m3.s) 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: ^(Tdb-Taa) = pXl (4.64) Chapter 4. Results and Discussion 161 and hence the thermodynamic state of the drying medium is represented by [107]: pXl2 Tdb - Taa Gu = — — = (4.65) bfl-db J-db where kf = heat conductivity of the gas-mixture (W/m.K) I = characteristic length (m) Tdb> Taa = dry bulb and asymptotic temperatures (K) Gu = 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 Discussion 162 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 = NcVvaJhd (4.66) The heat transfer coefficient in the presence of mass transfer was then formulated by: h = iphd (4.67) where hd is heat transfer coefficient of a dry body and 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 NcPmixCl/hd 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 and Discussion 163 ln(l + XX)jXX for ip where XX is defined by the following relationship: XX =cPat(Tgt-Tb)/\ (4.69) 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, Tdh <150°C, RH<80%). Nu = OM%ReosProzzGu0-2 (4.70) Sh = OmARe°-8Sc°-33Gu0-2 (4.71) A comparison between Equation 4.70 and heat heat transfer from a dry surface, Nud: Nud = 0M7 Re0SPr0-33 (4.72) results in the following relationship: N u =2.32Gu0'2 (4.73) Nu Their experiments on capillary porous bodies, under otherwise identical conditions, are represented within ±7% scatter by the following empirical equations: Nu = 0.08QRe2/3Pr1/3Gu01 (4.74) Chapter 4. Results and Discussion 164 Sh = 0.11Re2^Sc1/3Guou • (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 = ARe0-7 (4.76) 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 tempera-tures. The effect of mass transfer on Nu/Re07 was taken into account through introduc-tion of a Kutateladze number (Ku): Nv —S3 = f(Ku) « Ku02 (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 Chapter 4. Results and Discussion 165 the total solid surface is available for both heat and mass transfer, the heat and mass transfer J-factors are related by: JH = 1 .064# e d p - ° - 4 1 = 1.076JM for Re^ > 350 (4.78) and JH = IS.lRe^1 = 1.076JM for Re^ < 40 (4.79) Parti [113] examined the applicability of the analogy between heat and mass transfer in deeper beds of solids. The correlated results were: JH = 1.1 JM = OJSe^Re^-0^ for 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 •ApTim (4.81) anc . Rmax l^ds / . n n \ = , v (4.82) with T- — T in out and Tlm = LMTD = , i r i T . ° u t (4.83) Ylm = LMYD = ^°utY lin (4.84) Chapter 4. Results and Discussion 166 h = convective heat transfer coefficient (W/m2.K) Qc = convective rate of heat flow supplied by the gas (W) ky = mass transfer coefficient (kg/m2.s) Rmax = max rate of dring (kg H20/kg dry wood.s) Ap = total interfacial surface area in the column (ni2) wd8 = weight of the dried solid in the column (kg) Tim = Logarithmic Mean Temperature Difference, LMTD, (°C) = Logarithmic Mean Humidity Difference, LMYD, (kg H20/kg 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 Discussion 167 H 0 u t A cond Hevap A Hin Figure 4.52: Adiabatic Humidification of a Gas TTlaHin TftevapHevap — maHoui -\- TTlCOTid.Hcond Qsink 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 = r a t e of conductive heat transfer to the solid (W) Y = gas humidity (kg H 2 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 (4.85) (4.86) Chapter 4. Results and Discussion 168 Substituting Equation 4.86 into Equation 4.85 and replacing Ycond and Yevap for respec-tively = w and yields: Hin ~\~ YevapHevap — Hout ~\~ Ycondlicond -\- (4.87) ma Upon replacement of the following equations: Hin = CsinTin + YinX0 (4.88) Hout = Cs out T-out + YoutX0 (4.89) Hevap YevapCptTae (4.90) HCond — Ycond\cpmvTas Xat\ (4.91) Aa« = A 0 - Tas(cpt - cPwv) (4.92) 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 , * s Qt Q sens Qvap Csave(Tin - T o u t ) =AYcPwv(Tave - T a s ) + AYXas +Qaink (4.93) where cp = specific heat (kJ/kg.K) Cs = specific heat of mixture per unit dry gas (kJ/kg.K) Qvap — r ate of heat flow for vaporization of the moisture (W) Qsens — rate of heat flow for sensible heating of the evaporated moisture (W) Qt = total rate of heat flow (W) Ao,Aa„ = latent heat of vaporization (kJ/kg) 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 Tf P T) x 105 cp kf x 103 D W G a x l 0 5 °C kg/m3 kg/m-s J/kg-K W/m-K m2/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 72.5 1.11 1.98 1022 28.6 2.75 15 77.3 1.10 2.02 1014 28.9 2.83 16 75.4 1.10 1.99 1024 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 90.9 1.02 2.05 1034 29.9 3.13 20 73.5 1.10 1.99 1015 28.6 2.80 22 96.5 1.02 2.07 1039 30.4 3.17 23 100.5 1.00 1.90 1141 30.5 3.06 26 111.9 1.00 2.10 1065 31.4 3.31 29 102.2 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 1.98 1021 28.6 2.61 32 75.0 1.13 1.98 1026 28.8 2.72 34 70.6 1.14 1.98 1017 28.5 2.67 36 70.3 1.12 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 41 146.9 1.14 1.33 1982 35.7 2.00 42 138.5 1.13 1.29 1979 34.8 1.99 43 152.6 1.09 1.34 1983 36.2 2.12 44 146.4 1.11 1.32 1982 35.5 2.06 45 142.8 1.12 1.31 1980 35.2 2.03 46 142.2 1.12 1.31 1980 35.1 2.03 aValues denote Dww for Runs 38 to 46. Chapter 4. Results and Discussion 170 Table 4.15: Heat Transfer Coefficients and Dimensionless Groups Run h Nu Gu BiH Pr PeH stH JH W / m 2 -K xlO 3 xlO 3 xlO 3 0 572 55.4 13.5 1.00 30.7 1.4 0.70 403 33.6 26.6 1 616 43.0 13.5 0.99 82.4 1.5 0.71 435 31.1 24.7 3 380 62.8 12.9 0.99 124.8 1.5 0.71 270 47.8 38.0 4 514 55.0 12.0 0.99 80.3 1.3 0.71 364 32.9 26.1 8 476 63.9 13.4 0.99 107.1 1.5 0.71 337 39.8 31.7 9 386 45.8 10.0 0.99 88.0 1.1 0.71 273 36.6 29.1 10 386 37.7 8.1 0.98 99.8 0.9 0.71 273 29.6 23.5 11 397 40.1 8.9 0.99 74.8 0.9 0.71 280 31.7 25.1 12 436 43.5 9.8 0.99 59.3 1.0 0.71 308 31.7 25.2 13 396 39.7 8.7 0.99 78.9 0.9 0.71 280 30.9 24.6 14 316 40.2 7.0 0.99 74.9 0.8 0.71 223 31.5 25.0 15 678 37.5 14.3 0.98 93.2 1.6 0.71 479 29.8 23.6 16 439 43.6 10.6 0.99 80.6 1.1 0.71 310 34.2 27.1 17 190 41.1 4.3 0.99 73.0 0.5 0.71 134 32.2 25.6 18 559 46.0 14.3 0.99 85.6 1.6 0.71 395 36.3 28.8 19 345 46.3 9.7 0.99 109.1 1.1 0.71 244 39.9 31.7 20 393 46.9 10.3 0.99 82.4 1.1 0.71 278 37.2 29.5 22 341 43.5 9.0 0.99 118.3 1.0 0.71 242 37.3 29.6 23 380 38.4 7.9 0.98 85.5 0.9 0.71 271 29.3 23.3 26 316 56.8 11.4 0.98 135.3 1.3 0.71 225 50.6 40.3 29 381 63.7 13.0 0.99 90.6 1.5 0.71 271 48.2 38.4 30 420 41.1 8.3 0.98 81.3 1.0 0.71 300 27.8 22.2 31 402 41.4 9.1 0.99 75.8 0.9 0.71 284 32.0 25.4 32 400 40.4 8.8 0.99 77.3 0.9 0.71 283 31.3 24.8 34 407 51.3 11.3 0.99 77.1 1.2 0.71 287 39.4 31.3 36 402 60.7 13.4 0.99 77.9 1.4 0.71 284 47.2 37.4 38 338 50.9 8.7 0.98 93.8 1.2 0.74 249 34.9 28.5 39 414 60.9 11.2 0.99 27.2 1.4 0.74 305 36.7 30.0 41 373 50.9 9.0 0.99 55.5 1.2 0.74 274 32.7 26.7 42 398 53.6 9.7 0.99 38.7 1.3 0.74 293 33.2 27.0 43 347 46.5 8.1 0.98 70.5 1.1 0.74 255 31.7 25.9 44 368 50.1 8.9 0.98 56.7 1.2 0.74 271 32.8 26.8 45 386 52.9 9.5 0.99 48.5 1.3 0.74 284 33.3 27.2 46 390 53.6 9.6 0.99 47.2 1.3 0.74 287 33.5 27.3 Chapter 4. Results and Discussion Table 4.16: Mass Transfer Coefficients and Dimensionless Groups Run Red,, kY a x 103 Sh BiM Sc PeM StM JM kg/ m 2-s xlO 3 xlO 3 0 572 41.9 9.49 61.2 0.67 384 24.7 18.9 1 616 20.0 5.76 37.2 0.65 400 14.4 10.8 3 380 18.3 3.40 22.0 0.63 241 14.1 10.4 4 514 24.3 4.82 31.1 0.64 331 ' 14.6 10.9 8 476 15.3 2.93 18.9 0.64 305 9.6 7.1 9 386 21.9 4.37 28.2 0.65 250 17.5 13.1 10 386 26.0 5.09 32.9 0.64 249 20.5 15.3 11 397 23.6 4.80 31.0 0.65 258 18.6 14.0 12 436 28.9 5.94 38.4 0.65 283 21.0 15.7 13 396 21.6 4.32 27.9 0.65 256 16.9 12.6 14 316 15.9 2.55 16.5 0.65 205 12.5 9.3 15 678 21.7 7.53 48.6 0.65 440 17.1 12.8 16 439 18.9 4.20 27.1 0.65 284 14.8 11.1 17 190 13.4 1.30 8.4 0.65 123 10.5 7.9 18 559 24.4 6.96 44.9 0.65 361 19.2 14.4 19 345 14.7 2.82 18.2 0.64 221 12.7 9.5 20 393 . 18.7 3.77 24.3 0.65 255 14.8 11.1 22 341 15.5 2.94 19.0 0.64 219 13.4 10.0 23 380 21.3 3.99 25.7 0.62 235 16.9 12.3 26 316 19.2 3.51 22.6 0.63 200 17.5 12.9 29 381 14.4 2.70 17.4 0.62 237 11.4 8.3 30 420 31.1 5.72 36.9 0.60 253 22.6 16.1 31 402 25.7 5.17 33.4 0.65 260 19.9 14.8 32 400 26.0 5.21 33.6 0.65 259 20.1 15.1 34 407 32.2 6.54 42.2 0.65 265 24.7 18.6 36 402 32.9 6.68 43.1 0.65 262 25.5 19.2 38 338 3.9 1.06 6.9 0.58 196 5.4 3.8 39 414 8.0 2.59 16.7 0.57 236 11.0 7.5 41 373 7.5 2.37 15.3 0.58 216 11.0 7.6 42 398 6.5 2.06 13.3 0.57 228 9.0 6.2 43 347 7.4 2.19 14.2 0.58 201 10.9 7.6 44 368 8.1 2.48 16.0 0.58 212 11.7 8.1 45 386 7.6 2.35 15.2 0.57 222 10.6 7.3 46 390 7.9 2.47 15.9 0.57 224 11.0 7.6 "Values represent kc (kg / m2-s-(mol/m3) )for Runs 38 to 46. Chapter 4. Results and Discussion 172 The inequality of the rate of heat flow supplied by the gas, Qt, and that consumed for 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 Ze along the bed height as the vapour pressure of water at the solid surface becomes smaller than Chapter 4. Results and Discussion 1 7 3 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 Ze and Zt that the gas travels before exiting the column. The humidity of the gas will remain constant at Yzc if the gas exiting the column is unsaturated. Figure 4 . 5 4 ilustrates the state of a 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 Ze are indicative of the likelihood of the occurance of case A for more intense 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 Zt: *M = Y ° V Y I N ( 4 . 9 4 ) which actually correspondts to height Ze up to which the number of heat, 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 Ze and Zt can be obtained through Equation 4 . 9 5 : 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 Re-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 Chapter 4. Results and Discussion 175 Z = Z 2 (Co lumn out le t ) • P v at T s • S ta te of the gas t r a v e l l i n g a l o n g the column Z = Z Z = Zj ( C o l u m n in let ) Figure 4.54: State of Drying Gas Traveling Along the Column (case A) Chapter 4. Results and Discussion 176 temperature via the following expression: H H = T i n ~ T o u t (4.96) 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 = ZE for case A. Even though the section between inlet and ZE constitutes the mass transfer zone, the mass transfer coefficients, ky, in Table 4.16 are evaluated over the whole bed height ZT. This would indicate that the Kjvf follows the dashed hne in 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 col-umn 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 tempera-ture, the ratio only corresponds to the surface area of the fraction of the particles having surface temperature of Tas. Despite this fact, the height of desorption zone is calculated and tabulated in Table 4.19. Tze is determined through equality of Qt and Qevap in Equation 4.93. A comparison between Tze and the recorded temperature profile along 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 and Discussion 177 Table 4.17: Rates of Heat Flow at Different Heat Transfer Modes ( W ) Run Qc Qr Qt Qvap Qsens Qevap Qet 0 2083 2083 1942 29 1971 0.95 1 4356 4356 3437 160 3598 0.83 3 7258 7258 5314 415 5729 0.79 4 5165 5165 4037 187 4224 0.82 8 7247 > 7247 4295 278 4573 0.63 9 3704 3704 2720 137 2857 0.77 10 3106 3106 2595 152 2747 0.88 11 4114 4114 3242 136 3378 0.82 12 3496 3496 3024 99 3123 0.89 13 4366 4366 3833 173 4006 0.92 14 4157 4157 3119 132 3252 0.78 15 3269 3269 2493 133 2626 0.80 16 3853 3853 2904 134 3038 0.79 17 4131 4131 3512 145 3656 0.89 18 3746 3746 2968 146 3114 0.83 19 5294 5294 3690 242 3933 0.74 20 4096 4096 3104 145 3249 0.79 22 5749 5749 4161 301 4462 0.78 23 4904 4904 4077 219 4296 0.88 26 5664 5664 3509 306 3814 0.67 29 5148 5148 3609 207 3816 0.74 30 5098 5098 4751 251 5002 0.98 31 4350 4350 3290 142 3432 0.79 32 4347 4347 3460 153 3614 0.83 34 3955 17 3973 3663 159 3822 0.96 36 4073 10 4083 3705 162 3867 0.95 38 4250 274 4524 3233 244 3477 0.77 39 2692 125 2816 2465 50 2516 0.89 41 4749 325 5074 4105 179 4284 0.84 42 3417 197 3614 2638 78 2716 0.75 43 5589 406 5995 4704 263 4967 0.83 44 4769 297 5066 4377 193 4570 0.90 45 4273 253 4525 3631 136 3767 0.83 46 4207 239 4446 3721 135 3856 0.87 Chapter 4. Results and Discussion 178 Table 4.18: Summary of Temperature and Humidity Data Run T,„ "C Ta, °C Tf °C rp a x dew °c Yb(d..b.) RH,n % HHout % RHavt % meu. calc.c in out as 0 62.3 22.7 25.3 23.7 33.1 22.1 0.0021 0.0168 0.0180 1.72 96.91 31.33 1 151.8 51.0 70.3 44.4 72.9 40.1 0.0114 0.0449 0.0573 0.40 58.66 14.17 3 241J 59.2 102.4 56.3 103.3 52.6 0.0263 0.0854 0.1085 0.12 73.74 8.56 4 155.7 56.0 75.9 49.5 77.7 46.1 0.0306 0.0649 0.0779 0.92 62.52 18.50 8 204.0 58.0 112.9 52.8 91.9 45.8 0.0246 0.0626 0.0914 0.23 56.27 9.96 9 154.8 60.0 82.8 45.8 76.6 40.1 0.0168 0.0465 0.0639 0.53 38.70 13.19 10 158.1 80.0 90.4 47.9 83.5 42.0 0.0233 0.0516 0.0716 0.66 18.25 11.74 11 147.8 43.3 63.9 44.2 69.9 41.1 0.0139 0.0487 0.0584 0.53 89.57 17.31 12 126.3 44.4 54.7 45.2 65.3 43.8 0.0261 0.0567 0.0617 1.85 96.98 27.40 13 158.4 48.0 60.2 48.2 75.7 46.9 0.0239 0.0659 0.0723 0.68 94.98 19.25 14 150.7 46.0 70.4 46.6 72.5 43.3 0.0212 0.0550 0.0666 0.74 87.57 18.68 15 151.2 68.6 85.9 44.6 77.3 37.7 0.0139 0.0406 0.0597 0.48 23.39 11.13 16 152.0 55.0 76.9 47.3 75.4 43.3 0.0233 0.0549 0.0692 0.78 56.89 16.95 17 148.4 44.0 58.5 46.0 71.1 44.4 0.0201 0.0582 0.0647 0.75 102.15 20.32 18 153.9 59.0 76.6 46.6 76.5 42.5 0.0211 0.0535 0.0679 0.66 45.62 15.27 19 204.8 56.5 97.2 51.2 90.9 46.4 0.0210 0.0660 0.0883 0.19 61.85 9.96 20 154.0 50.0 73.1 44.9 73.5 40.6 0.0145 0.0479 0.0615 0.46 62.91 14.69 22 . 220.7 59.8 99.4 52.8 96.5 48.2 0.0205 0.0713 0.0941 0.13 58.35 8.68 23 196.4 68.5 88.1 68.6 100.5 68.5 0.1422 0.2004 0.2116 1.39 99.83 24.94 26 246.8 81.1 137.3 59.8 111.9 53.8 0.0450 0.0925 0.1312 0.18 30.91 7.60 29 202.1 70.3 106.6 68.2 102.2 66.7 0.1347 0.1848 0.2066 1.16 85.74 21.99 30 201.7 78.0 85.4 77.8 108.8 78.6 0.2856 0.3638 0.3679 2.08 102.49 29.74 31 154.4 . 46.0 70.6 47.6 73.9 44.5 0.0195 0.0546 0.0660 0.65 92.83 18.26 32 156.2 47.6 68.1 48.1 75.0 45.6 0.0226 0.0600 0.0700 0.69 90.54 18.68 34 146.2 48.0 54.6 44.1 70.6 42.5 0.0130 0.0512 0.0568 0.53 76.42 17.58 36 148.1 46.0 54.4 43.6 70.3 41.9 0.0114 0.0504 0.0561 0.43 81.68 16.88 38 250.8 155.0 179.8 121.2 162.0 120.9 0.0474 0.0580 0.0635 4.35 36.54 30.27 39 170.9 118.5 124.1 122.6 133.6 122.2 0.0583 0.0661 0.0662 25.10 112.75 70.17 41 220.5 120.0 137.3 123.6 146.9 123.2 0.0541 0.0679 0.0681 8.38 110.84 49.16 42 188.9 120.0 137.5 122.6 138.5 122.2 0.0560 0.0658 0.0662 16.18 107.40 60.66 43 245.7 119.6 144.8 122.6 152.6 122.2 0.0499 0.0659 0.0662 4.97 108.80' 40.62 44 221.3 119.0 131.4 122.6 146.4 122.2 0.0523 0.0660 0.0662 7.98 110.93 48.37 45 206.9 119.0 135.0 122.6 142.8 122.2 0.0539 0.0660 0.0662 10.80 110.93 53.60 46 204.7 119.0 131.6 122.6 142.2 122.2 0.0542 0.0660 0.0662 11.34 110.93 54.49 "Dew point of the outcoming gas. ^Corresponds to molar concentration (mol/m 3) for Runs 38 to 46. cThe outlet temperature should the analogy between the transfer processes exist. Chapter 4. Results and Discussion 179 Table 4.19: Summary of data Determining the Analogy between the Transfer Processes Run ReD Re^ Rmax x 10 3 s-1 JHI JM K M ze cm 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 12252 380 1.81 3.65 4.16 1.27 0.31 7.9 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 1.96 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 A 1.92 18 12617 559 1.00 2.00 2.16 1.18 0.55 13.8 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 A 2.99 31 12980 402 1.34 1.71 2.15° 1.41 32 12909 400 1.41 1.65 2.32 A 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 A 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 A 44 11858 368 1.65 3.31 2.57° 45 12453 386 1.37 3.71 2.65 A 46 12578 390 1.41 3.59 2.59 A a Denotes infinitely long heat transfer section (see Appendix A ). Chapter 4. Results and Discussion 180 The J-factors for the section where the bed height does not exceed the thickness of the desorption layer can be calculated by replacing Qevap for Qc and Tze for Tout 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, conserva-tively, 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 to-ward 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^Redp)0-812Pr°-333Gu0 0 9 5 (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 ro.333G i to.o 9 5 = 0-112fle° p 8 1 2 (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 Num 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 Discussion 181 10 1—I I I I I T 1 1—I I I I A Experimental Fitted 2 CD C/3 ^ II ^ 1 0 <L> S S ' A a o 3 10 10 ' • ' • 10 Re dp J i i i i i i 10 Figure 4.55: A Plot of Modified Nusselt Number as a Function of Reynolds number Chapter 4. Results and Discussion 182 in Equation 4.97 seems to be contrary to the previous argument that the mass trans-fer 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 in-creasing 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 re-moval 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 Discussion 183 kg water/kg dry wood (23% < M' < 40% wet basis ) is sufficient to guarantee an effi-ciency 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, irre-spective 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 H20/kg 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 2 is permitted to 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 2 used for the North American ones. 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? 20/kg dry wood. Even though a similar 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 dp > 9 mm. A comparison between the two figures indicates that the effect of particle Chapter 4. Results and Discussion 184 0 2 0 4 0 6 0 8 0 100 Pe rcen 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 Heat ing Value of 8 7 5 0 B tu / l b for Wood and B a r k . S t a c k Temperature 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 4.0 CD 3.0 II Z 2.0 CD 1.0 0.0 h -1.0 X "| "T»T-T Xref - o L 10 cm -A dp 3 m m -• T a i r 100 ° C * o Tsteam 100 ° C -• Y,n 0.1 d.b. -— -- / _ • / -— / --• ®< ft A -6. Q • ^~ -" • — — - A -• cr • Qret — 1 , , , 600 s 0.0 1.0 2.0 3.0 x / x 4.0 5.0 r e f Figure 4.57: The Effect of Various Parameters on the Normalized Drying Time to Reach M = 0.6 Chapter 4. Results and Discussion 186 7 . 0 X 6.0 - o L 10 c m A dp 3 m m • Tair 100 °C 5.0 Tsteam 100 °C • Yin 0.1 d . b . CD 4 .0 h CO © II CO 0.0 I I I I I I I I I I I I I I I A / 3 . 0 h 2 . 0 h * - - _ 1.0 h x -A. — A— \ ^ e \ •o Bret = 600 S 1 1 1 1 1 • 1 1 ' 1 1 1 1 1 1 1 • 1 • 1 i i i ' 1 1 0.0 1.0 2 .0 3 . 0 4 .0 x / x 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 Discussion 187 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 repre-sentative 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 20/kg dry wood, a 30% increase in the 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 2. Extrapolating 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 \ 204 . . V grate heat release rate) ~ \ bed height ) 1014L 4- 204 ^ where L denotes the final bed height in m. Increases in humidity at Tin = 202° C would very gradually reduce the required residence 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 rela-tively 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 veloc-ity 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 < Mcr < 1.1 kg water /kg dry sohd. Generally, Mcr 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 e , has a finite value. MCT, Me,u; and 189 Chapter 5. Concluding Remarks 190 more specifically Rmax have been used to quantify the drying process with respect to the particle thickness (dp), the initial moisture content of the sample (Ma) and the height of the bed (L), and to the inlet temperature (T^), velocity (V;n) and composition of the 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 Me, and the critical 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, MD. Neither of these parameters has any effect on the drying behaviour during the falling rate period and hence on u). There is a linear relationship between R m a x and L ~ 2 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 for approximately a 31% rise in velocity. This suggests that Rmax, 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 mass flow rate. 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 Remarks 191 temperature. Particularly at lower temperatures, the falling rate period remains rela-tively 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 < Tin < 221°C indicate that both Rmax and u increase with increases in temper-ature. Due to spontaneous ignition of wood there was no data collected at T;n = 221°C for M < 0.4; however, the remaining runs are indicative of a linear relationship between u> and Tin < 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, ex-ists between Rmax and T;n with superheated steam drying at 215 kPa absolute pressure and 171 < T;n < 246°C. At a constant mass flow of the drying medium, evaporation 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 con-tent decreases with increasing temperature for air drying while it remains approximately constant for superheated steam drying at T;n > 190°C. In air there are limitations on predrying due to fire hazards, particularly at temperatures above 200°C. Drying with su-perheated 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(92 content of the drying gas. However, 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 in-version 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 Remarks 193 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 (Mfinai = 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 par-ticle 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 pro-cesses 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 there-fore, 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 corre-sponds 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 a0,ai,a2 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 m 2 /m 3 Aij coefficient in Equation A. 15 Ap specific surface area m 2 /m 3 As solid surface area in the column m 2 b thickness of the slab m bi average thickness of zth thickness fraction m B constant in Equation 4.26 cp specific heat in the gaseous state J/kg-K cp specific heat in the gaseous state J/kmol-K C molar concentration kmol/m3 Cf molar concentration at film temperature kmol/m3 C j m logarithmic mean concentration difference kmol/m3 CL specific heat in the liquid state J/kg-K Cr correction factor for radiation heat transfer Cs specific heat of gas mixture per unit dry air J/kg-K 195 Nomenclature Symbol Description Units Cs specific heat of gas mixture per unit dry air J/kmol-K Cw molar concentration of water kmol/m3 dh hydraulic diameter Equation 4.58 m dp Sauter mean or arithmetic mean thickness m D diameter of the column m Da apparent moisture diffusivity within wet material m2/s Dv apparent vapour diffusivity within dry material m2/s DWG water diffusivity within gas medium m2/s Dww water vapour self diffusivity m2/s E emissive power in radiation heat transfer EV energy used for volumetric evaporation W/m 3 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/m2-s G superficial total gas mass velocity kg/m2-s Gb Gibbs function G' superficial dry gas mass velocity kg/m2-s h convective heat transfer coefficient W/m2-K hd convective heat transfer coefficient with no mass transfer W/m2 -K H enthalpy per unit either dry gas or incoming steam J/kg H enthalpy of gas per unit gas J/kg Nomenclature 197 Symbol Description Units I lave k kc kf K ky Ky kc Kys eq 771 / m M grate heat release rate higher heating value of dry sohd drying intensity drying intensity at the bed inlet mean drying intensity along the column Boltzmann's constant humidity dependent mass transfer coefficient conductivity of fluid conductivity of solid humidity dependent mass transfer coefficient humidity independent mass transfer coefficient humidity independent mass transfer coefficient humidity independent mass transfer coefficient during surface evaporation humidity independent mass transfer coefficient during sub-surface evaporation characteristic length height of the column equivalent wet length radiating beam length total mass flow rate dry gas mass flow rate dry basis wood moisture content kW/m 2 kJ/kg m m m J/molecule-K kg/m2-s-(mol/m3) W/m-K W/m-K kg/m2-s kg/m2-s kg/m2-s-(mol/m3) kg/m2-s kg/m2-s m m m m kg/hr or kg/s kg/hr or kg/s kg H20/kg dry sohd Nomenclature 198 Symbol Description Units M0 initial dry basis wood moisture content kg H20/kg dry solid M„ critical dry basis wood moisture content kg H20/kg dry solid Me equilibrium dry basis wood moisture content kg H20/kg dry solid M , dry basis wood moisture content at the surface kg H20/kg dry solid M' weight percent wood moisture content M average dry basis wood moisture content kg H20/kg dry solid M„ average critical dry basis wood moisture content kg H20/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 kmol rii number of ith point, Equation 4.9 N mass transfer flux kg/m2-s N° mass transfer flux at the inlet conditions kg/m2-s Nmax maximum mass transfer flux, corresponding to Rmax kg/m2-s Nw mass transfer flux for water kg/m2-s N molal flux of mass transfer kmol/m2-s N number of transfer units N# number of heat transfer units number of mass transfer units Nomenclature Symbol Description Units P number of parameters P pressure Pa Pc critical pressure Pa Pt total pressure Pa Pv vapour pressure Pa P partial pressure Pa Pco2 partial pressure of CO2 Pa Pw partial pressure of water Pa pp 0.5(Pt + p) Pa p volumetric power kg/m3-s 1 flux of heat transfer W/m 2 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-1 RE experimental rate of drying per dry weight of sohd s"1 RP fitted rate of drying per dry weight of sohd s-1 Rg gas constant J/kmol-K Nomenclature 200 Symbol Description Units RG molecular separation at collision for dry gas nm Rmax maximum drying rate per dry weight of sohd s-1 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 (p/pv) RM MW/MG R' 3R/d6 R" dR'/dd S cross sectional area of the column m 2 SEE residual sum of squares due to pure experimental error s-2 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"2 SP sum of squares of the predicted values s-2 SR residual sum of squares of the fitted curve s"2 cross sectional area of the column m 2 T temperature °C or K T J- as adiabatic saturation temperature °C or K T ave average temperature °C or K T dew dew point temperature °C or K Nomenclature 201 Symbol Description Units Tf film temperature °C or K T -1 in inlet temperature °C or K Tim logarithmic mean temperature difference °C or K T, surface temperature °C or K Tz gas temperature at point Z along the column °C or K U overall heat transfer coefficient W/m2-K Vb volumetric bulk flow rate of solids m3/s Vg molar volume of gas m3/kmol Vt molar volume of liquid m3/kmol Vs volumetric flow rate of solids m3/s V velocity m/s v, sohd volume m 3 vt total volume m 3 vv void volume m 3 wds weight of dry sohd in the column kg w yy ws weight of wet sohd in the column kg X distance m Xi the ith point of an independent quantity, Equation 4.9 X x mean value of the independent quantities, Equation 4.9 X mole fraction Y dry basis air humidity kg # 20/kg Yi the fitted value of the ith point, Equation 4.9 Nomenclature 202 Symbol Description Units Yim logarithmic mean humidity difference kg H20/kg wet gas Y' wet basis air humidity kg H20/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 Zc critical compressibility factor Ze position along the column up to which heat and mass transfer processes occur simultaneously m Zr Ze/Zr  Greek a hygrothermal ratio am fitting parameter Equation 4.60 m (3 BiH/BiM 7 evaporative resistance coefficient 8 thickness of the boundary layer m £ deviation within 95% confidence interval s _ 1 8ee experimental errors within 95% confidence interval s _ 1 8P standard deviation of the predicted value within 95% confidence interval s _ 1 8ee relative experimental errors with 95% confidence limit s _ 1 A denotes a change Ap pressure drop Pa Nomenclature 203 Symbol Description Units e voidage in the bed m3/m3 gas emittance £» sohd emittance C depth of recession m V viscosity kg/m-s 6 time s K, overall mass transfer coefficient kg/m2-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 o-p 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 Nomenclature 204 Symbol Description Units crn_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 m (f> humidity potential coefficient {fi^wt weight fraction of ith thickness fraction kg/kg 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 m/m tp porosity of the wood . m3/m3 \P sphericity ui slope during falling rate period s - 1 u' du/de s" 2 Subscripts Description Subscripts Description a air b boiling a apparent c conduction as adiabatic saturation c critical ave average cr critical 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 206 Dimensionless Groups Biff heat transfer Biot number B%M mass transfer Biot number Eu Euler number Euh hydraulic Euler number Gu Gukhman number JH heat transfer J-factor JM mass transfer J-factor Ku Kutateladze number Le Lewis number Lu Luikov number Nu Nusselt number P&H heat transfer Peclet number PeM mass transfer Peclet number Pr Prandtl number Re Reynolds number Sc Schmidt number Sh Sherwood number Stjf heat transfer Stanton number StjM mass transfer Stanton number Definition hl/k. 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[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 Evap-oration," 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 Pro-cesses (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 Refer-ence 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. 219-223. [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. References 223 [126] Keey, R.B., Drying Operations, Oxford, Pergamon Press, 1978, p. 171. [127] Perry, R.H. and Chilton, C.H., Chemical Engineers' Handbook, 5th Edition, New-York, McGraw-Hill Book Company, 1973, p. 5-52. Appendix A Sample Calculations Determination of Factors Affecting the Properties of the Fluid 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) Rg — gas constant (J/kmole-K) T = Temperature (K). Specific heat, cp, of the components of the drying medium is calculated [114] using the equations given in Table 2. The heat capacity of the mixture is obtained through: Cpmi* =~Y1 UiCPi ( A- 2) where denotes the number of molecules of the ith component and n is the the total number of molecules in mixture. 224 Appendix A. Sample Calculations 225 Table A.l: Heat Capacities of the Components of the Drying Medium Subst. State cp x 1(T3 (J/kmole-K) Range of T (K) Uncertainty % C 0 2 g 43.294 + 0.00115T - 818558.5/T2 34.626 + 0.00108T - 785899.9/T2 273-1200 l\ N 2 g 300-5000 3 o 2 g 27.216 + 0.004187r 2 300-3000 3 H 2 0 g 34.417 + 0.00063T + 0.00000561T2 300-2500 -3. Viscosity, 77, of pure substances is calculated [115] via Equations A.3 to A.7 for Nonpolar gases: 77A = 10-7 x (4.61T,0-618 - 2.04e- a 4 4 9 7 ; + 1.94e-4-058T' + 0.1) Polar gases, hydrogen-bonding, Tr < 2.0: 77A = 10 - 7 x (0.755TP - 0.055)ZC~5/4 polar gases, non-hydrogen-bonding, Tr < 2.5 : 77A = 10~7 x (1.97; - 0.29) 4 / 5Z c- 2 / 3 A = T}'6M-l/2pV3 C r c log Vc 0.371 - 0.0343 The mixture viscosity is determined using the following expression: XiTji VTUIX ^ ^ i = l where: = [1 + (r; i/nj) 1 / 2(Mj/Mi) 1 / 4] 2 [8(1 + Mi/M^l2 4>ji = (•nihi){MilMj)<t>ii (A.3) (A.4) (A.5) (A.6) (A.7) (A.8) (A.9) (A.10) endix A. Sample Calculations 226 and T = temperature (K) M = molecular weight Z = compressibility factor 77 = viscosity (kg/m-s) c,r = denote critical and reduced properties, respectively Xi = mole fraction of the ith component. Thermal conductivity of the fluid, kf, is obtained [115] via thermal conductiv-ities 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. kfil = (c„, + 18715.9)-g- (A.ll) kfi2 = (1.32c,, + 18715.9)-|r (A.12) kh = 0.5(kfil+kft2) (A.13) Conductivity of mixture is determined using the following expression: h = t where kf= heat conductivity (W/m-K) cv = specific volume (J/kmole) v = viscosity (P) M— molecular weight (kg/kmole) i = denotes properties of the ith component. l3 . (A.14) Appendix A. Sample Calculations 227 Aij can be estimated using Lindsay Bromley relation: {1 + Vi,MJ}3/4,T + Si -I 1/2 •\2(T + Sjj * {T + Si} Si = 1.5Tbi Si:i = CiSiS^2 9- — (A.15) (A.16) (A.17) (A.18) where C = 1, T is temperature (K) and Tbi is the boiling point temperature of the ith component in degrees Kelvin. 5. Diffusivity of water vapor in the dry 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-4(1.084 - 0 . 2 4 9 M ^ G)T 3' 2M M G , A I M  = PT(RWG)2f(kT/EWG) ( A A 9 ) 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) = R w ^ R q EWG — energy of molecular attraction (J/molecule) f(kT/EwG) = collision function [118]. Appendix A. Sample Calculations 228 6. Inlet temperature, T; n, is the average value over the length of a run. 7. Instantaneous mean temperature, Tm(6), 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, Tag, is determined by solving the following Equations 4.21 to 4.24 simultaneously. 10. Vapor pressure, pv, of the water is calculated via interpolation of Equation A.21 between 20 and 100°C as is shown in Equation A.22. inp„ = -—^—+const (A.21) Kgl -4986.667 / A x \npv = + 24.9 (A.22) where Rg, X and T denote the gas constant (J/kmole-K), the molal latent heat of 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 tempera-ture, Tdew, of a diluted sample, mixture, and its subsequent substitution for T in Appendix A. Sample Calculations 229 Equation A.22. Substitution of pv in Equation A.23 would provide the humidity of the mixture: Y = . ^ (A.23) MG{pt-Pv) K where pt is the total pressure (Pa) and Mw and MG, respectively, represent the molecular weight of water and that of dry gas. The humidity of undiluted sample taken at the inlet and outlet of the drying column (Yin, Yout) are obtained through humidity of the mixture as represented by: Ymixmmix • YfiaTTicla . CIA\ tam — \ A . Z 4 J 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;n, and the inlet humidity, Y{n, as is represented by: m' = m i n ( l + Yin) (A.25) 3. Instantaneous drying rate, R(9), is determined through Equation A.26 for su-perheated steam runs and through Equation A.27 for remainder of the runs. R(6) = ( m ° u ; ~ m , n ) (A.26) R(6) = ^-(Yout-Yin) (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. crR{6) = 0.04 x 10~3 (A.28) Appendix A. Sample Calculations 230 c r m = VQQIR2 + 88 x 10-6 x 10-3 (A.29) For an average value of Rmax = 1.5 x 10 - 3 for superheated steam runs and Rmax = 1.2 x 10 - 3 for rest of drying runs, the following approximation is obtained: = = 0-025 (A.30) 4. Instantaneous mean superficial mass flow velocity along the column, Gm(t9), is obtained through the following Equation: Gm{6) = 0.5{min+moutl)/Sx (A.31) where Sx = cross sectional area of the column (m) mout = min + WdaR(6) 5. Inlet velocity, Vin, and Instantaneous mean velocity along the bed,Vm(0), are determined by, respectively, substituting T, n and Tave(9) in Equation A. l and subsequent substitution of pin and pm(d) in : Vin = ^  (A.32) Pin or Vm(0) = ^  (A.33) 6. Average properties, Tave, pave, G a v e and Vave are determined by averaging the instantaneous properties (i.e. Tm(0), pm(9), Gm{Q) and Vm(0)) over the length of a run. Appendix A. Sample Calculations 231 A.3 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: Numerical values are included in Tables C.l to C.34. 2. Particle thickness in a thickness fraction, dPi, is the arithmetic mean thick-ness in fraction which was determined using a Wennberg classifier [70, 71]. 3. Particle density, pg, is taken as 506.5 kg dry bark/m3 green volume as is sug-gested by Smith and Kozak [121]. 4. Conductivity of the wood, k,y is determined by averaging the two relationships [120] for respectively weight percent moisture contents of M' < 40% and M' > 40%. ktl = p,(0.2006 + 0.0040M') x 10~3 + 0.02379 (A.35) (A.34) k ^(0.2006 + 0.0055M') x 10 - 3 + 0.02379 (A.36) k3 = 0.5(ktl+k.2) W/m-K (A.37) where ps is in kg dry solid/m3 green volume. 5. Porosity of the solid, -0, is approximated using the Skarr's [46] analysis of mois-ture in wood suggesting that complete uptake of water by capillaries will increase Appendix A. Sample Calculations 232 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 3 of space (p„ ~500kg/m3), the pore volume would be: = = 1.2 x (1000kg water)/(1000kg/m3) = 1.2 m 3 (A.38) PH20 Thus the porosity becomes: 1 2 •tjj = — = 0.6 m 3 /m 3 (A.39) 6. Krischer's diffusion resistance coefficient in a porous body, po, is defined by: pD = ^ (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. Vapour diffusivity through dry out material, DV, is calculated via: Dv = ?m (A .42) PD where DWG is the water vapour diffusivity in the dry gaseous phase. Appendix A. Sample Calculations 233 8. Apparent moisture diffusivity through the wet material, Da, is approxi-mated as 0.0015 x l O - 6 m2/s from the experimental data [123]. A.4 Factors Affecting Hydrodynamics of a Packed Bed 1. Bed Volume , Vt, is measured prior to and just after each run via weighing a volume equivalent bucket of water. 2. Voidage , e, is determined by a comparison between the dry solid, Va, and the bulk volumes, Vt. The former is calculated using a dry solid density of 506.5 kg dry wood/ m 3 green wood. An average value of initial and final voidage is used for sub-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, dp, is expressed by the arithmetic mean thickness, dPi, 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) dPi where (<f>i)wt is the weight fraction of the ith thickness fraction. 4. Specific solid surface, Ap, is calculated via: 6 ( 1 - 0 dp (A.44) Appendix A. Sample Calculations 234 where e is voidage and dp is particle size. 5. B e d height , L, is obtained through the following expression: L = 4s (A.45) 4 where Vt and D are bed volume and diameter, respectively. 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 unifor-mity 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. Sample Calculations 235 A.5 Determination of Heat and Mass Transfer Coefficients and Dimension-less groups during Constant Rate Period 1. Humid heat, Cs, is obtained through the following equation: C s = Y^- + ^ - (A.46) Mw MG v ' where Y = humidity (kg H 20/kg dry gas) • . cPw — specific heats of water (J/kg-K) Cp g = specific heats of dry gas (J/kg-K) 2. Outlet temperature, T o u f , 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. m {Yout — Yi n ) (CLTOB — X0) + CsinTin . J-out(calc) = ^ l A - 4 ' J T rnincPinTin + Am(CLTas - Xa) J-out{calc) = (A.48J moutcpout where CL = specific heat of liquid (J/kg-K) A0 = latent heat of evaporation at 0°C 3. Average temperature, Tave, 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(Tave + Tas) (A.50) Appendix A. Sample Calculations 236 where Tag 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. 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: where c and Z, respectively, represent heat conduction to the solid and enthalpy of the net evaporated moisture. Substituting the corresponding values for H1, H2 and 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. •Hi + Hi = H2 (A.51) -Hi + Hi = H2 + Hc (A.52) Qt = m'Ca1(Tl-T2) (A.53) Qt = m ^ ( T i - r a ) Am[Xaa + cps(T2 - Ta3)] + mlHc (A.54) Csx = Cp^Fx + c, (A.55) where m' = mass flow rate of dry air (kg/s) endix A. Sample Calculations 237 Table A.2: Enthalpy of various streams Parameter Humid air Steam (J/kg dry air) (J/kg incoming steam) # i Cs1T1 + X0Y1 cpiTi + A 0 H2 Cs2T2 + X0Y2 Hi CL(Y2 — Yi)Ta, CL(m2 - mi)Ta8 mi — mass flow of total incoming steam (kg/s) cPa, cPw, cPs = respectively denote specific heats of air, water and steam at film temperature (J/kmole.K) Flux of radiative heat transfer, qr, between a radiating gas and a surface is calculated [124] using emissive power of a real body through the Stefan-Boltzman law: where k = Stefan-Boltzman's constant, 1.3805xlO-23 T = Temperature (K) £g, e, — emittance of the radiating gas and that of the sohd surface. Both eg and £, are temperature dependent. eg is approximately constant at 0.85 while eg at 1 atm total pressure is given [125] as a function of radiating gas partial endix A. Sample Calculations 238 pressure, pw, temperature and radiating beam length, Lr. For radiation within the packed ped, Lr is determined by: Volume of eas L ' = 3 \ r e a of bounding surface = ZAW^7) ( A ' 5 7 ) The beam length for radiation between the solid surface and the gas volume occu-pying the space above the packed layer is approximated by: Lr = 0.9D (A.58) where e = voidage in the bed (m3/m3) dp= particle size (m) D = Column diameter (m). Therefore, the total rate of radiative flow will be obtained through the following equation: QT = qTlAs + qr2Sx (A.59) 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, Cr, to account for the effect of pressure. For superheated steam at 1 atm total pressure and at 250°C< T < 350°C, eg is relatively constant at 0.08 for radiation within the packed layer; eg increases to a constant value of 0.32 for the radiation in the space above the packed layer. Appendix A. Sample Calculations 239 Table A.3: Ernissivities of CO2 p (Pa) LT (cm) pLT x 10~3 N/m 0.06 0.882 0.499 0.008 0.06 18.281 0.97 0.048 0.12 0.832 0.998 0.015 0.12 18.29 21.95 0.063 Although no data is available for pp = 0.5(pw + pt) > 1.2 atm, the asymptotic shape of the correction factor curves indicate that Cr(pp= 2atm) = l-lC r^ p p = 1 2atm) can provide a good approximation for superheated steam runs. This would result in Cr=1.87 for the former and C r = 1.6 for the later. Ernissivities of carbon dioxide at 1 atm total pressure between the surface and av-erage gas temperature of, respectively, 40 and 120°C at required p~cOiLT values are given in Table A.3. Cr is unity as air drying runs have taken place at approximately 1 atm total pressure. 7. Rate of convective heat transfer, Qc, is obtained through the following rela-tionship: Qc = Qt~Qr. (A.60) 8. Logarithmic mean temperature difference, Tj m , is determined using Equation Appendix A. Sample Calculations 240 A.61 for a heat transfer process with a phase change. Tlm = ^V" TTU\ (A.61) ln(i" y ) s ^ out " J u l ' 9. Convective heat transfer coefficient, 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 a s , Figure A.1(a), the total rate of convective heat flow between 1 and 2, Qc, is calculated for an infinetly long heat exchanger ( A s —> oo) by: Qc = hAT{1) (A.63) where AT(i) = Tx — Tas. 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, Qc is determined through the following summation: Qc = h(AT{1) + AT{2)) (A.64) where AT(2) — T2 — T» (2) ~ 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 T 1 (a ) 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. The Ackerman coefficient, tp, is determined using the following relationship: In [X + 1] <P X (A.66) where X = Nc„„„/h N = Flux of mass transfer (kg/m2-s) cPvaP = 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 242 180 160 140 h 120 h o 100 h 80 60 h 40 20 1 1 1 I 1 1 1 I I I I I I Run 11 o o o o o o o o j 8 f l f i o o . | A A • D D o ° ° • • o o o o A • T h e r m , No. 1 2 3 4 _1 L 1 1 1 1 1 J _ l _ 0 600 1200 1800 6 (s) 2400 3000 3600 Figure A.2: Plot of Temperature Distribution along the Bed Appendix A. Sample Calculations 243 A.68. kY = (A.67) kc = ^ (A.68) where Nmax represents maximum flux of mass transfer, Y/m and Cim respectively denote the logarithmic mean humidity and concentration difference as defined by the following equations: Ylm = ?%~_Y\ (A.69) C0Ut ~ C; ln(,?3a'~ff" ) where C = p/RgT denotes the molar concentration of superheated steam. As dis-cussed for Tim, Equations A.69 and A.70 approach the limiting value of, respectively, Ysat — Yin and Caat — Cin for a saturated outcoming gas. The F-type mass transfer coefficient for humid air is determined via: F = ^ - (A.71) MG y 1 and its corresponding value for superheated steam is represented by: F = kcCf (A. 72) where Cf is molar concentration at the film temperature. 12. Reynolds number, Re, representing the ratio of inertial to viscous forces is eval-uated both based on the column diameter, D, and on the particle size, dP32, for both inlet and average film temperatures and flow rates through: Gl Rei = — . (A.73) V Appendix A. Sample Calculations 244 where I denotes the characteristic length, D or dPi2. 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: S h = k y d ^ . (A.75) D W G C } M G Sh = (A.76) Dww 15. Prandtl number, Pr, representing the relative effect of momentum and heat diffusivities at film temperature is obtained via: Pr = ^ (A.77) kf 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. PeH = Re^Pr (A.80) PeM = Re^Sc (AM) Appendix A. Sample Calculations 245 18. Stanton number, St, is evaluated for both processes at film temperature. St» = H^Fr (A.82) S t M = (A.83) riedj)bc 19. J-factors are calculated at T — Tj using the following expressions: JH = StHPr2/3 (A.84) JM = StMSc2/3 (A.85) (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: Bi" = iBk  (A'88) Substitution of Dv, apparent vapour diffusivity, from Equation A.42 and replacing Tjr C D W G KY, = —-g—MG would result in: BiM = liD-8 (A.89) where pu is the Krischer's diffusion resistance corfficient in a porous body. Appendix A. Sample Calculations 246 21. Gukhman number, Gu, represents the ratio of thermal potential of mass transfer to that of heat transfer and is evaluated using: Gu = (A.90) 1f 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 abso-lute humidity, or molar concentration for mass transfer, across the column. The corresponding values are respectively shown by Equations A.91 andA.92. T- — T -L i n -£ out Tim hApL CSlG' (A.91) Yin or Gout — Ci-i KyAvh 23. Height of transfer units, H*, is determined via: r r - L (A.92) 24. Height of desorption zone, Ze, is determined, considering that the heat trans-fer process prolongs along the total height of packed bed, throught the following relationship: Z. = L$r) (A-93) Appendix A. Sample Calculations 247 A.6 Determination of the Factors Affecting Characteristic Drying Curve 1. Hygrothermal ratio, a, is a function of wet bulb temperature, Tw0. 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 t p r j ) and a is the hygrothermal ratio. 3. Drying intensity, N, is evaluated through the following Equation: N d N = iV"7 ^ (A.95) paM0Da K } where ' kYYlm N — or kcClm is the initial mass transfer flux along the column, and MQ and Da 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 Calculations 248 1 + jBiM where BIM is the mass transfer Biot number based on the depth of recession. (A.96) 5. Charac ter i s t i c mois ture content , $, is denned by Equation 2.25 for a hygro-scopic 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 the Re la ted Propert i e s 1. A v e r a g e pressure d r o p , Ap, is determined via: T ]=m m n—1 L (A.97) 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 ve-locity at the inlet conditions. 3. Spher ic i ty , '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 Calculations 249 4. Modified friction factor, / m y, is determined using Equation 4.56. The exponent of the bracketed value, [yz^]2_n, is a function of Reynolds number. A spline function 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 differ-entiating: R = ® ^ (A.99) i = l with respect to M ; therefore: dR _ (if) _ d2M de dM dM(6) d62 dM Using Equation A.99 the following would yield: (A.100) dR u> i t a ^ e - ^ - c ' ^ (A.101) dM Rlri 1 0 3. Standard deviation of the slope, 0 " ( w ) , is evaluated through Equation A.102. * M = 0 2 * H + O S V , (A.102) Substituting the following expressions in the above equation: , , d M , , . * ( M ) = (afi) H o (A.103) Appendix A. Sample Calculations 250 would yield: °-2n = 2 ( ^ ) v w (A.105) The bracketed parameter: du du dd . k , . m  = Tem (A106) is calculated by differentiation of Equations A.101 and A.99 with respect to 6 and their subsequent replacement in Equation A. 106 as is shown in the folio wings: ^=R> = ^a[6b'.e-V[)-c[] (A.107) du R\ R" R' / A thus, where du; 1 . R" R'J 8R = R [ - R J + R ] fl(dR\ LI LI R" = 86 = ^ <dKe~C'6^i ~ <)2 ~ P (A-110) 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 Calculations 251 Table A.4: Maximum Drying Rates at Various Temperatures at Mass Flow of 142 kg/hr Run m T--1- in P*max iCa* x 103 s"1 kg/hr ° c s-1 at 142 kg/hr 12 152.5 126.3 1.02 0.97 11&20 141.9 150.9 1.07 1.07 19 126.8 204.8 1.25 1.36 22 126.7 220.7 1.41 1.53 39 97.9 170.9 0.93 1.22 42 95.5 189.5 1.00 1.34 45&46 94.0 205.8 1.39 1.88 41&44 90.9 220.9 1.61 2.24 43 86.3 245.7 1.730 2.46 A.9 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 ): ^ o c V ^ a m 0 - 7 1 (A.112) 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 Vin = 1.35 m/s and Tin = 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. Appendix A. Sample Calculations 252 Based on the experimental data ( see Section 4-3 ), a relationship of the form: Rmax = "'^ L + 0-823 X 10"3 (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 at 247°C to the one at 202°C is determined. This would yield to a corrected value of R m a x = 1.32 m/s for both temperature and weight of the wet solid. A.11 Effect of Bed Height on the Grate Heat Release Rate The grate heat release rate (h~g) is a function of both the bed height, L, and the residence time of the fuel on the grate hearth as expressed by: A hg = hs— =%,p.{l - e) - = A— = A- (A.114) where h~s = heigher heating value of dry fuel (kJ/kg) Vf,, vs = bulk and solid volumetric flow rate (m3/s) 6 = residence time (s) Thus, the effect of bed height on the grate heat release rate is determined through the following equation: dh^^dh^ 8^d6_ = A _ ALd6_ f A 115^ 1 dL dL 86 dL 6 0* dL ' Appendix A. Sample Calculations 253 Equation A. 115 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 (A.116) Substitution of Equation A. 116 in Equation A. 115 and subsequent integration would yield: = 2 0 4 (A.117) hx L x 204 + 1014Z,2 v ; where subscripts 1 and 2 indicate, respectively, the initial and final conditions. Appendix B Drying 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 0.0032 0.0028 •O 0.0024 o o » K 0.0020 0.0016 S* 0.0012 o • 0.0008 Experimental Pitted Run 1A T , . 62.3 *C V,. 1.40m/s L 23.1 om M. 1.14 d.b. d» 0.0 mm CO, O.OvolX Y „ 0.0021 d.b. -0.0004 0.0028 0.0024 -0.0020 -800 1600 2400 3200 4000 4800 9600 0 (a) -0.0004 O Experimental Pitted Run 1 T,. 101.8 *C v , » 1.43 m/s L 32.3om U. 1.14d.b. d, 6.3 mm CO, l.OvolX Y i . 0.0114d.b. _ i _ L 800 1600 2400 e (») 3200 4000 4800 0.0028 0.0024 Experimental Pitted -0.0004 Run 3 T „ E4i.3*C V,D 1.57 m/a -L 29.8 om Mo 1.41 d.b. d» 6.3 mm -CO, 1.7voIX Y , „ 0.0263d.b. _ l _ - L 0.0028 0.0024 I •rt o o • u TS a « u « «• 400 800 1200 6 («) 1600 2000 2400 0.0020 0.0016 0.0012 -0.0008 0.0004 0.00001 -0.0004 Experimental Pitted Run 4 T„ 106.7 *C v , „ 1.77m/» L 28.0 em M. 1.41 d.b. <h 6.3mm CO, l.OvolX Y „ 0.0306 d.b. _ l _ 400 800 1200 9 (a) 1600 2000 2400 Figure B . l : Drying Rates versus Time Appendix B. Drying Rate Curves 256 0.0028 0.0084 --0.0004 Experimental Pitted Run 8 T„ 204.0*C V,D 1.84 m/a L 28.4 om Mo 1.41d.b. d. 8.3 mm CO, l.SvolX T„ 0.0246d.b. 0.0004 K o.oooo< • 0.0028 0.0024 -0.0020 400 800 1200 1800 0 (e) 2000 2400 -0.0004 1 1 I 1 1 1 I 1 1 1 I O Experimental Pitted Run 0 T„ 154.8*C V,D 1.34 m/a L 16.1 om M. 1.41d.b. a. 8.3mm CO. 1.0 vol* Y.. 0.0168d.b. 800 1800 2400 3200 6 (a) 4000 4800 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 ) 0.0004 J.0000< ? -0.0004 Experimental Pitted Run 10 T„ lSB.l'C V,. 1.36m/s L 12.3 om Mo 1.41d.b. d. 6.3 mm CO. l.OvolX Y,. 0.0233 d.b. 0.0028 0.0024 -o 0.0020 o t o.ooie •a 800 1600 2400 3200 4000 4800 e (a) -0.0004 Experimental Pitted Run 11 • T„ 147.8 *C • V,D 1.33 m/a -L 24.0om M . 1.41d.b. o» 6.3mm -CO, l.OvolX Yi. 0.0139d.b. _i_L 800 1600 2400 3200 4000 4800 6 (a) Figure B.2: Drying Rates versus Time Appendix B. Drying Ra.te Curves 257 0.0028 0.0024 0.0020 u 0.0016 0.0012 0.0008 0.0004 Ot 0.00OOC >• -0.0004 Experimental Pitted Run 12 T„ 126.3 *C V,D 1.37 m/a L 27.0 om M. 1.41d.b. dt. 6.3mm CO, l.OvolX Y,. 0.0261 d.b. 0.0028 0.0024 0.0020 I •a o o u 0.0016 800 1600 2400 3200 4000 4800 0 (a) -0.0004 O Experimental Pitted Run 13 198.9 *C • vto 1.39 m/a -L 32.0om * M. 1.41 d.b. d. 6.3mm -CO. l.OvolX • Y« 0.0238 d.b. I 800 1600 2400 3200 0 (a) 4000 4800 0.0028 0.0024 -0.0020 0.0016 0.0012 0.0008 Experimental Pitted -0.0004 Run 14 100.7*C v,. 1.39m/a L 26.9 am M. 1.41d.b. d. 4 - 6mm CO, l.OvolX Y,. 0.0212d.b. _ u J _ _ i _ L 0.0028 0.0024 -I IB O e • U 800 1600 2400 3200 4000 4800 0 (a) 0.0020 -0.0016 -0.0012 -0.0008 0.0004 -0.0000 -0.0004 800 1600 2400 3200 B (a) 4000 4800 Figure B.3: Drying Rates versus Time Appendix B. Drying Rate Curves 258 0.0028 0.0024 -I o 0.0020 o » u 0.0016 •0 0.0012 0.0008 0.0004 os o.oooo< • -0.0004 Experimental Pitted Run 16 T„ 102.0'C v,» 1.33 m/s L 24.1 om M. 1.41d.b. dp 6 - 8mm CO. l.OvolX Y,. 0.0233d.b. 0.0028 0.0024 0.0020 800 1600 2400 0 (a) 3200 4000 4800 -0.0004 Experimental Pitted Run 17 T„ 148.8 "C v,„ 1.33 m/a L 30.2 om M. 1.41 d.b. dp 2 - 4 mm CO. l.OvolX 0.0201 d.b. 400 800 1200 « («) 1600 2000 2400 0.0028 0.0024 0.0020 0.0016 0.0012 0.0008 0.0004 03 0.0000( •)--0.0004 Experimental Pitted Run 18 T,. 163.8'C V,D 1.37m/e L 29.3 om Mo 1.41d.b. d. 8 - 10mm CO. l.OvolX Y„ 0.0211 d.b. I I I I t 0.0028 0.0024 0.0020 I D o o u 0.0016 •a 0.0012 0.0008 0.0004 06 O.OOOOC • 800 1600 2400 6 (a) 3200 4000 4800 -0.0004 Experimental Pitted Run 19 T,. 204.8*C V,B 1.39m/a L 29.3 om M. 1.14d.b. d. 6.3mm CO. l.OvolX Y„ 0.0210d.b. 400 800 1200 0 (a) 1600 2000 2400 Figure B.4: Drying Rates versus Time Appendix B. Drying Raie Curves 259 0.0028 0.0024 0.0020 Experimental Fitted I •O o e * b 0.0016 •o -0.0004 Run 20 T,. 1B4.0*C V,. 1.37 m/s L 26.4 cm Mo 1.41 d.b. d. 6.3 mm CO, l.OvolX Y„ 0.0149d.b. J . 0.0028 0.0024 -I o 0.0020 o u 0.0016 •0 800 1600 2400 6 («) 3200 4000 4800 -0.0004 Experimental Pitted Run 22 T t o 220.7 *C v„ 1.41 m/a L 24 .Bom U . 1.41d.b. d. 6.3mm CO, l.OvolX 0.0209d.b. 400 800 1200 6 (a) 1600 2000 2400 0.0028 0.0024 -0.0004 I 1 ' 1 I 1 1 1 I Experimental Pitted T Run 23 T„ 186.0'C v,D 1.32 m/a L 26.8 om M. 1.41 d.b. d. 6.3mm CO, l.OvolX T|. 0.1422d.b. 0.0096 0.0048 I •d o o » u •0 «* M V . o. 0.0040 0.0032 0.0024 M 0.0016 0.0008 400 800 1200 1600 0 (e) 2000 2400 -0.0008 O Experimental Pitted Run 26 T„ 246.8*C V,. 1.39 m/a -L 12.3cm M. 1.41d.b. • dp 6.3mm CO, 2.0volX • Y.» 0.0490d.b. _ l _ (X o.ooooc r 400 800 1200 1600 0 (a) 2000 2400 Figure B.5: Drying Rates versus Time Appendix B. Drying Rate Curves 260 0.0028 0.0024 -0.0020 0.0018 -0.0012 0.0008 0.0004 0.00001 -0.0004 Experimental Pitted Run 28 T„ 202.2 *C V,D 1.38 m/a L 2S.0om Mo 1.41d.b. d. 6.3mm CO, l.OvolX T,B 0.1347d.b. 0.0028 0.0024 I •e o o > u T J t* M \ It 0.0020 0.0016 0.0012 Li e « OS 400 800 1200 « <•) 1600 2000 2400 0.0008 0.0004 0.00001 -0.0004 Experimental Pitted O Run 30 T„ 201.7 *C • V,. 1.39 m/a -L 20.6 om U. 1.41d.b. • d. 6.3mm -CO, l.OvolX • Y„ 0.2896 d.b. • 2000 2400 Experimental Pitted 0.0000( • Run 31 T„ 194.3*C v, D 1.30m/a L 18.9om Mo 1.92 d.b. d> 6.3 mm CO, l.OvolX T „ 0.0199d.b. 0.0028 0.0024 -0.0020 -800 1600 2400 3200 0 (a) 4000 4800 -0.0004 T - r " Experlmental Pitted Run 32 • T i . 196.2 'C * v„ 1.33 m/a -L 21.9cm M. 1.92 d.b. • <«- 6.3mm -CO, l.OvolX Y„ 0.0226d.b. • 800 1600 2400 3200 4000 6 (a) 4800 Figure B.6: Drying Rates versus Time Appendix B. Drying Rate Curves 261 Exper iment*! Fi t ted Run 34 T „ 148.2'C V 1 D 1.29m/s L 24.0om M. 1.41 d.b. d . 8 .3mm CO, U . 7 v o l X Y, D 0.0130d.b. 0.0028 800 1000 2400 3200 6 (a) 4000 4800 -0.0004 800 1800 2400 3200 4000 4800 6 (a) 0.0096 0.0048 I o 0.0040 o ft h 0.0032 •e 0.0024 0.0016 0.0008 06 o.oooo( >• -0.0008 Exper imenta l Fi t ted Run 38 T „ 200.8 *C V , B 0.86 m / a L 12.lorn M. 1.41d.b. d . 6 .3mm Y„ ~d.b. 400 800 1200 0 (a) 0.0028 0.0024 0.0020 I •>3 C O ft U 0.0016 m >' e ft 0.0012 0.0008 0.0004 06 0.0000( • 1600 2000 2400 -0.0004 Expe r imen ta l Fi t ted R u n 39 T„ 170.0 «C V t o 900.69 m / a L 9029.1 om M. 1.41d.b. d . 6 .3mm Y„ •d .b . _1_ 800 1600 2400 0 (a) 3200 4000 4800 Figure B.7: Drying Rates versus Time Appendix B. Drying Rate Curves 262 0.0028 0.0024 0.0020 0.0016 -0.0004 Exper imenta l Pi t ted R u n 41 Ti . 280.8 *C V , . 0 .80m/a L 27.3cm M. 1.41 d.b. d . 6 .3mm T„ ••d.b. 0.0028 0.0024 I •O o o » •o of M V . P. e u • tt » OS 0.0020 0.0016 0.0012 0.0008 0.0004 0.0000< Vi 400 800 1200 B (a) 1600 2000 2400 -0.0004 ' 1 1 1 1 ' ' 1 1 ' 1 1 1 1 1 1 1 1 1 • o Exper imenta l Pit ted • R u n 42 • T„ 180.8 *C * - V,« 0.81 m / a -L 27.7 om M . 1.41d.b. • d, Yla 8 .3mm -d .b . • o p O ] JO q • O 800 1600 2400 0 (a) 3200 4000 4800 0.0028 0.0024 0.0004 OS 0.0000C • -0.0004 Exper imenta l Pi t ted R u n 43 T„ 248.7 *C v,» 0.82 m / a 1. 22.0 om M. 1.41 d.b. d, 6.3 m m T„ - d . b . JL _1_ 400 800 1200 0 (a) 0.0028 0.0024 1800 2000 2400 -0.0004 I ' ' ' I 1 1 ' I Exper imenta l • Pitted Run 44 • Tim 221.3*C * v,B 0.81 m / a -h 23.8 om M . 1.41d.b. • d> 6.3mm -d .b . • J L '<*> -L 400 800 1200 0 (a) 1800 2000 2400 Figure B.8: Drying Rates versus Time Appendix B. Drying Rate Curves 263 0.0028 0.0024 -0.0020 -0.0018 -0.0012 -0.0008 -0.0004 0.0000( • -0.0004 I 1 1 ' I O Exper imenta l Fitted i | i i i I i i i R u n 40 T„ 200.8 *C V , . 0.82 m / » L 24.8cm M. 1.41 d.b. d . 8 .3mm ~d.b. I • • • I _1_ 0.0028 0.0024 0.0020 400 800 1200 1800 « («) 2000 2400 -0.0004 I 1 1 1 I 1 1 1 I 1 Exper imenta l - Fit ted T R u n 4 0 2 0 4 . 7 *C • v „ 0 . 8 2 m / a -L 2 0 . 2 c m • U . 1 . 4 1 d.b. • <», 8.3mm -T» - d . b . • I 1 I I I 400 800 1200 0 (a) 1800 2000 2400 Figure B.9: Drying Rates versus Time Appendix B. Drying Rate Curves 264 Table B . l : Parameters in the Fit" of Drying Rate Curve R u n a ' i b'i c'-i ' a'3 c ' , s ~ ] s - 1 s " 3 s - 1 s - 1 s - 1 0 0.13E-09 0.20E+01 0.93E-03 0.65E-11 0.30E+01 0.28E-02 0.38E-06 0 15E+01 0.59E-02 1 0.24E-O7 0.15E+01 0.14E-02 0.17E-07 0.20E+01 0.39E-02 0.84E-09 0 30E+01. 0.27E-01 3 0.26E-10 0.35E+01 0.81E-02 0.16E-08 0.20E+01 O.21E-02 0.39E-08 0 30E+01 0.17E-01 4 0.21E-07 0.15E+01 0.16E-02 0.28B-07 0.20E+01 0.39E-02 0.12E-08 0 30E+01 0.14E-01 8 0.18E-05 0.15E+01 0.80E-02 O.21E-07 0.20E+01 0.88E-02 0.72E-10 0 30E+01 0.49E-02 9 0.32E-06 0.15E+01 0.28E-02 0.18E-06 0.20E+01 0.11E-01 0.20E-07 0 30E+01 0.49E-01 10 0.16E-06 0.-15E+01 0.24E-02 0.14E-06 0.20E+01 0.80E-02 0.12E-O7 0 30E+01 0.28E-01 11 0.28E-06 0.15E+01 0.25E-02 0.24E-07 0.20E+01 0.77E-02 0.95E-09 0 30E+01 0.17E-01 12 0.16E-06 0.15E+01 0.21E-02 0.15E-06 0.20E+01 0.13E-01 0.14E-09 0 30E+01 0.84E-02 13 0.17E-06 0.15E+01 0.20E-O2 0.29E-06 0.20E+01 0.30E-01 0.35E-09 0 30E+01 0.10E-01 14 0.14E-O5 0.15E+01 0.84E-02 0.10E-08 0.20E+01 0.16E-02 0.64E-10 0 30E+01 0.50E-02 15 0.17E-04 0.30E+00 0.42E-03 0.19E-24 0.75E+01 0.42E-02 0.48E-23 0 80E+01 0.89E-02 1(5 0.82E-06 0.15E+01 0.63E-02 0.72E-08 0.20E+01 0.24E-02 0.87E-08 0 30E+01 0.38E-01 17 0.14E-05 0.15E+01 0.80E-02 0.12E-08 0.20E+01 0.18E-02 0.67E-10 0 30E+01 0.48E-02 18 0.56E-07 0.15E+01 0.17E-02 0.20E-07 0.20E+01 0.41E-02 0.72E-09 0 30E+01 0.14E-01 19 0.38E-06 0.15E+01 0.28E-02 0.42E-07 0.20E+01 0.82E-02 0.27E-08 0 30E+01 0.25E-01 20 0.42E-06 0.15E+01 0.40E-02 0.58E-07 0.20E+01 0.96E-02 0.86E-11 0 30E+01 0.29E-02 22 0.38E-10 . 0.35E+01 0.99E-02 0.11E-10 CI.32E+01 0.40E-02 0.37E-08 0 30E+01 0.22E-01 23 0.26E-11 0.35E+01 0.44E-02 0.51E-09 0.32E+01 0.25E-01 0.18E-09 0 30E+01 0.76E-02 26 0.19E-04 0.15E+01 0.32E-01 0.11E-06 0.20E+01 0.58E-02 0.47E-08 0 30E+01 0.18E-01 29 0.12E-11 0.35E+01 0.38E-02 0.21E-09 0.32E+01 0.21E-01 0.16E-09 0 30E+01 0.68E-02 30 0.26E-10 0.30E+01 0.37E-02 0.14E-16 0.60E+01 0.11E-01 0.18E-10 0 40E+01 0.24E-01 31 0.11E-05 0.15E+01 0.60E-02 0.84E-07 0.20E + 01 0.16E-01 0.34E-10 0 30E+01 0.35E-02 32 0.19E-07 0.15E+01 0.17E-02 0.85E-07 0.20E+01 0.74E-02 0.43E-10 0 30E+01 0.39E-02 34 0.88E-06 0.15E+01 0.50E-02 0.79E-11 0.30E+01 0.29E-02 0.37E-06 0 20E+01 0.20E-01 36 0.24E-O6 0.15E+01 0.25E-02 0.14E-06 0.20E+01 0.99E-02 0.22E-07 0 30E+01 0.42E-01 38 0.13E-04 0.15E+01 0.24E-01 0.18E-06 0.20E+01 0.69E-02 0.68E-09 0 30E+01 0.14E-01 39 0.78E-06 0.15E+01 0.77E-02 0.71E-10 0.20E+01 0.64E-03 0.47E-10 0 30E+01 0.42E-02 41 0.59E-06 0.20E+01 0.19E-01 0.11E-07 0.25E+01 0.10E-01 0.83E-10 0 30E+01 0.49E-02 42 0.68E-08 0.20E+01 0.24E-02 0.13E-09 0.30E+01 0.82E-02 0.18E-05 0 15E+01 0.10E-01 43 0.46E-05 0.15E+01 0.13E-01 0.22E-07 0.20E+01 0.37E-02 0.34E-09 0 30E+01 0.94E-02 44 0.43E-05 0.15E+01 0.22E-01 0.19E-07 0.20E+01 0.35E-02 0.26E-08 0 30E+01 0.14E-01 45 0.13E-06 0.15E + 01 0.21E-O2 0.84E-07 0.20E+01 0.67E-02 0.13E-07 0 30E+01 0.39E-01 46 a 0.36E-06 0.15E+01 0.29E-O2 0.18E-06 0.20E+01 0.11E-01 0.30E-07 0 30E+01 0.49E-01 a Equat ion 4.1 Appendix B. Drying Rate Curves Table B.2: Summary of Data Representing the Goodness of the Fit Run n SR X 10 6 ov 2 x 10 6 <TT x 10 3 S p x 10 6 6/ x 10 6 <5P x 10 3 s- 2 s " 2 s - 1 s- 2 s - 2 s - 1 0 113 0.004 0.0000 0.006 2.100 0.004 0.0000 0.006 1 99 0.322 0.0035 0.059 2.100 0.366 0.0039 0.063 3 30 0.171 0.0071 0.084 2.490 0.277 0.0116 0.107 4. 48 0.119 0.0028 0.053 2.340 0.159 0.0038 0.062 8 34 0.283 0.0101 0.101 2.450 0.432 0.0154 0.124 9 76 0.452 0.0065 0.080 2.220 0.538 0.0077 0.088 10 132 2.838 0.0225 0.150 2.100 3.122 0.0248 0.157 11 75 0.044 0.0006 0.025 2.240 0.053 0.0008 0.028 12 96 0.078 0.0009 0.030 2.220 0.090 0.0010 0.032 13 70 0.479 • 0.0075 0.086 2.240 0.579 0.0091 0.095 14 85 0.107 0.0014 0.037 2.230 0.125 0.0016 0.040 15 99 0.155 0.0017 0.041 2.220 0.178 0.0019 0.044 16 68 0.088 0.0014 0.038 2.250 0.108 0.0017 0.042 17 61 0.134 0.0024 0.049 2.250 0.167 0.0030 0.055 18 82 0.139 0.0018 0.043 2.250 0.164 0.0022 0.046 19 62 0.035 0.0006 0.025 2.250 0.044 0.0008 0.028 20 86 0.027 0.0003 0.018 2.250 0.031 0.0004 0.020 22 27 0.029 0.0014 0.037 2.560 0.049 0.0024 0.049 23 43 0.293 0.0079 0.089 2.380 0.407 0.0110 0.105 26 36 0.745 0.0248 0.158 2.420 1.106 0.0369 0.192 29 42 1.309 0.0364 0.191 2.380 1.829 0.0508 0.225 30 41 3.229 0.0923 0.304 2.310 4.508 0.1288 0.359 31 48 1.636 0.0390 0.197 2.310 2.176 0.0518 0.228 32 88 0.408 0.0050 0.071 2.200 0.473 0.0058 0.076 34 134 0.069 0.0005 0.023 2.100 0.076 0.0006 0.024 36 113 0.046 0.0004 0.021 2.180 0.052 0.0005 0.022 38 25 0.506 0.0266 0.163 2.700 0.938 0.0494 0.222 39 67 0.214 0.0035 0.059 2.250 0.262 0.0043 0.065 41 44 0.250 0.0066 0.081 2.380 0.345 0.0091 0.095 42 49 0.245 0.0057 0.075 2.300 0.323 0.0075 0.087 43 58 0.245 0.0047 0.069 2.300 0.309 0.0060 0.077 44 43 0.227 0.0061 0.078 2.340 0.314 0.0085 0.092 45 45 0.144 0.0037 0.061 2.340 0.195 0.0050 0.071 46 31 0.208 0.0067 0.082 2.400 0.305 0.0098 0.099 aa' = 0.05; therefore, 95% confidence region 6 fit of drying rates versus time(see Equation 4-1 )• Appendix C Tabulated Instantaneous Drying Rate Data The Instantaneous experimental and predicted (Equation 4.1) drying rates, their resid-ual 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 char-acteristic moisture contents, $, used for prepration of the drying rate curves. 266 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.l: Summary of Data for Run 1A 267 6 s R E x 103 s-1 R P x 103 s-1 (RE -RP)x 103 s-1 cT p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.140 0.000 1.113 50 0.122 0.103 0.019 0.001 1.138 0.213 1.111 95 0.230 0.210 0.021 0.001 1.131 0.435 1.104 134 0.284 0.285 -0.001 0.002 1.121 0.592 1.094 173 0.342 0:342 0.001 0.002 1.109 0.710 1.082 212 0.381 0.382 -0.000 0.003 1.095 0.793 1.068 251 0.406 0.409 -0.002 0.003 1.079 0.849 1.053 336 0.425 0.437 -0.012 0.003 1.043 0.909 1.017 375 0.437 0.443 -0.006 0.002 1.026 0.920 1.000 414 0.443 0.446 -0.003 0.002 1.008 0.927 0.983 453 0.450 0.448 0.002 0.002 0.991 0.931 0.965 492 0.452 0.450 0.002 0.002 0.973 0.934 0.948 531 0.455 0.452 0.003 0.002 0.956 0.939 0.930 570 0.470 0.454 0.016 0.002 0.938 0.944 0.913 655 0.473 0.461 0.012 0.002 0.899 0.957 0.874 694 0.466 0.465 0.001 0.002 0.881 0.965 0.856 733 0.472 0.468 0.003 0.002 0.863 0.972 0.838 772 0.467 0.472 -0.005 0.002 0.845 0.980 0.820 811 0.481 0.475 0.006 0.002 0.826 0.986 0.802 850 0.475 0.477 -0.003 0.002 0.808 0.992 0.783 895 0.484 0.480 0.004 0.002 0.786 0.997 0.762 974 0.481 0.481 -0.001 0.002 0.748 1.000 0.724 1013 0.481 0.481 -0.000 0.002 0.729 0.999 0.705 1052 0.476 0.479 -0.003 0.002 0.711 0.996 0.687 1091 0.475 0.477 -0.002 0.002 0.692 0.991 0.668 1130 0.437 0.474 -0.037 0.002 0.674 0.984 0.650 1175 0.467 0.469 -0.002 0.002 0.652 0.973 0.629 1215 0.464 0.463 0.001 0.002 0.634 0.962 0.610 1293 0.455 0.450 0.004 0.002 0.598 0.935 0.575 1332 0.447 0.443 0.004 0.002 0.581 0.920 0.557 1371 0.437 0.435 0.002 0.002 0.564 0.903 0.540 1410 0.423 0.426 -0.003 0.002 0.547 0.885 0.524 1474 0.418 0.411 0.007 0.002 0.520 0.853 0.497 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.l: Summary of Data for Run 1A -(Continued) 268 e s RE x 103 s-1 RP x 103 s-1 (RE - RP) x 103 s-1 <7p X 103 s-1 M / $ 1495 0.409 0.405 0.004 0.002 0.511 0.842 0.488 1534 0.401 0.395 0.005 0.002 0.496 0.821 0.473 1612 0.377 0.375 0.002 0.002 0.466 0.779 0.443 3454 0.079 0.078 0.000 0.002 0.121 0.163 0.100 3468 0.077 0.077 -0.001 0.002 0.120 0.161 0.099 3482 0.076 0.077 -0.001 0.002 0.118 0.159 0.098 3511 0.076 0.075 0.001 0.002 0.116 0.156 0.096 3525 0.076 0.075 0.001 0.002 0.115 0.155 0.095 3539 0.074 0.074 0.001 0.002 0.114 0.153 0.094 3582 0.071 0.072 -0.001 0.002 0.111 0.149 0.090 3596 0.071 0.071 -0.000 0.002 0.110 0.148 0.089 3611 0.070 0.070 -0.000 0.002 0.109 0.146 0.088 3639 0.069 0.069 -0.000 0.002 0.107 0.143 0.086 3653 0.068 0.068 -0.000 0.002 0.106 0.142 0.086 3668 0.067 0.068 -0.001 0.002 0.105 0.141 0.085 3696 0.065 0.067 -0.001 0.001 0.103 0.138 0.083 3725 0.065 0.065 -0.000 0.001 0.101 0.136 0.081 3753 0.063 0.064 -0.001 0.001 0.099 0.133 0.079 3767 0.063 0.064 -0.000 0.001 0.099 0.132 0.078 3782 0.063 0.063 0.000 0.001 0.098 0.131 0.077 3810 0.062 0.062 -0.000 0.001 0.096 0.129 0.075 3825 0.060 0.061 -0.001 0.001 0.095 0.127 0.074 3839 0.060 0.061 -0.001 0.001 0.094 0.126 0.074 3882 0.059 0.059 0.000 0.001 0.091 0.123 0.071 3896 0.058 0.059 -0.001 0.001 0.091 0.122 0.070 3910 0.058 0.058 -0.000 0.002 0.090 0.121 0.069 3939 0.056 0.057 -0.001 0.002 0.088 0.119 0.068 3953 0.056 0.057 -0.001 0.002 0.087 0.118 0.067 3967 0.056 0.056 -0.001 0.002 0.087 0.117 0.066 3996 0.055 0.055 -0.000 0.002 0.085 0.115 0.065 4024 0.054 0.054 -0.001 0.002 0.083 0.113 0.063 4053 0.053 0.053 -0.001 0.002 0.082 0.111 0.061 4067 0.053 0.053 -0.000 0.002 0.081 0.110 0.061 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.l: Summary of Data for Run 1A -(Continued) 269 6 s RE X 103 s-1 RP x 103 s-1 { R E - R P ) X 103 s-1 cT p X 103 s-1 M / $ 4081 0.051 0.053 -0.001 0.002 0.080 0.109 0.060 4110 0.051 0.052 -0.001 0.002 0.079 0.107 0.058 4124 0.050 0.051 -0.001 0.002 0.078 0.106 0.058 4138 0.050 0.051 -0.001 0.002 0.077 0.106 0.057 4181 0.049 0.050 -0.001 0.002 0.075 0.103 0.055 4195 0.048 0.049 -0.001 0.002 0.075 0.102 0.054 4210 0.048 0.049 -0.001 0.001 0.074 0.101 0.053 4238 0.047 0.048 -0.001 0.001 0.072 0.100 0.052 4252 0.047 0.048 -0.000 0.001 0.072 0.099 0.051 4267 0.047 0.047 0.000 0.001 0.071 0.098 0.051 4295 0.047 0.046 0.000 0.001 0.070 0.096 0.049 4324 0.045 0.046 -0.001 0.001 0.068 0.095 0.048 4352 0.045 0.045 -0.000 0.001 0.067 0.093 0.047 4367 0.044 0.045 -0.000 0.001 0.067 0.092 0.046 4381 0.044 0.044 -0.001 0.001 0.066 0.092 0.046 4395 0.044 0.044 -0.000 0.001 0.065 0.091 0.045 4424 0.044 0.043 0.000 0.001 0.064 0.090 0.044 4438 0.043 0.043 0.000 0.001 0.063 0.089 0.043 4492 0.042 0.041 0.000 0.001 0.061 0.086 0.041 4531 0.040 0.041 -0.001 0.001 0.060 0.084 0.039 4570 0.041 0.040 0.001 0.001 0.058 0.082 0.038 4615 0.039 0.039 0.001 0.001 0.056 0.080 0.036 4655 0.039 0.038 0.001 0.001 0.055 0.079 0.034 4694 0.038 0.037 0.001 0.001 0.053 0.077 0.033 4733 0.036 0.036 0.000 0.001 0.052 0.075 0.032 4812 0.036 0.035 0.002 0.001 0.049 0.072 0.029 4851 0.034 0.034 0.001 0.001 0.048 0.070 0.028 4890 0.034 0.033 0.001 0.001 0.046 0.069 0.026 4954 0.034 0.032 0.002 0.001 0.044 0.066 0.024 4975 0.034 0.032 0.002 0.001 0.044 0.066 0.023 5014 0.033 0.031 0.002 0.001 0.042 0.064 0.022 5053 0.032 0.030 0.002 0.001 0.041 0.063 0.021 5132 0.032 0.029 0.003 0.001 0.039 0.060 0.019 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.2: Summary of Data for Run 1 270 e s RE x 103 s-1 RP x 103 s-1 {RE - Rp)x 103 s-1 <7p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.140 0.000 1.383 66 0.095 0.110 -0.015 0.046 1.137 0.149 1.379 109 0.258 0.212 0.045 0.039 1.130 0.289 1.371 153 0.198 0.303 -0.105 0.036 1.119 0.411 1.357 196 0.566 0.383 0.183 0.035 •1.104 0.520 1.339 240 0.272 0.461 -0.189 0.027 1.086 0.626 1.316 283 0.572 0.531 0.041 0.023 1.064 0.722 1.289 327 0.630 0.595 0.035 0.023 1.039 0.808 1.259 370 0.695 0.645 0.050 0.023 1.013 0.877 1.226 413 0.710 0,684 0.026 0.023 0.984 0.930 1.190 457 0.727 0.712 0.015 0.021 0.953 0.968 1.152 500 0.719 0.729 -0.010 0.020 0.922 0.990 1.114 544 0.746 0.736 0.011 0.018 0.890 1.000 1.074 588 0.703 0.734 -0.031 0.017 0.858 0.998 1.034 631 0.719 0.726 -0.007 0.017 0.826 0.987 0.995 675 0.680 0.712 -0.032 0.016 0.795 0.967 0.956 718 0.675 0.694 -0.018 0.017 0.764 0.943 0.919 762 0.676 0.672 0.005 0.017 0.734 0.913 0.882 805 0.636 0.647 -0.012 0.017 0.706 0.880 0.847 849 0.631 0.621 0.010 0.017 0.678 0.844 0.812 892 0.597 0.594 0.003 0.016 0.652 0.808 0.780 935 0.555 0.567 -0.012 0.016 0.627 0.771 0.749 979 0.468 0.539 -0.071 0.016 0.603 0.733 0.719 1022 0.471 0.513 -0.042 0.015 0.580 0.696 0.691 1066 0.475 0.486 -0.011 0.015 0.558 0.660 0.664 1109 0.467 0.460 0.007 0.014 0.538 0.625 0.639 1153 0.433 0.435 -0.003 0.014 0.518 0.592 0.615 1196 0.443 0.412 0.031 0.013 0.500 0.560 0.592 1240 0.404 0.389 0.015 0.013 0.482 0.529 0.571 1284 0.392 0.368 0.024 0.013 0.466 0.500 0.550 1327 0.361 0.348 0.013 0.013 0.450 0.473 0.531 1371 0.353 0.329 0.024 0.013 0.435 0.447 0.513 1414 0.335 0.311 0.024 0.013 0.421 0.423 0.496 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.2: Summary of Data for Run 1 -(Continued) 271 e s R E x 103 s"1 R P x 103 s-1 (RE - RP) x 103 s-1 cTp x 103 s-1 M / $ 1457 0.337 0.295 0.043 0.013 0.408 0.401 0.480 1501 0.311 0.279 0.032 0.013 0.396 0.379 0.464 1544 0.308 0.265 0.043 0.013 0.384 0.360 0.450 1588 0.183 0.251 -0.068 0.013 0.373 0.341 0.436 1631 0.581 0.238 0.342 0.013 0.362 0.324 0.423 1675 0.049 0.226 -0.177 0.013 0.352 0.307 0.410 1718 0.111 0.215 -0.104 0.013 0.343 0.292 0.398 1762 0.325 0.205 0.121 0.012 0.333 0.278 0.387 1805 0.215 0.195 0.020 0.012 0.325 0.265 0.376 1849 0.186 0.186 0.000 0.012 0.316 0.252 0.366 1892 0.179 0.177 0.002 0.012 0.309 0.241 0.356 1936 0.168 0.169 -0.001 0.012 0.301 0.229 0.347 1979 0.139 0.161 -0.023 0.011 0.294 0.219 0.338 2022 0.132 0.154 -0.022 0.011 0.287 0.210 0.330 2066 0.098 0.147 -0.050 0.011 0.281 0.200 0.322 2110 0.126 0.141 -0.015 0.011 0.274 0.191 0.314 2153 0.121 0.135 -0.014 0.010 0.268 0.183 0.306 2197 0.108 0.129 -0.022 0.010 0.262 0.175 0.299 2240 0.101 0.124 -0.023 0.010 0.257 0.168 0.293 2284 0.086 0.119 -0.033 0.010 0.252 0.161 0.286 2327 0.091 0.114 -0.023 0.010 0.247 0.154 0.280 2371 0.0.90 0.109 -0.019 0.009 0.242 0.148 0.274 2414 0.067 0.105 -0.038 0.009 0.237 0.142 0.268 2458 0.082 0.100 -0.018 0.009 0.233 0.136 0.263 2501 0.066 0.096 -0.031 0.009 0.228 0.131 0.257 2545 0.066 0.092 -0.026 0.009 0.224 0.125 0.252 2588 0.066 0.089 -0.022 0.009 0.220 0.120 0.247 2631 0.065 0.085 -0.020 0.009 0.217 0.115 0.243 2675 0.053 0.082 -0.028 0.009 0.213 0.111 0.238 2718 0.057 0.078 -0.021 0.009 0.210 0.106 0.234 2762 0.049 0.075 -0.026 0.009 0.206 0.102 0.230 2806 0.053 0.072 -0.019 0.009 0.203 0.098 0.226 2849 0.058 0.069 -0.011 0.010 0.200 0.094 0.222 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.2: Summary of Data for Run 1 -(Continued) 272 9 s R E X 103 s-1 R P x 103 s-1 (RE - RP) x 103 s-1 cT p x 103 s-1 M / $ 2893 0.041 0.066 -0.025 0.010 0.197 0.090 0.219 2936 0.046 0.064 -0.018 0.010 0.194 0.086 0.215 2980 0.056 0.061 -0.005 0.010 0.191 0.083 0.212 3023 0.047 0.059 -0.012 0.010 0.189 0.080 0.209 3067 0.041 0.056 -0.015 0.010 0.186 0.076 0.205 3110 0.053 0.054 -0.001 0.010 0.184 0.073 0.202 3154 0.047 0.052 -0.005 0.010 0.182 0.070 0.200 3197 0.042 0.049 -0.008 0.010 0.180 0.067 0.197 3241 0.038 0.047 -0.009 0.010 0.177 0.064 0.194 3284 0.049 0.045 0.004 0.010 0.175 0.062 0.192 3328 0.061 0.044 0.017 0.009 0.173 0.059 0.189 3371 0.078 0.042 0.037 0.009 0.172 0.057 0.187 3415 0.075 0.040 0.035 0.009 0.170 0.054 0.185 3458 0.083 0.038 0.045 0.009 0.168 0.052 0.183 3502 0.074 0.037 0.038 0.009 0.166 0.050 0.181 3545 0.059 0.035 0.024 0.009 0.165 0.048 0.179 3589 0.047 0.034 0.013 0.009 0.163 0.046 0.177 3632 0.041 0.032 0.009 0.009 0.162 0.044 0.175 3676 0.036 0.031 0.005 0.009 0.161 0.042 0.174 3719 0.058 0.029 0.028 0.009 0.159 0.040 0.172 3763 0.044 0.028 0.015 0.008 0.158 0.038 0.170 3806 0.038 0.027 0.011 0.008 0.157 0.037 0.169 3850 0.046 0.026 0.020 0.008 0.156 0.035 0.168 3893 0.044 0.025 0.019 0.008 0.155 0.034 0.166 3937 0.068 0.024 0.045 0.008 0.154 0.032 0.165 3980 0.036 0.023 0.013 0.008 0.153 0.031 0.164 4024 0.046 0.022 0.024 0.007 0.152 0.029 0.162 4067 0.053 0.021 0.033 0.007 0.151 0.028 0.161 4111 0.065 0.020 0.045 0.007 0.150 0.027 0.160 4154 0.057 0.019 0.039 0.007 0.149 0.026 0.159 4198 0.073 0.018 0.055 0.007 0.148 0.024 0.158 4241 0.058 0.017 0.041 0.007 0.147 0.023 0.157 4285 0.046 0.016 0.030 0.000 0.147 0.022 0.156 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.3: Summary of Data for Run 3 273 e s R E x 103 s-1 R P x 103 s-1 (RE - RP) x 103 s"1 <7p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.042 1.410 0.000 1.376 65 0.153 0.400 -0.247 0.058 1.402 0.221 1.368 109 1.130 0.968 0.162 0.050 1.372 0.535 1.338 152 1.420 1.414 0.006 0.048 1.320 0.781 1.287 196 1.599 1.679 -0.080 0.048 1.251 .0.927 1.219 239 1.862 1.789 0.073 0.044 1.176 0.988 1.145 283 1.781 1.811 -0.030 0.041 1.097 1.000 1.066 326 1.787 1.784 0.002 0.041 1.019 0.985 0.990 370 1.697 1.731 -0.034 0.041 0.942 0.956 0.913 413 1.666 1.662 0.004 0.039 0.869 0.918 0.841 457 1.587 1.578 0.009 0.036 0.798 0.872 0.770 500 1.467 1.484 -0.018 0.034 0.732 0.820 0.705 544 1.385 1.379 0.006 0.035 0.669 0.762 0.642 587 1.308 1.270 0.038 0.036 0.612 0.702 0.586 631 1.178 1.157 0.022 0.037 0.558 0.639 0.533 675 1.129 1.044 0.085 0.037 0.510 0.577 0.485 718 0.988 0.938 0.050 0.036 0.467 0.518 0.443 761 0.619 0.839 -0.221 0.034 0.429 0.464 0.405 805 0.525 0.746 -0.221 0.033 0.394 0.412 0.371 848 0.636 0.664 -0.027 0.033 0.364 0.367 0.341 892 0.580 0.589 -0.009 0.034 0.337 0.325 0.313 935 0.478 0.525 -0.047 0.034 0.313 0.290 0.290 979 0.504 0.467 0.037 0.033 0.291 0.258 0.268 1022 0.460 0.419 0.041 0.032 0.272 0.232 0.249 1066 0.418 0.377 0.040 0.030 0.254 0.208 0.232 1109 0.362 0.342 0.020 0.029 0.239 0.189 0.217 1152 0.322 0.312 0.010 0.029 0.225 0.172 0.203 1196 0.292 0.286 0.006 0.031 0.212 0.158 0.190 1239 0.271 0.264 0.007 0.036 0.200 0.146 0.178 1283 0.235 0.245 -0.010 0.043 0.189 0.135 0.167 1326 0.219 0.229 -0.010 0.053 0.178 0.126 0.157 1370 0.180 0.214 -0.035 0.000 0.169 0.118 0.147 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.4: Summary of Data for Run 4 274 6 s R E x 103 s - 1 R P x 103 s - 1 {RE - RP) x 103 s - 1 crp x 103 s - 1 M / $ 0 0.001 0.000 0.001 0.025 1.410 0.000 1.418 51 0.107 0.144 -0.037 0.030 1.408 0.106 1.416 124 0.714 0.693 0.021 0.027 1.378 0.507 1.386 160 1.022 0.944 0.078 0.026 1.348 0.691 1.355 226 1.217 1.240 -0.023 0.024 1.275 0.907 1.281 263 1.273 1.320 -0.047 0.023 1.227 0.966 1.232 335 1.362 1.366 -0.004 0.021 1.130 1.000 1.133 365 1.429 1.361 0.069 0.020 1.089 0.996 1.091 431 1.324 1.325 -0.002 0.019 1.000 0.970 1.000 467 1.316 1.299 0.016 0.019 0.953 0.951 0.952 533 1.214 1.245 -0.031 0.018 0.869 0.912 0.866 569 1.166 1.213 -0.047 0.018 0.825 0.888 0.821 635 1.203 1.149 0.053 0.017 0.747 0.841 0.742 672 1.080 1.111 -0.030 0.017 0.705 0.813 0.699 744 1.042 1.031 0.011 0.016 0.628 0.755 0.620 774 0.946 0.997 -0.050 0.016 0.598 0.730 0.589 840 0.953 0.919 0.034 0.015 0.534 0.672 0.525 876 0.879 0.876 0.003 0.015 0.502 0.641 0.492 942 0.826 0.797 0.029 0.015 0.447 0.584 0.436 978 0.831 0.755 0.076 0.015 0.419 0.553 0.407 1044 0.672 0.681 -0.010 0.015 0.371 0.499 0.359 1074 0.623 0.649 -0.026 0.015 0.352 0.475 0.338 1146 0.536 0.575 -0.039 0.015 0.308 0.421 0.293 1176 0.499 0.546 -0.047 0.015 0.291 0.400 0.276 1248 0.481 0.481 0.000 0.015 0.254 0.352 0.239 1278 0.484 0.456 0.028 0.014 0.240 0.334 0.224 1344 0.455 0.405 0.050 0.014 0.211 0.296 0.195 1380 0.494 0.379 0.115 0.015 0.197 0.277 0.181 1446 0.361 0.336 0.025 0.016 0.174 0.246 0.157 1482 0.309 0.315 -0.005 0.018 0.162 0.230 0.145 1555 0.198 0.275 -0.078 0.023 0.140 0.201 0.123 1585 0.218 0.261 -0.043 0.026 0.132 0.191 0.115 1621 0.256 0.244 0.012 0.000 0.123 0.179 0.105 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.5: Summary of Data for Run 8 275 e s R E x 103 s-1 R P x 103 s"1 (RE - Rp) x 103 s-1 * p x 103 s-1 M / 0 0.001 0.000 0.001 0.000 1.410 0.000 1.324 48 0.684 0.451 0.232 0.065 1.400 0.309 1.315 84 0.589 0.817 -0.228 0.060 1.377 0.560 1.293 114 1.118 1.054 0.064 0.050 1.349 0.723 1.266 150 1.195 1.254 -0.059 ' 0.049 1.307 0.860 1.226 186 1.334 1.376 -0.043 0.049 1.260 0.944 1.181 216 1.460 1.431 0.028 0.047 1.218 0.982 1.141 289 1.510 1.455 0.055 0.039 1.112 0.998 1.040 325 1.391 1.433 -0.041 0.039 1.060 0.982 0.990 361 1.410 1,399 0.011 0.040 1.009 0.959 0.941 391 1.311 1.366 -0.055 0.039 0.967 0.937 0.902 427 1.198 1.323 -0.125 0.037 0.919 0.907 0.856 457 1.289 1.285 0.004 0.035 0.880 0.881 0.819 493 1.327 1.239 0.088 0.033 0.834 0.850 0.775 566 1.086 1.144 -0.058 0.032 0.747 0.785 0.692 602 0.987 1.097 -0.110 0.032 0.707 0.752 0.654 632 0.937 1.057 -0.121 0.033 0.674 0.725 0.623 668 1.024 1.009 0.015 0.033 0.637 0.692 0.588 704 1.070 0.961 0.109 0.033 0.602 0.659 0.554 734 0.999 0.921 0.079 0.032 0.574 0.631 0.527 770 0.803 0.872 -0.070 0.030 0.541 0.598 0.496 836 0.817 0.784 0.033 0.028 0.487 0.538 0.444 872 0.803 0.737 0.067 0.027 0.459 0.505 0.418 909 0.798 0.689 0.109 0.027 0.433 0.472 0.393 945 0.721 0.643 0.077 0.029 0.409 0.441 0.370 981 0.639 0.599 0.040 0.030 0.387 0.411 0.349 1011 0.576 0.564 0.012 0.032 0.369 0.387 0.332 1047 0.471 0.522 -0.052 0.035 0.350 0.358 0.314 1113 0.378 0.451 -0.073 0.039 0.317 0.309 0.283 1149 0.368 0.415 -0.047 0.040 0.302 0.285 0.268 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.6: Summary of Data for Run 9 276 9 s RE x 103 s"1 RP x 103 s"1 {RE - Rp) x 103 s-1 <TP x 103 s"1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.275 51 0.556 0.594 -0.039 0.075 1.397 0.434 1.264 81 0.947 0.883 0.064 0.059 1.375 0.644 1.243 117 1.075 1.089 -0.015 0.056 1.339 0.795 1.210 153 1.141 1.233 -0.092 0.043 1.297 0.900 1.172 183 1.360 1.313 0.048 0.043 1.259 0.958 1.137 249 1.295 1.370 -0.075 0.035 1.170 1.000 1.055 285 1.371 1.352 0.019 0.032 1.120 0.987 1.010 322 1.392 1.314 0.077 0.032 1.071 0.959 0.964 358 1.333 1.269 0.064 0.032 1.025 0.926 0.922 394 1.242 1.221 0.021 0.031 0.980 0.891 0.880 424 1.253 1.182 0.071 0.029 0.944 0.863 0.847 490 1.088 1.102 -0.014 0.025 0.868 0.805 0.778 526 1.029 1.063 -0.034 0.023 0.829 0.776 0.743 556 1.013 1.032 -0.019 • 0.022 0.798 0.754 0.714 592 0.899 0.998 -0.099 0.022 0.761 0.728 0.680 622 1.017 0.970 0.047 0.022 0.732 0.708 0.653 658 0.845 0.937 -0.092 0.022 0.698 0.684 0.622 724 0.771 0.879 -0.108 0.022 0.638 0.642 0.567 760 0.760 0.848 -0.088 0.022 0.607 0.619 0.538 790 0.669 0.822 -0.153 0.021 0.581 0.600 0.515 826 0.845 0.791 0.054 0.021 0.552 0.577 0.488 863 0.869 0.759 0.110 0.020 0.524 0.554 0.462 899 0.745 0.728 0.017 0.019 0.497 0.531 0.438 965 0.862 0.671 0.190 0.017 0.451 0.490 0.395 1001 0.753 0.641 0.112 0.017 0.427 0.468 0.374 1031 0.656 0.616 0.040 0.016 0.408 0.450 0.356 1067 0.649 0.586 0.063 0.016 0.387 0.428 0.336 1097 0.621 0.562 0.058 0.015 0.370 0.410 0.321 1133 0.507 0.534 -0.026 0.015 0.350 0.390 0.303 1206 0.525 0.478 0.047 0.015 0.313 0.349 0.269 1243 0.484 0.452 0.033 0.015 0.296 0.330 0.253 1279 0.381 0.427 -0.046 0.015 0.280 0.311 0.238 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.6: Summary of Data for Run 9 -(Continued) 277 e s RE x 103 s"1 RP x 103 s-1 ( R E - R P ) x 103 s-1 <jp x 103 s-1 M / $ 1315 0.460 0.403 0.058 0.015 0.265 0.294 0.225 1345 0.378 0.383 -0.005 0.015 0.253 0.280 0.214 1381 0.330 0.361 -0.031 0.015 0.240 0.263 0.202 1447 0.417 0.322 0.095 0.015 0.217 0.235 0.181 1484 0.280 0.302 -0.022 0.015 0.206 0.220 0.170 1520 0.283 0.283 -0.000 0.015 0.195 0.207 0.161 1557 0.304 0.265 0.039 0.015 0.185 0.194 0.151 1593 0.248 0.248 -0.000 0.015 0.176 0.181 0.143 1630 0.184 0.232 -0.048 0.015 0.167 0.169 0.135 1703 0.175 0.202 -0.028 0.014 0.151 0.148 0.120 1739 0.176 0.189 -0.013 0.014 0.144 0.138 0.114 1775 0.128 0.176 -0.049 0.013 0.137 0.129 0.108 1805 0.153 0.166 -0.013 0.013 0.132 0.122 0.103 1841 0.093 0.155 -0.062 0.013 0.127 0.113 0.098 1871 0.039 0.146 -0.108 0.012 0.122 0.107 0.094 1943 0.130 0.127 0.003 0.012 0.112 0.093 0.085 1973 0.092 0.119 -0.028 0.011 0.108 0.087 0.081 2009 0.159 0.111 0.048 0.011 0.104 0.081 0.077 2039 0.129 0.105 0.024 0.010 0.101 0.076 0.074 2075 0.182 0.097 0.085 0.010 0.097 0.071 0.071 2112 0.137 0.090 0.047 0.010 0.094 0.066 0.068 2184 0.035 0.078 -0.043 0.009 0.088 0.057 0.062 2214 0.024 0.073 -0.049 0.008 0.086 0.053 0.060 2250 -0.034 0.068 -0.101 0.008 0.083 0.049 0.058 2280 -0.087 0.063 -0.150 0.008 0.081 0.046 0.056 2316 -0.110 0.059 -0.168 0.007 0.079 0.043 0.054 2346 -0.102 0.055 -0.158 0.007 0.077 0.040 0.053 2419 -0.048 0.047 -0.095 0.006 0.074 0.034 0.049 2455 0.031 0.044 -0.012 0.006 0.072 0.032 0.048 2491 -0.016 0.040 -0.056 0.006 0.070 0.029 0.046 2521 -0.101 0.038 -0.139 0.005 0.069 0.028 0.045 2557 -0.088 0.035 -0.123 0.005 0.068 0.026 0.044 2587 -0.042 0.033 -0.075 0.005 0.067 0.024 0.043 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.7: Summary of Data for Run 10 278 6 s RE x 103 s-1 RP x 103 s-1 {RE - Rp) x 103 s-1 Op x 103 M / $ 0 0.002 0.000 0.002 0.000 1.410 0.000 1.230 55 0.779 0.760 0.000 0.083 1.407 0.182 1.227 100 1.589 1.475 0.000 0.076 1.395 0.434 1.217 144 1.803 1.727 0.000 0.072 1.372 0.677 1.197 189 1.732 1.748 -0.000 0.065 1.343 0.842 1.170 233 1.648 1.702 -0.000 0.056 1.308 0.938 1.140 278 1.534 1.638 -0.000 0.056 1.271 0.985 1.107 322 1.497 1.563 -0.000 0.053 1.231 1.000 1.071 367 1.377 1.474 -0.000 0.047 1.192 0.997 1.037 411 1.412 1.378 0.000 0.043 1.154 0.986 1.003 456 1.387 1.275 0.000 0.042 1.116 0.971 0.970 500 1.200 1.175 0.000 0.042 1.077 0.953 0.936 545 1.157 1.077 0.000 0.041 1.041 0.934 0.904 589 0.911 0.989 -0.000 0.039 1.005 0.914 0.872 634 0.901 0.908 -0.000 0.037 0.971 0.892 0.841 678 0.782 0.837 -0.000 0.034 0.935 0.867 0.810 723 0.778 0.772 0.000 0.032 0.902 0.841 0.781 767 0.630 0.717 -0.000 0.031 0.870 0.814 0.752 811 0.704 0.667 0.000 0.031 0.839 0.786 0.725 856 0.713 0.622 0.000 0.031 0.810 0.757 0.699 900 0.606 0.583 0.000 0.031 0.780 0.727 0.672 945 0.540 0.546 -0.000 0.031 0.752 0.698 0.648 989 0.474 0.513 -0.000 0.030 0.726 0.670 0.625 1034 0.394 0.483 -0.000 0.030 0.701 0.642 0.602 1078 0.333 0.455 -0.000 0.029 0.675 0.614 0.580 1123 0.286 0.428 -0.000 0.028 0.652 0.589 0.559 1167 0.334 0.404 -0.000 0.026 0.630 0.564 0.540 1212 0.307 0.380 -0.000 0.025 0.608 0.541 0.521 1256 0.363 0.358 0.000 0.024 0.587 0.518 0.502 1301 0.357 0.337 0.000 0.023 0.568 0.497 0.485 1345 0.263 0.317 -0.000 0.022 0.549 0.477 0.468 1389 0.667 0.298 0.000 0.022 0.531 0.459 0.452 1434 0.982 0.280 0.001 0.022 0.513 0.441 0.436 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.7: Summary of Data for Run 10 -(Continued) 279 e s RE x 103 s - 1 RP x 103 s - 1 [RE - Rp) x 103 s"1 (TP X 103 s - 1 M / $ 1478 0.469 0.263 0.000 0.021 0.496 0.424 0.421 1523 0.386 0.246 0.000 0.021 0.480 0.409 0.407 1567 0.349 0.231 0.000 0.021 0.464 0.394 0.393 1612 0.302 0.216 0.000 0.021 0.449 0.381 0.380 1656 0.191 0.202 -0.000 0.022 0.434 0.367 0.367 1701 0.148 0.188 -0.000 0.022 0.420 0.355 0.354 1745 0.061 0.176 -0.000 0.022 0.407 0.343 0.342 1790 0.024 0.164 -0.000 0.022 0.394 0.332 0.331 1834 0.013 0.153 -0.000 0.022 0.381 0.321 0.319 1879 0.037 0.142 -0.000 0.021 0.369 0.311 0.308 1923 0.021 0.132 -0.000 0.021 0.357 0.302 0.298 1967 0.024 0.123 -0.000 0.021 0.345 0.293 0.288 2012 0.026 0.114 -0.000 0.020 0.334 0.284 0.278 2056 0.031 0.106 -0.000 0.020 0.323 0.275 0.268 2101 0.286 0.098 0.000 0.020 0.312 0.267 0.259 2145 0.063 0.091 -0.000 0.019 0.302 0.259 0.250 2190 0.010 0.084 -0.000 0.019 0.292 0.252 0.241 2234 -0.016 0.078 -0.000 0.018 0.282 0.244 0.232 2279 -0.042 0.072 -0.000 0.017 0.273 0.237 0.224 2323 -0.024 0.067 -0.000 0.017 0.264 0.230 0.216 2368 -0.045 0.062 -0.000 0.016 0.255 0.224 0.208 2412 0.031 0.057 -0.000 0.016 0.246 0.217 0.200 2457 0.053 0.053 0.000 0.015 0.238 0.210 0.193 2501 -0.061 0.049 -0.000 0.014 0.230 0.204 0.186 2546 -0.125 0.045 -0.000 0.014 0.222 0.198 0.179 2590 -0.148 0.041 -0.000 0.013 0.215 0.192 0.172 2635 -0.116 0.038 -0.000 0.012 0.207 0.186 0.166 2679 0.026 0.035 -0.000 0.012 0.200 0.181 0.159 2724 0.148 0.032 0.000 0.011 0.193 0.175 0.153 2768 0.591 0.030 0.001 0.011 0.187 0.170 0.147 2813 0.344 0.027 0.000 0.010 0.180 0.165 0.142 2857 0.076 0.025 0.000 0.010 0.174 0.160 0.136 2902 0.039 0.023 0.000 0.009 0.168 0.155 0.131 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.8: Summary of Data for Run 11 280 6 s R E x 103 s-1 R P x 103 s-1 (RE - RP) x 103 s"1 Op x 103 s"1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.463 66 0.180 0.281 -0.101 0.018 1,403 0.258 1.456 110 0.616 0.574 0.042 0.017 1.384 0.526 1.436 153 0.848 0.805 0.043 0.015 1.354 0.738 1.404 197 0.947 0.957 -0.010 0.015 1.315 0.877 1.363 240 1.016 1.038 -0.022 0.014 1.272 0.951 1.318 327 1.064 1.090 -0.026 0.012 1.179 0.999 1.220 371 1.076 1.091 -0.015 0.012 1.131 1.000 1.169 415 1.104 1.085 0.018 0.012 1.083 0.995 1.119 458 1.162 1,076 0.086 . 0.011 1.036 0.986 1.070 502 0.906 1.064 -0.157 0.011 0.989 0.975 1.020 545 1.095 1.049 0.046 0.011 0.944 0.961 0.972 633 0.990 1.010 -0.020 0.010 0.853 0.925 0.877 676 0.970 0.987 -0.016 0.009 0.810 0.904 0.832 720 0.937 0.960 -0.024 0.009 0.767 0.880 0.787 763 0.933 0.933 0.001 0.008 0.727 0.855 0.744 807 0.864 0.903 -0.038 0.008 0.686 0.827 0.701 851 0.877 0.871 0.006 0.007 0.647 0.798 0.660 938 0.804 0.805 -0.001 0.007 0.574 0.738 0.583 981 0.759 0.772 -0.013 0.007 0.540 0.708 0.548 1025 0.747 0.738 0.010 0.007 0.507 0.676 0.513 1069 0.703 0.703 -0.000 0.007 0.476 0.644 0.479 1112 0.672 0.670 0.002 0.007 0.446 0.614 0.448 1156 0.650 0.636 0.014 0.007 0.417 0.583 0.418 1243 0.602 0.571 0.031 0.006 0.365 0.523 0.363 1287 0.555 0.539 0.016 0.006 0.340 0.494 0.337 1330 0.528 0.509 0.019 0.006 0.318 0.467 0.314 1374 0.501 0.479 0.022 0.006 0.296 0.439 0.291 1418 0.455 0.451 0.005 0.005 0.276 0.413 0.269 1461 0.425 0.424 0.001 0.005 0.257 0.389 0.249 1549 0.384 0.372 0.012 0.005 0.222 0.341 0.212 1592 0.353 0.349 0.004 0.005 0.206 0.320 0.196 1636 0.329 0.326 0.002 0.005 0.191 0.299 0.180 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.8: Summary of Data for Run 11 -(Continued) 281 6 s R E x 103 s-1 R P x 103 s-1 {RE -Rp)x 103 s-1 cT p x 103 s-1 M / $ 1679 0.311 0.305 0.006 0.005 0.178 0.280 0.166 1723 0.292 0.285 0.008 0.005 0.165 0.261 0.153 1767 0.267 0.265 0.002 0.005 0.153 0.243 0.140 1854 0.239 0.230 0.009 0.005 0.131 0.211 0.117 1897 0.222 0.214 0.008 0.005 0.122 0.196 0.107 1941 0.195 0.199 -0.004 0.005 0.113 0.182 0.098 1985 0.183 0.185 -0.001 0.005 0.104 0.169 0.089 2028 0.162 0.171 -0.009 0.005 0.097 0.157 0.081 2072 0.145 0.159 -0.013 0.005 0.089 0.146 0.073 2159 0.140 0.136 0.003 0.005 0.077 0.125 0.060 2202 0.124 0.126 -0.003 0.004 0.071 0.116 0.054 2246 0.109 0.117 -0.008 0.004 0.066 0.107 0.048 2290 0.101 0.108 -0.007 0.004 0.061 0.099 0.043 2333 0.088 0.100 -0.012 0.004 0.056 0.091 0.038 2377 0.080 0.092 -0.013 0.004 0.052 0.084 0.034 2464 0.074 0.078 -0.005 0.004 0.045 0.072 0.026 2508 0.054 0.072 -0.018 0.003 0.041 0.066 0.022 2551 0.047 0.067 -0.020 0.003 0.038 0.061 0.019 2595 0.047 0.061 -0.015 0.003 0.035 0.056 0.016 2638 0.039 0.057 -0.017 0.003 0.033 0.052 0.014 2682 0.035 0.052 -0.017 0.003 0.030 0.048 0.011 2769 0.031 0.044 -0.014 0.003 0.026 0.040 0.007 2813 0.030 0.041 -0.011 0.002 0.024 0.037 0.005 2856 0.011 0.037 -0.026 0.002 0.023 0.034 0.003 2900 0.020 0.034 -0.014 0.002 0.021 0.031 0.001 2944 0.019 0.031 -0.012 0.002 0.020 0.029 -0.000 2987 0.005 0.029 -0.024 0.002 0.018 0.026 -0.002 3074 0.007 0.024 -0.017 0.002 0.016 0.022 -0.004 3118 0.006 0.022 -0.016 0.002 0.015 0.020 -0.005 3162 0.002 0.020 -0.019 0.002 0.014 0.019 -0.006 3205 -0.003 0.019 -0.022 0.001 0.013 0.017 -0.007 3249 -0.007 0.017 -0.024 0.001 0.013 0.016 -0.008 3292 -0.033 0.016 -0.049 0.001 0.012 0.014 -0.009 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.9: Summary of Data for Run 12 282 6 s RE x 103 s-1 RP x 103 s-1 (RE - RP) x 103 s-1 CT-p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.299 65 0.278 0.371 -0.093 0.020 1.400 0.364 1.290 109 0.691 0.654 0.036 0.019 1.377 0.642 1.268 152 0.906 0.840 0.066 0.016 1.345 0.825 1.238 196 0.937 0.949 -0.012 0.016 1.305 0.931 1.201 240 0.962 1.001 -0.039 0.016 1.262 0.982 1.161 283 1.011 1.019 -0.008 0.014 1.219 1.000 1.120 327 1.030 1.018 0.012 0.013 1.174 0.999 1.078 370 0.987 1.006 -0.019 0.013 1.130 0.987 1.038 414 0.979 0.988 -0.008 0.013 1.086 0.969 0.997 457 0.979 0.966 0.014 0.013 1.044 0.948 0.957 501 0.929 0.941 -0.012 0.012 1.002 0.923 0.918 545 0.962 0.915 0.047 0.011 0.962 0.898 0.880 588 0.888 0.889 -0.000 0.011 0.923 0.872 0.844 632 0.846 0.862 -0.016 0.011 0.884 0.846 0.808 675 0.877 0.836 0.041 0.011 0.848 0.820 0.774 719 0.797 0.809 -0.012 0.011 0.812 0.794 0.740 762 0.774 0.784 -0.009 0.010 0.777 0.769 0.708 806 0.786 0.758 0.028 0.010 0.743 0.744 0.676 849 0.711 0.734 -0.023 0.009 0.711 0.720 0.646 893 0.686 0.709 -0.023 0.009 0.680 0.696 0.616 937 0.688 0.684 0.003 0.008 0.649 0.672 0.588 980 0.656 0.661 -0.005 0.008 0.620 0.649 0.561 1024 0.603 0.637 -0.035 0.008 0.591 0.625 0.534 1067 0.605 0.614 -0.009 0.008 0.565 0.603 0.509 1111 0.574 0.591 -0.017 0.008 0.538 0.580 0.484 1155 0.563 0.568 -0.005 0.008 0.513 0.558 0.460 1198 0.525 0.546 -0.021 0.008 0.489 0.536 0.438 1242 0.488 0.524 -0.036 0.008 0.465 0.514 0.416 1285 0.513 0.502 0.011 0.008 0.443 0.493 0.395 1329 0.447 0.481 -0.033 0.007 0.421 0.472 0.375 1373 0.457 0.459 -0.002 0.007 0.401 0.451 0.356 1416 0.456 0.439 0.017 0.007 0.381 0.431 0.338 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.9: Summary of Data for Run 12 -(Continued) 283 6 s RE x 103 s-1 RP x 103 s"1 (RE - Rp) x 103 s-1 o-p x 103 s-1 M / $ 1460 0.423 0.419 0.004 0.007 0.363 0.411 0.320 1503 0.416 0.399 0.017 0.006 0.345 0.392 0.304 1547 0.415 0.380 0.035 0.006 0.328 0.373 0.288 1591 0.390 0.361 0.029 0.006 0.312 0.355 0.272 1634 0.390 0.343 0.047 0.006 0.296 0.337 0.258 1678 0.333 0.326 0.007 0.006 0.282 0.320 0.245 1721 0.298 0.309 -0.011 0.006 0.268 0.303 0.232 1765 0.326 0.293 0.033 0.005 0.255 0.287 0.219 1809 0.283 0.277 0.006 0.005 0.242 0.272 0.208 1852 0.284 0.262 0.021 0.005 0.231 0.257 0.197 1896 0.248 0.248 0.000 0.005 0.219 0.243 0.186 1940 0.252 0.234 0.018 0.005 0.209 0.230 0.176 1983 0.243 0.221 0.023 0.005 0.199 0.217 0.167 2027 0.230 0.208 0.022 0.005 0.190 0.204 0.158 2070 0.240 0.196 0.044 0.005 0.181 0.193 0.150 2114 0.197 0.185 0.012 0.005 0.173 0.181 0.143 2158 0.172 0.174 -0.002 0.005 0.165 0.171 0.135 2201 0.160 0.164 -0.004 0.005 0.157 0.161 0.128 2245 0.167 0.154 0.013 0.005 0.150 0.151 0.122 2288 0.155 0.145 0.010 0.005 0.144 0.142 0.116 2332 0.145 0.136 0.009 0.005 0.138 0.133 0.110 2376 0.130 0.127 0.003 0.005 0.132 0.125 0.105 2419 0.112 0.119 -0.008 0.005 0.127 0.117 0.100 2463 0.121 0.112 0.009 0.005 0.122 0.110 0.095 2506 0.120 0.105 0.015 0.005 0.117 0.103 0.091 2550 0.101 0.098 0.003 0.005 0.112 0.097 0.086 2593 0.087 0.092 -0.005 0.005 0.108 0.090 0.083 2637 0.059 0.086 -0.027 0.005 0.104 0.085 0.079 2681 0.072 0.081 -0.008 0.004 0.101 0.079 0.076 2724 0.092 0.075 0.017 0.004 0.097 0.074 0.072 2768 0.063 0.070 -0.008 0.004 0.094 0.069 0.069 2812 0.043 0.066 -0.023 0.004 0.091 0.065 0.067 2855 0.052 0.062 -0.009 0.004 0.089 0.060 0.064 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.9: Summary of Data for Run 12 -(Continued) 284 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 cTp x 103 s-1 M / $ 2899 0.048 0.057 -0.009 0.004 0.086 0.056 0.062 2942 0.031 0.054 -0.022 0.004 0.084 0.053 0.059 2986 0.023 0.050 -0.027 0.003 0.081 0.049 0.057 3029 0.017 0.047 -0.030 0.003 0.079 0.046 0.055 3073 0.024 0.044 -0.019 0.003 0.077 0.043 0.053 3117 0.011 0.041 -0.029 0.003 0.075 0.040 0.052 3160 0.014 0.038 -0.024 0.003 0.074 0.037 0.050 3204 0.013 0.035 -0.022 0.003 0.072 0.035 0.049 3247 0.014 0.033 -0.018 0.003 0.071 0.032 0.047 3291 -0.002 0.031 -0.033 0.003 0.069 0.030 0.046 3334 -0.026 0.029 -0.054 0.002 0.068 0.028 0.045 3378 -0.020 0.027 -0.047 0.002 0.067 0.026 0.044 3422 0.010 0.025 -0.015 0.002 0.066 0.024 0.043 3465 0.015 0.023 -0.008 0.002 0.065 0.023 0.042 3509 -0.008 0.021 -0.029 0.002 0.064 0.021 0.041 3552 -0.018 0.020 -0.038 0.002 0.063 0.020 0.040 3596 -0.033 0.018 -0.051 0.002 0.062 0.018 0.039 3640 0.003 0.017 -0.014 0.002 0.061 0.017 0.038 3683 -0.052 0.016 -0.068 0.002 0.060 0.016 0.038 3727 -0.031 0.015 -0.046 0.002 0.060 0.015 0.037 3770 -0.019 0.014 -0.033 0.001 0.059 0.014 0.036 3814 -0.011 0.013 -0.024 0.001 0.058 0.013 0.036 3857 -0.016 0.012 -0.028 0.001 0.058 0.012 0.035 3901 -0.021 0.011 -0.032 0.001 0.057 0.011 0.035 3945 -0.035 0.010 -0.045 0.001 0.057 0.010 0.035 3988 -0.026 0.009 -0.035 0.001 0.057 0.009 0.034 4032 -0.035 0.009 -0.043 0.001 0.056 0.009 0.034 4075 -0.042 0.008 -0.050 0.001 0.056 0.008 0.033 4119 -0.026 0.008 -0.033 0.001 0.055 0.007 0.033 4163 -0.045 0.007 -0.052 0.001 0.055 0.007 0.033 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.10: Summary of Data for Run 13 285 6 s R E x 103 s-1 R P x 103 s-1 {RE - RP) x 103 s-1 cTp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.350 66 0.271 0.307 -0.037 0.083 1.400 0.318 1.340 109 0.504 0.436 0.068 0.063 1.384 0.451 1.324 153 0.574 0.566 0.007 0.057 1.362 0.585 1.303 196 0.651 0.696 -0.045 0.044 1.335 0.719 1.276 240 0.660 0.810 -0.149 0.045 1.301 0.837 1.244 283 0.892 0.890 0.002 0.044 1.265 0.920 1.209 327 1.103 0.940 0.163 0.039 1.224 0.972 1.169 414 0.940 0.968 -0.028 0.034 1.141 1.000 1.088 458 0.862 0,960 -0.098 0.035 1.098 0.992 1.047 502 1.033 0.945 0.088 0.034 1.057 0.976 1.006 545 1.039 0.927 0.112 0.033 1.016 0.958 0.967 589 0.844 0.908 -0.064 0.030 0.976 0.938 0.928 632 0.896 0.889 0.007 0.028 0.937 0.918 0.891 676 0.786 0.870 -0.083 0.026 0.899 0.899 0.853 720 0.763 0.851 -0.088 0.025 0.861 0.880 0.816 807 0.748 0.815 -0.067 0.025 0.788 0.843 0.746 850 0.864 0.798 0.066 0.025 0.754 0.824 0.712 894 0.731 0.779 -0.048 0.025 0.719 0.805 0.679 937 0.670 0.760 -0.090 0.025 0.686 0.786 0.646 981 1.100 0.741 0.359 0.025 0.653 0.765 0.614 1025 0.859 0.720 0.139 0.024 0.621 0.744 0.583 1068 0.734 0.700 0.035 0.023 0.590 0.723 0.553 1112 0.700 0.678 0.022 0.022 0.560 0.701 0.524 1199 0.581 0.635 -0.054 0.020 0.503 0.656 0.469 1243 0.632 0.612 0.020 0.019 0.475 0.632 0.442 1286 0.800 0.590 0.210 0.018 0.449 0.609 0.417 1330 0.774 0.567 0.207 0.018 0.424 0.586 0.392 1374 0.525 0.544 -0.019 0.017 0.399 0.562 0.368 1417 0.531 0.522 0.009 0.017 0.377 0.540 0.346 1461 0.401 0.500 -0.099 0.016 0.354 0.517 0.324 1504 0.366 0.478 -0.113 0.016 0.333 0.494 0.304 1592 0.336 0.436 -0.100 0.016 0.293 0.450 0.265 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.10: Summary of Data for Run 13 -(Continued) 286 e s RE x 103 s-1 RP x 103 s-1 ( R E - R P ) x 103 s-1 cTp x 103 s-1 M / •$ 1635 0.568 0.416 0.152 0.016 0.275 0.429 0.247 1679 0.539 0.396 0.143 0.016 0.257 0.409 0.230 1722 0.425 0.376 0.048 0.016 0.240 0.389 0.214 1766 0.377 0.358 0.020 0.017 0.224 0.370 0.198 1810 0.256 0.339 -0.083 0.017 0.209 0.351 0.183 1853 0.488 0.322 0.166 0.017 0.194 0.333 0.169 1897 0.467 0.305 0.162 0.017 0.181 0.315 0.156 1984 0.222 0.274 -0.052 0.017 0.155 0.283 0.132 2028 0.192 0.259 -0.066 0.016 0.144 0.267 0.120 2071 0.160 0.244 -0.085 0.016 0.133 0.253 0.110 2115 0.169 0.231 -0.061 0.016 0.122 0.238 0.100 2158 0.161 0.218 -0.057 0.016 0.113 0.225 0.090 2202 0.179 0.205 -0.027 0.016 0.104 0.212 0.081 2246 0.133 0.194 -0.061 0.015 0.095 0.200 0.073 2289 0.117 0.182 -0.065 0.015 0.087 0.189 0.065 2376 0.126 0.162 -0.036 0.014 0.072 0.167 0.050 2420 0.282 0.152 0.130 0.014 0.065 0.157 0.044 2463 0.272 0.143 0.129 0.014 0.058 0.148 0.037 2507 0.266 0.134 0.131 0.013 0.052 0.139 0.031 2551 0.102 0.126 -0.024 0.013 0.047 0.130 0.026 2594 0.180 0.119 0.062 0.013 0.041 0.123 0.021 2638 0.119 0.111 0.008 0.012 0.036 0.115 0.016 2681 0.074 0.104 -0.031 0.012 0.032 0.108 0.011 2769 0.023 0.092 -0.068 0.011 0.023 0.095 0.003 2812 0.130 0.086 0.044 0.011 0.019 0.089 -0.001 2856 0.116 0.080 0.035 0.010 0.016 0.083 -0.004 2900 0.045 0.075 -0.031 0.010 0.012 0.078 -0.008 2943 0.101 0.071 0.030 0.009 0.009 0.073 -0.011 2987 0.050 0.066 -0.016 0.009 0.006 0.068 -0.014 3030 0.024 0.062 -0.038 0.009 0.003 0.064 -0.016 3074 0.011 0.058 -0.047 0.008 0.001 0.060 -0.019 3161 -0.040 0.050 -0.091 0.008 -0.004 0.052 -0.023 3205 -0.004 0.047 -0.051 0.007 -0.006 0.049 -0.025 Appendix C. Tabulated Instantaneous Drying Rate Data Table C l l : Summary of Data for Run 14 287 6 s R E x 103 s-1 R P x 103 {RE - RP) x 103 s-1 <Tp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.479 51 0.263 0.344 -0.080 0.018 1.402 0.327 1.470 81 0.576 0.550 0.026 0.022 1.389 0.523 1.456 117 0.733 0.739 -0.006 0.022 1.365 0.702 1.431 147 0.869 0.849 0.020 0.019 1.341 0.807 1.406 183 0.956 0.938 0.018 0.018 1.309 0.892 1.371 220 0.992 0.994 -0.002 0.017 1.273 0.945 1.333 256 1.017 1.025 -0.008 0.018 1.237 0.974 1.294 293 1.067 1.042 0.024 0.018 1.198 0.990 1.254 329 1.048 1.050 -0.003 0.017 1.161 0.998 1.214 366 1.015 1.052 -0.038 0.016 1.122 1.000 1.172 402 1.063 1.051 0.012 0.015 1.084 0.998 1.132 438 1.036 1.046 -0.010 0.014 1.046 0.994 1.092 468 1.059 1.040 0.019 0.014 1.015 0.988 1.058 504 1.011 1.031 -0.020 0.014 0.978 0.979 1.019 534 0.996 1.020 -0.024 0.014 0.947 0.969 0.986 570 1.007 1.005 0.001 0.014 0.910 0.955 0.947 606 1.000 0.988 0.012 0.014 0.875 0.939 0.909 636 0.955 0.971 -0.016 0.013 0.845 0.923 0.878 672 0.953 0.948 0.004 0.013 0.811 0.901 0.841 702 0.926 0.928 -0.001 0.012 0.782 0.881 0.811 738 0.950 0.901 0.049 0.012 0.750 0.856 0.776 774 0.856 0.872 -0.016 0.012 0.718 0.829 0.742 804 0.852 0.847 0.004 0.011 0.692 0.805 0.715 840 0.939 0.817 0.122 0.011 0.662 0.776 0.683 877 0.629 0.784 -0.155 0.011 0.632 0.745 0.651 913 0.784 0.752 0.032 0.011 0.605 0.715 0.622 943 0.713 0.726 -0.013 0.011 0.582 0.689 0.598 979 0.715 0.694 0.021 0.011 0.557 0.659 0.571 1016 0.660 0.661 -0.002 0.011 0.532 0.628 0.544 1052 0.643 0.631 0.013 0.011 0.509 0.599 0.520 1088 0.618 0.601 0.017 0.011 0.486 0.571 0.496 1118 0.577 0.577 -0.000 0.011 0.469 0.548 0.477 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C l l : Summary of Data for Run 14 -(Continued) 288 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 cy, x 103 s-1 M / $ 1154 0.551 0.549 0.002 0.011 0.448 0.522 0.456 1184 0.506 0.527 -0.021 0.010 0.432 0.501 0.439 1220 0.512 0.501 0.011 0.010 0.414 0.476 0.419 1256 0.475 0.477 -0.002 0.010 0.396 0.453 0.400 1286 0.455 0.457 -0.002 0.009 0.382 0.435 0.385 1322 0.414 0.435 -0.022 0.009 0.366 0.414 0.368 1352 0.419 0.418 0.001 0.009 0.353 0.397 0.355 1388 0.378 0.398 -0.020 0.009 0.339 0.378 0.339 1424 0.345 0.380 -0.034 0.009 0.325 0.361 0.324 1454 0.382 0.365 0.016 0.009 0.313 0.347 0.312 1490 0.552 0.349 0.203 0.009 0.301 0.331 0.299 1520 0.265 0.336 -0.071 0.009 0.290 0.319 0.288 1556 0.300 0.321 -0.021 0.009 0.279 0.305 0.275 1586 0.344 0.309 0.034 0.009 0.269 0.294 0.265 1622 0.321 0.297 0.025 0.009 0.258 0.282 0.253 1658 0.300 0.284 0.016 0.009 0.248 0.270 0.242 1688 0.296 0.275 0.021 0.009 0.239 0.261 0.233 1724 0.289 0.264 0.025 0.009 0.230 0.251 0.223 1754 0.284 0.255 0.028 0.009 0.222 0.243 0.215 1790 0.272 0.246 0.027 0.009 0.213 0.233 0.205 1826 0.235 0.237 -0.001 0.009 0.204 0.225 0.196 1856 0.236 0.229 0.007 0.009 0.197 0.218 0.188 1892 0.215 0.221 -0.006 0.009 0.189 0.210 0.180 1922 0.208 0.215 -0.007 0.009 0.183 0.204 0.173 1958 0.198 0.207 -0.010 0.008 0.175 0.197 0.165 1995 0.201 0.200 0.001 0.008 0.167 0.190 0.157 2031 0.149 0.193 -0.044 0.008 0.160 0.184 0.149 2067 0.138 0.187 -0.049 0.008 0.153 0.178 0.142 2097 0.145 0.182 -0.036 0.008 0.148 0.173 0.136 2133 0.168 0.176 -0.008 0.008 0.142 0.167 0.129 2163 0.197 0.171 0.026 0.008 0.136 0.163 0.124 2199 0.151 0.166 -0.015 0.008 0.130 0.157 0.117 2229 0.158 0.161 -0.003 0.008 0.125 0.153 0.112 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C l l : Summary of Data for Run 14 -(Continued) 289 e s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 (TP x 103 s-1 M / $ 2265 0.137 0.156 -0.020 0.008 0.120 0.148 0.106 2302 0.116 0.151 -0.035 0.008 0.114 0.144 0.100 2338 0.155 0.147 0.009 0.008 0.109 0.139 0.094 2375 0.197 0.142 0.055 0.008 0.103 0.135 0.089 2411 0.209 0.137 0.071 0.008 0.098 0.131 0.083 2447 0.269 0.133 0.136 0.008 0.093 0.126 0.078 2477 0.289 0.130 0.160 0.009 0.089 0.123 0.074 2513 0.305 0.126 0.180 0.009 0.085 0.119 0.069 2543 0.326 0.122 0.204 0.009 0.081 0.116 0.065 2579 0.284 0.118 0.166 0.009 0.077 0.113 0.060 2615 0.217 0.115 0.102 0.009 0.073 0.109 0.056 2645 0.236 0.112 0.124 0.009 0.069 0.106 0.052 2681 0.202 0.108 0.094 0.009 0.065 0.103 0.048 2711 0.156 0.105 0.051 0.010 0.062 0.100 0.045 2747 0.123 0.102 0.021 0.010 0.058 0.097 0.041 2777 0.145 0.099 0.045 0.010 0.055 0.094 0.038 2813 0.081 0.096 -0.015 0.010 0.052 0.091 0.034 2850 0.092 0.093 -0.000 0.010 0.048 0.088 0.030 2886 0.146 0.090 0.056 0.010 0.045 0.085 0.027 2922 0.212 0.087 0.125 0.010 0.042 0.083 0.023 2952 0.178 0.084 0.093 0.010 0.039 0.080 0.020 2988 0.144 0.082 0.062 0.010 0.036 0.078 0.017 3018 0.071 0.079 -0.009 0.010 0.034 0.075 0.015 3054 0.064 0.077 -0.013 0.010 0.031 0.073 0.012 3084 0.053 0.075 -0.022 0.010 0.029 0.071 0.009 3120 0.031 0.072 -0.041 0.011 0.026 0.069 0.006 3156 0.029 0.070 -0.041 0.010 0.024 0.066 0.004 3186 0.031 0.068 -0.037 0.010 0.021 0.064 0.002 3222 0.043 0.065 -0.023 0.010 0.019 0.062 -0.001 3252 0.025 0.063 -0.039 0.010 0.017 0.060 -0.003 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.12: Summary of Data for Run 15 290 e s RE x 103 s-1 RP x 103 s"1 (RE -RP)x 103 s-1 Op x 103 s-1 M / $ 0 0.001 0.001 -0.000 0.000 1.410 0.001 1.479 65 0.102 0.071 0.031 0.012 1.406 0.085 1.475 109 0.124 0.080 0.044 0.013 1.403 0.095 1.471 152 0.125 0.086 0.040 0.013. 1.399 0.102 1.467 196 0.133 0.091 0.042 0.014 1.395 0.108 1.463 239 0.136 0.098 0.038 0.014 1.391 0.117 1.459 283 0.145 0.110 0.034 0.014 1.387 0.131 1.454 326 0.149 0.130 0.019 0.013 1.382 0.155 1.449 370 0.147 0.160 -0.013 0.012 1.375 0.191 1.442 413 0.140 0.202 -0.062 0.011 1.368 0.241 1.434 457 0.145 0.257 -0.113 0.011 1.358 0.306 1.423 501 0.146 0.323 -0.177 0.011 1.345 0.385 1.409 544 0.362 0.395 -0.034 0.012 1.329 0.471 1.393 588 0.598 0.473 0.125 0.013 1.310 0.563 1.373 631 0.542 0.549 -0.007 0.014 1.288 0.654 1.349 675 0.571 0.623 -0.052 0.015 1.263 0.742 1.322 719 0.719 0.689 0.030 0.015 1.234 0.821 1.291 762 0.835 0.743 0.091 0.015 1.203 0.885 1.258 806 0.831 0.787 0.045 0.016 1.169 0.937 1.222 893 0.730 0.834 -0.104 0.016 1.098 0.994 1.147 936 0.691 0.839 -0.149 0.016 1.062 1.000 1.109 980 0.615 0.834 -0.219 0.016 1.025 0.994 1.070 1024 0.627 0.819 -0.193 0.017 0.989 0.976 1.031 1067 0.827 0.798 0.030 0.017 0.954 0.950 0.994 1111 0.946 0.770 0.175 0.016 0.920 0.918 0.957 1154 0.779 0.740 0.039 0.016 0.887 0.881 0.923 1198 0.680 0.706 -0.027 0.015 0.855 0.841 0.889 1241 0.631 0.673 -0.041 0.014 0.826 0.802 0.857 1285 0.562 0.639 -0.077 0.013 0.797 0.761 0.826 1329 0.511 0.606 -0.095 0.012 0.769 0.722 0.797 1372 0.497 0.575 -0.078 0.011 0.744 0.685 0.770 1416 0.537 0.546 -0.008 0.011 0.719 0.650 0.744 1459 0.574 0.519 0.055 0.011 0.697 0.619 0.720 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.12: Summary of Data for Run 15 -(Continued) 291 9 s RE x 103 s-1 RP x 103 s-1 (RE— Rp) x 103 s"1 <7p x 103 s-1 M / $ 1503 0.542 0.495 0.048 0.011 0.674 0.589 0.696 1547 0.544 0.472 0.072 0.011 0.653 0.562 0.673 1590 0.528 0.452 0.076 0.011 0.633 0.539 0.652 1634 0.504 0.434 0.071 0.011 0.614 0.517 0.632 1677 0.452 0.417 0.035 0.011 0.595 0.497 0.612 1764 0.364 0.388 -0.024 0.011 0.560 0.462 0.575 1808 0.309 0.375 -0.066 0.011 0.544 0.447 0.557 1851 0.316 0.363 -0.047 0.010 0.528 0.432 0.540 1895 0.342 0.351 -0.009 0.010 0.512 0.418 0.523 1939 0.331 0.340 -0.009 0.010 0.497 0.405 0.507 1982 0.328 0.329 -0.001 0.009 0.482 0.392 0.492 2026 0.320 0.318 0.001 0.009 0.468 0.379 0.477 2069 0.303 0.308 -0.005 0.009 0.455 0.367 0.462 2113 0.282 0.298 -0.016 0.009 0.441 0.355 0.448 2156 0.284 0.288 -0.004 0.009 0.429 0.343 0.435 2200 0.269 0.278 -0.009 0.009 0.416 0.331 0.422 2244 0.264 0.268 -0.003 0.009 0.404 0.319 0.409 2287 0.257 0.258 -0.001 0.009 0.393 0.307 0.397 2331 0.292 0.248 0.044 0.009 0.382 0.296 0.385 2374 0.259 0.238 0.020 0.009 0.371 0.284 0.374 2418 0.262 0.229 0.033 0.009 0.361 0.273 0.363 2461 0.229 0.220 0.009 0.009 0.352 0.262 0.353 2505 0.206 0.210 -0.005 0.009 0.342 0.250 0.343 2549 0.176 0.201 -0.025 0.009 0.333 0.240 0.333 2636 0.161 0.184 -0.022 0.009 0.316 0.219 0.315 2679 0.163 0.175 -0.012 0.009 0.309 0.209 0.307 2723 0.162 0.167 -0.005 0.009 0.301 0.199 0.299 2766 0.149 0.160 -0.010 0.008 0.294 0.190 0.291 2810 0.149 0.152 -0.003 0.008 0.287 0.181 0.284 2853 0.139 0.145 -0.006 0.008 0.281 0.173 0.277 2897 0.136 0.138 -0.002 0.008 0.275 0.164 0.271 2941 0.132 0.131 0.001 0.008 0.269 0.156 0.264 2984 0.122 0.125 -0.003 0.007 0.263 0.149 0,259 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.12: Summary of Data for Run 15 -(Continued) 292 6 s RE x 103 s-1 RP x 103 s-1 {RE - Rp) x 103 s-1 <TP x 103 s-1 M / $ 3028 0.125 0.119 0.006 0.007 0.258 0.142 0.253 3072 0.133 0.113 0.020 0.007 0.253 0.135 0.247 3115 0.121 0.108 0.013 0.007 0.248 0.128 0.242 3159 0.111 0.103 0.008 0.007 0.243 0.122 0.238 3202 0.100 0.098 0.002 0.006 0.239 0.117 0.233 3246 0.104 0.093 0.011 0.006 0.235 0.111 0.228 3289 0.092 0.089 0.003 0.006 0.231 0.106 0.224 3333 0.084 0.085 -0.001 0.006 0.227 0.101 0.220 3377 0.075 0.081 -0.006 0.006 0.223 0.097 0.216 3420 0.074 0.077 -0.004 0.006 0.220 0.092 0.213 3507 0.076 0.071 0.005 0.006 0.214 0.085 0.206 3551 0.084 0.068 0.016 0.007 0.210 0.081 0.203 3594 0.067 0.065 0.001 0.007 0.208 0.078 0.200 3638 0.072 0.063 0.010 0.007 0.205 0.075 0.197 3682 0.063 0.060 0.003 0.007 0.202 0.072 0.194 3725 0.067 0.058 0.009 0.007 0.200 0.069 0.191 3769 0.059 0.056 0.003 0.007 0.197 0.066 0.188 3812 0.057 0.054 0.003 0.007 0.195 0.064 0.186 3856 0.048 0.052 -0.004 0.007 0.192 0.062 0.183 3900 0.066 0.050 0.016 0.008 0.190 0.060 0.181 3943 0.062 0.048 0.014 0.008 0.188 0.058 0.179 3987 0.063 0.047 0.016 0.008 0.186 0.056 0.177 4030 0.056 0.045 0.011 0.008 0.184 0.054 0.174 4074 0.054 0.044 0.010 0.008 0.182 0.052 0.172 4117 0.043 0.043 0.001 0.008 0.180 0.051 0.170 4161 0.038 0.041 -0.004 0.008 0.178 0.049 0.168 4205 0.013 0.040 -0.027 0.008 0.176 0.048 0.166 4248 0.018 0.039 -0.022 0.008 0.175 0.047 0.165 4292 0.033 0.038 -0.005 0.008 0.173 0.045 0.163 4379 0.035 0.036 -0.001 0.008 0.170 0.043 0.159 4423 0.042 0.035 0.006 0.009 0.168 0.042 0.158 4466 0.017 0.035 -0.018 0.009 0.167 0.041 0.156 4510 0.019 0.034 -0.014 0.009 0.165 0.040 0.155 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.13: Summary of Data for Run 16 293 e s RE x 103 s- 1 RP x 103 s- 1 (RE - Rp) x 103 s- 1 Op x 103 s- 1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.376 66 0.529 0.526 0.003 0.036 1.395 0.536 1.361 110 0.727 0.726 0.001 0.028 1.366 0.740 1.333 153 0.795 0.810 -0.014 0.025 1.333 0.826 1.300 197 0.871 0.873 -0.003 0.020 1.296 0.891 1.263 240 0.999 0.924 0.074 0.020 1.257 0.943 1.225 284 0.903 0.960 -0.057 0.019 1.216 0.979 1.184 327 0.980 0.977 0.003 0.016 1.174 0.997 1.143 371 0.979 0.981 -0.001 0.014 1.131 1.000 1.100 458 0.920 0.960 -0.040 0.014 1.046 0.979 1.016 502 0.964 0.943 0.021 0.014 1.004 0.961 0.975 545 0.915 0.924 -0.009 0.014 0.964 0.942 0.935 589 0.958 0.903 0.055 0.013 0.924 0.921 0.895 632 0.867 0.883 -0.016 0.012 0.886 0.900 0.857 676 0.876 0.862 0.014 0.011 0.847 0.879 0.819 720 0.828 0.841 -0.013 0.011 0.810 0.858 0.782 763 0.843 0.821 0.022 0.010 0.774 0.837 0.747 807 0.815 0.800 0.014 0.010 0.739 0.816 0.711 894 0.772 0.759 0.013 0.010 0.671 0.774 0.644 937 0.721 0.739 -0.018 0.011 0.638 0.753 0.612 981 0.694 0.717 -0.023 0.011 0.606 0.731 0.581 1025 0.656 0.695 -0.039 0.011 0.575 0.709 0.550 1068 0.628 0.674 -0.045 0.011 0.546 0.687 0.521 1112 0.668 0.651 0.016 0.011 0.517 0.664 0.492 1155 0.615 0.629 -0.014 0.010 0.489 0.642 0.465 1199 0.733 0.606 0.127 0.010 0.462 0.618 0.438 1242 0.753 0.584 0.169 0.010 0.436 0.595 0.412 1330 0.603 0.538 0.065 0.009 0.387 0.548 0.364 1373 0.500 0.515 -0.015 0.009 0.365 0.526 0.341 1417 0.496 0.493 0.003 0.008 0.342 0.503 0.319 1460 0.479 0.471 0.008 0.008 0.322 0.480 0.299 1504 0.499 0.449 0.050 0.008 0.301 0.458 0.279 1548 0.618 0.427 0.190 0.008 0.282 0.436 0.259 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.13: Summary of Data for Run 16 -(Continued) 294 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 <TP x 103 s-1 M / $ 1591 0.317 0.407 -0.089 0.008 0.264 0.415 0.242 1635 0.341 0.386 -0.045 0.008 0.247 0.394 0.224 1678 0.359 0.367 -0.008 0.008 0.231 0.374 0.208 1765 0.323 0.329 -0.006 0.007 0.200 0.335 0.179 1809 0.366 0.311 0.055 0.007 0.186 0.317 0.165 1852 0.308 0.294 0.014 0.007 0.173 0.299 0.152 1896 0.325 0.277 0.048 0.007 0.161 0.282 0.139 1940 0.292 0.261 0.031 0.007 0.149 0.266 0.128 1983 0.310 0.246 0.064 0.007 0.138 0.251 0.117 2027 0.246 0,231 0.015 0.007 0.127 0.236 0.106 2070 0.184 0.217 -0.033 0.007 0.118 0.222 0.097 2114 0.180 0.204 -0.024 0.007 0.109 0.208 0.088 2201 0.141 0.179 -0.039 0.007 0.092 0.183 0.071 2245 0.192 0.168 0.024 0.007 0.084 0.171 0.064 2288 0.246 0.157 0.088 0.007 0.077 0.160 0.057 2332 0.195 0.147 0.048 0.007 0.071 0.150 0.050 2375 0.174 0.138 0.036 0.006 0.064 0.140 0.044 2419 0.160 0.128 0.031 0.006 0.059 0.131 0.038 2463 0.255 0.120 0.136 0.006 0.053 0.122 0.033 2506 0.157 0.112 0.046 0.006 0.048 0.114 0.028 2550 0.088 0.104 -0.017 0.006 0.043 0.106 0.023 2637 0.096 0.091 0.006 0.005 0.035 0.092 0.015 2680 0.074 0.084 -0.010 0.005 0.031 0.086 0.011 2724 0.066 0.078 -0.013 0.005 0.028 0.080 0.008 2767 0.028 0.073 -0.045 0.005 0.024 0.074 0.004 2811 0.069 0.068 0.001 0.005 0.021 0.069 0.001 2855 0.046 0.063 -0.017 0.004 0.018 0.064 -0.002 2898 0.011 0.058 -0.047 0.004 0.016 0.060 -0.004 2942 0.002 0.054 -0.053 0.004 0.013 0.055 -0.007 2985 0.017 0.050 -0.033 0.004 0.011 0.051 -0.009 3073 0.011 0.043 -0.032 0.003 0.007 0.044 -0.013 3116 -0.024 0.040 -0.064 0.003 0.005 0.041 -0.015 3160 -0.008 0.037 -0.045 0.003 0.003 0.038 -0.016 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.14: Summary of Data for Run 17 295 6 s RE x 103 s-1 RP x 103 s-1 { R E - RP) x 103 s-1 cTp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.022 1.410 0.000 1.695 54 0.158 0.381 -0.222 0.026 1.401 0.321 1.684 84 0.554 0.597 -0.043 0.025 1.386 0.504 1.666 120 0.918 0.799 0.119 0.022 1.361 0.675 1.635 157 0.991 0.945 0.046 0.020 1.328 0.798 1.595 193 1.063 1.040 0.023 0.020 1.292 0.878 1.552 229 1.103 1.101 0.002 0.020 1.254 0.930 1.505 259 1.170 1.134 0.035 0.020 1.220 0.958 1.464 295 1.133 1.160 -0.027 0.019 1.179 0.979 1.413 332 1.146 1.175 -0.030 0.018 1.136 0.992 1.361 368 1.170 1.183 -0.012 0.017 1.093 0.999 1.309 398 1.183 1.185 -0.002 0.016 1.058 1.001 1.265 434 1.155 1.184 -0.029 0.016 1.015 1.000 1.213 470 1.174 1.179 -0.006 0.016 0.972 0.996 1.162 500 1.158 1.172 -0.015 0.016 0.937 0.990 1.118 536 1.104 1.161 -0.057 0.016 0.895 0.980 1.067 566 1.136 1.149 -0.013 0.016 0.860 0.970 1.025 602 1.109 1.130 -0.022 0.015 0.819 0.955 0.975 638 1.115 1.109 0.006 0.015 0.779 0.936 0.926 668 1.138 1.088 0.049 0.014 0.746 0.919 0.886 704 1.119 1.061 0.058 0.014 0.707 0.896 0.838 741 1.061 1.030 0.031 0.014 0.669 0.870 0.791 777 1.010 0.997 0.012 0.014 0.632 0.842 0.747 813 0.999 0.963 0.036 0.014 0.597 0.813 0.704 843 1.008 0.933 0.075 0.014 0.569 0.788 0.669 879 0.910 0.896 0.014 0.014 0.536 0.757 0.629 909 0.872 0.865 0.007 0.014 0.509 0.730 0.597 945 0.817 0.827 -0.010 0.014 0.479 0.699 0.559 975 0.733 0.796 -0.063 0.014 0.454 0.672 0.530 1011 0.758 0.758 -0.000 0.013 0.426 0.640 0.496 1047 0.725 0.721 0.004 0.013 0.400 0.609 0.463 1077 0.667 0.690 -0.024 0.013 0.379 0.583 0.437 1113 0.622 0.655 -0.033 0.012 0.354 0.553 0.408 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.14: Summary of Data for Run 17 -(Continued) 296 e s RE x 103 s"1 RP x 103 s"1 (RE - Rp) x 103 s"1 (Tp x 103 s-1 M / $ 1143 0.624 0.626 -0.002 0.012 0.335 0.528 0.384 1179 0.562 0.592 -0.031 0.012 0.313 0.500 0.358 1216 0.512 0.559 -0.047 0.012 0.292 0.472 0.332 1252 0.522 0.528 -0.006 0.012 0.272 0.446 0.308 1288 0.435 0.499 -0.065 0.012 0.254 0.421 0.285 1318 0.461 0.476 -0.015 0.012 0.239 0.402 0.267 1354 0.397 0.449 -0.052 0.012 0.223 0.379 0.247 1384 0.382 0.428 -0.047 0.013 0.210 0.362 0.231 1420 0.447 0.404 0.042 0.013 0.195 0.341 0.213 1457 0.402 0.381 0.021 0.013 0.180 0.322 0.195 1493 0.346 0.360 -0.014 0.013 0.167 0.304 0.179 1529 0.361 0.340 0.021 0.013 0.154 0.287 0.164 1559 0.398 0.325 0.074 0.013 0.144 0.274 0.151 1595 0.396 0.307 0.089 0.013 0.133 0.259 0.138 1625 0.332 0.293 0.039 0.012 0.124 0.248 0.127 1661 0.262 0.278 -0.016 0.012 0.113 0.234 0.114 1691 0.270 0.265 0.005 0.012 0.105 0.224 0.104 1727 0.293 0.252 0.042 0.012 0.096 0.212 0.093 1763 0.335 0.239 0.096 0.012 0.087 0.202 0.082 1793 0.408 0.229 0.179 0.012 0.080 0.193 0.073 1829 0.318 0.217 0.101 0.012 0.072 0.183 0.064 1859 0.226 0.208 0.017 0.012 0.066 0.176 0.056 1895 0.218 0.198 0.020 0.013 0.058 0.167 0.047 1931 0.212 0.189 0.023 0.014 0.052 0.159 0.038 1961 0.194 0.181 0.013 0.015 0.046 0.153 0.032 1997 0.158 0.173 -0.014 0.015 0.040 0.146 0.024 2027 0.149 0.166 -0.017 0.017 0.035 0.140 0.018 2063 0.131 0.159 -0.028 0.018 0.029 0.134 0.011 2099 0.125 0.151 -0.027 0.019 0.023 0.128 0.004 2129 0.117 0.146 -0.029 0.020 0.019 0.123 -0.002 2165 0.098 0.139 -0.041 0.021 0.014 0.118 -0.008 2195 0.136 0.134 0.001 0.000 0.009 0.113 -0.013 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.15: Summary of Data for Run 18 297 6 s R E x 103 s-1 R P x 103 s-1 (RE - Rp) x 103 s-1 <rp x 103 s"1 M / 0 0.001 0.000 0.001 0.016 1.410 0.000 1.390 66 0.051 0.174 -0.122 0.024 1.406 0.173 1.386 109 0.393 0.401 -0.008 0.025 1.394 0.400 1.374 196 0.850 0.783 0.067 0.021 1.341 0.782 1.321 240 0.815 0.892 -0.077 0.021 1.304 0.891 1.284 284 0.933 0.955 -0.021 0.021 1.263 0.953 1.243 371 0.994 1.000 -0.006 0.018 1.177 0.998 1.157 414 0.968 1.001 -0.033 0.018 1.134 1.000 1.114 458 1.101 0.996 0.105 0.018 1.090 0.994 1.070 545 0.966 0.970 -0.004 0.017 1.005 0.968 0.985 588 0.996 0.951 0.045 0.016 0.963 0.950 0.943 632 0.946 0.928 0.018 0.015 0.922 0.927 0.902 719 0.854 0.874 -0.020 0.013 0.844 0.873 0.824 763 0.869 0.843 0.026 0.013 0.806 0.842 0.786 806 0.841 0.812 0.030 0.013 0.770 0.810 0.750 894 0.655 0.744 -0.089 0.013 0.702 0.743 0.682 937 0.655 0.710 -0.056 0.013 0.670 0.709 0.650 981 0.639 0.676 -0.038 0.012 0.640 0.675 0.620 1068 0.639 0.611 0.028 0.012 0.584 0.610 0.564 1111 0.577 0.581 -0.004 0.011 0.558 0.580 0.538 1155 0.586 0.550 0.035 0.011 0.533 0.550 0.513 1242 0.496 0.494 0.001 0.010 0.488 0.494 0.468 1286 0.473 0.468 0.005 0.010 0.467 0.467 0.447 1329 0.414 0.444 -0.030 0.010 0.447 0.443 0.427 1417 0.396 0.398 -0.002 0.010 0.410 0.397 0.390 1460 0.410 0.377 0.033 0.010 0.394 0.376 0.374 1504 0.378 0.357 0.021 0.010 0.378 0.357 0.358 1591 0.349 0.321 0.028 0.010 0.348 0.321 0.328 1634 0.294 0.305 -0.011 0.010 0.335 0.304 0.315 1678 0.284 0.289 -0.005 0.010 0.322 0.289 0.302 1765 0.231 0.260 -0.029 0.009 0.298 0.260 0.278 1809 0.219 0.247 -0.028 0.009 0.287 0.247 0.267 1852 0.243 0.235 0.008 0.009 0.276 0.235 0.256 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.15: Summary of Data for Run 18 -(Continued) 298 6 s R E x 103 s"1 R P x 103 s-1 (RE - RP) x 103 . s-1 Op x 103 s-1 M / 1939 0.203 0.212 -0.009 0.009 0.257 0.212 0.237 1983 0.247 0.202 0.045 0.008 0.248 0.201 0.228 2026 0.259 0.192 0.067 0.008 0.239 0.191 0.219 2113 0.150 0.173 -0.023 0.008 0.223 0.173 0.203 2157 0.146 0.165 -0.019 0.008 0.216 0.165 0.196 2201 0.122 0.157 -0.035 0.008 0.209 0.156 0.189 2288 0.129 0.142 -0.013 0.007 0.196 0.142 0.176 2331 0.110 0.135 -0.025 0.007 0.190 0.135 0.170 2375 0.149 0.128 0.021 0.007 0.184 0.128 0.164 2462 0.107 0.116 -0.009 0.008 0.173 0.116 0.153 2506 0.084 0.110 -0.027 0.008 0.169 0.110 0.149 2549 0.065 0.105 -0.040 0.008 0.164 0.105 0.144 2636 0.057 0.095 -0.038 0.008 0.155 0.095 0.135 2680 0.035 0.090 -0.055 0.008 0.151 0.090 0.131 2723 0.024 0.086 -0.061 0.008 0.147 0.085 0.127 2811 0.030 0.077 -0.047 0.008 0.140 0.077 0.120 2854 0.021 0.073 -0.052 0.008 0.137 0.073 0.117 2898 0.069 0.070 -0.000 0.008 0.134 0.069 0.114 2985 0.116 0.063 0.053 0.008 0.128 0.063 0.108 3029 0.064 0.059 0.005 0.008 0.125 0.059 0.105 3072 0.087 0.056 0.030 0.008 0.123 0.056 0.103 3159 0.110 0.051 0.059 0.008 0.118 0.051 0.098 3203 0.093 0.048 0.045 0.008 0.116 0.048 0.096 3246 0.067 0.046 0.022 0.008 0.114 0.046 0.094 3334 0.032 0.041 -0.009 0.007 0.110 0.041 0.090 3377 0.078 0.039 0.039 0.007 0.109 0.039 0.089 3421 0.114 0.037 0.077 0.007 0.107 0.037 0.087 3508 0.048 0.033 0.015 0.007 0.104 0.033 0.084 3551 0.092 0.031 0.061 0.007 0.102 0.031 0.082 3595 0.112 0.030 0.082 0.000 0.101 0.030 0.081 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.16: Summary of Data for Run 19 299 6 s RE x 103 s - 1 RP x 103 s" 1 (RE - RP) x 103 s"1 <7p x 103 s - 1 M / $ 0 0.001 0.000 0.001 0.015 1.410 0.000 1.598 48 0.206 0.264 -0.058 0.018 1.405 0.211 1.592 84 0.592 0.569 0.023 0.015 1.390 0.455 1.575 120 0.834 0.804 0.030 0.015 1.365 0.643 1.546 150 0.910 0.936 -0.026 0.014 1.339 0.748 1.516 186 1.040 1.042 -0.003 0.012 1.303 0.833 1.475 222 1.126 1.115 0.012 0.012 1.264 0.891 1.430 252 1.146 1.159 -0.013 0.012 1.230 0.927 1.391 288 1.166 1.199 -0.033 0.012 1.188 0.959 1.342 325 1.246 1.228 0.018 0.011 1.143 0.982 1.291 361 1.285 1.245 0.040 0.010 1.098 0.995 1.239 391 1.179 1.251 -0.072 - 0.010 1.061 1.000 1.196 427 1.246 1.250 -0.004 0.010 1.016 0.999 1.144 463 1.264 1.241 0.023 0.009 0.971 0.992 1.093 493 1.215 1.228 -0.013 0.009 0.934 0.982 1.050 529 1.182 1.208 -0.026 0.009 0.890 0.966 1.000 566 1.188 1.182 0.006 0.008 0.846 0.945 0.949 602 1.142 1.154 -0.011 0.008 0.804 0.922 0.901 638 1.068 1.122 -0.054 0.007 0.763 0.897 0.854 668 1.159 1.094 0.065 0.007 0.729 0.875 0.815 704 1.051 1.059 -0.008 0.007 0.691 0.846 0.771 734 1.027 1.029 -0.001 0.007 0.659 0.822 0.735 770 1.020 0.991 0.029 0.007 0.623 0.792 0.693 806 0.946 0.953 -0.007 0.007 0.588 0.762 0.653 836 0.876 0.922 -0.046 0.007 0.560 0.737 0.621 872 0.878 0.883 -0.005 0.007 0.527 0.706 0.583 908 0.878 0.845 0.033 0.007 0.496 0.676 0.547 938 0.774 0.813 -0.039 0.007 0.471 0.650 0.519 974 0.766 0.776 -0.010 0.006 0.443 0.620 0.486 1004 0.741 0.745 -0.004 0.006 0.420 0.596 0.460 1040 0.696 0.709 -0.013 0.006 0.394 0.567 0.430 1070 0.726 0.679 0.047 0.006 0.373 0.543 0.406 1106 0.669 0.644 0.025 0.006 0.349 0.515 0.378 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.16: Summary of Data for Run 19 -(Continued) 300 9 s RE x 103 s-1 RP x 103 s-1 ( R E -RP)X 103 s-1 <7p x 103 s-1 M / $ 1142 0.592 0.611 -0.018 0.005 0.327 0.488 0.352 1172 0.603 0.583 0.019 0.005 0.309 0.466 0.332 1208 0.605 0.551 0.054 0.005 0.288 0.441 0.308 1244 0.509 0.521 -0.012 0.005 0.269 0.416 0.286 1274 0.505 0.496 0.009 0.005 0.254 0.396 0.269 1310 0.478 0.467 0.011 0.005 0.236 0.374 0.249 1347 0.404 0.439 -0.035 0.005 0.220 0.351 0.229 1383 0.405 0.413 -0.008 0.005 0.204 0.330 0.212 1419 0.408 0.388 0.020 0.005 0.190 0.310 0.195 1449 0.350 0.368 -0.018 0.005 0.178 0.294 0.182 1485 0.343 0.345 -0.002 0.005 0.166 0.276 0.167 1515 0.337 0.327 0.010 0.005 0.156 0.262 0.156 1551 0.299 0.307 -0.008 0.005 0.144 0.245 0.143 1588 0.274 0.286 -0.012 0.005 0.133 0.229 0.130 1624 0.285 0.268 0.017 0.005 0.123 0.214 0.119 1660 0.270 0.250 0.020 0.005 0.114 0.200 0.108 1690 0.232 0.236 -0.004 0.005 0.107 0.189 0.100 1726 0.219 0.221 -0.002 0.005 0.098 0.176 0.090 1763 0.189 0.205 -0.017 0.005 0.090 0.164 0.081 1799 0.177 0.192 -0.015 0.005 0.083 0.153 0.073 1835 0.174 0.178 -0.005 0.005 0.077 0.143 0.065 1865 0.182 0.168 0.013 0.005 0.071 0.134 0.059 1901 0.138 0.156 -0.018 0.005 0.066 0.125 0.052 1938 0.139 0.145 -0.006 0.005 0.060 0.116 0.046 1974 0.137 0.135 0.002 0.004 0.055 0.108 0.040 2010 0.104 0.126 -0.022 0.004 0.050 0.100 0.035 2040 0.104 0.118 -0.014 0.004 0.047 0.094 0.031 2076 0.112 0.110 0.003 0.004 0.043 0.088 0.026 2113 0.101 0.101 -0.000 0.004 0.039 0.081 0.021 2149 0.091 0.094 -0.003 0.000 0.035 0.075 0.017 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.17: Summary of Data for Run 20 301 e s RE x 103 s-1 RP x 103 s-1 (RE - RP)x 103 s-1 cT p x 103 s"1 M / $ 0 0.001 0.000 0.001 0.011 1.410 0.000 1.376 66 0.210 0.306 -0.096 0.011 1.402 0.293 1.368 109 0.579 0.554 0.025 0.010 1.383 0.530 1.349 196 0.923 0.893 0.030 0.009 •1.318 0.854 1.285 240 0.960 0.980 -0.020 0.008 1.277 0.938 1.244 283 1.025 1.026 -0.001 0.008 1.234 0.982 1.202 370 1.019 1.045 -0.027 0.007 1.143 1.000 1.112 414 1.025 1.034 -0.009 0.007 1.097 0.989 1.067 457 1.009 1.017 -0.008 0.007 1.053 0.973 1.023 544 0.981 0.972 0.009 0.007 0.967 0.929 0.937 588 0.959 0.947 0.012 0.006 0.924 0.906 0.895 632 0.927 0.922 0.005 0.006 0.883 0.882 0.855 719 0.880 0.871 0.009 0.006 0.805 0.834 0.777 762 0.871 0.846 0.024 0.006 0.768 0.810 0.741 806 0.810 0.821 -0.011 0.006 0.732 0.785 0.705 893 0.749 0.769 -0.021 0.006 0.662 0.736 0.636 936 0.739 0.744 -0.005 0.005 0.630 0.712 0.604 980 0.714 0.718 -0.003 0.005 0.598 0.686 0.572 1067 0.660 0.666 -0.005 0.005 0.538 0.637 0.512 1111 0.612 0.639 -0.027 0.005 0.509 0.611 0.484 1154 0.600 0.614 -0.014 0.005 0.482 0.587 0.457 1241 0.545 0.563 -0.017 0.005 0.431 0.538 0.407 1285 0.541 0.537 0.004 0.005 0.407 0.514 0.383 1328 0.490 0.513 -0.023 0.005 0.384 0.490 0.360 1416 0.452 0.464 -0.012 0.005 0.341 0.444 0.318 1459 0.455 0.441 0.014 0.005 0.322 0.422 0.299 1503 0.422 0.418 0.003 0.004 0.303 0.400 0.280 1590 0.378 0.375 0.003 0.004 0.268 0.359 0.246 1633 0.361 0.355 0.006 0.004 0.253 0.339 0.230 1677 0.346 0.334 0.012 0.004 0.237 0.320 0.215 1764 0.317 0.297 0.020 0.004 0.210 0.284 0.188 1807 0.304 0.279 0.024 0.004 0.198 0.267 0.176 1851 0.267 0.262 0.004 0.004 0.186 0.251 0.164 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.17: Summary of Data for Run 20 -(Continued) 302 6 s RE x 103 s-1 RP x 103 s-1 {RE - Rp) x 103 s-1 o-p x 103 s-1 M / 1938 0.245 0.231 0.014 0.004 0.164 0.221 0.143 1981 0.222 0.216 0.006 0.004 0.155 0.207 0.133 2025 0.203 0.202 0.001 0.004 0.145 0.193 0.124 2112 0.186 0.176 0.010 0.004 0.129 0.168 0.108 2156 0.174 0.164 0.010 0.004 0.121 0.157 0.100 2199 0.132 0.153 -0.021 0.004 0.115 0.146 0.094 2286 0.119 0.132 -0.014 0.004 0.102 0.127 0.081 2330 0.116 0.123 -0.007 0.004 0.097 0.118 0.076 2373 0.116 0.114 0.002 0.004 0.092 0.109 0.071 2460 0.096 0.098 -0.003 0.003 0.082 0.094 0.062 2504 0.096 0.091 0.005 0.003 0.078 0.087 0.058 2548 0.081 0.084 -0.003 0.003 0.074 0.080 0.054 2635 0.082 0.072 0.010 0.003 0.068 0.069 0.047 2678 0.069 0.066 0.003 0.003 0.065 0.064 0.044 2722 0.063 0.061 0.002 0.003 0.062 0.059 0.041 2809 0.043 0.052 -0.009 0.003 0.057 0.050 0.036 2852 0.039 0.048 -0.009 0.003 0.055 0.046 0.034 2896 0.023 0.044 -0.021 0.003 0.053 0.042 0.032 2983 0.017 0.037 -0.020 0.003 0.049 0.036 0.029 3027 0.040 0.034 0.006 0.002 0.048 0.033 0.027 3070 0.019 0.031 -0.012 0.002 0.046 0.030 0.026 3157 0.022 0.026 -0.004 0.002 0.044 0.025 0.023 3201 0.014 0.024 -0.011 0.002 0.043 0.023 0.022 3244 0.026 0.022 0.003 0.002 0.042 0.021 0.021 3331 0.012 0^ 019 -0.007 0.002 0.040 0.018 0.020 3375 -0.004 0.017 -0.021 0.002 0.039 0.016 0.019 3418 0.003 0.016 -0.012 0.002 0.038 0.015 0.018 3505 0.002 0.013 -0.011 0.001 0.037 0.012 0.017 3549 0.002 0.012 -0.009 0.001 0.036 0.011 0.016 3593 -0.003 0.011 -0.014 0.001 0.036 0.010 0.016 3680 -0.012 0.009 -0.021 0.000 0.035 0.009 0.015 3723 -0.005 0.008 -0.013 0.000 0.035 0.008 0.015 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.18: Summary of Data for Run 22 303 6 s R E x 103 s-1 R P x 103 s-1 (RE - RP) x 103 s"1 (TP x 103 s-1 M / $ 0 0.001 0.000 0.001 0.018 1.410 0.000 1.511 51 0.155 0.182 -0.027 0.025 1.407 0.129 1.508 87 0.453 0.466 -0.013 0.021 1.396 0.330 1.495 117 0.692 0.681 0.011 0.021 1.378 0.482 1.476 153 0.912 0.878 0.034 0.022 1.350 0.621 1.446 190 1.036 1.027 0.009 0.021 1.315 0.727 1.407 226 1.074 1.141 -0.067 0.020 1.276 0.807 1.365 262 0.949 1.234 -0.285 0.020 1.233 0.873 1.318 292 1.313 1.298 0.016 0.019 1.195 0.919 1.277 328 1.351 1.356 -0.005 0.017 1.147 0.960 1.225 364 1.448 1.394 0.053 0.016 1.097 0.987 1.171 394 1.430 1.410 0.019 0.015 1.055 0.998 1.125 430 1.388 1.413 -0.025 0.015 1.004 1.000 1.070 460 1.363 1.403 -0.040 0.016 0.962 0.993 1.024 496 1.387 1.379 0.008 0.015 0.912 0.976 0.970 533 1.317 1.346 -0.029 0.015 0.862 0.952 0.915 569 1.272 1.307 -0.034 0.014 0.814 0.925 0.863 605 1.330 1.265 0.066 0.014 0.767 0.895 0.812 635 1.287 1.228 0.058 0.014 0.730 0.869 0.772 671- 1.169 1.185 -0.016 0.015 0.687 0.838 0.725 708 . 1.082 1.140 -0.058 0.015 0.644 0.807 0.678 744 1.114 1.098 0.017 0.015 0.603 0.777 0.634 780 1.060 1.056 0.003 0.014 0.565 0.748 0.592 810 1.011 1.023 -0.012 0.014 0.533 0.724 0.558 846 0.965 0.983 -0.019 0.015 0.497 0.696 0.519 883 0.987 0.944 0.043 0.019 0.462 0.668 0.480 919 0.899 0.906 -0.007 0.026 0.428 0.642 0.444 955 0.861 0.869 -0.008 0.000 0.396 0.615 0.409 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.19: Summary of Data for Run 23 304 e s RE x 103 s-1 RP x 103 s-1 (RE - R P ) x 103 s-1 <rp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.053 1.410 0.000 2.317 45 0.061 0.045 0.016 0.046 1.409 0.032 2.316 75 0.134 0.126 0.008 0.047 1.407 0.090 2.312 136 0.266 0.314 -0.048 0.041 1.393 0.223 2.289 166 0.404 0.406 -0.002 0.037 1.383 0.289 2.271 197 0.594 0.505 0.089 0.037 1.369 0.359 2.248 257 0.712 0.706 0.005 0.037 1.332 0.502 2.187 287 0.720 0.807 -0.087 0.035 1.310 0.574 2.149 318 1.021 0.908 0.113 0.033 1.283 0.645 2.105 378 1.073 1.081 -0.008 0.030 1.223 0.768 2.005 408 1.098 1.154 -0.056 0.031 1.190 0.820 1.949 438 1.118 1.218 -0.099 0.031 1.154 0.865 1.890 499 1.315 1.316 -0.001 0.031 1.077 0.936 1.761 529 1.485 1.351 0.135 0.030 1.037 0.960 1.694 560 1.358 1.377 -0.019 0.028 0.994 0.979 1.624 620 1.418 1.404 0.014 0.026 0.911 0.998 1.484 650 1.366 1.407 -0.041 0.026 0.868 1.000 1.414 681 1.512 1.404 0.108 0.026 0.825 0.998 1.341 741 1.489 1.380 0.108 0.027 0.741 0.981 1.202 772 1.449 1.361 0.088 0.028 0.699 0.967 1.131 802 1.331 1.338 -0.007 0.028 0.658 0.951 1.064 862 1.252 1.282 -0.031 0.027 0.580 0.911 0.933 893 1.265 1.249 0.016 0.026 0.540 0.888 0.867 923 0.989 1.215 -0.226 0.025 0.503 0.863 0.806 983 1.145 1.140 0.005 0.024 0.433 0.810 0.688 1014 1.182 1.100 0.082 0.025 0.398 0.782 0.630 1044 1.048 1.060 -0.011 0.026 0.366 0.753 0.576 1104 1.086 0.978 0.108 0.031 0.304 0.695 0.474 1135 0.978 0.935 0.043 0.035 0.275 0.665 0.425 1165 0.937 0.894 0.044 0.038 0.247 0.635 0.379 1226 0.718 0.811 -0.093 0.000 0.195 0.577 0.292 1256 0.885 0.772 0.114 0.000 0.172 0.548 0.253 1286 0.596 0.733 -0.137 0.000 0.149 0.521 0.215 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.20: Summary of Data for Run 26 305 6 s RE x 103 s"1 RP x 103 s-1 (RE - Rp) x 103 s-1 <7p x 103 s-1 M / 0 0.002 0.000 0.002 0.000 1.410 0.000 1.580 35 1.382 1.494 -0.113 0.142 1.382 0.623 1.548 58 2.103 1.883 0.220 0.099 1.343 0.785 1.503 81 1.933 2.041 -0.108 0.101 1.297 0.850 1.451 104 2.155 2.143 0.012 0.088 1.249 0.893 1.397 127 2.034 2.236 -0.202 0.079 1.199 0.932 1.339 150 2.375 2.316 0.058 0.080 1.146 0.965 1.280 196 2.349 2.400 -0.051 0.071 1.037 1.000 1.156 219 2.334 2.396 -0.062 0.066 0.982 0.999 1.093 242 2.402 2.367 0.035 0.065 0.927 0.986 1.031 266 2.100 2.316 -0.216 0.065 0.871 0.965 0.967 289 2.238 2.252 -0.014 0.065 0.819 0.938 0.908 312 2.286 2.180 0.106 0.062 0.768 0.908 0.850 335 2.130 2.102 0.028 0.057 0.718 0.876 0.794 381 2.076 1.941 0.135 0.052 0.625 0.809 0.688 404 1.595 1.859 -0.263 0.051 0.582 0.775 0.638 427 1.727 1.777 -0.050 0.052 0.540 0.741 0.591 450 1.785 1.696 0.089 0.053 0.500 0.707 0.545 473 1.576 1.616 -0.040 0.053 0.462 0.673 0.502 496 1.673 1.537 0.136 0.052 0.426 0.640 0.461 519 1.682 1.458 0.224 0.050 0.391 0.608 0.422 565 1.303 1.306 -0.003 0.045 0.328 0.544 0.350 588 1.350 1.232 0.118 0.043 0.298 0.513 0.316 611 1.033 1.160 -0.126 0.042 0.271 0.483 0.285 634 1.035 1.089 -0.055 0.042 0.245 0.454 0.256 658 0.999 1.019 -0.019 0.043 0.220 0.424 0.227 681 0.744 0.953 -0.209 0.045 0.197 0.397 0.201 704 0.784 0.890 -0.106 0.048 0.176 0.371 0.177 750 0.718 0.772 -0.054 0.054 0.138 0.322 0.134 773 1.043 0.718 0.325 0.056 0.121 0.299 0.114 796 0.887 0.666 0.221 0.059 0.105 0.277 0.096 819 0.423 0.616 -0.194 0.060 0.090 0.257 0.079 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.21: Summary of Data for Run 29 306 9 s RE x 103 s-1 RP x 103 s-1 {RE - Rp) x 103 s-1 crp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.125 1.410 0.000 1.805 57 -0.236 0.047 -0.284 0.111 1.409 0.038 1.804 94 0.278 0.135 0.142 0.101 1.406 0.109 1.800 169 0.558 0.363 0.195 0.098 1.387 0.292 1.776 207 0.464 0.485 -0.021 0.086 1.371 0.390 1.755 244 0.566 0.604 -0.038 0.082 1.351 0.485 1.729 320 0.860 0.832 0.028 0.083 1.296 0.668 1.658 357 1.052 0.929 0.123 0.079 1.264 0.746 1.615 395 0.806 1.015 -0.209 0.073 1.227 0.815 1.567 470 0.961 1.141 -0.181 0.067 1.146 0.917 1.462 508 1.320 1.185 0.135 0.067 1.101 0.951 1.404 545 1.394 1.215 0.179 0.069 1.057 0.975 1.347 621 1.007 1.244 -0.237 0.067 0.963 0.999 1.225 658 1.270 1.245 0.025 0.064 0.917 1.000 1.165 696 1.088 1.239 -0.152 0.061 0.870 0.995 1.104 771 1.137 1.211 -0.074 0.057 0.778 0.972 0.984 808 ' 0.867 1.190 -0.323 0.057 0.734 0.956 0.927 846 1.462 1.165 0.297 0.057 0.689 0.936 0.869 921 1.187 1.108 0.079 0.059 0.603 0.890 0.758 959 0.782 1.076 -0.294 0.060 0.562 0.864 0.704 996 1.207 1.043 0.164 0.059 0.523 0.838 0.653 1072 1.266 0.972 0.294 0.056 0.446 0.780 0.553 1109 0.934 0.936 -0.002 0.054 0.411 0.752 0.508 1147 0.986 0.898 0.087 0.052 0.376 0.722 0.462 1222 0.844 0.824 0.019 0.051 0.311 0.662 0.378 1260 0.996 0.786 0.210 0.053 0.281 0.632 0.339 1297 0.602 0.750 -0.148 0.057 0.252 0.602 0.302 1373 0.486 0.677 -0.191 0.067 0.198 0.543 0.231 1410 0.828 0.642 0.186 0.073 0.174 0.516 0.200 1448 0.361 0.607 -0.246 0.079 0.150 0.487 0.169 1523 0.402 0.541 -0.139 0.000 0.107 0.434 0.113 1561 0.586 0.509 0.077 0.000 0.087 0.409 0.087 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.22: Summary of Data for Run 30' 307 e s RE x 103 s"1 RP x 103 s"1 {RE - Rp) x 103 s-1 <rp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.675 46 -0.088 0.029 -0.118 0.060 1.410 0.018 1.674 76 0.306 0.110 0.196 0.185 1.408 0.066 1.672 106 0.182 0.214 -0.032 0.289 1.403 0.129 1.666 137 -1.516 0.313 -1.829 0.323 1.395 0.189 1.656 167 -0.673 0.391 -1.064 0.305 1.384 0.236 1.643 197 -0.561 0.458 -1.019 0.271 1.371 0.277 1.628 227 -0.183 0.529 -0.712 0.238 1.356 0.319 1.610 258 0.725 0.617 0.108 0.202 1.339 0.372 1.589 288 0.855 0.720 0.134 0.163 1.319 0.435 1.565 318 0.612 0.841 -0.228 0.132 1.295 0.508 1.537 349 1.080 0.976 0.103 0.125 1.267 0.589 1.503 379 0.758 1.111 -0.352 0.141 1.236 0.671 1.465 409 1.350 1.240 0.109 0.163 1.201 0.749 1.422 440 0.649 1.362 -0.713 0.181 1.160 0.822 1.374 470 -0.235 1.462 -1.698 0.188 1.118 0.883 1.323 500 9.729 1.543 8.186 0.187 1.073 0.932 1.268 531 9.239 1.604 7.635 0.178 1.024 0.968 1.210 561 2.841 1.640 1.200 0.164 0.975 0.990 1.151 591 2.724 1.656 1.068 0.147 0.926 1.000 1.091 622 1.823 1.653 0.170 0.131 0.874 0.998 1.029 652 1.806 1.633 0.173 0.116 0.825 0.986 0.970 682 1.978 1.600 0.378 0.106 0.777 0.966 0.911 713 1.286 1.554 -0.268 0.098 0.728 0.938 0.853 743 1.504 1.501 0.003 0.094 0.682 0.906 0.797 773 1.048 1.442 -0.395 0.092 0.638 0.871 0.744 804 1.562 1.378 0.184 0.090 0.594 0.832 0.691 834 0.850 1.313 -0.463 0.088 0.554 0.793 0.643 864 1.571 1.248 0.324 0.086 0.515 0.753- 0.597 894 0.748 1.183 -0.435 0.083 0.479 0.714 0.553 925 1.437 1.118 0.319 0.080 0.443 0.675 0.510 955 0.656 1.057 -0.401 0.076 0.410 0.638 0.470 986 1.328 0.997 0.331 0.073 0.379 0.602 0.432 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.22: Summary of Data for Run 30 -(Continued) 308 e s RE x 103 s-1 RP x 103 s-1 (RE -Rp)x 103 s-1 cTp x 103 s-1 M / $ 1016 0.943 0.941 0.002 0.070 0.350 0.568 0.397 1046 0.897 0.889 0.009 0.068 0.322 0.537 0.364 1077 0.794 0.837 -0.043 0.066 0.295 0.506 0.332 1107 0.978 0.791 0.188 0.066 0.271 0.478 0.302 1137 0.982 0.747 0.234 0.067 0.248 0.451 0.275 1168 0.614 0.705 -0.091 0.068 0.225 0.426 0.247 1198 0.635 0.666 -0.031 0.070 0.205 0.402 0.223 1228 0.699 0.630 0.069 0.071 0.185 0.381 0.199 1259 0.985 0.595 0.390 0.073 0.166 0.359 0.176 1289 0.405 0.563 -0.158 0.075 0.149 0.340 0.155 1319 1.068 0.533 0.536 0.076 0.133 0.322 0.136 1350 0.140 0.503 -0.364 0.077 0.117 0.304 0.116 1380 0.753 0.477 0.276 0.077 0.102 0.288 0.099 1410 0.334 0.451 -0.117 0.078 0.088 0.272 0.082 1441 2.091 0.426 1.665 0.077 0.074 0.257 0.065 1471 -0.224 0.403 -0.627 0.077 0.062 0.243 0.050 1501 0.890 0.381 0.509 0.076 0.050 0.230 0.036 1532 0.333 0.360 -0.027 0.075 0.039 0.217 0.022 1562 0.674 0.340 0.334 0.074 0.028 0.205 0.010 1592 -0.260 0.321 -0.582 0.072 0.018 0.194 -0.002 1623 0.486 0.303 0.183 0.070 0.009 0.183 -0.014 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.23: Summary of Data for Run 31 309 6 s RE x 103 RP x 103 s-1 (RE - Rp) x 103 s-1 <Tp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.165 1.920 0.000 1.810 67 0.403 0.525 -0.122 0.130 1.904 0.393 1.795 112 0.903 0.849 0.054 0.142 1.873 0.635 1.765 157 1.163 1.056 0.107 0.148 1.830 0.790 1.723 202 2.062 1.178 0.884 0.139 1.779 0.881 1.675 246 1.150 1.246 -0.096 0.130 1.726 0.932 1.624 291 2.337 1.286 1.051 0.123 1.669 0.962 1.570 336 1.226 1.309 -0.083 0.114 1.610 0.979 1.514 381 2.320 1.323 0.997 0.103 1.551 0.989 1.458 426 1.264 1.331 -0.067 0.095 1.491 0.995 1.401 471 1.560 1.336 0.224 0.093 1.431 0.999 1.344 516 1.393 1.338 0.055 0.094 1.371 1.000 1.287 560 1.715 1.336 0.379 0.094 1.312 0.999 1.231 605 1.367 1.332 0.035 0.093 1.252 0.996 1.173 650 1.718 1.324 0.394 0.088 1.192 0.990 1.117 695 0.801 1.312 -0.511 0.082 1.133 0.981 1.060 740 1.307 1.296 0.011 0.075 1.074 0.969 1.004 785 1.160 1.276 -0.116 0.069 1.016 0.954 0.949 830 1.195 1.252 -0.057 0.064 0.960 0.936 0.895 875 1.094 1.223 -0.129 0.061 0.904 0.915 0.842 920 1.043 1.191 -0.148 0.059 0.849 0.891 0.790 964 1.258 1.157 0.101 0.059 0.798 0.865 0.741 1009 0.794 1.118 -0.324 0.058 0.747 0.836 0.692 1054 1.447 1.077 0.371 0.058 0.697 0.805 0.645 1099 0.621 1.033 -0.412 0.057 0.650 0.773 0.600 1144 1.108 0.988 0.119 0.056 0.604 0.739 0.556 1189 1.128 0.942 0.186 0.054 0.561 0.704 0.515 1234 1.232 0.895 0.337 0.053 0.519 0.669 0.476 1278 1.153 0.849 0.305 0.052 0.481 0.635 0.439 1323 1.214 0.802 0.412 0.050 0.444 0.599 0.404 1368 0.290 0.755 -0.465 0.050 0.409 0.565 0.370 1413 0.774 0.709 0.065 0.049 0.376 0.530 0.339 1458 0.675 0.664 0.011 0.049 0.345 0.497 0.310 C o n t i n u e d Appendix C. Tabulated Instantaneous Drying Rate Data Table C.23: Summary of Data for Run 31 -(Continued) 310 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 (TP x 103 s-1 M / $ 1503 0.623 0.621 0.002 0.049 0.316 0.464 0.282 1548 0.336 0.579 -0.243 0.050 0.289 0.433 0.256 1593 0.700 0.538 0.161 0.051 0.264 0.403 0.232 1638 1.412 0.500 0.913 0.051 0.241 0.374 0.210 1683 0.251 0.463 -0.212 0.052 0.219 0.346 0.190 1727 1.396 0.429 0.967 0.052 0.199 0.320 0.171 1772 0.195 0.395 -0.201 0.052 0.181 0.296 0.153 1817 0.766 0.364 0.402 0.052 0.164 0.272 0.137 1862 0.228 0.335 -0.107 0.052 0.148 0.250 0.122 1907 0.971 0.307 0.664 0.051 •0.134 0.230 0.108 1952 0.087 0.282 -0.195 0.050 0.120 0.210 0.096 1997 0.649 0.258 0.392 0.049 0.108 0.193 0.084 2042 0.054 0.235 -0.182 0.048 0.097 0.176 0.074 2086 0.288 0.215 0.073 0.047 0.087 0.161 0.064 2131 0.254 0.196 0.058 0.045 0.078 0.147 0.055 2176 0.427 0.178 0.249 0.043 0.070 0.133 0.047 2221 0.639 0.162 0.476 0.042 0.062 0.121 0.040 2266 0.125 0.147 -0.022 0.040 0.055 0.110 0.033 2311 0.899 0.133 0.766 0.038 0.049 0.100 0.027 2356 0.070 0.121 -0.051 0.036 0.043 0.090 0.022 2401 0.021 0.109 -0.088 0.034 0.038 0.082 0.017 2446 0.102 0.099 0.003 0.032 0.033 0.074 0.013 2490 0.164 0.089 0.074 0.030 0.029 0.067 0.009 2535 0.205 0.081 0.125 0.029 0.025 0.060 0.005 2580 0.108 0.073 0.035 0.027 0.022 0.054 0.002 2625 1.064 0.065 0.999 0.025 0.019 0.049 -0.001 2670 0.233 0.059 0.174 0.023 0.016 0.044 -0.004 2715 0.199 0.053 0.146 0.022 0.013 0.039 -0.006 2760 0.067 0.047 0.020 0.000 0.011 0.035 -0.008 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.24: Summary of Data for Run 32 311 6 s R E x 103 s"1 R P x 103 s-1 (RE - RP) x 103 s"1 o> x 103 s"1 M / $ 0 0.001 0.000 0.001 0.000 1.920 0.000 1.610 46 0.165 0.138 0.028 0.019 1.918 0.098 1.608 76 0.372 0.307 0.065 0.027 1.911 0.218 1.603 106 0.568 0.490 0.078 0.030 1.899 0.348 1.593 136 0.638 0.667 -0.029 0.031 1.882 0.474 1.578 167 0.723 0.830 -0.107 0.030 1.858 0.590 1.558 197 0.904 0.966 -0.061 0.028 1.831 0.686 1.535 227 1.046 1.077 -0.031 0.026 1.801 0.765 1.509 258 1.172 1.170 0.002 0.025 1.766 0.831 1.480 288 1.266 1.241 0.026 0.025 1.730 0.881 1.449 318 1.314 1.295 0.019 0.025 1.692 0.920 1.417 349 1.378 1.336 0.042 0.025 1.651 0.949 1.382 379 1.431 1.365 0.066 0.024 1.610 0.970 1.348 409 1.484 1.385 0.099 0.024 1.569 0.984 1.313 439 1.489 1.398 0.091 0.024 1.527 0.993 1.277 470 1.433 1.405 0.027 0.024 1.484 0.998 1.240 500 .1.389 1.408 -0.019 0.024 1.442 1.000 1.205 530 1.241 1.406 -0.165 0.024 1.399 0.999 1.169 560 1.211 1.401 -0.190 0.025 1.357 .0.995 1.133 591 0.712 1.393 -0.681 0.025 1.314 0.990 1.097 621 0.668 1.382 -0.715 0.025 1.272 0.982 1.061 651 0.828 1.369 -0.541 0.025 1.231 0.973 1.026 682 1.008 1.353 -0.345 0.024 1.189 0.961 0.990 712 1.251 1.336 -0.085 0.024 1.148 0.949 0.956 742 1.416 1.316 0.100 0.023 1.109 0.935 0.923 773 1.303 1.294 0.009 0.022 1.068 0.919 0.888 803 1.200 1.270 -0.070 0.021 1.030 0.902 0.856 833 1.183 1.245 -0.063 0.020 0.992 0.884 0.824 863 1.180 1.218 -0.039 0.020 0.955 0.865 0.792 894 1.260 1.189 0.071 0.019 0.918 0.845 0.761 924 1.360 1.160 0.200 0.018 0.882 0.824 0.731 954 1.266 1.129 0.137 0.018 0.848 0.802 0.702 985 1.206 1.096 0.1.10 0.017 0.814 0.779 0.673 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.24: Summary of Data for Run 32 -(Continued) 312 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 cTp x 103 s-1 M / 1015 1.115 1.064 0.052 0.017 0.781 0.755 0.645 1045 1.049 1.030 0.019 0.017 0.750 0.732 0.618 1075 1.013 0.997 0.017 0.017 0.719 0.708 0.593 1106 0.930 0.961 -0.032 0.017 0.689 0.683 0.567 1136 0.889 0.927 -0.038 0.017 0.661 0.659 0.543 1166 0.866 0.893 -0.027 0.017 0.633 0.634 0.520 1197 0.829 0.858 -0.028 0.017 0.606 0.609 0.497 1227 0.719 0.824 -0.104 0.017 0.581 0.585 0.476 1257 0.678 0.790 -0.112 0.016 0.557 0.561 0.455 1288 0.638 0.756 -0.118 0.016 0.533 0.537 0.435 1318 0.641 0.723 -0.082 0.016 0.511 0.514 0.416 1348 0.608 0.691 -0.083 0.016 0.490 0.491 0.398 1378 0.628 0.660 -0.032 0.015 0.469 0.469 0.381 1409 0.624 0.629 -0.005 0.015 0.449 0.446 0.364 1439 0.558 0.599 -0.041 0.015 0.431 0.425 0.348 1469 0.576 0.570 0.006 0.015 0.413 0.405 0.333 1500 0.606 0.541 0.065 0.015 0.396 0.385 0.319 1530 0.581 0.514 0.067 0.015 0.380 0.365 0.305 1560 0.578 0.489 0.090 0.015 0.365 0.347 0.293 1590 0.577 0.464 0.114 0.015 0.351 0.329 0.280 1621 0.544 0.439 0.105 0.015 0.337 0.312 0.269 1651 0.472 0.416 0.056 0.015 0.324 0.295 0.258 1681 0.470 0.394 0.076 0.015 0.312 0.280 0.247 1711 0.450 0.373 0.077 0.015 0.301 0.265 0.238 1742 0.395 0.352 0.043 0.015 0.289 0.250 0.228 1773 0.252 0.332 -0.080 0.015 0.279 0.236 0.219 1803 0.186 0.314 -0.128 0.015 0.269 0.223 0.211 1833 0.181 0.296 -0.115 0.014 0.260 0.210 0.203 1863 0.207 0.280 -0.072 0.014 0.251 0.199 0.196 1894 0.205 0.263 -0.058 0.014 0.243 0.187 0.189 1924 0.222 0.249 -0.027 0.014 0.235 0.177 0.182 1954 0.215 0.234 -0.019 0.014 0.228 0.167 0.176 1984 0.225 0.221 0.004 0.014 0.221 0.157 0.170 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.24: Summary of Data for Run 32 -(Continued) 313 6 s R E x 103 s-1 R P x 103 s-1 (RE - RP) x 103 s-1 <T p x 103 s-1 M / $ 2015 0.247 0.208 0.039 0.014 0.214 0.148 0.165 2045 0.246 0.196 0.050 0.013 0.208 0.139 0.160 2075 0.244 0.185 0.060 0.013 0.203 0.131 0.155 2106 0.160 0.174 -0.014 0.013 0.197 0.123 0.150 2136 0.160 0.164 -0.004 0.013 0.192 0.116 0.146 2166 0.182 0.154 0.028 0.013 0.187 0.110 0.142 2196 0.173 0.145 0.028 0.013 0.183 0.103 0.138 2227 0.150 0.137 0.013 0.013 0.178 0.097 0.134 2257 0.151 0.129 0.022 0.013 0.174 0.091 0.131 2288 0.135 0.121 0.014 0.013 0.171 0.086 0.128 2318 0.128 0.114 0.013 0.013 0.167 0.081 0.125 2348 0.118 0.107 0.010 0.013 0.164 0.076 0.122 2378 0.122 0.101 0.020 0.014 0.161 0.072 0.119 2409 0.093 0.095 -0.002 0.014 0.158 0.068 0.117 2439 0.082 0.090 -0.008 0.014 0.155 0.064 0.114 2469 0.040 0.085 -0.045 0.015 0.152 0.060 0.112 2500 0.030 0.080 -0.049 0.015 0.150 0.057 0.110 2530 0.023 0.075 -0.052 0.016 0.147 0.053 0.108 2560 0.043 0.071 -0.028 0.016 0.145 0.050 0.106 2590 0.059 0.067 -0.008 0.017 0.143 0.048 0.104 2621 0.060 0.063 -0.003 0.017 0.141 0.045 0.103 2651 0.080 0.059 0.020 0.018 0.139 0.042 0.101 2681 0.103 0.056 0.047 0.018 0.137 0.040 0.100 2712 0.055 0.053 0.002 0.019 0.136 0.038 0.098 2742 0.045 0.050 -0.005 0.019 0.134 0.036 0.097 2772 0.046 0.047 -0.002 0.020 0.133 0.034 0.096 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.25: Summary of Data for Run 34 314 6 s R E x 103 s-1 R P x 103 s"1 {RE - Rp) x 103 s-1 t T p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.014 1.410 0.000 1.264 76 0.885 0.878 0.000 0.012 1.399 0.434 1.254 137 1.203 1.186 0.000 0.012 1.378 0.712 1.234 197 1.191 1.233 -0.000 0.010 1.348 0.878 1.207 258 1.229 1.218 0.000 0.009 1.313 0.962 1.175 318 1.150 1.190 -0.000 0.009 1.277 0.993 1.142 379 1.109 1.152 -0.000 0.008 1.240 1.000 1.109 440 1.146 1.103 0.000 0.007 1.203 0.996 1.075 500 1.062 1.048 0.000 0.007 1.165 0.988 1.041 561 0.985 0.988 -0.000 0.007 1.128 0.977 1.008 621 0.922 0.928 -0.000 0.007 1.093 0.965 0.975 682 0.889 0.869 0.000 0.006 1.056 0.950 0.942 743 0.822 0.814 0.000 0.006 1.021 0.934 0.910 803 0.737 0.764 -0.000 0.006 0.987 0.916 0.879 864 0.708 0.718 -0.000 0.005 0.952 0.895 0.848 925 0.697 0.675 0.000 0.005 0.920 0.873 0.818 985 0.616 0.636 -0.000 0.005 0.888 0.850 0.789 1046 0.599 0.599 0.000 0.005 0.856 0.825 0.760 1107 0.561 0.565 -0.000 0.005 0.826 0.801 0.732 1167 0.497 0.533 -0.000 0.005 0.796 0.777 0.706 1228 0.513 0.502 0.000 0.005 0.768 0.753 0.680 1289 0.444 0.472 -0.000 0.005 0.740 0.728 0.654 1349 0.451 0.443 0.000 0.005 0.713 0.705 0.630 1410 0.397 0.416 -0.000 0.004 0.688 0.683 0.607 1471 0.402 0.389 0.000 0.004 0.662 0.660 0.584 1531 0.372 0.363 0.000 0.004 0.638 0.640 0.562 1592 0.345 0.338 0.000 0.004 0.615 0.620 0.541 1653 0.317 0.314 0.000 0.004 0.591 0.600 0.519 1713 0.302 0.292 0.000 0.004 0.569 0.582 0.500 1774 0.263 0.270 -0.000 0.004 0.548 0.565 0.480 1834 0.250 0.249 0.000 0.004 0.527 0.547 0.461 1895 0.247 0.229 0.000 0.004 0.507 0.531 0.443 1956 0.216 0.211 0.000 0.004 0.488 0.516 0.425 C o n t i n u e d Appendix C. Tabulated Instantaneous Drying Rate Data Table C.25: Summary of Data for Run 34 -(Continued) 315 e s RE x 103 s-1 RP x 103 s-1 { R E - RP) x 103 s-1 <Tp x 103 s-1 M / $ 2016 0.198 0.193 0.000 0.004 0.468 0.500 0.408 2077 0.208 0.177 0.000 0.004 0.450 0.486 0.391 2138 0.167 0.161 0.000 0.004 0.432 0.472 0.375 2199 0.170 0.147 0.000 0.004 0.415 0.458 0.359 2259 0.138 0.134 0.000 0.004 0.398 0.445 0.344 2320 0.133 0.121 0.000 0.004 0.382 0.432 0.329 2380 0.143 0.110 0.000 0.003 0.365 0.419 0.314 2441 0.105 0.099 0.000 0.003 0.350 0.407 0.300 2502 0.091 0.089 0.000 0.003 0.335 0.395 0.287 2563 0.067 0,081 -0.000 0.003 0.320 0.383 0.273 2623 0.070 0.073 -0.000 0.003 0.307 0.371 0.260 2684 0.076 0.065 0.000 0.003 0.293 0.360 0.248 2745 0.037 0.058 -0.000 0.003 0.279 0.348 0.236 2805 0.046 0.052 -0.000 0.003 0.267 0.337 0.224 2866 0.035 0.047 -0.000 0.002 0.255 0.326 0.213 2927 0.007 0.042 -0.000 0.002 0.242 0.315 0.202 2987 0.022 0.037 -0.000 0.002 0.231 0.305 0.192 3048 0.011 0.033 -0.000 0.002 0.220 0.295 0.182 3109 0.018 0.030 -0.000 0.002 0.209 0.284 0.171 3169 0.014 0.026 -0.000 0,002 0.198 0.275 0.162 3230 -0.002 0.023 -0.000 0.002 0.188 0.265 0.153 3291 -0.018 0.021 -0.000 0.001 0.178 0.255 0.144 3351 -0.005 0.018 -0.000 0.001 0.169 0.246 0.136 3412 -0.002 0.016 -0.000 0.001 0.160 0.237 0.127 3473 -0.013 0.014 -0.000 0.001 0.152 0.228 0.120 3533 0.008 0.013 -0.000 0.001 0.143 0.219 0.112 3594 -0.027 0.011 -0.000 0.001 0.135 0.210 0.105 3655 -0.020 0.010 -0.000 0.001 0.128 0.202 0.098 3716 0.002 0.009 -0.000 0.001 0.120 0.194 0.091 3776 -0.031 0.008 -0.000 0.001 0.113 0.186 0.084 3837 -0.009 0.007 -0.000 0.001 0.106 0.178 0.078 3898 -0.035 0.006 -0.000 0.001 0.100 0.171 0.072 3958 -0.015 0.005 -0.000 0.001 0.093 0.164 0.067 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.26: Summary of Data for Run 36 316 e s RE x 103 s-1 RP x 103 s-1 (RE - RP) x 103 s-1 cT p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.264 46 0.559 0.555 0.004 0.017 1.400 0.446 1.255 76 0.886 0.891 -0.005 0.014 1.378 0.715 1.234 106 1.045 1.036 0.009 0.014 1.349 0.831 1.208 137 1.091 1.110 -0.019 0.012 1.315 0.891 1.177 167 1.170 1.165 0.006 0.010 1.281 0.935 1.146 197 1.206 1.209 -0.003 0.010 1.245 0.970 1.114 258 1.252 1.246 0.005 0.009 1.170 1.000 1.046 288 1.232 1.240 -0.007 0.008 1.133 0.995 1.012 318 1.195 1.221 -0.026 0.007 1.096 0.980 0.978 349 1.171 1.193 -0.022 0.007 1.058 0.957 0.944 379 1.118 1.162 -0.043 0.007 1.023 0.932 0.912 409 1.127 1.128 -0.001 0.007 0.989 0.905 0.881 440 1.099 1.093 0.006 0.007 0.954 0.877 0.849 500 1.071 1.030 0.041 0.006 0.891 0.826 0.792 530 0.972 1.000 -0.028 0.006 0.860 0.803 0.764 561 0.976 0.972 0.004 0.006 0.830 0.780 0.736 591 0.999 0.946 0.052 0.005 0.801 0.759 0.710 621 0.947 0.922 0.025 0.005 0,773 0.740 0.684 651 0.906 0.898 0.008 0.005 0.746 0.721 0.660 682 0.917 0.875 0.042 0.005 0.718 0.702 0.635 742 0.805 0.832 -0.027 0.005 0.667 0.668 0.588 773 0.857 0.811 0.046 0.005 0.641 0.651 0.565 803 0.758 0.790 -0.032 0.005 0.617 0.634 0.543 833 0.787 0.769 0.018 0.005 0.594 0.617 0.522 864 0.738 0.748 -0.010 0.005 0.571 0.600 0.500 894 0.722 0.728 -0.005 0.005 0.548 0.584 0.480 924 0.693 . 0.707 -0.014 0.005 0.527 0.567 0.461 985 0.626 0.665 -0.039 0.004 0.485 0.534 0.423 1015 0.665 0.644 0.021 0.004 0.465 0.517 0.405 1045 0.650 0.624 0.026 0.004 0.446 0.501 0.388 1076 0.545 0.603 -0.058 0.004 0.427 0.484 0.370 1106 0.565 0.582 -0.018 0.004 0.410 0.467 0.354 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.26: Summary of Data for Run 36 -(Continued) 317 6 s RE x 103 s"1 RP x 103 s-1 {RE - Rp) x 103 s-1 <rp x 103 s-1 M f $ 1136 0.566 0.562 0.004 0.004 0.392 0.451 0.339 1167 0.525 0.542 -0.017 0.004 0.375 0.435 0.323 1227 0.473 0.503 -0.030 0.004 0.344 0.404 0.294 1257 0.443 0.484 -0.040 0.003 0.329 0.388 0.281 1288 0.458 0.465 -0.007 0.003 0.314 0.373 0.268 1318 0.438 0.446 -0.009 0.003 0.301 0.358 0.255 1348 0.455 0.429 0.027 0.003 0.288 0.344 0.243 1379 0.437 0.411 0.026 0.003 0.275 0.329 0.231 1409 0.394 0.394 0.000 0.003 0.263 0.316 0.221 1470 0.362 0.361 0.001 0.003 0.240 0.289 0.200 1500 0.356 0.345 0.011 0.003 0.229 0.277 0.190 1530 0.337 0.330. 0.008 0.003 0.219 0.265 0.181 1561 0.329 0.315 0.015 0.003 0.209 0.253 0.172 1591 0.301 0.301 0.001 0.003 0.200 0.241 0.163 1621 0.298 0.287 0.011 0.003 0.191 0.230 0.155 1651 0.284 0.274 0.010 0.003 0.182 0.220 0.148 1712 0.248 0.249 -0.000 0.003 0.166 0.200 0.133 1742 0.246 0.237 0.009 0.003 0.159 0.190 0.127 1772 0.246 0.226 0.020 0.003 0.152 0.181 0.120 1803 0.220 0.215 0.006 0.003 0.145 0.172 0.114 1833 0.232 0.204 0.028 0.003 0.139 0.164 0.108 1863 0.212 0.194 0.018 0.003 0.133 0.156 0.103 1894 0.211 0.184 0.027 0.003 0.127 0.148 0.098 1955 0.178 0.166 0.012 0.003 0.117 0.133 0.088 1985 0.178 0.158 0.021 0.003 0.112 0.127 0.083 2015 0.181 0.150 0.031 0.003 0.107 0.120 0.079 2046 0.157 0.142 0.015 0.003 0.103 0.114 0.075 2076 0.152 0.135 0.017 0.003 0.099 0.108 0.071 2106 0.141 0.128 0.013 0.003 0.095 0.103 0.068 2137 0.133 0.121 0.012 0.003 0.091 0.097 0.064 2197 0.088 0.109 -0.020 0.003 0.084 0.087 0.058 2227 0.100 0.103 -0.003 0.002 0.081 0.083 0.055 2258 0.088 0.097 -0.009 0.002 0.078 0.078 0.052 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.26: Summary of Data for Run 36 -(Continued) 318 6 s RE x 103 s-1 RP x 103 s-1 ( R E - RP) x 103 s-1 <TP x 103 s-1 M / $ 2288 0.075 0.092 -0.017 0.002 0.075 0.074 0.050 2318 0.077 0.087 -0.010 0.002 0.072 0.070 0.047 2349 0.084 0.082 0.001 0.002 0.069 0.066 0.045 2379 0.078 0.078 -0.000 0.002 0.067 0.063 0.043 2439 0.057 0.070 -0.013 0.002 0.063 0.056 0.039 2470 0.071 0.066 0.006 0.002 0.060 0.053 0.037 2500 0.057 0.062 -0.005 0.002 0.059 0.050 0.035 2531 0.059 0.059 0.001 0.002 0.057 0.047 0.033 2561 0.054 0.055 -0.002 0.002 0.055 0.045 0.032 2591 0.058 0.052 0.005 0.002 0.053 0.042 0.030 2622 0.061 0.049 0.012 0.002 0.052 0.040 0.029 2682 0.051 0.044 0.007 0.001 0.049 0.035 0.026 2713 0.031 0.042 -0.010 0.001 0.048 0.033 0.025 2743 0.028 0.039 -0.011 0.001 0.046 0.031 0.024 2773 0.026 0.037 -0.011 0.001 0.045 0.030 0.023 2804 0.039 0.035 0.004 0.001 0.044 0.028 0.022 2834 0.028 0.033 -0.005 0.001 0.043 0.026 0.021 2864 0.022 0.031 -0.008 0.001 0.042 0.025 0.020 2925 0.022 0.027 -0.005 0.001 0.040 0.022 0.019 2955 0.010 0.026 -0.015 0.001 0.040 0.021 0.018 2986 0.014 0.024 -0.011 0.001 0.039 0.020 0.017 3016 0.009 0.023 -0.014 0.001 0.038 0.018 0.016 3046 -0.002 0.022 -0.023 0.001 0.037 0.017 0.016 3077 0.010 0.020 -0.011 0.001 0.037 0.016 0.015 3107 0.022 0.019 0.003 0.001 0.036 0.015 0.015 3168 0.004 0.017 -0.013 0.001 0.035 0.014 0.014 3198 -0.010 0.016 -0.026 0.001 0.035 0.013 0.013 3228 -0.014 0.015 -0.029 0.001 0.034 0.012 0.013 3259 -0.026 0.014 -0.040 0.001 0.034 0.011 0.012 3289 -0.010 0.013 -0.023 0.001 0.033 0.011 0.012 3319 -0.011 0.013 -0.024 0.001 0.033 0.010 0.012 3349 -0.009 0.012 -0.021 0.001 0.033 0.009 0.011 3410 -0.017 0.010 -0.027 0.001 0.032 0.008 0.011 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.27: Summary of Data for Run 38 319 e s R E x 103 s-1 R P x 103 s-1 {RE - RP) x 103 s"1 C T p x 103 s-1 M / $ 0 0.002 0.000 0.002 0.139 1.410 0.000 1.738 78 2.119 2.132 -0.013 0.127 1.308 0.879 1.610 130 2.368 2.337 0.032 0.096 1.191 0.963 1.463 181 2.429 2.407 0.022 0.096 1.070 0.992 1.312 233 2.270 2.427 -0.157 0.081 0.944 1.000 1.155 285 2.484 2.361 0.123 0.079 0.819 0.973 0.998 337 2.201 2.210 -0.009 0.077 0.700 0.911 0.849 389 2.050 1.998 0.052 0.069 0.590 0.823 0.712 441 1.938 1.755 0.182 0.064 0.492 0.723 0.590 493 1.337 1.507 -0.170 0.064 0.407 0.621 0.484 544 1.035 1.274 -0.240 0.063 0.337 0.525 0.396 596 0.850 1.058 -0.208 0.059 0.276 0.436 0.320 648 0.970 0.866 0.104 0.054 0.226 0.357 0.258 700 0.961 0.702 0.259 0.050 0.186 0.289 0.207 752 0.696 0.563 0.133 0.048 0.153 0.232 0.166 804 0.691 0.448 0.243 0.048 0.127 0.184 0.133 856 0.312 0.353 -0.042 0.048 0.106 0.146 0.107 907 0.238 0.278 -0.041 0.047 0.090 0.115 0.087 959 0.201 0.217 -0.016 0.045 0.077 0.089 0.071 1011 -0.002 0.168 -0.170 0.042 0.067 0.069 0.059 1063 0.111 0.130 -0.019 0.038 0.059 0.053 0.049 1115 0.035 0.099 -0.064 0.034 0.053 0.041 0.042 1167 -0.037 0.076 -0.113 0.030 0.049 0.031 0.036 1219 0.125 0.058 0.067 0.025 0.045 0.024 0.032 1271 -0.096 0.044 -0.140 0.021 0.043 0.018 0.028 1323 -0.125 0.033 -0.158 0.018 0.041 0.014 0.026 1375 -0.014 0.025 -0.039 0.015 0.039 0.010 0.024 1427 -0.093 0.019 -0.112 0.012 0.038 0.008 0.023 1478 0.016 0.014 0.002 0.010 0.037 0.006 0.022 1530 -0.162 0.011 -0.173 0.008 0.037 0.004 0.021 1582 -0.024 0.008 -0.032 0.006 0.036 0.003 0.020 1634 0.034 0.006 0.028 0.000 0.036 0.002 0.020 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.28: Summary of Data for Run 39 320 6 s RE x 103 s-1 RP x 103 s-1 ( R E - RP) x 103 s-1 O p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.034 1.410 0.000 1.738 78 0.317 0.313 0.004 0.035 1.399 0.336 1.723 130 0.542 0.489 0.054 0.030 1.377 0.525 1.697 182 0.560 0.608 -0.048 0.027 1.349 0.653 1.661 234 0.666 0.691 -0.025 0.027 1.315 0.742 1.619 338 0.896 0.802 0.094 0.025 1.237 0.861 1.521 390 0.811 0.843 -0.033 0.023 1.194 0.906 1.467 442 0.974 0.878 0.096 0.022 1.149 0.942 1.411 494 0.799 0.904 -0.105 0.021 1.103 0.971 1.353 546 0.991 0,923 0.069 0.021 1.055 0.991 1.294 650 1.019 0.931 0.089 0.021 0.959 0.999 1.173 701 0.859 0.921 -0:062 0.020 0.911 0.989 1.114 753 0.876 0.902 -0.027 0.020 0.864 0.969 1.055 805 0.934 0.876 0.058 0.019 0.818 0.941 0.997 857 0.793 0.843 -0.051 0.019 0.773 0.906 0.941 961 0.701 0.764 -0.064 0.020 0.689 0.820 0.836 1013 0.827 0.720 0.107 0.021 0.651 0.773 0.788 1065 0.664 0.675 -0.010 0.021 0.614 0.724 0.743 1117 0.717 0.629 0.089 0.022 0.580 0.675 0.700 1169 0.434 0.584 -0.150 0.022 0.549 0.626 0.661 1273 -1.714 0.497 -2.210 0.022 0.493 0.534 0.591 1325 -0.620 0.457 -1.077 0.021 0.468 0.490 0.560 1377 -0.725 0.419 -1.144 0.020 0.445 0.450 0.532 1429 0.242 0.384 -0.142 0.020 0.424 0.412 0.505 1481 0.365 0.351 0.014 0.018 0.405 0.377 0.482 1585 0.312 0.294 0.017 0.016 0.372 0.316 0.440 1637 0.226 0.270 -0.044 0.015 0.357 0.290 0.421 1689 0.348 0.248 0.100 0.014 0.344 0.266 0.405 1741 0.226 0.228 -0.002 0.014 0.331 0.245 0.389 1793 0.225 0.210 0.014 0.013 0.320 0.226 0.375 1897 0.104 0.181 -0.077 0.013 0.300 0.195 0.350 1949 0.120 0.169 -0.050 0.013 0.291 0.182 0.338 2001 0.070 0.159 ' -0.089 0.013 0.282 0.170 0.328 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.28: Summary of Data for Run 39 -(Continued) 321 6 s R E x 103 s- 1 R P x 103 s-1 (RE - RP) x 103 s-1 cTp x 103 s-1 M / $ 2053 0.207 0.150 0.058 0.013 0.274 0.161 0.317 2105 0.070 0.142 -0.072 0.013 0.266 0.152 0.308 2209 0.141 0.129 0.012 0.013 0.252 0.139 0.290 2261 0.265 0.124 0.141 0.013 0.246 0.133 0.282 2313 0.074 0.120 -0.046 0.013 0.239 0.128 0.274 2365 0.231 0.116 0.115 0.013 0.233 0.125 0.267 2417 0.129 0.113 0.016 0.013 0.227 0.121 0.259 2521 0.027 0.108 -0.081 0.012 0.216 0.116 0.245 2573 0.165 0.106 0.059 0.012 0.210 0.114 0.238 2625 0.046 0.104 -0.059 0.012 0.205 0.112 0.231 2677 0.116 0.103 0.013 0.012 0.200 0.111 0.224 2729 0.082 0.102 -0.020 0.011 0.194 0.109 0.218 2833 0.065 0.100 -0.035 0.011 0.184 0.108 0.205 2885 0.102 0.099 0.003 0.011 0.178 0.107 0.198 2937 0.071 0.099 -0.028 0.011 0.173 0.106 0.192 2989 0.121 0.098 0.022 0.011 0.168 0.105 0.185 3042 0.137 0.098 0.040 0.011 0.163 0.105 0.179 3146 0.123 0.097 0.026 0.011 0.153 0.104 0.166 3198 0.054 0.096 -0.043 0.012 0.148 0.103 0.160 3250 0.103 0.096 0.007 0.012 0.143 0.103 0.154 3302 0.086 0.096 -0.010 0.013 0.138 0.103 0.147 3354 0.137 0.095 0.042 0.013 0.133 0.102 0.141 3458 0.035 0.094 -0.060 0.015 0.123 0.101 0.129 3510 0.157 0.094 0.064 0.015 0.118 0.101 0.123 3562 0.138 0.093 0.045 0.016 0.113 0.100 0.117 3614 0.190 0.093 0.097 0.017 0.109 0.100 0.111 3666 0.071 0.092 -0.021 0.018 0.104 0.099 0.105 3770 0.123 0.091 0.032 0.019 0.094 0.098 0.093 3822 0.192 0.091 0.101 0.020 0.089 0.097 0.087 3874 0.071 0.090 -0.019 0.021 0.085 0.097 0.081 3926 0.175 0.089 0.086 0.022 0.080 0.096 0.075 3978 0.089 0.089 0.000 0.022 0.075 0.095 0.069 4082 0.090 0.087 0.003 0.000 0.066 0.094 0.058 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.29: Summary of Data for Run 41 322 6 s RE x 103 s-1 RP x 103 s-1 {RE - Rp) x 103 s-1 c T p x 103 s-1 M / 0 0.001 0.000 0.001 0.000 1.410 0.000 1.311 67 0.864 0.971 -0.108 0.072 1.381 0.623 1.284 156 1.381 1.559 -0.178 0.054 1.260 1.000 1.170 201 1.550 1.553 -0.002 0.047 1.189 0.996 1.103 290 1.547 1.438 0.109 0.044 1.056 0.922 0.977 335 1.317 1.382 -0.064 0.041 0.993 0.886 0.918 425 1.354 1.286 0.067 0.036 0.873 0.825 0.805 469 1.142 1.243 -0.102 0.036 0.817 0.798 0.752 559 1.056 1.154 -0.099 0.033 0.709 0.741 0.650 603 1.178 1.108 0.070 0.031 0.659 0.711 0.603 693 1.112 1.005 0.107 0.028 0.564 0.645 0.513 738 0.884 0.949 -0.065 0.028 0.520 0.609 0.472 827 0.802 0.835 -0.033 0.028 0.441 0.536 0.397 872 0.753 0.776 -0.024 0.027 0.405 0.498 0.363 961 0.691 0.661 0.030 0.025 0.341 0.424 0.303 1006 0.505 0.605 -0.100 0.023 0.312 0.388 0.276 1096 0.480 0.499 -0.019 0.022 0.263 0.320 0.229 1140 0.519 0.451 0.067 0.022 0.242 0.290 0.209 1230 0.408 0.363 0.045 0.022 0.205 0.233 0.175 1274 0.327 0.325 0.002 0.022 0.190 0.208 0.160 1364 0.286 0.256 0.030 0.022 0.164 0.164 0.136 1409 0.238 0.226 0.012 0.022 0.153 0.145 0.126 1498 0.031 0.175 -0.144 0.021 0.135 0.112 0.109 1543 0.201 0.153 0.048 0.020 0.128 0.098 0.102 1632 0.161 0.117 0.045 0.018 0.116 0.075 0.091 1677 0.043 0.102 -0.058 0.017 0.111 0.065 0.086 1766 -0.017 0.077 -0.094 0.014 0.103 0.049 0.079 1811 0.104 0.066 0.037 0.013 0.100 0.042 0.076 1901 0.096 0.049 0.047 0.011 0.095 0.032 0.071 1946 -0.067 0.042 -0.109 0.010 0.093 0.027 0.069 1991 0.001 0.036 -0.035 0.009 0.091 0.023 0.067 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.30: Summary of Data for Run 42 323 9 s R E x 103 s-1 R P x 103 s-1 (RE -Rp)x 103 s-1 crp x 103 s-1 M / $ 0 0.001 0.000 0.001 0.129 1.410 0.000 1.252 78 0.905 0.603 0.301 0.070 1.387 0.605 1.231 130 0.816 0.851 -0.035 0.049 1.348 0.854 1.197 182 1.038 0.962 0.076 0.054 1.301 0.966 1.154 234 0.970 0.997 -0.027 0.049 1.250 1.000 1.108 286 0.675 0.993 -0.318 0.043 1.198 0.996 1.061 338 0.899 0.972 -0.073 0.042 1.147 0.975 1.015 390 0.917 0.945 -0.028 0.041 1.097 0.948 0.970 442 1.040 0.917 0.123 0.038 1.048 0.920 0.926 494 0.760 0.889 -0.129 0.035 1.001 0.892 0.884 546 0.880 0.863 0.017 0.032 0.956 0.866 0.843 598 0.798 0.839 -0.042 0.031 0.912 0.842 0.803 650 0.883 0.817 0.066 0.031 0.869 0.820 0.764 702 0.813 0.795 0.018 0.030 0.827 0.798 0.727 754 0.640 0.775 -0.134 0.029 0.786 0.777 0.690 806 0.623 0.754 -0.132 0.027 0.746 0.757 0.654 858 0.710 0.734 -0.024 0.026 0.707 0.736 0.619 910 0.974 0.713 0.261 0.025 0.670 0.716 0.585 961 0.800 0.692 0.108 0.024 0.634 0.695 0.553 1013 0.872 0.671 0.201 0.024 0.598 0.673 0.521 1065 0.664 0.648 0.016 0.024 0.564 0.650 0.490 1117 0.647 0.625 0.022 0.024 0.531 0.627 0.460 1169 0.559 0.601 -0.042 0.024 0.499 0.603 0.432 1221 0.668 0.577 0.091 0.023 0.469 0.579 0.404 1273 0.143 0.553 -0.410 0.023 0.439 0.555 0.378 1325 0.479 0.528 -0.049 0.022 0.411 0.530 0.352 1377 0.392 0.503 -0.111 0.021 0.384 0.505 0.328 1430 0.392 0.478 -0.086 0.019 0.358 0.480 0.305 1482 0.343 0.453 -0.110 0.019 0.334 0.455 0.283 1533 0.412 0.430 -0.018 0.018 0.312 0.431 0.263 1585 0.448 0.406 0.042 0.017 0.290 0.407 0.243 1637 0.398 0.383 0.015 0.017 0.269 0.384 0.225 1689 0.382 0.360 0.021 0.016 0.250 0.362 0.207 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.30: Summary of Data for Run 42 -(Continued) 324 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 <Tp x 103 s-1 M / $ 1741 0.362 0.339 0.024 0.016 0.232 0.340 0.191 1793 0.363 0.318 0.045 0.017 0.215 0.319 0.175 1845 0.312 0.297 0.014 0.017 0.199 0.299 0.161 1897 0.310 0.278 0.032 0.017 0.184 0.279 0.148 1949 0.225 0.260 -0.035 0.017 0.170 0.261 0.135 2001 0.277 0.242 0.035 0.017 0.157 0.243 0.123 2053 0.175 0.226 • -0.050 0.017 0.145 0.226 0.112 2105 0.244 0.210 0.034 0.017 0.133 0.210 0.102 2157 0.092 0.195 -0.102 0.017 0.123 0.195 0.093 2209 0.231 0.181 0.050 0.017 0.113 0.181 0.084 2261 0.126 0.168 -0.041 0.017 0.104 0.168 0.076 2313 0.283 0.155 0.128 0.017 0.096 0.156 0.068 2365 0.096 0.143 -0.048 0.016 0.088 0.144 0.061 2417 0.147 0.133 0.014 0.016 0.081 0.133 0.055 2469 0.116 0.122 -0.007 0.015 0.074 0.123 0.049 2521 0.032 0.113 -0.081 0.015 0.068 0.113 0.043 2573 0.151 0.104 0.047 0.015 0.062 0.104 0.038 2625 -0.102 0.096 -0.198 0.014 0.057 0.096 0.033 2677 0.155 0.088 0.067 0.014 0.052 0.088 0.029 2729 0.004 0.081 -0.077 0.013 0.048 0.081 0.025 2781 0.177 0.074 0.102 0.012 0.044 0.075 0.022 2833 0.075 0.068 0.006 0.000 0.040 0.069 0.018 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.31: Summary of Data for Run 43 325 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s"1 <TP x 103 s-1 M / 0 0.001 0.000 0.001 0.046 1.410 0.000 1.311 45 . 0.786 0.825 -0.039 0.042 1.393 0.464 1.295 75 1.342 1.278 0.064 0.035 1.361 0.719 1.265 106 1.408 1.562 -0.153 0.035 1.316 0.879 1.223 136 1.849 1.705 0.144 0.034 1.267 0.960 1.176 166 1.791 1.766 0.025 0.032 1.215 0.994 1.127 197 1.750 1.777 -0.028 0.031 1.160 1.000 1.075 227 1.829 1.760 0.069 0.032 1.107 0.990 1.025 257 1.660 1.727 -0.067 0.033 1.054 0.972 0.976 287 1.573 1.686 -0.113 0.034 1.003 0.949 0.927 318 1.178 1.638 -0.461 0.033 0.952 0.922 0.879 348 1.162 1.589 -0.427 0.031 0.903 0.894 0.833 378 1.501 1.538 -0.036 0.028 0.856 0.865 0.789 408 1.532 1.485 0.047 0.026 0.811 0.835 0.746 438 1.481 1.430 0.050 0.024 0.767 0.805 0.705 468 1.500 1.375 0.124 0.024 0.725 0.774 0.665 499 1.465 1.318 0.147 0.023 0.683 0.742 0.626 529 1.130 1.263 -0.132 0.023 0.645 0.710 0.589 559 1.185 1.207 -0.023 0.023 0.608 0.679 0.554 589 1.120 1.153 -0.033 0.022 0.572 0.649 0.521 620 1.039 1.098 -0.059 0.021 0.537 0.618 0.488 651 1.125 1.044 0.081 0.020 0.504 0.587 0.457 681 0.842 0.993 -0.151 0.020 0.474 0.559 0.428 712 0.864 0.942 -0.078 0.019 0.444 0.530 0.400 742 0.937 0.894 0.044 0.019 0.416 0.503 0.374 773 0.825 0.846 -0.021 0.019 0.389 0.476 0.348 803 0.765 0.802 -0.037 0.019 0.364 0.451 0.325 834 0.785 0.758 0.027 0.019 0.340 0.426 0.302 864 0.754 0.717 0.037 0.019 0.318 0.403 0.281 894 0.763 0.677 0.086 0.019 0.297 0.381 0.262 925 0.635 0.638 -0.004 0.019 0.277 0.359 0.242 955 0.619 0.602 0.017 0.018 0.258 0.339 0.225 986 0.627 0.567 0.060 0.018 0.240 0.319 0.208 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.31: Summary of Data for Run 43 -(Continued) 326 6 s RE x 103 s-1 RP x 103 s-1 { R E - RP) x 103 s-1 <rv x 103 s"1 M / $ 1016 0.499 0.534 -0.035 0.017 0.224 0.300 0.192 1047 0.503 0.501 0.001 0.016 0.208 0.282 0.177 1077 0.491 0.472 0.019 0.016 0.193 0.265 0.163 1108 0.431 0.442 -0.012 0.015 0.179 0.249 0.150 1138 0.455 0.415 0.040 0.015 0.166 0.234 0.138 1169 0.362 0.389 -0.026 0.015 0.153 0.219 0.126 1199 0.382 0.364 0.018 0.014 0.142 0.205 0.115 1230 0.355 0.340 0.015 0.014 0.131 0.191 0.105 1260 0.299 0.318 -0.020 0.015 0.121 0.179 0.096 1291 0.334 0.297 0.037 0.015 0.112 0.167 0.087 1321 0.287 0.277 0.009 0.015 0.103 0.156 0.079 1352 0.131 0.258 -0.127 0.015 0.095 0.145 0.071 1382 0.284 0.241 0.043 0.015 0.087 0.136 0.064 1413 0.193 0.224 -0.031 0.015 0.080 0.126 0.057 1443 0.217 0.209 0.008 0.016 0.074 0.117 0.051 1473 0.253 0.194 0.059 0.016 0.068 0.109 0.045 1504 0.079 0.180 -0.101 0.016 0.062 0.101 0.040 1534 0.180 0.167 0.012 0.016 0.057 0.094 0.035 1565 0.156 0.155 0.001 0.016 0.052 0.087 0.030 1595 0.159 0.144 0.015 0.016 0.047 0.081 0.026 1626 0.165 0.133 0.032 0.016 0.043 0.075 0.022 1656 0.088 0.123 -0.036 0.015 0.039 0.069 0.018 1687 0.130 0.114 0.016 0.015 0.035 0.064 0.015 1718 0.087 0.105 • -0.019 0.015 0.032 0.059 0.011 1748 0.026 0.097 -0.072 0.014 0.029 0.055 0.008 1779 0.158 0.090 0.068 0.014 0.026 0.051 0.006 1809 0.065 0.083 -0.018 0.000 0.023 0.047 0.003 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.32: Summary of Data for Run 44 327 e s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 cT p x 103 s"1 M / $ 0 0.001 0.000 0.001 0.000 1.410 0.000 1.275 67 0.907 0.900 0.007 0.077 1.379 0.544 1.247 156 1.569 1.550 0.019 0.052 1.266 0.937 1.143 201 1.647 1.653 -0.007 0.050 1.193 1.000 1.076 290 1.182 1.546 -0.364 0.047 1.048 0.935 0.944 336 1.301 1.421 -0.120 0.043 0.980 0.860 0.881 425 1.284 1.193 0.091 0.041 0.864 0.721 0.775 470 0.838 1.103 -0.265 0.037 0.813 0.667 0.727 559 0.959 0.975 -0.016 0.029 0.721 0.590 0.643 604 0.979 0;926 0.053 0.028 0.678 0.560 0.604 693 0.813 0.844 -0.031 0.027 0.599 0.511 0.531 738 0.868 0.805 0.062 0.027 0.562 0.487 0.497 827 0.720 0.728 -0.009 0.024 0.494 0.441 0.435 872 0.758 0.689 0.070 0.022 0.462 0.417 0.405 961 0.526 0.610 -0.084 0.020 0.404 0.369 0.352 1006 0.379 0.570 -0.191 0.019 0.378 0.345 0.328 1096 0.656 0.493 0.163 0.018 0.330 0.298 0.284 1141 0.529 0.457 0.073 0.019 0.308 0.276 0.265 1230 0.387 0.388 -0.001 0.019 0.271 0.235 0.230 1275 0.373 0.357 0.016 0.019 0.254 0.216 0.215 1364 0.244' 0.299 -0.055 0.019 0.225 0.181 0.188 1409 0.314 0.272 0.042 0.019 0.212 0.165 0.176 1498 0.292 0.226 0.067 0.018 0.190 0.136 0.156 1543 0.251 0.204 0.046 0.017 0.180 0.124 0.147 1633 0.096 0.167 -0.071 0.016 0.164 0.101 0.132 1677 0.153 0.151 0.002 0.016 0.157 0.091 0.125 1767 0.160 0.122 0.037 0.014 0.144 0.074 0.114 1812 0.076 0.110 -0.034 0.013 0.139 0.067 0.109 1902 0.013 0.088 -0.076 0.012 0.130 0.053 0.101 1946 0.133 0.079 0.054 0.011 0.127 0.048 0.098 1991 -0.008 0.071 -0.079 0.010 0.123 0.043 0.095 Appendix C. Tabulated Instantaneous Drying Rate Data Table C.33: Summary of Data for Run 45 328 9 s RE x 103 s"1 RP x 103 s-1 (RE - Rp) x 103 s-1 O p x 103 s-1 M / $ 0 0.001 0.000 0.001 0.058 1.410 0.000 1.404 67 0.566 0.585 -0.018 0.046 1.393 0.426 1.387 111 0.866 0.838 0.028 0.040 1.361 0.611 1.355 156 1.017 1.002 0.015 0.031 1.320 0.731 1.313 201 1.101 1.154 -0.053 0.032 1.271 0.841 1.264 245 1.219 1.272 -0.053 0.030 1.218 0.927 1.210 291 1.306 1.347 -0.040 0.026 1.157 0.982 1.149 335 1.392 1.372 0.020 0.024 1.097 1.000 1.088 380 1.395 1.360 0.035 0.024 1.036 0.991 1.026 425 1.432 1.319 0.112 0.025 0.975 0.962 0.965 469 1.310 1.262 0.048 0.026 0.919 0.920 0.908 514 1.224 1.194 0.030 0.026 0.863 0.870 0.852 559 1.328 1.121 0.207 0.025 0.811 0.817 0.799 604 0.848 1.048 -0.200 0.023 0.762 0.764 0.750 648 0.901 0.979 -0.078 0.021 0.718 0.713 0.705 693 0.802 0.912 -0.110 0.020 0.675 0.665 0.662 738 0.767 0.850 -0.082 0.018 0.636 0.619 0.622 783 0.787 0.792 -0.005 0.018 0.599 0.578 0.585 827 0.722 0.741 -0.019 0.017 0.565 0.540 0.551 872 0.793 0.694 0.099 0.017 0.533 0.506 0.518 917 0.607 0.651 -0.044 0.017 0.503 0.475 0.487 961 0.695 0.613 0.082 0.017 0.475 0.447 0.459 1006 0.529 0.577 -0.048 0.017 0.448 0.421 0.432 1051 0.464 0.544 -0.081 0.017 0.423 0.397 0.407 1096 0.551 0.514 0.037 0.016 0.399 0.375 0.383 1141 0.452 0.486 -0.034 0.016 0.376 0.354 0.360 1186 0.538 0.460 0.078 0.015 0.355 0.335 0.339 1230 0.421 0.436 -0.015 0.015 0.336 0.318 0.319 1275 0.542 0.413 0.129 0.014 0.316 0.301 0.299 1320 0.391 0.391 -0.000 0.014 0.298 0.285 0.281 1365 0.462 0.371 0.091 0.014 0.281 0.270 0.264 1409 0.362 0.352 0.010 0.013 0.265 0.256 0.248 1454 0.345 0.333 0.011 0.014 0.250 0.243 0.232 Continued Appendix C. Tabulated Instantaneous Drying Rate Data Table C.33: Summary of Data for Run 45 -(Continued) 329 6 s RE x 103 s-1 RP x 103 s-1 (RE - Rp) x 103 s-1 <Tp x 103 s-1 M / $ 1499 0.364 0.316 0.048 0.014 0.235 0.230 0.217 1543 0.215 0.299 -0.084 0.014 0.222 0.218 0.204 1588 0.301 0.283 0.018 0.014 0.209 0.206 0.191 1633 0.186 0.267 -0.082 0.015 0.196 0.195 0.178 1678 0.238 0.253 -0.015 0.015 0.185 0.184 0.166 1723 0.206 0.239 -0.033 0.016 0.174 0.174 0.155 1767 0.244 0.225 0.019 0.016 0.163 0.164 0.145 1812 0.247 0.213 0.034 0.016 0.153 0.155 0.135 1857 0.066 0.200 -0.134 0.017 0.144 0.146 0.125 1902 0.332 0.189 0.143 0.017 0.135 0.137 0.117 1946 0.055 0.178 -0.123 0.017 0.127 0.130 0.108 1991 0.178 0.167 0.010 0.017 0.120 0.122 0.101 2036 0.084 0.157 -0.074 0.017 0.112 0.114 0.093 2080 0.087 0.148 -0.061 0.017 0.106 0.108 0.086 2125 0.157 0.139 0.019 0.017 0.099 0.101 0.080 2170 0.091 0.130 -0.039 0.016 0.093 0.095 0.074 2215 0.145 0.122 0.023 0.000 0.087 0.089 0.068 Appendix C. Tabulated Instantaneous Drying Rate Data 330 Table C.34: Summary of Data for Run 46 0 s R E x 103 s"1 R P x 103 s-1 {RE - Rp) x 103 s"1 <rp x 103 s"1 M / 0 0.001 0.000 0.001 0.000 1.410 0.000 1.275 ' 68 0.885 0.895 -0.010 0.082 1.381 0.637 1.249 112 1.191 1.142 0.049 0.076 1.335 0.812 1.207 201 1.566 1.381 0.184 0.053 1.221 0.983 1.102 246 1.276 1.406 -0.130 . 0.044 1.159 1.000 1.044 291 1.483 1.380 0.103 0.040 1.096 0.982 0.987 380 1.019 1.268 -0.249 0.043 0.978 0.902 0.878 425 1.245 1.205 0.040 0.040 0.922 0.857 0.827 470 1.158 1.145 0.013 0.036 0.869 0.815 0.779 559 0.884 1.039 -0.155 0.030 0.772 0.739 0.690 604 0.986 0.990 -0.004 0.029 0.726 0.704 0.648 648 0.901 0.944 -0.043 0.029 0.684 0.672 0.609 738 0.815 0.854 -0.040 0.028 0.603 0.608 0.535 782 0.835 0.811 0.024 0.027 0.566 0.577 0.501 827 0.886 0.768 0.119 0.025 0.531 0.546 0.469 916 0.820 0.683 0.137 0.022 0.466 0.486 0.409 961 0.562 0.641 -0.080 0.021 0.436 0:456 0.382 1006 0.544 0.601 -0.057 0.020 0.408 0.427 0.356 1096 0.551 0.523 0.028 0.020 0.358 0.372 0.310 1140 0.419 0.487 -0.069 0.020 0.336 0.347 0.290 1185 0.284 0.452 -0.169 0.021 0.315 0.322 0.270 1274 0.373 0.388 -0.015 0.021 0.277 0.276 0.236 1319 0.406 0.358 0.048 0.022 0.260 -0.255 0.221 1364 0.207 0.330 -0.123 0.022 0.245 0.235 0.206 1453 0.278 0.279 -0.001 0.022 0.218 0.199 0.182 1498 0.301 0.256 0.045 0.021 0.206 0.182 0.171 1542 0.202 0.235 -0.033 0.021 0.195 0.167 0.161 1632 0.204 0.196 0.008 0.020 0.176 0.140 0.143 1676 0.122 0.180 -0.057 0.019 0.167 0.128 0.135 1721 0.242 0.164 0.078 0.019 0.160 0.116 0.128 1811 0.213 0.136 0.077 0.017 0.146 0.097 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, ap and 6P, are shown in Table D.l. The drying rate at fuel 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 - 1 ap x 103 s - 1 Sp x 103 s - 1 0 1.03 0.481 0.002 0.004 1 0.83 0.736 0.020 0.039 3 1.03 1.811 0.044 0.086 4 1.00 1.366 0.020 0.039 8 1.07 1.458 0.043 0.083 9 1.11 1.370 0.037 0.072 10 1.12 1.753 0.061 0.120 11 0.97 1.091 0.012 0.024 12 1.09 1.019 0.014 0.027 13 1.05 0.968 0.033 0.066 14 0.96 1.052 0.015 0.030 15 0.96 0.839 0.016 0.031 16 1.03 0.981 0.014 0.028 17 0.84 1.184 0.016 0.032 18 0.97 1.001 0.018 0.035 19 0.89 1.251 0.011 0.021 20 1.03 1.045 0.008 0.015 22 0.94 1.413 0.016 0.032 23 0.62 1.407 0.028 0.055 26 0.90 2.400 0.071 0.139 29 0.79 1.245 0.069 0.136 30 0.85 1.656 0.109 0.214 31 1.07 1.338 0.099 0.195 32 1.20 1.408 0.024 0.047 34 1.12 1.233 0.010 0.019 36 1.12 1.246 0.008 0.017 38 0.82 2.427 0.100 0.196 39 0.82 0.931 0.022 0.042 41 1.08 1.559 0.048 0.095 42 1.10 0.997 0.050 0.097 43 1.08 1.777 0.033 0.065 44 1.11 1.653 0.050 0.099 45 1.01 1.372 0.027 0.053 46 1.11 1.406 0.046 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 R x 103 s-1 <rHR) x 103 SP{R) x 103 M = 0.3 M = 0.4 M = 0.5 M = 0.6 s-1 s-1 0 0.235 0.324 0.398 0.451 0.002 0.004 1 0.169 0.287 0.412 0.539 0.013 0.026 3 0.495 0.756 1.019 1.247 0.035 0.069 4 0.561 0.730. 0.871 1.001 0.015 0.030 8 0.415 0.625 0.808 0.966 0.032 0.063 9 0.465 0.606 0.727 0.841 0.017 0.034 10 0.454 0.609 0.754 0.932 0.031 0.061 11 0.489 0.615 0.730 0.830 0.007 0.013 12 0.348 0.459 0.557 0.645 0.007 0.014 13 0.444 0.544 0.634 0.707 0.017 0.034 14 0.349 0.482 0.619 0.758 0.010 0.020 15 0.165 0.262 0.340 0.418 0.009 0.019 16 0.448 0.550 0.638 0.713 0.009 0.019 17 0.570 0.718 0.854 0.966 0.013 0.026 18 0.264 0.385 0.505 0.630 0.010 0.020 19 0.571 0.719 0.851 0.966 0.006 0.012 20 0.415 0.530 0.631 0.720 0.005 0.010 22 0.874 0.987 1.094 0.017 0.033 23 0.972 1.102 1.211 1.298 0.027 0.053 26 1.238 1.479 1.696 1.894 0.050 0.097 29 0.811 0.924 1.022 1.106 0.057 0.112 30 0.849 1.039 1.219 1.390 0.078 0.153 31 0.596 0.743 0.872 0.984 0.052 0.101 32 0.373 0.549 0.708 0.850 0.015 0.030 34 0.450 0.551 0.648 0.749 0.005 0.010 36 0.445 0.571 0.680 0.775 0.004 0.008 38 1.146 1.484 1.975 2.020 0.067 0.132 39 0.182 0.342 0.507 0.656 0.018 0.035 41 0.579 0.768 0.922 1.045 0.027 0.052 42 0.417 0.518 0.602 0.672 0.022 0.044 43 0.682 0.866 1.037 1.195 0.020 0.039 44 0.442 0.604 0.736 0.845 0.022 0.043 45 0.394 0.515 0.646 0.794 0.017 0.033 46 0.427 0.588 0.728 0.850 0.022 0.043 Appendix D. Tabulated Data on Maximum and Falling Drying Rates 334 Table D.3: Summary of Data Affecting the Slope of the Falling Rate Curve Run du/dR M = 0.3 M = 0.4 M = 0.5 M = 0.6 0.3 < M < 0.6 0 0.318 1.111 2.014 3.875 2.259 1 1.007 0.479 0.165 0.821 0.697 3 1.167 0.403 1.098 1.539 1.129 4 0.645 0.932 1.174 1.411 1.079 8 1.523 1.423 1.364 1.239 1.391 9 1.582 1.712 1.752 1.411 1.620 10 0.602 2.337 2.203 0.996 1.708 11 0.896 0.989 1.146 1.388 1.121 12 1.001 0.996 0.905 0.690 0.907 13 0.745 0.866 1.017 1.112 0.945 14 1.230 0.164 0.622 1.337 0.963 15 1.322 2.062 0.093 2.364 1.703 16 1.188 1.264 1.292 1.180 1.232 17 0.499 0.936 1.357 1.842 1.261 18 0.385 0.185 0.183 0.649 0.399 19 0.833 0.887 0.989 1.167 0.977 20 1.103 1.067 1.045 0.993 1.053 22 0.721 0.351 0.211 0.479 23 1.231 1.441 1.806 2.504 1.811 26 1.947 1.777 1.571 1.555 1.720 29 1.097 1.190 1.375 1.757 1.378 30 0.097 0.295 0.815 1.577 0.901 31 1.196 1.263 1.386 1.567 1.360 32 0.858 0.996 1.110 1.239 1.060 34 0.806 0.181 0.323 0.420 0.491 36 1.080 1.176 1.173 0.843 1.077 38 2.008 2.320 3.668 3.917 3.091 39 5.040 0.036 1.016 1.639 2.698 41 1.570 1.649 1.739 1.728 1.673 42 1.296 1.439 1.538 1.441 1.431 43 0.564 0.518 0.585 0.725 0.603 44 1.473 1.665 1.602 0.386 1.384 45 0.031 0.714 0.878 0.532 0.626 46 1.051 1.101 1.084 0.839 1.024 Appendix D. Tabulated Data on Maximum and Falling Drying Rates 335 Table D.4: Summary of Data on the Slope of the Falling Rate Curve Run ui x 10 d s- 1 s _ 1 6rM x s- 1 M = 0.3 M = 0.4 M = 0.5 M = 0.6 0.3 < M < 0.6 0 0.935 0.828 0.644 0.404 0.703a 0.7206 0.006 0.013 1 1.068 1.250 1.286 1.167 1.193 1.235 0.013 0.025 3 2.620 2.700 2.444 2.069 2.459 2.507 0.056 0.110 4 1.721 1.555 1.371 1.161 1.452 1.467 0.023 0.046 8 2.349 1.967 1.649 1.390 1.839 1.837 0.063 0.123 9 1.553 1.360 1.184 1.030 1.282 1.255 0.040 0.078 10 1.345 1.503 1.717 1.900 1.616 1.596 0.075 0.147 11 1.372 1.226 1.074 0.917 1.147 1.137 0.011 0.021 12 1.179 1.040 0.923 0.834 0.994 0.991 0.009 0.018 13 1.079 0.946 0.806 0.677 0.877 0.874 0.023 0.045 14 1.273 1.384 1.342 1.173 1.293 1.366 0.014 0.027 15 1.089 0.858 0.738 0.887 0.893 0.843 0.023 0.045 16 1.105 0.949 0.809 0.692 0.889 0.882 0.017 0.032 17 1.557 1.424 1.231 1.010 1.305 1.321 0.024 0.047 18 1.191 1.238 1.239 1.176 1.211 1.218 0.006 0.012 19 1.556 1.398 1.244 1.092 1.322 1.318 0.008 0.016 20 1.231 1.076 0.943 0.830 1.020 1.017 0.007 0.015 22 c 1.169 1.094 1.061 1.108 1.098 0.011 0.022 23 1.414 1.200 0.983 0.755 1.088 1.088 0.069 0.135 26 2.574 2.294 2.067 1.878 2.203 2.188 0.121 0.236 29 1.222 1.063 0.908 0.748 0.985 0.982 0.111 0.218 30 1.911 1.891 1.769 1.523 1.773 1.805 0.099 0.195 31 1.563 1.379 1.204 1.035 1.295 1.293 0.099 0.195 32 1.846 1.677 1.505 1.335 1.591 1.590 0.023 0.045 34 1.037 0.974 0.986 1.038 1.009 0.996 0.003 0.007 36 1.349 1.172 1.011 0.887 1.105 1.099 0.006 0.012 38 3.608 3.158 2.286 2.181 2.808 2.912 0.295 0.577 39 1.366 1.706 1.588 1.344 1.501 1.580 0.069 0.135 41 2.080 1.702 1.379 1.111 1.568 1.552 0.063 0.124 42 1.092 0.921 0.765 0.632 0.852 0.850 0.045 0.089 43 1.891 1.770 1.655 1.527 1.711 1.707 0.017 0.033 44 1.779 1.464 1.186 1.031 1.365 1.343 0.043 0.084 45 1.196 1.257 1.396 1.530 1.345 1.333 0.015 0.029 46 1.715 1.500 1.306 1.156 1.419 1.411 0.032 0.062 "average of the four values 6slope of the line connecting M = 0.3 and M = 0.6 cAverage values represent the region of 0.4 < M < 0.6 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 = 0.3 M = 0.4 M = 0.5 M = 0.6 0 2160 1800 1524 1288 1 1936 1479 1196 979 3 957 800 685 596 4 1160 1000 880 770 8 1149 960 818 700 9 1225 1043 900 768 10 1080 870 737 620 11 1360 1184 1035 906 12 1623 1373 1177 1009 13 1574 1375 1200 1054 14 1490 1248 1066 906 15 2729 2260 1930 1666 16 1506 1306 1138 990 17 1204 1050 920 810 18 1753 1442 1225 1043 19 1186 1030 902 794 20 1510 1298 1125 976 22 950 843 747 23 1108 1012 926 846 26 586 513 450 394 29 1235 1121 1019 924 30 1070 964 877 798 31 1529 1380 1256 1148 32 1711 1492 1332 1204 34 1334 1133 966 822 36 1320 1123 963 825 38 574 498 394 384 39 1893 1496 1260 1086 41 1027 878 760 659 42 1561 1346 1168 1010 43 890 760 655 566 44 1159 968 818 692 45 1315 1094 922 782 46 1219 1021 868 742 Appendix E Calibration Curves and Equations The following two tables provide the calibrated values of flowmetering devices and ther-mocouples. 337 Appendix E. Calibration Curves and Equations 338 Table E. l : Calibration Equations for Flowmeters Flowmeter Ch.E. No Substance m kg/hr Fisher rotameter 3162 Air @ STP — 1.61994-E - 07 + 0.742X0 Fisher rotameter 3227B Air @ STP 1.232523 + 0.344086X Matheson rotameter 3227B Air @ STP c0 + ClX + c2X2 + c3X3 b Brooks rotameter Water 32.5476 + 5.69366X Keiso rotameter Steam © 115 kPa -3.66793 + 8.6555X 3 inch orifice Air @ STP 1.7068^/Apc 2 inch orifice Air @ STP 1.745-/Sp l | inch orifice Air © STP 0.325V/A^ 1 inch orifice Air © STP 0 .079 v / £p Rosemount transducer^ -1.62634 + 0.394172X aX denotes flowmeter reading. c^o = 2.0 x 10-3, C l - 31.2 x 10-6, c2 = 4.7 x 10~6 and c 3 = -15.9 x 10~9  cAp is in Pa. dAp= 337.603-178.195X +23.170X2 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. Appendix E. Calibration Curves and Equations Table E.2: Calibration Equations for ThermocoupL Thermocouple No." rp b -L calib ° c 1 1.01067Ttafc.c -0.979519 2 1.01094Tta6 - 1.127330 3 1.00546Ttab - 1.069770 4 1.008007U - 1.080000 5 1.00916Tta6 - 1.094820 6 1.00900Tta6 - 0.855151 7 1.00303Tta6 - 0.628659 8 1.00832Ttafe - 1.092280 9 1.00747Ttab - 0.881030 10 1.0074lTtao - 0.884514 11 1.00804Ttab - 0.654781 12 1.00998Ttao - 0.800983 13 1.01188Tta6 - 1.005180 14 1.00982Tta6 - 0.909653 15 1.009387*6 - 0.726555 16 1.009327^6 - 0.729694 17 1.00747^ + 0.745452 18 1.01025Tta6 + 0.923989 19 1.00864^ + 1.223050 20 1.007267*06 + 1.188360 21 1.01158Tta6 + 1.249230 22 1.00747Tfo6 + 1.091800 23 1.004247*06 + 1.471470 24 1.01018Tto6 + 0.900685 25 0.99982Tta6 + 2.767340 28 1.00189Tte6 + 1.926900 29 1.00663Tta6 + 1.874640 30 1.00243Tta6 + 2.023960 31 1.00244Ttab + 1.815340 32 1.00842Tta6 + 1.892020 a As is marked on the flow diagram. ^Calibrated temperature. cTemperature calculated using tabulated linearized data. 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 com-puter 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 RATE C Program to calculate rate o l drying c _ C C AP= i n t e r f a c i a l surface/total bed vol. ;m**2/m**3 C AREBED= area of the bed ; m**2 C AVEMAS= time average GSAVE values C DPAVE= ave. effective p a r t i c l e diam. ; m C DEN= mean instantaneous density ; kg/m**3 C DENAVE= time averaged mean instantaneous density ; kg/m**3 C DENIN= ave. i n l e t density ; kg/m**3 C DENW0D= wood density ; kg/m**3 C E= voidage ; vol. s o l i d / v o l . bed C EPS=error tolerance prescribed by the user C F= vapor press, of water at dew point of outlet gas ; itimHg C GMS1= in l e t dry a i r ; kg/hr C GMAS1= i n l e t t o t a l a i r ; kg/hr : i n the READ statement , i t i s C the mass through 3" o r i f i c e and i n the output i t i s the C t o t a l mass throug the bed. C GS1,GS2= i n and out t o t a l gas/cross section.time ; kg/hr.m**2 C GSAVE= ave tot. 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 point temp readings C KS= last no of reading before the contact of s o l i d ft gas starts C KSFLAG= i s "0" when read. no. KS+1 not considered i n eval. of Yl C KB= no of reading after which the gas was by-passed C KJ= the last KJ no of readings axe averaged to get the incoming C mass flow f or the steam runs ; chosen as 4 i n the program C N= degree of the polynomial i n RPDLY2 subroutine C NRUN= Run no. C PT= t o t a l press. ; mmHg C RATEIN= rate of drying ; kg water/hr.m**2 of i n t e r f a c i a l area C RATE= rate of drying ; (kg water/kg dry wood)/sec C RATEVP=rate of evaporation ; kg water/sec C RATEX= rate of drying ; kg water/hr.m**2 of cross section C SUPVEL= average s u p e r f i c i a l velocity (mean of VEL values) ; m/hr C TDP2= outlet gas dew point temp ; oC C TDPAIR= dew point temp of the d i l u t i n g a i r ; oC C TIME= time dew point temp, measured ; sec C TG1= in l e t gas temp. ; oC C TG1KS= ave. i n l e t gas temp, when the bypass l i n e i s shut off; oC C TG2= outlet gas temp, (thermo. #4 i n steam runs;#7 for rest); oC C TGAVE= ave. temp, of icoming and outgoing gas .5*(TG1+TG2); oC C TGAVER= ave. of TGAVE values; oC Appendix F. Computer Programs 342 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C VEL= mean instantaneous s u p e r f i c i a l velocity of gas ; m/s C VELAVE= ave. s u p e r f i c i a l v e l o c i t y of gas ; m/s C VELIN= ave. i n l e t s u p e r f i c i a l velocity of gas ; m/s C VOLBED= bed volume ; m**3 C WODDRY= mass of dry wood ; kg C W0DMAS= mass of wet wood ; kg C Y1,Y2= inl e t and outlet gas humidity , dry basis C Zl= i n i t i a l wood moisture content , dry basis 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 ; f i r s t f i l e contains * C * the following values and the second f i l e i s the one obtained by * C * PC contains temperature data. * C * * C ******************************************************************** Appendix F. Computer Programs 343 Table F. l : Program to Calculate the Instantaneous Drying Rates -(Continued) READ(5,LIST) NRUN,K,KB,KS,KSFLAG READ(5,LIST) 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 CONTINUE 26 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 Appendix F. Computer Programs 344 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 in l e t flow for 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 CONTINUE C 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) Appendix F. Computer Programs Table F. l : Program to Calculate the Instantaneous Drying Rates -(Continued) TIMCOR(I)=0. 35 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 in 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 article by Smith and Kozak in 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 WRITE INITIAL CONDITIONS C 65 WRITE(6,10) 10 FORMAT('1') IF(STFLAG.EQ.L) WRITE(6,11) 11 F0RMAT(/,10X,'STEAM IS THE DRYING MEDIUM'/) WRITE(6,12)NRUN,GMAS1 12 FORMAT('RUN=',I3,/,'INLET TOTAL MASS FL0W= \F6.2,' kg/hr') IF(STFLAG.EQ.1.) GO TO 16 WRITE(6,15)GMS1,Y1 15 FORMAT('INLET DRY GAS= ',F6.2,' kg/hr',/, 1 'DRY BASIS GAS HUMIDITY=',F7.4) 16 WRITE(6,17)TG1,VELIN 17 FORMAT('AVE. INLET GAS TEMP= '.F6.2,' oC 1,/,'AVE. INLET SUPERFICIAL GAS VELOCITY= >,F4.2,' m/sec') WRITE(6,50)TG1KS,VELIKS,DENIKS 50 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 55 FORMAT('Re BASED ON BED DIAMETER=',F7.0,/,'Rep=',F5.0) WRITE(6,20)WODMAS,WODDRY,Z1,HTBED 20 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 30 FORMAT('VOIDAGE=',F6.3) C WRITE(6,31) YAS.TAS C31 FORMAT(2D15.6) C 60 CONTINUE C C CALCULATE RATE (kg water/kg dry wood/sec) C and RATEX (kg water/sq.m of cross sect./hr) C SUMVEL=0. SUMMAS=0. Appendix F. Computer Programs 347 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) SUMTG=0. DO 70 1=1,K XX(I)=TIME(I) C 70 CONTINUE C 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. 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.) 72 CONTINUE C 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 CALCULATE AVE PARTICLE DIAM .SPECIFIC SURFACE AND RATE (RATEIN) C DPAVE=DP32 120 AP=(6.*(1.-E))/DPAVE DO 140 1=1,K RATEIN(I)=RATEX(I)/(AP*HTBED) 140 CONTINUE C C WRITE DATA C WRITE(6,220) AVEMAS,SUPVEL 220 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',/, Appendix F. Computer Programs 348 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) l'Rint = kg water/hr.m**2 ol interfacial 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 TIME ') oC TIME Revp kg/sec l/sec' 252 254 258 WRITE(6,230) FORMAT01',/,' I TG2 Y2 1' R Rint WRITE(6,235) FORMAT(' 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 260 470 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) 232 F0RMAT(4X,F7.0,8X,F8.4,F8.0,2F10.6,F9.3) 234 F0RMAT(1X,I3,F7.0,F8.2,F8.4) 238 F0RMAT(1X,I3,F7.0,F8.2,F8.4,F8.0,2F10.6,F9.3) 260 KI=KSP2 Appendix F. Computer Programs Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) KF=KFSAVE GO TO 236 239 IF(KF.GE.K)GO TO 240 KI=KF+1 GO TO 229 240 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 241 FORMAT(' 1' , //,' TIME RATE WT 1' '//,3I5/,2F15.6,2I5) WRITE(6,242) (TIMCOR(I),RATE(I),WEIT(I),I=KSP,K) 242 FORMAT(3F15.6) C NEVAP=1 WRITE(6,245) KCOR,KCOR,NRUN,Z1,WODDRY,NEVAP,NAREA 245 FORMAT (.'1',//,' TIME Revap WT 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 Appendix F. Computer Programs 350 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 NR= no. of readings C P(I,J)= no. of points C TIME(I)= time at which the data was recorded C R0T= rotameter readings C PRES0= upstream orifice pressure C TDPAIR= dew point temperature of diluting air C 1 FORMAT(' ') S FORMAT(F8.2) 10 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) 30 CONTINUE 20 CONTINUE C 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) C C In C IF(STEAM.LT.50.)G0 TO 43 steam Runs YDSAM is the mass flow through the 3" orifice 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. IF(NRUN.Eq. IF(NRUN.Eq. IF(NRUN.Eq. IF(NRUN.Eq. IF(NRUN.Eq. IF(NRUN.Eq, IF(NRUN.Eq. IF(NRUN.Eq. IF (NRUN. Eq. IF(NRUN.Eq, IF(NRUN.Eq, IF (NRUN. Eq, IF(NRUN.Eq, 38.AND. 38.AND. 38.AND. 38. AND. 39. AND. 40. AND. 40. AND. 41. AND. 43. AND. 44. AND. 45. AND, 46. AND, 46.AND, 46.AND, I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE I.GE .13.AND .19.AND .28.AND .40.AND .13.AND .15.AND .17.AND .13.AND .17.AND .14.AND .15.AND .12.AND .13.AND .15.AND I.LE.18) I.LE.20) I.LE.39) .I.LE.43) .I.LE.29) .I.LE.16) .I.LE.17) •I.LE.19) .I.LE.23) •I.LE.14) .I.LE.17) .I.LE.12) •I.LE.14) .I.LE.15) PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= PRES0= 15.7 15.5 14.5 14.7 17.0 17.8 17. 17.7 16.7 18. 17. 20. 18. 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 therefore, the panel reading should i d e a l l y be equl to the comp. C recorded value . That was the reason 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 for c a l i b . i n Aug 87 to include any changes C from the ideal 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******************** c a l i b . f or small Fisher rot. i n Aug 86 C C02=DUMC02*(0.0452867+0.0126428*RCD2)*60.*.4536 C C In the following 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 Programs 353 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C IF(NRUN.NE.20)GO TO 49 DO 52 1=5,44 P(I,27)=10.15 52 CONTINUE C 49 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. 55 IF(NRUN.GT.24.)GO TO 56 C C******************** calib. for small Fisher rot. in Aug 86 C GAIR=0.0452867+0.0126428+ROT GO TO 58 C 3 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. in 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 is 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 Appendix F. Computer Programs 354 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) C C A l l the points used for the c a l i b . of the 1" o r i f i c e ( f i l e orlmet) C C********************** used for a l l runs C GSTD(I)=(0.394172D0*P(I,27)-0.162634D1)/60./.4536 C C************ Dec 21/87 calibrations to check previos ones C they agree well. C C F i r s t point i s l e f t out i n c a l i b . of the 1" o r i f i c e ( f i l e orl2) C C GSTD(I)=(0.395075D0*P(I,27)-0.170554D1)/60./.4536 C C A l l the points used for the c a l i b . of the 1" o r i f i c e ( f i l e o r l l ) 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********************* for Run# 23 C IF(NRUN.NE.23.0R.I.LT.3) GO TO 60 IF(I.GT.3)G0 TO 64 1=1+30 64 GWSAM(I)=GWSAM(I+30) 60 SGSAM=SGSAM+GWSAM(I) NNR=NNR+1 IF(I.EQ.NR) GO TO 51 51 CONTINUE Appendix F. Computer Programs Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) GSAM=SGSAM/NNR IF(NRUN.EQ.O.) GSAM=4./60./.4536 C 80 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 356 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 Appendix F. Computer Programs 357 Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) NM=N-1 C DO 5 1=1,N X(I)=TGF(I) Y(I)=VIS(I) 5 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 DO 5 1=1,N X(I)=TGF(I) Y(I)=VIS(I) 5 CONTINUE C CALL SPLINE C TG=(TGAVE*9./5.)+32. VISAVE=(F(TG))*1.488 C RETURN END Appendix F. Computer Programs Table F.l: Program to Calculate the Instantaneous Drying Rates -(Continued) c C SPLINE * C************************ c SUBROUTINE SPLINE C C Interpolation using cubic splines with fitted end points. C C Input: X Array of independent x-values C Y Array of dependent y-values C N Number of data points C NM N-l C C Output: Q,R,S Coefficients of cubic spline equations C 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 Coefficient matrices for end point cubics C INTEGER FLAG DATA M/4/ IS=0 FLAG=0 MP=M+1 MM=M-1 10 DO 20 1=1,M II=I+IS C0EFF(I,MP)=Y(II) C0EFF(I,1)=1. DO 20 J=2,M 20 C0EFF(I,J)=C0EFF(I,J-1)*X(II) C C Gauss elimination to find A4 and B4 C DO 30 K=1,MM KP=K+1 DO 30 I=KP,M DO 30 J=KP,MP 30 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) A4=C0EFF(M,MP)/COEFF(M,M) FLAG=1 IS=N-M GO TO 10 40 B4=C0EFF(M,MP)/C0EFF(M,M) C C Calculate H(I) C DO 50 1=1,NM 50 H(I)=X(I+1)-X(I) C C Coefficients of tridiagonal equations C 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) 60 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 C Call Thomas algorithm to solve tridiagonal set C CALL TDMA(A,B,C,D,R,N) C C Determine Q(I) and S(I) C DO 70 1=1,NM IP=I+1 Q(I)=(Y(IP)-Y(I))/H(I)-B(I)*(2.*R(I)+R(IP))/3. 70 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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