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Wax deposition from kerosene onto cooled surfaces Ghedamu, Michael Abraha 1995

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W A X DEPOSITION F R O M K E R O S E N E ONTO C O O L E D SURFACES By Michael Abraha Ghedamu B . A . S c , Addis Ababa University, 1989  A THESIS SUBMITTED I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF M A S T E R OF APPLIED SCIENCE  IN T H E F A C U L T Y OF G R A D U A T E STUDIES C H E M I C A L ENGINEERING  We accept this thesis as conforming to the standard  T H E U N I V E R S I T Y OF BRITISH C O L U M B I A May 1995 Cc), Michael Abraha Ghedamu , 1 9 9 5  In  presenting  degree  this  at the  thesis  in  University of  partial  fulfilment  of  of  department  this or  thesis for by  his  or  scholarly purposes may be her  representatives.  permission.  The University of British Columbia Vancouver, Canada  for  an advanced  Library shall make it  agree that permission for extensive  It  publication of this thesis for financial gain shall not  DE-6 (2/88)  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  Abstract  Wax fouling is a major problem in some oil refineries. The main objective of this project was to test different surfaces with the aim of eliminating or at least reducing wax deposits in heat exchangers. Wax is separated in oil refineries by cooling the wax-laden petroleum stream in chillers and then scraping off the deposited wax mechanically from the surfaces of the heat exchangers (chillers). The solid wax is separated from the liquid petroleum stream by means of filters.  An experimental test rig was set up to study ways of eliminating or reducing wax deposits by changing some of the operating conditions as well as the surface type of the heat transfer area. A double pipe heat exchanger 0.72 m long with inner tube (ID=9.96 mm, OD=12.45 mm) and outer pipe (ID=25.4 mm) was used. The solution tested was wax dissolved in kerosene, which flowed through the annular section while the cooling water flowed countercurrently in the inner tube. The effects of flow velocity of waxkerosene, of bulk temperature, of wax-kerosene concentration and of heat transfer surface type have been studied. Two types of wax were used: refined wax and slack wax. The surfaces used were: uncoated stainless steel, sand-blasted stainless steel, chrome-plated stainless steel, n-C18 silane-coated chrome-plated stainless steel, Heresite Si 57 E coated stainless steel (shiny), Heresite P-400/L-66 coated stainless steel (dull) and n-C18 silane coated stainless steel.  The cloud point for each wax-kerosene concentration investigated (5, 10, 15 and 20 wt. % wax) was measured using A S T M procedures. The rheology of wax-kerosene was also investigated to determine if the mixtures were Newtonian or non-Newtonian. All mixtures were found to be Newtonian. The mixture viscosity was determined at temperatures from the cloud point upwards at each concentration.  ii  9  A Kern-Seaton (1959) equation was used to determine R* and 9 from the f  C  resistance vs. time experimental data. The wax deposit showed a decrease in R* with f  increasing Re, with increasing T and with decreasing concentration. Similar results were b  found by Bott and Gudmundsson (1977b). From the plots of R* vs. Re, the hierarchy in f  increasing R* was found to be: Heresite-coated stainless steel (dull and shiny) < n-C18 f  silane coated stainless steel < n-C18 silane-coated chrome-plated stainless steel < chrome-plated stainless steel < uncoated stainless steel < sand-blasted stainless steel.  A  similar hierarchy with four of the seven tubes was shown with respect to R* vs. T . That f  b  plastics show a lower wax deposit compared to metal surfaces has been shown by previous investigations.  After some deposition had occurred, the removal of wax chunks from the surface and occasional bare patches were visually observed on all tubes except the two Heresite-coated tubes and the sand-blasted stainless steel. The phenomenon of deposit sliding was observed on the chrome-plated stainless steel, where the sliding velocity was recorded.  The concentration and bulk temperature of a petroleum stream may be fixed by refinery conditions. However, a lower wax deposit on heat transfer surfaces can be obtained by using a smooth surface material which has a low affinity for wax, and high flow velocity or turbulence.  iii  Table of Contents Abstract  ii  List of Tables  vii  List of Figures  ix  Acknowledgments  xii  1. Introduction  1  2. Literature Survey  3  3. Experimental Setup  24  3.1 The Test Rig  24  3.1.1 Test Section  24  3.1.2 Pump  27  3.1.3 Flow Rate Measurement  27  3.2 Temperature Measurement and Calibration  28  3.3 Cloud Point and Viscosity  29  3.3.1 Cloud Point  29  3.3.2 Viscometry  31  4. 4 Experimental Procedures  33  4.1 System Cleaning  33  4.2 Preparation of Wax-Kerosene Mixture  33  4.3 Fouling Test  33  4.4 Cloud Point Test  34  5. Properties of Wax and Kerosene  36  iv  5.1 Waxes  36  5.2 Kerosene  36  5.3 Could Point of Wax-Kerosene Mixtures  37  5.4 Viscosity of Wax-Kerosene Mixtures  37  6. Data Analysis  45  6.1 Calculation of Fouling Resistance  45  6.2 Data Fitting and Determination of Parameters  46  7. Results and Discussion  50  7.1 Test of Reproducibility  51  7.2 Fouling Results  51  7.2.1 Effect of Flow Velocity  51  7.2.2 Effect of Bulk Temperature  62  7.2.3 Effect of Surface Conditions  69  7.2.4  Effect of Concentration  72  7.2.5 Removal and Sliding of Fouling Deposit  79  7.2.6 Uncertainty  80  7.2.7 Prior Work at U B C  82  8. Conclusions  83  Nomenclature  87  References  90  Appendices A. Rotameter Calibration  93  V  B. Thermocouple Calibration Equations  94  C. Computer Program  95  D . Experimental Results  107  vi  List of Tables  Table 1. Effect of surface preparation on deposition Table 2. Summary of literature review of  21  vs. wax-solvent velocity, T and b  concentration effects  21  Table 3. Cloud Point Temperature (°C) for Refined and Slack Waxes in Kerosene  37  Table 4. Viscosity runs for refined wax at 5 % by wt. in kerosene  40  Table 5. Viscosity runs for refined wax at 10% by wt. in kerosene  40  Table 6. Viscosity runs for refined wax at 15 % by wt. in kerosene  40  Table 7. Viscosity runs for refined wax at 20 % by wt. in kerosene  40  Table 8. Viscosity runs for slack wax MCT-10 at 5 % by wt. in kerosene  40  Table 9. Viscosity runs for slack wax MCT-10 at 10 % by wt. in kerosene  40  Table 10. Viscosity runs for slack wax MCT-10 at 15 % by wt. in kerosene  41  Table 11. Viscosity runs for slack wax MCT-10 at 20 % by wt. in kerosene  41  Table 12. Viscosity Coefficients a and b for Refined Wax  42  Table 13. Viscosity Coefficients a and b for MCT-10 Slack Wax  42  Table 14. Results for refined wax at 10 % by wt. using stainless steel. T =32.6±0.2°C, Cloud Point= 21.1 ° C , t =9.5+0.5 °C, V =2.5 m/s  53  Table 15. Results for slack wax MCT-10 at 20% by wt. using stainless steel. T =31.4±0.3 °C, Cloud Point= 27.8 °C , f =10.4±1.5°C, V = l . l m/s  53  b  b  b  w  6  w  Table 16. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel. T = 31.3+0.1°C ,CloudPoint=27.8 °C, / =7.6±0.4°C, V = l . l m/s....54 b  fc  w  Table 17. Results for slack wax MCT-10 at 20% by wt. using sand-blasted stainless steel. T = 31.2+0.1 °C, Cloud Point= 27.8°C, f =11.4±0.6 °C, V = l . l m/s 54 b  6  w  Table 18. Results for slack wax MCT-10 at 20% by wt. using n-C18 silane-coated chrome- plated stainless steel. T =31.3+0.1 °C, Cloud Point=27.8°C , t =13.6± 0.7°C, V = l . l m/s b  b  w  vii  54  Table 19. Results for slack wax MCT-10 at 20% by wt using Heresite Si 57 E coated stainless steel. T„ =31.3±0.2 °C, Cloud Point=27.8 ° C , / =13.5±0.9 °C, V = l . l m/s  55  Table 20. Results for slack wax MCT-10 at 20% by wt. using Heresite P-400/L-66 coated stainless steel. 7^= 31.2+0.1 °C, Cloud Point=27.8°C, f =13.2±0.4 oc, V = l . l m/s  55  6  w  6  w  Table 21. Results for slack wax MCT-10 at 20% by wt. using monolayer n-C18 silane coated stainless steel. T =31.5+0.1 °C, Cloud Point=27.8 ° C , f =13.2+0.2°C, V = l . l m/s 55 b  6  w  Table 22. Results for refined wax at 10% by wt. using stainless steel and wax-kerosene atRe=12155. Cloud Point=27.8 ° C , f =10.0+0.3 °C, V = l . l m/s 63 b  w  Table 23. Results for slack wax MCT-10 at 20% by wt. using stainless steel at Re=9074. Cloud Point=27.8 ° C , f =7.9±0.5°C, V = l . l m/s 6  w  63  Table 24. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel at Re= 9629. Cloud Point=27.8°C , f =9.6±1.5 °C, V = l . l m/s 63 6  w  Table 25. Results for slack wax MCT-10 at 20% by wt. using sand-blasted stainless steel at Re= 9357. Cloud Point= 27.8°C , f =11.7±0.8°C, V = l . l m/s 64 6  w  Table 26. Results for slack wax MCT-10 at 20% by wt. using n-C18 silane-coated chrome-plated stainless steel at Re=9391, Cloud Point=27.8°C , f =12.8±0.5°C, V = l . l m/s 6  w  64  Table 27. Results for refined wax using stainless steel and wax-kerosene at Re=10664 and ^=32.5±0.1°C, Cloud Point= 27.8 ° C , / =9.3±0.5°C, V =2.5 m/s 73 6  w  Table 28. Results for slack wax MCT-10 using stainless steel at Re= 10003 and T =29.2 ±0.1 ° C , Cloud Point=27.8 <>C , f =13.9±0.9 °C, V = l . l m/s b  6  w  Table. 29. Summary of removal and sliding of wax deposit  73 80  Table. 30. Sliding velocity for chrome-plated stainless steel tube using slack wax MCT-10 at 20% by wt. T = 31.3±0.1°C , Cloud Point=27.8 ° C , 4=7.6±0.4°C, V = l . l m/s 80 b  w  Table 31. Lists of run number, disk number, tube type, wax type and U  viii  0  107  List of Figures Fig. 1. Plot ofEq. (7), after Kern-Seaton (1959)  9  Fig. 2. Typical curve of amount of wax deposited vs. flowrate by Bott and Grudmundsson (1977b)  16  Fig. 3. Effect of velocity on rate of deposition of Delhi DU-184-1 crude oil at 106 °F  18  Fig. 4. Weights of paraffin deposited on polished, sand-blasted, mill-scaled, corroded and rough-ground steel as a function of deposition surface temperature (roughness factors in parentheses)  20  Fig. 5. Flow diagram of wax fouling rig. TC=thermocouple  25  Fig. 6. Apparatus for cloud point measurement  31  Fig. 7. Typical graph of shear stress vs. shear rate for refined wax in kerosene at 10 % by wt. and 21.1 °C. Cloud point of solution= 21.1 °C Fig. 8. Typical graph of shear stress vs. shear rate for slack wax MCT-10 in kerosene at 5 % by wt. and 15.0 °C. Cloud point of solution=15.0 °C  39  Fig. 9. G C chromatogram for refined wax  43  Fig. 10. G C chromatogram for slack MCT-10 wax  44  39  Fig. 11. Result for slack wax at 20% by wt on chrome-plated stainless steel tube, Re=9224and 5=31.2 ° C  50  Fig. 12. Result for slack wax at 20% by wt. on chrome-plated stainless steel tube, Re=9208 and 5=31.2 ° C  50  Fig. 13 a. Rf vs. time for slack wax MCT-10 at 10 % by wt. using stainless steel. Re = 6645, 7^=31.4 °C, Cloud Point = 27.8°C  56  Fig. 13b. R vs. time for slack wax MCT-10 at 10 % by wt. using f  stainless steel. Re = 8722, 7^=31.4 °C, Cloud Point = 27.8°C  56  Fig. 13 c. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=10615, 5=31.4 °C, Cloud Point=27.8°C  ix  57  Fig. 13d. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=12184, 5=31.4 °C, Cloud Point=27.8°C  57  Fig. 13e. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=14430, 5=31.4 °C, Cloud Point=27.8°C  58  Fig. 14 Results for refined wax at 10% by wt. on stainless steel tube at5 32.6°C =  59  Fig. 15a. Result of R* vs. Re for MCT-10 slack wax, 20% by wt at 5=31.3+0.2 ° C for different surfaces 60 f  Fig. 15b. Result of Log (R* ) vs. Log (Re) for MCT-10 slack wax, 20 % by wt at f  5= 31.3+0.2 °C for different surfaces  61  Fig. 16a. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=9430, 5= 28.9 °C, Cloud Point=27.8°C  64  Fig. 16b. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=9430, 5 = 31.2 °C,Cloud Point=27.8°C  65  Fig. 16c. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=9430, 5= 34.0 °C,Cloud Point=27.8°C  65  Fig. 16d. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=9430,5 = 38.1 °C,Cloud Point=27.8°C  66  Fig. 16e. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=9430, 5 =40.6 °C, Cloud Point=27.8°C  66  Fig. 17. Results for refined wax at 10% by wt. on stainless steel tube at Re=12155  67  Fig. 18. Graph of R* vs. 5 for MCT-10 slack wax at 20% by wt. and Re =9452+277  68  Fig. 19. Graph for slack wax MCT-10 at 20 % by wt. and 5= 31.3±0.3 °C for different surfaces  71  f  Fig. 20a. R vs. time for slack wax MCT-10 at 5 % by wt.using stainless steel. f  Re=10003, 5 =29.2 °C, Cloud Point=27.8°C  73  Fig. 20b. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=10003, T„ =29.2 °C, Cloud Point=27.8°C  74  Fig. 20c R vs. time for slack wax MCT-10 at 15 % by wt.using stainless steel. f  Re=10003, 7^=29.2 °C, Cloud Point=27.8°C  74  Fig. 20d. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. f  Re=10003, 7^=29.2 °C, Cloud Point=27.8°C  75  Fig. 21. Results for refined wax on stainless steel tube at Re=10664 and 7^=32.5 °C  76  Fig. 22. Results for slack wax MCT-10 on stainless steel tube at Re= 10003 and T =29.2°C  77  b  Fig. 23. Graph of R^ vs. T -T b  c  for slack wax MCT-10 on uncoated stainless steel tube.  Re =10003 and 7^=29.2 °C. Fig. 24. Calibration curve of rotameter  92  xi  Acknowledgments I would like to express my sincere gratitude to Professors A. P. Watkinson and N . Epstein for their guidance and suggestions which played a very important role in the completion of this study. M y thanks also go to Dr. Tom Broadhurst and the Imperial Oil Limited staff, and to Heresite Protective Coatings Inc., for their valuable advice and service.  Thanks are also due to the staff of the Department of Chemical Engineering Workshop, Office and Stores for their invaluable assistance.  xii  Chapter 1  1. Introduction  P e t r o l e u m w a x e s are b r o a d l y defined as w a x e s w h i c h naturally o c c u r i n the v a r i o u s fractions o f crude petroleum. S o m e crudes contain little o r n o wax, whereas others are so w a x y that they are semisolid at r o o m temperature.  T h e r e are three m a i n types o f petroleum waxes: paraffin waxes, microcrystalline waxes, and petrolatum. Paraffin w a x e s are mainly c o m p o s e d o f straight-chain m o l e c u l e s w i t h a small n u m b e r o f branched chains and crystallize i n large, w e l l f o r m e d , distinct crystals o f plate and needle types. T y p i c a l l y paraffin w a x e s contain 18-56 c a r b o n atoms. M i c r o c r y s t a l l i n e w a x e s have molecules o f 4 0 - 5 0 carbon atoms and crystals f o r m e d are small and indistinct. T h i s type o f w a x contains m o r e branched h y d r o c a r b o n s c o m p a r e d to paraffin. P e t r o l a t u m contains b o t h solid and liquid hydrocarbons.  W a x is r e c o v e r e d as a p r o d u c t f r o m some refineries. T h e separation o f w a x f r o m a paraffin distillate is made possible b y the fact that the solubility o f w a x i n the distillate decreases w i t h decreasing temperature. exchangers  T h e petroleum stream is first chilled in heat  to a l o w temperature to solidify the wax, w h i c h is then r e m o v e d from the heat  transfer surface b y scraping. T h e chilling may be accompanied by incremental dilution as in the  DILCHILL  process w h e r e a petroleum stream is diluted b y a solvent s u c h  as propane, w h i c h is a g o o d solvent for oil but a p o o r one for wax, and then chilled.  T h e scraped w a x is r e c o v e r e d usually by a v a c u u m type filter. A s a further means  l  of reducing the oil content a fresh solvent is used to wash the filter cake on the vacuum drum. Scraped surfaces provide good heat transfer but a non-optimum environment for the crystallization of wax. This is because the wax which is deposited on the cold chiller wall, and subsequently scraped off, has poor filtration performance. Therefore, industrial research has been targeted at ways to crystallize the wax and recover it in an easily filterable form.  The objective of this research was to investigate the factors which control the accumulation of wax from petroleum streams on heat exchange surfaces. The effects on the buildup of the wax layer, of flow velocity, bulk temperature, and concentration of wax in solvent kerosene were therefore studied. Experiments were done using different tube surfaces to determine the effect on wax attachment and removal. The theology of wax in kerosene was investigated to aid in interpretation of the deposition results.  Chapter 2 2. Literature Survey  The desired precipitation of wax for recovery as a product in oil refineries was described in Chapter 1. In the oil industry, the formation of any predominantly organic matter in oil well tubing, surface flowlines and other production equipment (Hunt, 1962 ) is referred as paraffin deposition. This undesired precipitation gives rise to operating problems in oil production and pipeline systems. The deposits consist mainly of n-paraffins with smaller amounts of branched and cyclic paraffins and aromatics (Jorda, 1966). Paraffins in oil show normal solubility-temperature behavior, i.e. solubility decreases as temperature is lowered. Heat treatment has therefore been found beneficial in the improvement of pumping of certain waxy crude oils. The temperature at which wax crystals first appear in cooling a solution is defined as the cloud point. Standard empirical tests (Standard Test Methods, A S T M D2500-91 and IP 219/93) have been devised to determine this temperature.  The crystalline nature of paraffins has been investigated by a number of workers (Holder and Winkler, 1965). Modification of the wax crystal structure by additives during deposition or gelling can improve the flow properties (Brod et al., 1971).  Wax deposition as a fouling problem Fouling can be defined as the accumulation of undesired solid material at a phase  3  interface (Epstein, 1983). The five primary categories of fouling are crystallization, particulate, chemical reaction, corrosion, and biological fouling.  In the oil industry, fouling is taken to mean the formation of any undesirable deposit on heat exchanger surfaces which increases resistance to heat transmission or flow. The deposition of wax on cooled surface is therefore a fouling problem.  Epstein (1983) has discussed the sequential events which occur in most fouling systems as initiation, transport of foulant to the surface (mass transfer), attachment (adhesion), removal (spalling, sloughing off) and aging.  The effect of fouling in terms of thermal resistance on heat transfer equipment is expressed in the fundamental equation for the overall heat transfer coefficient U at the outside of the surfaces as: -L = R, +-  u  °  f  + R +^R  h  W  0  fi  +  4  (1)  4  h  Here R and R refer to the thermal resistance of the fouling deposit on the fo  fi  outside and inside of the surface, respectively. While the fouling resistance can be described by a time function starting at zero and proceeding asymptotically, a constant value of the fouling resistance is generally used for design. This value is then interpreted as the thermal resistance to be reached in some "reasonable" time interval after which the equipment is cleaned. However, the fact that at time zero, the equipment is clean and, therefore, may operate under drastically different conditions than just before cleaning, is rarely examined. Allocation of exaggerated R values does not guarantee longer operating f  4  time. On the contrary, in many cases it can contribute to more rapid deterioration of the overall heat transfer coefficient.  The fouling resistance at any time can be calculated as R =—-—  (2)  f  where U is the overall heat transfer coefficient at time zero. R can also be written 0  f  as  for a small thickness x with respect to diameter.  Many researchers have studied fouling problems based on measurement of R, f  x, or m. Work pertinent to this project is summarized below.  The effect of operational variables While many other effects may be present in a specific fouling process, the following process variables appear to be most important (Taborek et al., 1972). 1. Flow velocity- Moderate to very strong effects on most fouling processes, because of the influence on deposition and removal rates. 2. Surface temperature -Affects most fouling processes; particularly, crystallization and chemical reaction fouling because of strong influence on rates. 3. Fluid bulk temperature- Affects reaction and crystallization rates, and solubility of fouling species.  Effects of surface material and structure  1. Material- Possible catalytic effect on reaction; corrosion can affect adhesion. 2. Surface- Roughness, size and density of cavities will affect crystalline nucleation, sedimentation and adhesion of deposits. Both surface material and structure have their greatest influence in fouling initiation rather than for the continued fouling process. The fouling resistance versus time curves generally follow one of the four types of behavior-linear, falling rate, asymptotic, or saw-tooth. Hunt (1962), and Patton and Jessen (1970) found that paraffin deposition increased asymptotically with time.  Kem-Seaton Equation  Kern and Seaton (1959) derived an equation for asymptotic fouling, which can be used for fitting of the data for fouling of wax in kerosene.  Deposition of wax can be considered to involve two steps-transport of paraffin molecules to the cooled surface, and integration of the molecules into the deposit structure. Removal of wax deposits can also occur due to the effects of shear on the wax structure. The net rate of deposit accumulation is the difference between deposition and removal rates.  Deposition The component must be transported from the bulk of the fluid, where its  6  concentration is Q , to the heat transfer surface where its concentration in the adjacent fluid is C . Assuming turbulent flow, s  m =k (C -C.) d  t  (4)  b  where k is a turbulent mass transport coefficient. The surface integration step is then given t  by m =k C: d  (4a)  r  where k is the surface integration constant and n the order of the integration step. r  Removal  Removal of the deposit may or may not begin right after deposition has started. That it does so is an assumption implicit in the removal model originally proposed by Kern and Seaton, and further developed by Taborek et al. (1972). Bmx.  (5)  This equation states that removal rate increases linearly with deposit thickness and hence with m, and with the shear stress x . The fact that removal increases with increasing s  layer thickness suggests that the shear strength of the deposit is decreasing, or other mechanisms which reduce the stability of the layer are taking place. Although the continuous coexistence of removal with deposition (especially particulate deposition) is more readily rationalized in turbulent than in laminar flow, the fouling rate at any time according to this assumption is given by dm . — = m -m =m d9 d  r  Bmx '\y s  d  7  (6)  Integration of Eq. (6) from the initial conditions 9= 0,m = 0 on the assumption that the only variables in Eq. (6) during the course of fouling are 6 and m yields the well-known Kern-Seaton equation represented in Fig. 1. /w = m*(l-e*)  (7)  where m* is the asymptotic mass per unit surface area and the time constant is given by  e,=^=^=-f m  r  m  d  (8)  Bx,  m  d  c  3d c  Fig. 1. Plot of Eq. (7), after Kern and Seaton (1959).  Since deposit removal is desirable to obviate the need for scraping the surface in wax chillers, some discussion of deposit strength and removal processes is appropriate.  From Eq. (8) it is seen that 9 can be interpreted as the average residence time of an C  element of fouling deposit on the heat transfer surface, as well as the time it would take to accumulate the asymptotic fouling deposit m* if the fouling proceeded linearly at the initial deposition rate m . B y putting 9- 9 in Eq.(7), m works out to be 0.632m*, so that 9 is d  C  C  also the actual time required to achieve 63.2% of the asymptotic fouling resistance. 6 can C  also be interpreted as one-third the actual time required to achieve 95% of the asymptotic fouling resistance. It is generally recommended that 9 for an experimental run be at least equal to 3 9 in order to determine a reliable value of R* . Since m =m 9 C  f  d  c  and  9 oc 1/r, <X1/M? in turbulent flow, it follows that even if m is directly proportional to w„, C  d  as would be the case under conditions of turbulent mass transfer control at high values of Sc, m* and hence R* would still decrease as the velocity increases. This generalization f  has commonly been found in practice, at least when deposit removal occurs (Gudmundsson, 1981). Only if deposit strength \\i is also directly proportional to u,, as inferred by Gudmundsson (1977) from the inverse proportionality of G with fluid velocity c  for wax deposits solidifying from hydrocarbon streams, might this generalization falter. The evidence for a velocity dependence of \\i is still tenuous.  Nevertheless, deposit removal has been observed to occur simultaneously with deposition ( Epstein, 1981) in certain instances, and for those cases 9 can reasonably be C  represented by Eq.(8). According to Cleaver and Yates (1976), it is not simple viscous shear that lifts (or is capable of lifting) particles from the deposit back to the mainstream, but the periodic bursts that are randomly distributed over less that 0.5% of the surface at any instant. They referred to these bursts as miniature tornadoes, and that this  9  characterization is not a metaphor has been vindicated by experiments (Dinkelacker, 1979) which showed that there is a measurable wall suction associated with the turbulent bursting.  For a given deposit and fluid, a minimum friction velocity u , is required before the turbulent bursts can become effective in removing some of the deposit. B y reference to Eq. (8 ), it is reasonable to generalize the criterion to be fulfilled by any deposit as  '.<('.L or, since  () 9  0 ac(y//T )<X(y//ul), c  S  oo)  where the subscript "crit" denotes some critical value for a given fluid. Note that the numerator in Eq. (10) represents hydrodynamic forces tending to disrupt the deposit while the denominator represents the adhesive or cohesive strength of the deposit, depending on which is weaker.  Taborek et al. ( 1972) have explained the deposit strength in a different way. The removal potential is given by (11) where Rf, is deposit bond resistance. This may be considered the adhesive strength of the deposit per unit area at the plane of the weakest adhesion. The following speculations are made based on limited observation.  1. Rf, increases with uniformity of the deposit structure (highest for pure crystals and  10  polymers, lowest for discrete particles). 2. R,, may decrease with deposit thickness due to increasing number of planes of potential weakness. This may be expressed mathematically as  X.  where v|/ is a function of the deposit structure and m is a constant to be determined experimentally. 3. R,, is a function of the original surface characteristics only if the deposit-surface interface adhesion is weaker than deposit internal cohesion. This accounts for the fact that specially prepared smooth surfaces retard fouling in some instances and not in others.  Eq. (7) can be differentiated to find the initial rate of fouling, i.e. dm ~dd t=0  = "L_  (13)  &c  Models of wax deposition Fredensland et al. (1988) have developed a new theory for precipitation of wax from hydrocarbon solutions based on the theory of multicomponent polymer solutions. The wax appearance points were determined and agree in most cases within ± 4 K with the measured ones.  Majid et al. (1990) used the equilibrium model developed by Erbar (1973) to predict deposition. The model is developed by using material balances and equilibrium values of components of an oil containing wax. It assumes that none of the wax which  ll  diffuses to the wall and deposits is removed by shear forces. Calculations done on a crude oil pipeline have shown that wax deposition goes through a maximum with flowrates. The wax-equilibrium model requires a very detailed oil analysis as input data, however.  Svendsen (1993) has developed a mathematical model for the prediction of wax deposition in both open and closed pipeline systems, using a combination of analytical and numerical methods. The model includes phase equilibria, phase transition and fluid dynamics. It is known that wax deposition occurs i f there is a negative radial temperature gradient present in the flow and if the wall temperature is below the cloud point. The cloud point is sometimes referred to as the precipitation temperature of the particular oil, or the wax appearance point (WAP). The amount of deposition depends on the oil composition. The model is consistent with these experimental observations. If the liquid/solid phase transition expressed by the change in moles of liquid with temperature,  is small at the wall temperature, then the model predicts that wax  deposition can be considerably reduced even when the wall temperature is below the W A P . If, in addition, the coefficient of thermal expansion, a„ is sufficiently large, some components may separate and move in opposite radial directions at temperatures below the WAP. Thus the wax would move to the bulk fluid from the wall region. N o comparison of the theoretical results to experimental data was given.  Experimental studies of wax deposition Jessen and Howell (1958) studied the effect of flowrate on paraffin wax deposition in steel and plastic coated steel pipe. Microcrystalline wax at concentrations of about 2.3 to 8.4 g/L in kerosene solutions and several crude oils were circulated at bulk temperatures from 29 ° C to 42°C, which were below the cloud point. In laminar flow, the deposition increased with flowrate, reaching a maximum prior to transition to turbulent  12  flow, and then decreased with increasing flowrate. In laminar flow, the positive effect of flowrate was explained in terms of more particles being carried by the moving stream, providing a greater opportunity for deposition on the pipe surface. At high velocities viscous drag exerted by the stream tended to remove the accumulation. Where drag becomes equal to or exceeds the shear stresses within the deposited wax, a removal mechanism is provided. Paraffin deposited at high flowrates was observed to be considerably harder than paraffin deposited at lower flowrates. The increase in both viscous drag and shearing stresses on the paraffin deposit at high flowrates was considered to account for the gradual decrease in deposition at high flowrates. Experiments were not done to determine the effects of T and concentration. b  The effect of flowrate on paraffin deposition was studied by Toronov (1969) using a 5 % solution of technical paraffin in kerosene. The apparatus consisted of a room temperature reservoir from which the solution flowed to an experimental chamber. The paraffin deposited on the outside of a jacketed tube cooled from the inside with water 10°C below ambient. Neither the melting point of the wax used nor the solution cloud point were given. The thickness of the paraffin deposit was measured after 2 minutes by a camera fitted with a microscope. The results showed that the deposit thickness decreases with increasing velocity and that the deposit hardness, as expressed by the velocity required to remove it from the tube wall, increases with velocity. Toronov explained that as the flowrate increases only those wax crystals and crystal clusters capable of firm attachment to the surface, and having good cohesion between themselves, will not be removed from the deposit.  Patton and Casad (1970) studied paraffin deposition on a cold surface inserted into  13  a well stirred wax solution maintained above its cloud point temperature. They found that the amount deposited increased asymptotically with time. The initial rate of deposition and the asymptotic deposit amount both decreased with increased stirring. Water was circulated at 29°C through the annulus of the test cell to maintain the solution temperature 3 ° C above its cloud point. The deposits which formed on the cold probes tended to slide off smooth surfaces and flake off roughened surfaces. But roughness seemed to have no effect with a high molecular weight wax. Plastic coatings on the surface showed a decrease in wax deposit which was solely attributed to reduction in heat transfer. Deposit weight decreased with increasing stirring rate, and increased as the temperature differential between the solution cloud point and the probe face temperature increased. This work is discussed further below under the effects of surface properties.  Bott and Gudmundsson (1977b) reported that Armenski et al. (1971), in a study analyzing reduction in pipe diameter due to paraffin deposition, observed slight removal of deposits following their establishment. During the cooling of waxy kerosene in simulated heat exchanger tubes, a fluctuating deposit thickness was observed.  Eaton and Weeter (1976), using a rotating disc apparatus, showed that deposition was low at extreme velocities and much higher at intermediate values. In their work, the fluid velocity was accurately maintained by varying the disk rotational speed, and the paraffin deposition determined by weighing. The bulk temperature of the oil was varied from 4 to 30° C .The wax deposition reached a maximum at around 17 °C. The rotational speed of the disk was varied from 0 to 2500 rpm to simulate different flow rates. The paper states that the wax deposit rate increases from 0 to a peak value at 1000 rpm and decreases thereafter up to 2500 rpm, but does not indicate whether the rpm range  14  is for laminar or turbulent flow.  Experimental results have been obtained by Bott and Gudmundsson (1977a) for a flowing system where paraffin wax-kerosene solutions were cooled in tubular heat exchangers. It was found that the overall heat transfer resistance increased rapidly to some average value that fluctuated at random with time. These fluctuations were apparently caused by continuous buildup and break-down processes of the wax deposit. The creation of planes of weakness and the increase in shear stress at the wall as deposits build up were probably the main factors causing break-down and removal.  Bott and Gudmundsson (1977b) have studied the factors affecting the deposition of paraffin wax from its solution with hydrocarbons onto surfaces in pipelines and process equipment. Deposition studies showed that the amount of paraffin deposited increases with time to an asymptotic value. The asymptotic value showed significant fluctuations around the mean value with time.  15  200 I  i i—i i—|—i—|—i—i—j—i—\—r—i—|—i—i—i  ;  -  Cloud point T  j  _ Average bulk temp. T  i^-150— ! TJ  = 23 °C  c  b  r  = 28°C  Time t  = 15 min.  -  Qr 0  i  i  1 1  i  i  i  i  i  i  i  i  i  i  11  0-05 0-10 0-15 W — F l o w r a t e (kg/s)  i  i  i  i  0-2(  Fig. 2. Typical curve of amount of wax deposited vs. flowrate by Bott and Gudmundsson (1977b).  It was suggested that paraffin deposition is controlled by the cohesive properties of the wax. For the given studies, there appeared to be a critical deposit thickness at which deposits break up and slough away, giving rise to the fluctuating condition. The equipment used by Bott and Gudmundsson essentially consisted of two closed circulation loops where paraffin wax from wax- kerosene mixtures flowing in a rectangular duct was allowed to deposit on a copper plate cooled by water. A long entry section to the duct was provided to ensure that the velocity profile in the experimental section had been fully developed before the plate was reached by the fluid. The bulk temperature of the paraffin wax-kerosene solution was kept 5 ° C above its cloud point temperature. The solution flowrate varied from about 0.04 kg/s to 0.18 kg/s such that Reynolds number was greater than 5000 and the flow conditions therefore turbulent. The amount of paraffin deposition was determined by weighing. The deposition decreased with increasing flowrate (Fig. 2)  16  and bulk temperature but increased with concentration. The asymptotic fouling resistance varied inversely as Re squared.  Surface properties Since deposition and particularly the adhesion of the deposit onto a surface will be a function of the surfaces properties, investigations into the effects of different surfaces have been carried out.  Jessen and Howell (1958) report that crude oil field observations have indicated that plastic coated pipe not only reduced paraffin accumulation but in some cases eliminated deposition completely. However, data were needed to demonstrate the relative effectiveness of plastic materials. Steel, butyrate, rigid P V C , kralastic resin type plastic pipes and aluminum pipe were tested. The rate of paraffin deposition at all velocities and temperatures was greatest in steel pipes but considerable paraffin deposition was also found in butyrate pipe. The least amount of paraffin accumulation was noted in the rigid P V C and kralastic pipe. All plastic pipes tested showed less tendency for accumulation of paraffin than did steel or aluminum pipe, as shown in Fig. 3.  17  I  Fig. 3. Effect of velocity on rate of deposition of Delhi DU-184-1 crude oil atl06°F.  In laminar flow, a gradual increase in the rate of paraffin deposition was obtained with increased velocity, the maximum rate being reached when the flow changed from viscous to turbulent flow. At higher velocities the rate of deposition decreased rapidly. At Re greater than 4,000, the plastic pipe surfaces were free of any paraffin accumulation. The tendency for the rate of paraffin deposition to increase with velocity to velocities approximately equal to the transition velocity (Re=1980) was clearly shown for the steel pipe. Fig 3 shows the turbulent case. Paraffin deposited at high rate of flow was found to be considerably harder than paraffin deposited at low flow rates. Hunt (1962) studied the effect of roughness on paraffin deposition and concluded that deposits do not adhere to metals themselves but are held in place by surface roughness. A cold finger assembly was immersed in a wax-oil slurry contained in a 300  18  ml beaker surrounded by water at 120 °F. The temperature of the water circulating through the cold finger was lowered from a temperature just above the slurry temperature at a constant rate of 1.2 °F/hour over a period of 15 1/2 hours. An increased deposit was found on sand-blasted stainless steel compared to polished cold-rolled steel. The deposit did not adhere to plastic coatings such as epoxy-phenolic, isophthalic ester, coal tar-epoxy and epoxy.  Jorda (1966) found that paraffin deposition increased with surface roughness. A wax-oil solution composition of 25 percent by weight of refined petroleum wax in a refined petroleum solvent at a temperature of 41°C and 300 rpm was used. It was observed that the weight of the paraffin deposit increased as the temperature of the deposition surface decreased from 2, 6, 8, and 10°C below the cloud point. Roughness was found to play an important role as can be seen in Figure 4. Sliding of paraffin on polished surfaces and flaking on roughened surfaces was also observed. Smooth phenolformaldehyde (roughness <2u), epoxy-phenolic ( <5|_i) and polyurethane (<3u.) have shown less deposit compared to surfaces covered by mill scale (30-40u). Tetrafluoroethylene provides a zero micron surface roughness, which was expected to provide a superior surface for paraffin control; however, in the tests with tetra-fluoroethylene, polyethylene and polypropylene surfaces, massive deposits of paraffin of extreme hardness were collected.  19  350  ROUGH GROUND /(60-70/x)  300 \—  38 100.4  36 96.8  34 32 30 28 *C 93.2 89.6 86.0 82.4 ' F C O L D SPOT T E M P E R A T U R E (CLOUD POINT T E M P E R A T U R E = 3 8 * C )  Fig. 4. Weights of paraffin deposited on polished, sand-blasted, mill-scaled, corroded and rough-ground steel as a function of deposition surface temperature (roughness factors in parentheses).  Patton and Casad (1970) performed similar studies and concluded that no correlation could be observed between surface roughness and amount of deposit. However, they argued that the adhesion bond at a surface should be proportional to the total contact area and therefore related to surface roughness. An experiment done using 10percent RHI wax-soltrol 170 solution is shown in Table 1. Plastic coatings resulted in about a 30 % reduction in deposit weight over 6 hours.  20  TABLE t —  E F F E C T O F S U R F A C E PREPARATION ON DEPOSITION 10 P E R C E N T RHI WAX — S O L T R O L 170 SOLUTION  Ar = c  Stirring Rate =  Preparat ion  Deposit Wt. (mg) 6 hours  Polished 240-Grit 50-Grit Coating Coating Coating Coating  X Y Y* Z  4°C 300 rpm Deposit Wt. (mg) 16 hour s  Percent Change  86.6 90.0 90.3 59.8 55.3 60.4  1 19.0 1 13.5 103.2 81.9 74.4  —  3.9 + 4.3 -30.9  -f  -36.7 -30.2  84.5 78.3  P ercent Change —  -  4.6 13.3  -31.2 -37.5 -29.0 -34.2 (22 hours)  •Roughened with 50-grit paper. Percent Change = Wt. Deposited — Wt. Deposited on Polished Surface Wt. Deposited on Polished Surface Coating X = Unmodified phenolic Coating Y = Epoxy-phenolic Coating Z = Polyurethane  Summary of literature review The key studies on velocity, temperature and concentration effects are listed in Table 2. Table 2. Summary of literature review of R* vs. wax-solvent velocity, T and f  b  concentration effects. lessen and Howell Velocity Effects Temperature Effects Concentration  Jorda  Toronov  *  Not studied Not studied Not studied  * Not studied  Patton and Cassad *  Not studied  Not studied  Not studied  Not studied  21  Eaton and Weeter  ± ± Not studied  Bott and Gudmundsson * * +  + when indicated variable increases , R^- increases. * when indicated variable increases, R* decreases. f  ± when indicated variable increases, both an increase and decrease in R* are observed. f  Jorda reported that as the cold surface temperature was increased, the wax deposit decreased. Since the wax-kerosene solution temperature as reported was 41 °C, which was presumably the inlet bulk temperature, then it can be inferred that the bulk temperature of the solution inside the apparatus must have been increasing with increasing temperature of the cold surface. If the above assumption holds true, then it can be safely concluded that Jorda's results signify that as the bulk temperature of the wax-oil solution increased, the mass of wax deposit decreased, which is indicated in the above Table 2.  Eaton and Weeter presented their data as wax deposition vs. rpm. Therefore it was not possible to determine whether their experiment was in the laminar or turbulent region or both. The other four studies agree that R* decreases with increasing velocity. Bott and f  Gudmundsson indicate that R* decreases as T increases, but little was reported f  b  by others on temperature effects.  Four studies of surface effects were reviewed. It was concluded by most authors that plastics generally have lower deposits compared to metal surfaces. This was mainly attributed to smoothness of the surfaces. However, it was also found that ultra-smooth surfaces such as tetra-fluoroethylene showed a good adhesion to wax, and formation of hard deposits. On the other hand, when steel was compared with other rough surfaces  22  and plastic, the plastics and polished steel showed less deposit, persuading some researchers that wax is held by surface roughness. Therefore, adhesion of wax to surfaces must be both a function of roughness and material type.  23  Chapter 3 3. Experimental Setup 3.1. The Test Rig The test rig included a tank, a pump, a chilled test section and associated flow meters. The annular test section consisted of a 750 mm long double pipe heat exchanger, which was opearted in counter-current flow. The hydrocarbon solvent containing wax flowed in the annular section, and the wax deposited on the outside surface of the inner tube through which the coolant flowed. The test rig is shown in Fig. 5. The test section and flow lines both from and to the supply tank were insulated. The flow lines and manometer lines were equipped with heating tapes to warm up the solution when the experiment was started.  3.1.1 Test section The test section was composed of a 1/2-inch Type 316 stainless steel tube concentrically surrounded by a 1-inch pipe. The geometry of the test section was as follows: Outer pipe: stainless steel with a transparent glass viewing section, ID=25.4 mm, L=750 mm Inner tube: stainless steel, wall thickness =1.245 mm ID=9.96 mm, OD= 12.45 mm Distance between inlet and outlet lines for the wax-kerosene mixture: 720 mm  24  Fig. 5. Flow diagram of wax fouling. TC=thermocouple  Samples of the stainless steel tubes (with roughness 2.5 pm) were sent to ESSO Petroleum Canada, and to Heresite Protective Coatings, Inc. for surface modification. ESSO provided a sand-blasted stainless steel tube (5 pm roughness), a chrome-plated stainless steel tube (0.5 pm), and tubes coated with n-C18 silane on stainless steel and on chrome-plated stainless steel. ESSO also provided the roughness values of the tubes. Heresite Protective Coatings, Inc. provided stainless steel coated with Heresite Si 57 E (shiny) and Heresite P-400/L-66 (dull). The Si series type of coating is produced from complex mixtures of liquid thermosetting plastics (phenol, formaldehyde, silicone, epoxide resins) and is produced with special flooding or spraying techniques. The Heresite P400/L-66 is made of a phenolic coating. Both Si 57 E and P-400/L-66 have thicknesses of about 6-8 mils (152-203u,m).  The tubes were tested in turn by substituting them for the original stainless steel tube in the unit. A Heresite Protective Coatings, Inc. brochure states: "The fact that Si 14 E G and Si 57 E G have practically no effect on heat transfer is important in practice. Tube bundles protected with such resin formulations do not, therefore, require to have increased surface area. This is confirmed by heat transfer figures:Steel tube drawn  422  Steel tube sandblasted  425  Steel tube, with Si 14 E G and Si 57 E G  396 "  N o units were given for the numbers recorded above. The brochure also states that "By using suitable silicone formulations the frictional resistance to the flowing liquids is considerably lowered. It was shown that the frictional losses were lower compared to uncoated pipes." This indicates that the surface is more smooth than steel tubes. The surface smoothness is characterized by a smooth to enamel-like finish.  26  3.1.2. Pump  The pump used for circulating the wax-kerosene mixture was an ACE-5100 end suction mild steel centrifugal pump. Running with water, the specified head was 100 ft at a capacity of 12 US gallons/minute. The drive motor (J13509A), made by Baldor Electric Co., drew a current of 11A at 115V (or 5.5A at 230V).  3.1.3 Flow rate measurement  Measurements of flow rate were made for both the cooling water and the waxkerosene mixture. A rotameter and an orifice meter, respectively, were used for the measurements.  Cooling water flow rate The cooling water flow rate was measured by means of a rotameter upstream of the double pipe heat exchange tube. The calibration curve and its equation are given in Appendix A .  Wax-kerosene mixture flowrate The flow rate of the wax-kerosene mixture was measured by an orifice meter. The volumetric flow rate was calculated from: (14) where M =  h(p - )g  ,  hg  Pw  C , the discharge coefficient, was determined by calibration (Zhang, 1992) over d  the Re-range studied and was found to be 0.62 (confirmed at Reynolds No. of  27  orifice=4000). A P , the pressure drop across the orifice meter, was measured by using a manometer filled with mercury. To prevent wax deposition on the manometer and the pressure transmitting tubes, the wax-kerosene was separated from the water in small cylindrical pots (about 50 mm diameter by 110 mm height). The pots contained about half clean water and half kerosene solution. The clean water (transmission liquid ) transmitted the pressure difference to the differential pressure manometer.  3.2 Temperature Measurement and Calibration The following temperatures and temperature difference were measured: •  cooling water inlet temperature  •  cooling water outlet temperature  •  wax-kerosene mixture inlet temperature  •  wax-kerosene mixture outlet temperature  •  bulk temperature in the supply tank  •  cooling water temperature rise  The thermocouples used were chromel (nickel-chromium)-constantan (copper-nickel) E type. All thermocouples were calibrated in the range 0°C to 60°C . The temperatureelectrical voltage calibrations for the thermocouples used are given in Appendix B. For temperature display a direct-reading digital thermometer was used (an O M E G A serial number 2170 digital thermometer and a 12-way selector switch). The automatic cold-junction-compensated thermometer had a range of -99.8 °C to 999.8 °C. Its resolution and repeatability were ±0.2 °C.  For temperature recording on the test rig, a Digitrend 235 data logger was used.  28  The datalogger could record either temperature or thermoelectric voltage . The temperature difference between the inlet and outlet of either the cooling water or the wax-kerosene mixture was normally about 1°C. This small differential temperature requires a high accuracy in the measurement to give a reasonable accuracy for heat flow calculations. Therefore, a ±0.5 u,v or ±0.008 °C resolution was used, which was the best possible accuracy one could get from the datalogger. The differential temperature of the cooling water side was measured by connecting the chromel sides of the two chromel-constantan thermocouples together and the constantan sides to the datalogger, for measurement of the voltage difference. This voltage difference was converted to temperature rise by the calibration equation. 3.3. Cloud Point and Viscosity 3.3.1 Cloud Point According to standards ( A S T M D2500-91 and IP 219/93), the cloud point of a petroleum oil is the temperature at which paraffin wax or other solid substances start to crystallize out or separate from solution when the oil is chilled under definite prescribed conditions. The cloud point was determined in separate experiments so that the waxkerosene solution inlet bulk temperature could be appropriately controlled to stay above the cloud point in the wax fouling experiments.  Apparatus:  The apparatus shown in Fig. 6 was designed to meet the specification of A S T M D2500-91 and IP 219/93. The components of the apparatus are as follows: a) Test jar: A test jar, a, of clear glass, cylindrical form, 33 mm in inside diameter and  29  115 mm in height. b) Thermometer: An A S T M cloud test thermometer, b, having a range -38 to + 50 ° C (or -36 to 120 °F). c) Cork: A cork, c, to fit the test jar, bored centrally to take the test thermometer. d) Jacket: A jacket, d, of glass, water tight, of cylindrical form, flat bottom, about 114 mm in depth, with inside diameter 13.7 mm: greater than the outside diameter of the test jar. e) Disk: A disk of cork, e, 6 mm in thickness, and of the same diameter as the inside of the jacket. f) Gasket: A ring gasket, f, about 5 mm in thickness, to fit snugly around the outside of the test jar and loosely inside the jacket. This gasket was made of cork. The purpose of the ring gasket was to prevent the test jar from touching the jacket. g) Bath: A cooling bath, g, made of a transparent glass cylinder of 152 mm diameter and 152 mm height with a transparent glass support for the jacket, d.  30  b  Fig. 6. Apparatus for cloud point measurement.  3.3.2 Viscometry The flow behavior of waxy crudes is reported to be considerably modified by the crystallization of paraffins. Viscometer measurements were undertaken to determine whether the wax-kerosene solutions were Newtonian or non-Newtonian at their operating temperatures and, if Newtonian, to determine the viscosity.  A rotary viscometer was used to measure the shear stress vs. shear rate behaviour of the wax-kerosene mixtures at different concentrations and temperatures. The H A A K E Rotovisco is a computer-controlled rotary viscosity-testing apparatus. It consists of a stationary outer cup which contains the fluid to be tested. A motor-driven inner cup (rotor) is placed into the fluid and rotated. The torque of the rotor is measured by a force sensor and the data are logged to memory. The shear rate is measured as 1/second.  31  For a Newtonian fluid in the absence of turbulence, the rate of shear D [1/s] is directly proportional to the shear stress (x ). In this case the viscosity is defined by the s  Newtonian equation M =%  05)  If the rate of deformation (shear rate D) is not directly proportional to the shear stress (x ), s  then the fluid is said to be non-Newtonian.  32  Chapter 4 4. Experimental Procedures 4.1 System Cleaning Before cleaning, the wax-kerosene mixture was drained out from the test rig via the drain valve at the bottom of the mixing tank. The test rig was washed with about 10 litres clean hot kerosene (50°C or less) by pumping this liquid through the flow loop for about 30 minutes. The whole system including the pump and filter was then drained. 4.2 Preparation of Wax-Kerosene Mixture Wax concentration was determined in weight percent i.e. concentration  of wax-kerosene  mixture (wt. %) =  ^ wax weight  weight  _  + kerosene weight  The total volume of the mixing tank was about 30 liters. The general procedure was: 1) The tank was filled with' 10 liters of kerosene (minus a portion set aside for washing). 2) The kerosene was recirculated by the pump and heated up to 40°C . 3) The melted wax was then poured into the tank. The funnel and fill port were washed with heated kerosene, which had been set aside for this purpose. 4) The mixture was recirculated for 10 minutes at 50°C before a test was started. 4.3 Fouling Test The general protocol for the fouling runs is described as follows: 1) Power to the datalogger is turned on. The time and run number are put into the instrument. The functions of measuring points are programmed and the compensation voltage, E , of the datalogger is recorded. 2) All display instruments in the test rig are turned on. A particular temperature display  33  +10Q  can be selected using the selector switch. 3) The pump is started and the wax-kerosene mixture is circulated through the test system. 4) The tank heating tape is turned on using the potentiometer (max. 13 amps.) i f necessary. 5) The pipe heating tape can be turned on by using the switch but heating the pipe is optional depending on the wax-kerosene condition in the pipeline. Once the wax-kerosene starts to flow, power to the heating tape must be stopped. 5) The wax-kerosene flow rate is adjusted to the desired value using the two flow valves. 6) When the bulk temperature reaches a steady state, the readings of the manometer pressure drops are recorded. 7) The datalogger is started with a scanning sequence of 2 minutes.  <.  8) The cooling water through the test section is set at 20% on the rotameter scale. The flow rate corresponding to this setting can be calculated using the calibration Eq. 43 in Appendix A . 9) Data are gathered over three hours, and visual observations of the wax deposit made. The run is then stopped by turning off all heating tapes and the data logger. 10) The cooling water is turned off, allowing the wax-kerosene mixture to heat up. If required, the system is washed by running hot liquid through the test rig. 11) The pump is stopped, and all power is shut off.  4.4. Cloud Point Test Procedure for cloud point Following is the procedure for measuring the cloud point temperature, using the  34  apparatus of Fig. 6. a) The oil temperature to be tested was brought to a temperature of at least 14 °C above the approximate cloud point. b) The clear oil was poured into the test jar, a , to a height of not less than 51 mm or more than 57 mm. c) The test jar was tightly closed by the cork, c, carrying the test thermometer, b, in a vertical position in the center of the jar, with the thermometer bulb resting on the bottom of the jar. d) The disk, e, was placed at the bottom of the jacket, d, and the test jar was inserted into the jacket with the ring gasket, f, 25 mm above the bottom. e) The temperature of the cooling bath, g, was maintained at -1.1 to 1.7 °C. f) At each test thermometer reading that is a multiple of 1.1 °C( 2°F), the test jar was removed from the jacket, quickly but without disturbing the oil, inspected for cloud, and replaced in the jacket. g) When such inspection first revealed a distinct cloudiness or haze in the oil at the bottom of the test jar, the reading of the test thermometer was recorded as the cloud point.  35  Chapter 5  5. Properties of Wax and Kerosene  5.1. Waxes  In this investigation, three waxes were used. A refined wax marketed by ESSO was purchased locally. ESSO Petroleum Canada, Research Department supplied two slack waxes from the Sarnia refinery, which were designated MCT-10 and MCT-30.  Waxes were characterized by measuring the amount of oil in the wax and obtaining a boiling point distribution using a GC chromatogram which permits identification of the normal paraffins present in the wax. The amount of oil is measured using the procedure A S T M (D3235). The results provided by ESSO for the two types of wax used, including important physical properties, are shown in Fig. 9 and Fig. 10. Slack wax is an intermediate product before refining. The figures show that both refined wax and slack wax MCT-10 contain mostly molecules with about 20 to 30 carbon atoms. M C T slack wax contains more branched hydrocarbons and oil compared to refined wax.  5.2 Kerosene The kerosene utilized in these experiments was bought from ESSO. Commercial kerosene is defined by the A S T M as a "refined petroleum distillate suitable for use as illuminant when burned in a wick lamp" (Handbook of Petroleum Processing, 1967). The properties are summarized below: Boiling point range  195-260 °C  Flash point  46 °C  Burning test  16 hr  36  Sulfur, % mass  0.13  Color, Saybolt chrom, no darker than  +21  Color, Saybolt chrom, after heating 16 hr, no darker than  +16  Cloud point  -15 °C  Specific gravity (15.6 °C)  0.80  5.3 Cloud Point of Wax-Kerosene Mixtures The cloud point of a wax-kerosene mixture is the temperature at which paraffin wax or other solid substances start to crystallize out or separate from solution when the oil is chilled under definite prescribed conditions. The bulk temperature outside the heat exchanger was maintained above the cloud point. This would ensure that the wax precipitates only inside the heat exchanger. The cloud point measurements taken for refined wax, slack wax MCT-10 and MCT-30 are tabulated below.  Table 3. Cloud Point Temperature (°C) for ]Refined and Slack Waxes in Kerosene. MCT-30 MCT-10 Refined wax Cone (% by wt.) 31.1 15.0 15.6 5 36.7 21.1 21.1 10 40.0 23.3 25.6 15 42.2 27.8 28.9 20  5.4 Viscosity of Wax^Kerosene Mixtures The wax-kerosene mixtures were found to be Newtonian near and above the cloud point. The test was made by using the Rotovisco mentioned in the previous two Chapters and the range of the shear rate used was from 0 to 468 1/s. Two typical graphs (Fig. 7  37  and Fig. 8) show shear stress vs. shear rate for refined wax at 10% by wt. concentration and slack wax MCT-10 at 5 % by wt. concentration. All the data points at each concentration and temperature were fitted using a linear equation of the formr= b +aD, an equation of the form r = a+bD" and a third equation of the form T= bD". The best fit was found in each case by the linear equation, which is equivalent to the second equation with n=l. For refined wax at 10 % by wt and a temperature of 21.1 °C, the standard deviation for the linear fit was 0.021 and the x intercept was -0.007, so it could be inferred that the intercept was not significant and could be assumed to pass through zero, since the absolute value of the intercept was less than the standard deviation. The slack wax M C T 10 was tested at 5 % concentration and a temperature of 15 °C (Fig. 8), at which the standard deviation and the % intercept for the linear fit were 0.023 and -0.008 respectively. As the absolute value of the intercept was again less than the standard deviation, it could again be stated that the significance of the intercept was negligible. Therefore, the wax-kerosene solution was taken to be Newtonian at the given temperature and concentration. The wax-kerosene solution viscosities were found from the slope of x the best line passing through the origin, i.e.// = —.  38  S h e a r rate (1 /s)  Fig. 7. Typical graph of shear stress vs. shear rate for refined wax in kerosene at 10 % by wt. and 21.1 °C. Cloud point of solution= 21.1 °C  0  100  200  Shear  300  Rate  400  500  (1/s)  Fig. 8. Typical graph of shear stress vs. shear rate for slack wax MCT-10 in kerosene at 5 % by wt. and 15.0 °C. Cloud point of solution=15.0 °C  39  Viscosity was measured as a function of temperature for wax-kerosene, mixtures as described in section 3.3.2. The viscosity runs taken at some intervals of temperature starting near the cloud point are tabulated below.  Table 4: Viscosity runs for refined wax at 5 % by wt. in kerosene. T[°C] u.rPa.sl.10-  15.6 1.30  3  25.0 0.89  30.0 0.82  35.0 0.76  40.0 0.78  Table 5: Viscosity runs for refined wax at 10% by wt. in kerosene. 21.1 T[0C1 p. [Pa.s].10- 1.02 3  25.0 1.26  30.0 1.00  35.0 0.87  40.0 0.80  Table 6: Viscosity runs for refined wax at 15 % by wt. in kerosene. T[°C] p |Ta.sl.lO-  3  25.6 1.25  30.0 1.10  35.0 0.93  40.0 0.82  Table 7: Viscosity runs for refined wax at 20 % by wt. in kerosene. Tr°ci u[Pa.s].10-  3  28.9 1.10  35.0 1.00  40.0 0.80  Table 8: Viscosity runs for slack wax MCT-10 at 5 % by wt. in kerosene. T[°C] p[Pa.s].10-  3  15.0 1.37  20.0 1.03  25.0 1.03  30.0 0.90  35.0 0.90  40.0 0.81  Table 9: Viscosity runs for slack wax MCT-10 at 10 % by wt. in kerosene. TTO uTPa.sl.10-  3  21.1 1.27  25.0 1.14  30.0 1.07  40  35.0 0.95  40.0 0.87  45.0 0.81  Table 10: Viscosity runs for slack wax MCT-10 at 15 % by wt. in kerosene. TPCI u.rPa.sl.10-  40.0 0.84  35.0 0.98  30.0 1.10  23.3 1.40  3  45.0 0.78  Table 11: Viscosity runs for slack wax MCT-10 at 20 % by wt. in kerosene.  T r°ci nlTa.sl.10-  45.0 0.80  40.0 0.81  35.0 0.91  27.8 1.04  3  The physical properties which are used in the heat transfer and flow computations involve densities, viscosity, and heat capacities of the wax-kerosene mixture.  The properties of water were regressed using data obtained from the Handbook of Chemistry and Physics(1987). The accuracy of the equations has not been given.  Density of water (kg/m ) 3  280 54253 x 10" f p„ = (999.83952 +16.945176f -7.9870401 x IO"** -46.170461 x IO"** + 105.56302 x \Qr*t* n  3  5  3  4  for 0 °C <t < 20 °C b  Viscosity of water (Pa.s) log /U0 1 0  3  1301 998.333 + 8.1855(f - 20) + 0.00575(f - 2 0 ) fc  t  b  inO  — 1.30233  2  fc  C  Heat capacity of water (kJ/kg °C) =4.21765-3.74987 x 10- r +1.49921 x IO"** -3.35545x 1CT\ +4.27292x IO":, - 2.30244 xlO" /, 3  4  3  8  4  10  t  where  The density and heat capacity of the wax-kerosene mixtures were experimentally measured  41  5  by Zhang (1992) using refined wax. The results are as follows. Density (kg/m ): p = 816.25 - 0.748927;,  T in ° C  3  k  b  The presence of different concentrations of wax in kerosene did not change the density of the mixture much, so the above equation was used for all concentrations. The waxkerosene solutions were measured from about 25 to 80 °C. Heat capacity (kJ/kg °C): C  M  = 1.18143 + 0.0122467; , where T = 2 L ± £ b  j in ° C b  The effect of wax on the wax-kerosene specific heat capacity was minimal, so the above equation was used for all concentrations. Viscosity:  , T inK.  ju =aexp  b  k  K » RT  The above equation for viscosity was fitted using data from Tables 4-7 for refined wax and Tables 8-11 for slack wax MCT-10. The corresponding values of a and b are given in Tables 12 and 13 for refined wax and MCT-10 slack wax, respectively.  Table 12: Viscosity Coefficients a and b for Refined Wax. Wax concentration (wt. %) a b  20  15  5  10  1.83x10-* 15525  7.58X10"  6  12147  1.27xl022830  7  1.65xl022171  7  Table 13: Viscosity Coefficients a and b for MCT-10 Slack Wax. Wax concentration (wt %) a b  5  4.16X10"  13676  6  10  15  3.80x10-* 14160  1.86xl021993  42  20  7  5.92xl018820  7  0  (J o  N ol  U  9 N  5)-  >^ J3  <  6  0  CO C\2  z  <^  z  1  V  pn Oi  (A  y  !£  <  in  -J o  x  ft  h  01  O  •rt o UJ I— Ul  <  —I—  in  —i— o  in  —r~  in  o ro  o CVJ  Fig. 9. G C chromatogram for refined wax.  43  —T—  in  o  in o  o o  in  o If)  u  10  0  o  to ^  Q  o h o CD  0  k o O  o m  5;  -J  o  5  '—.  UJ  o C  o  UJ  PQ  O  5  < S?0 LZ «-  C/l  •«  =3F  £3 0  o o  m  I  •H  o  UJ  •rt  <  '  1  cn  •  1  co  1  1  <~—i  •  r—  in  ID  _n  Fig. 10. G C chromatogram of slack wax MCT-10.  44  OJ  Chapter 6  6. Data Analysis The computations arising from wax fouling tests included calculation of the fouling resistance as a function of time, and fitting these data to the Kern-Seaton equation.  6.1 Calculation of fouling resistance The heat gained by the cooling water can be determined from Q =mC w  p w  (t -t ) 2  (16)  1  or by using the directly measured At (the differential temperature rise) for accuracy Q =mC w  p w  At  (17)  Equation (17) was preferred since the measurement of A/ was more accurate than that of (t - / , ) . Because of uncertainties in the heat capacity for the wax-kerosene mixture the heat 2  lost by this stream was not used in the calculation of Q. The overall heat transfer coefficient based on the inside surface of the inner tube was determined at time 9 as f  = T # V  08)  where A  ^  =  '  (  T  _\  '  (19)  The inside area was used because even with the coated tubes, 4 was constant for all tubes. The fouling resistance at any time 0 was then given by  *,={!-J-U  (20)  45  where U is the clean overall coefficient at 0=0. 0  The Reynolds number of wax-kerosene solution was calculated as (21)  Re = where d is the hydraulic diameter for the annulus, and u is the actual velocity in the h  annulus.  6.2. Data Fitting and Determination of Parameters From the fouling tests, it was found that most plots of R* vs. 9 followed f  asymptotic behaviour, i.e. the deposit was built up at a falling rate and eventually reached a constant value. Even without constancy of m and the other assumptions underlying d  Eq. (6), this type of behaviour can be represented by the well known KernSeaton equation Eq. (7), which can be rewritten as (22)  R =RU\-e«<) f  where R =  m  f  , and was calculated via Equation (20).  Pf f k  A computer program (Appendix C) was developed which fitted the experimental data by a non-linear least squares method to the above equation and found the two parameters R* and 6 . Given a set of data points (0 ,R ), f  C  t  fi  where i=l,....N, the values of  R* and 6 were calculated to minimize the sum, f  C  (23)  46  Uncertainty The uncertainty in the fouling resistance caculation has been explicitly derived by Crittenden et al. (1992) for crude oil fouling. The heat transferred in the heat exchanger can be calculated using Eq. (17), and the fouling resistance using Eq.(20). From Eq. (20), it is clear that the error in the calculated value of R is dependent upon the errors f  in the calculated values of both U and U . For the function n  (24)  R =R (U ,U) f  f  0  cR cR dR,=-^-dU +—^dU f  f  (25)  0  If the errors in U and U are 5 U and 8U respectively, and are small relative to U and U , 0  0  0  then the error induced in Rf is given by: cR  cR  d U °  cU  f  f  f  (26)  The worst possible value of SRf occurs when all of the terms on the right hand side of the equality are either positive or negative. Thus, taking 5 U and 8U to be positive, 0  SR = f  cR  W  0  su + 0  f  5U  (27)  FromEq. (20), (28)  u  2  (29)  4  Thus  47  SR = f  {Ul  (30)  IP) A,  Errors in U depend upon the accuracy of the heat exchanger data and are related solely to errors in Q, Ao and L M T D (Eq. 19).  Errors in operating parameters In the following analysis the worst scenario is considered, that is, the errors in each of the four end temperatures and in each of the two flowrates compound, rather than eliminate each other. The instantaneous coefficient U is given by: QJn-  U=  7 a - V  (31)  ^[(r-.O-te-O]  Thus neglecting errors in the calculation of A j , cU  5U  a + 2  32*  c57I  (32)  Hence  u  Q  w  w\ InX  1— InX  —1  a + 2  InX  ST  2  (33)  where W=  (T -t )-(T -t ) ]  T  Y=  2  l  (34) (35)  t  w (36)  {T -t ) W x  Z=  2-  2  2  (37)  48  Error in the duty The instantaneous thermal duty Qw is given by Eq. (16). Assuming that there is no error in C , then, based on individual measurement of t and t , x  32*  dm  dm + 3Q, a,  2  32.  (38)  dt,  a  2  or 5Q = C^-t^Sm+mC^St,  + AWC^<*  W  (39)  2  and 8Q  Sm  Q  ™  W  w  8t +a t  +  (40)  2  (t -t,) 2  The uncertainty as a percentage can be written by modifiying Eq. (30) SR  ' 1 5U  f  1 5U^  Q  :  JJ u u u) A\R +  0  0  (41)  100%  f  5UAJ is given by combining Eq. (40) and (33), i.e. 5t,+a  5U _bm  2  U ~ m  +  (t -t,) 2  |  1 \  -ia  x  W[ InX  +  + 1-  InX  \St + 2  InX  -w,+1-  ,  InX  < 5 r  u(42)  SU/U can be calculated from the corresponding values at time 0=0, the mass flowrate, 0  m, remaining constant throughout an experiment. The values for 6t,, Stj, 5Tj, 8T = 2  0.008 ° C for all cases. Sm/m was taken to be 1% from experimental observation. The uncertainty in the fouling r e s i s t a n c e s , ^ / ^ , was calculated by finding SUQAJO  and 8U/U from Eq. (42) and inserting the values in Eq. (41). This result is  reported in the next Chapter in %, which is the maximum error one can get in R . A f  slightly smaller maximum would have been reported if the above calculation were based on a single measurement of t -t or Af. x  2  49  Chapter 7 7. Results and Discussion  After addressing reproducibility, the results are presented in five sections, namely, the effect of velocity, the effect of bulk temperature, the effect of surface condition, the concentration effect, and deposit removal and sliding phenomena. Two types of wax were used, refined wax and slack wax MCT-10, the properties of which are summarized in Chapter 5.  6.1 Test of Reproducibility  A test was carried out twice to check for reproducibility. The test was carried out for the chrome-plated stainless steel with slack wax at 20 % by wt concentration.  1-8 IS  f  —  1-2'  5  1-0-  »  •° « » « . •  o-4H  AO  Time (min)  110  160  Fig. 11. Result for slack wax at 20% by wt on chrome-plated stainless steel tube, Re=9224 and T =31.2 °C. b  46  80  I2P  160  Time (min)  Fig. 12. Result for slack wax at 20% by wt. on chrome-plated stainless steel tube, Re=9208 and 7^=31.2 ° C . R =0.5814(1- <T")  i L =0.6031(1-e"")  f  50  As shown by Figures 11 and 12, the fouling resistance recorded as a function of time increased rapidly in the first 5-10 minutes and then assumed a constant fouling resistance. These results show that wax deposition is a rapid process with a small time constant 9 . C  Table 16 lists results for R* and 0 . For the two experiments, R * =0.592 m K/kW and the f  C  2  f  total range of Rf was 0.022 m K/kW, which is less than 4 % of the mean. The time 2  constants were 2.1 and 2.2 minutes, respectively, a disagreement of less than 5 %. The uncertainty was ISA % for Fig. 11 and 15.6 % for Fig. 12. The two graphs are representative for all the data except for those at the highest Re.  7.2. Fouling Results 7.2.1 Effect of Velocity For slack wax MCT-10 at 20 % by wt., Fig. 13 a-e shows R  f  versus time  plots and the corresponding fitted curves. It is apparent that at lower velocity, the R  f  values are larger. Table 15 shows that as the Reynolds number is roughly doubled from 6645 to 14,430, the R* value decreases by a factor of 1.5. For refined wax at 10 % by f  weight, the above trend with Reynolds number was similar for the same tube and in this case the time constant, 0 , also decreases as Re increases, i.e. the fouling resistance takes c  less time to reach 63 % of R* at higher flow velocities, as seen in Table 14. Figure 14 f  shows the Reynolds No. effect on R* for the refined wax runs. R f  f  vs. 0 data are shown in  Appendix D.  It was found that the asymptotic fouling resistance decreases with increasing flow velocity for all surface types and both waxes. The slack wax even at 20 wt. % concentration gave slightly lower values than did the refined wax at 10 wt. % concentration. For each tube the decreasing trend of R* with velocity was evident, but the f  time constants showed little in the way of trends with velocity. Conditions of 37  51  experimental runs with slack wax and values of the fitted parameters are given in Tables 15- 21. The Reynolds number effect on Rf is plotted for all surfaces in Figure 15a. The lines were determined by fitting a quadratic equation to the data points for each surface. The effect of velocity appears stronger with some surfaces than with others. For example, with the n-C18 silane-coated chrome-plated stainless steel tube, Rf appears almost independent of Re at Re>9000, whereas with both Heresite coated stainless steel tubes, R* drops markedly over the same range of Re. Fig. 15b shows a plot of log (Rf) vs. f  log (Re) for the data of Fig. 15a. The uncoated stainless steel (slope=-0.42), chromeplated stainless steel (-0.61), sand-blasted stainless steel (-0.81), n-C18 silane-coated chrome-plated stainless steel (-0.58) and n-C18 silane coated stainless steel (-0.84) each show a straight line fit on this plot. However, the two Heresite-coated tubes did not show this straight line fit. From the data of Bott and Gudmundsson (1977b) for a sand-blasted copper plate shown in Figure 2, log (Rf) vs. log (Re) would yield a slope of about -0.5. For the five straight line fits obtained on Fig. 15b, the slopes ranged from -0.4 to -0.8, while the average slope of the two curves for the Heresite-coated tubes was approximately -2.6.  One reason for the decrease in R* with velocity may be the increased shear f  acting on planes of weakness in the deposit such that as Re increases, progressively thinner wax layers can exist. The Kern and Seaton model, Eq. (7), suggests that removal increases with deposit thickness for this very reason. Another possible reason for the decrease is that as the flow velocity increases, the surface temperature where the wax deposition occurs increases.  Taking the derivative of Eq. (22) with respect to time yields the initial fouling rate  52  e (=0  c  The results of the above equation were calculated and presented in Tables 14-28. While the trends of R* /9 versus Re are widely scattered, this parameter tends to f  C  decrease as Reynolds increases for both types of waxes and for most tubes. Thus for refined wax at 10 % on stainless steel the initial fouling rate, R* J9 , F  C  decreases with  increasing Re (Table 14), i.e. lower initial rate of attachment. This was also found by Watkinson and Epstein (1969) for gas oil fouling. The same holds true for slack wax MCT-10 at 20 % on stainless steel, sand-blasted stainless steel and n-C18 silane-coated stainless steel (Tables 15, 16 and 21), but the two Heresite coated tubes do not show a consistent trend. Table 14. Results for refined wax at 10 % by wt. using stainless steel. T =32.6+0.2°C, Cloud Point= 21.1 ° C , f =9.5±0.5 <>C, V =2.5 m/s. b  K  Re  fc  w  0c (min.)  Uncertainty (%)  (m K/kW) 2  2.1890 0.8896 0.5122 0.3363 0.2249  7093 11414 14812 17332 19053  8.9 5.5 2.5 2.6 2.1  13.7 30.0 22.5 27.5 27.9  KI*.  (m K/kW-min) 0.2460 0.1617 0.2049 0.1293 0.1071 2  Table 15. Results for slack wax MCT-10 at 20% by wt. using stainless steel. T =31.4±0.3 °C, Cloud Point= 27.8 ° C , r =10.4±1.5°C, V = l . l m/s. b  Re  K  6  Q (min.) c  (m K/kW) 2  w  Uncertainty (%)  (m  2  R .»< = f  (m K/kW) 2  K/kW-min) 6645 8722 10615 12184 14430  0.9293 0.8244 0.7926 0.7244 0.6668  8.0 10.8 13.2 18.1 10.3  11.9 11.4 8.9 9.2 7.8  0.1162 0.0765 0.0600 0.0400 0.0645  53  2.2666 1.9197 1.6597 1.6142 1.4867  l° j  l u  +R  Table 16. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel. T = 31.3±0.1°C ,Cloud Point=27.8 ° C , r =7.6±0.4 C, V = l . l m/s. o  b  t  9 (min.)  Re  C  (m K/kW) 2  Uncertainty (%)  w  K.^^+R) (m  2  (m K/kW) 2  K/kW-min) 6586 9224 9208 11015 13156 14428  0.8238 0.6031 0.5814 0.5941 0.5240 0.4817  2.5841 1.9377 1.9258 1.6754 1.4183 1.3076  0.3980 0.2900 0.4184 0.3910 0.0749 0.2692  17.8 15.4 15.6 11.6 9.8 9.6  2.1 2.1 2.2 1.4 1.3 6.4  Table 17. Results for slack wax MCT-10 at 20% by wt. using sand-blasted stainless steel. T = 31.2±0.1 °C, Cloud Point= 27.8°C , / =11.4±0.6 °C, V = l . l m/s. b  Re  K  fc  & (min.) c  (m K/kW) 2  6418 8734 11340 12732 14440  1.2187 0.8227 0.7614 0.6609 0.6016  5.9 9.3 8.9 7.6 7.3  w  Uncertainty (%)  (m  10.1 11.7 7.6 7.7 6.7  K/kW-min) 0.2066 0.0863 0.0856 0.0870 0.0824  R* =\/U +R) f, tot 1 ° J 0  2  (m K7kW) 2  2.3548 1.9047 1.5304 1.3919 1.2142  Table 18. Results for slack wax MCT-10 at 20% by wt. using n-C18 silane-coated chrome- plated stainless steel. T =31.3±0.1 °C, Cloud Point=27.80C , r =13.6+0.7O b  Re  K  ®c (min.)  (m K/kW) 2  6629 8773 11314 12888 14642  0.7407 0.4854 0.4605 0.4572 0.4527  6  Uncertainty (%) (m K/kW-min) (m K/kW) 2.0159 0.0938 15.9 0.0232 1.7455 19.4 0.1123 1.2891 11.5 1.1567 0.0726 9.6 1.0383 0.0374 8.1 2  7.9 20.9 4.1 6.3 12.1  54  2  Cj  Table 19. Results for slack wax MCT-10 at 20% by wt using Heresite Si 57 E coated stainless steel. T =31.3±0.2 °C, Cloud Point=27.8 <>C, f =13.5±0.9 QC, V = l . l m/s. ft  b  9 (min.)  Re  C  w  Uncertainty  R  .<o< =  f  (m K/kW)  (%)  2  (m K/kW-min)  l ° *f  l U  +R  2  (m K/kW) 1.4979 1.3169 0.9410 0.8162 0.7314 2  6567 8819 11215 12697 14207  3.2 5.0 2.1 3.2 9.4  0.4406 0.4056 0.2263 0.1534 0.0700  0.1377 0.0811 0.1078 0.0479 0.0074  21.0 15.8 18.2 24.1 55.6  Table 20: Results for slack wax MCT-10 at 20% by wt. using Heresite P-400/L-66 coated stainless steel. T = 31.2+0.1 °C, Cloud Point=27.8°C, f =13.2±0.4 °C, V = l . l 6  b  m/s. Re  K  9 (min.) C  (m K/kW)  6616 8803 8765 11042 12674 14432  Uncertainty (m  (%)  2  6.4 2.0 2.3 3.7 7.9 4.9  0.5552 0.3804 0.3671 0.1912 0.1288 0.0520  w  21.1 17.2 16.3 28.2 47.2 155.1  2  K/kW-min)  (m  0.0868 0.1902 0.0517 0.0163 0.0106 0.1596  1.8305 1.3111 1.2295 1.0458 0.9277 0.8425  2  K/kW)  Table 21. Results for slack wax MCT-10 at 20% by wt. using monolayer n-C18 silane coated stainless steel. T =31.5+0.1 °C, Cloud Point=27.8 °C , f =13.2± 0.2°C, V = l . l 6  b  m/s. Re  K  9 (min.) C  (m K/kW) 6631 8734  0.7016 0.4639  11084 12672 14147  0.4496 0.3753 0.3574  4.4 14.2 10.0 4.2 6.9  K.«><  Uncertainty (%)  2  (m K7kW.min)  (m  0.1595 0.0327 0.0450 0.0894 0.0518  1.8546 1.4491  2  14.4 15.7 11.5 11.6 9.0  55  w  2  K/kW)  1.2543 1.1197 1.0402  =  / <> f  l  U  +R  2.0-1  1.81.61.41.2-  20  40  60  80  100  120  140  160  Time (min)  Fig. 13 a. R vs. time for slack wax MCT-10 at 20 % by wt. using stainless steel. f  Re = 6645, T =31.4 °C, Cloud Point = 27.8°C. b  2.0-1  1.81.61.41.2-  K/kV  >  1.0-  CM  E  OC  0.8•  0.60.40.20.00  20  40  60  80  100  120  140  160  Time (min) F i g . 13b. Rf  vs. time for slack w a x M C T - 1 0 at 20 % by wt. using stainless steel.  R e = 8722, 7^=31.4 ° C , C l o u d Point = 27.8°C.  56  2.0-,  1.81.61.4-  K/kV  1.21.0-  eg  E  DC  0.8•  0.60.40.20.00  20  40  60  80  100  120  140  160  Time (min)  Fig. 13 c. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. f  Re=10615, 7^=31.4 °C, Cloud Point=27.8°C.  1.81.61.41.2-  Time (min)  Fig. 13d. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. f  Re=12184, 7^=31.4 °C, Cloud Point=27.8°C.  57  20  n  1.8-  1.6  1.4 H 1.2  2  1.0 H  CM  E  0.8  °  o °  o  o  of  i—i— —i—•—i—'—i—'—i—'—i—'—i—'—i— 20 40 60 80 1  0  100  120  140  160  Time (min)  Fig. 13e. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=14430, 7^=31.4 °C, Cloud Point=27.8°C. f  58  59  •  Uncoated stainless steel tube  •  Chrome-plated stainless steel tube  O  Sand-blasted stainless steel tube  '+  n-C18 silane-coated chrome-plated stainless steel tube  1.4-1  t.2H  *  Heresite Si 57 E coated stainless steel tube (shiny)  A  Heresite P-400/L-66 coated stainless steel tube (dull)  o  n-C18 silane-coated stainless steel tube  1.0 H  0.8 ^  2 CM  E  0.6  K  a: 0.4  A  0.2  0.0 - | 6000  1  1  8000  1  1  •  10000  1  12000  1  1  14000  '  I 16000  Re Fig. 15a. Result of R} vs. Re for MCT-10 slack wax, 20% by wt at 7^=31.3+0.2 ° C for different surfaces.  60  • • +  Uncoated stainless steel Chrome-plated stainless steel Sand-blasted stainless steel n-C18 silane-coated chrome-plated stainless steel  A  Heresite Si 57 E coated stainless steel (shiny) Heresite P-40G7L-66 coated stainless steel (dull)  O  n-C18 silane-coated stainless steel  o  *  ------o.  N  A —I  3.8  1  1  1  3.9  \  4.0  i  —i  1  4.1  Log (Re) Fig. 15b. Result of Log (R}) vs. Log (Re) for MCT-10 slack wax, 20% by wt at 5=31.3+0.2 ° C for different surfaces.  61  1  4.2  7.2.2 Effect of Bulk Temperature  The bulk temperature here refers to the average of inlet and outlet bulk temperature of the wax-kerosene flow as defined in Chapter 5. The inlet and outlet temperatures typically differed by 1 ° C . The bulk temperature was varied from near the cloud point of the mixture to about 40 ° C . The effect of the bulk temperature was determined for refined wax on the stainless steel tube, and for slack wax on a total of four tubes. Figure 16a-e shows the R versus time curves for the case of slack wax. The trends f  shown in this figure are representative for the other tubes as indicated in Tables 22-26. At bulk temperatures near the cloud point, wax deposition was heaviest, and decreased with increasing bulk temperature as expected. For example, in Fig. 16a, at 7^=28.7 °C, R*  f  =1.5 m K/kW, whereas in Fig. 16d at 7^=38.1 °C, R* =0.22 m K/kW. Fig 17. and 2  2  f  Fig. 18 show the trends of R* with T .The most significant drop in R* occurs between the f  b  f  data near the cloud point and those at some 5 °C higher, where R* has decreased by f  almost an order of magnitude. While R* decreased sharply with increasing bulk f  temperature for all cases, the time constant did not show any consistent trend. Near the cloud point, 9 values tended to be high, and usually decreased with increasing C  temperature. In Table 23, for slack wax fouling on the stainless steel tube, a consistent drop in 9 with increasing temperature is observed, whereas in other cases (Table 22 and C  Table 26) there appears to be an increase in 0 at the highest temperatures. The initial e  fouling rate, R*fJ9 , for refined wax at 10 % on stainless steel showed a decrease with c  bulk temperature (Table 22).  The principal explanation for a decrease in R* with increasing T is that the higher f  b  the value of T , the smaller the zone of the hydrocarbon flow which is between the cloud b  point and the heat transfer surface, and hence the smaller the degree of wax crystallization.  62  This effect is enhanced by the steeper temperature gradient near the surface where the temperature is higher. Table 22. Results for refined wax at 10% by wt. using stainless steel and wax-kerosene Re=12155+1909. Cloud Point=21.1 ° C , f =10.0±0.3 °C, u=1.6 m/s, V =2.5 m/s. fe  T„(°C)  w  Q (min.)  Uncertainty  c  (%)  (m K/kW) 2  28.7 32.4 36.4 40.0 44.2  3.6474 0.8896 0.4632 0.3435 0.3070  12.0 5.5 6.6 4.4 111  21.0 30.0 27.3 18.6 14.2  (m K/kW-min) 0.3040 0.1617 0.0702 0.0781 0.0277 2  Table 23. Results for slack wax MCT-10 at 20% by wt. using stainless steel and Re=9430±l 166, Cloud Point=27.8 ° C , f =7.9±0.5QC, u= 1.6 m/s, V = l . l m/s. ft  U°c)  K  w  0 (min.)  Uncertainty  C  (m K/kW)  (%)  2  28.9 31.2 34.0 38.1 40.6 40.8  1.5241 0.8244 0.3788 0.2205 0.3916 0.2359  11.0 11.1 13.1 16.7 7.9 14.1  16.2 10.8 5.2 2.7 2.3 1.0  (m K/kW-min) 0.0943 0.0765 0.0727 0.0832 0.1733 0.2359 2  Table 24. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel and Re= 9629±626. Cloud Point=27.8°C , f =9.6±1.5 °C, u=1.6 m/s, V = l . 1 m/s ft  T rc) b  K  9 (min.)  Uncertainty  C  (m K/kW)  (%)  2  31.2 35.9 37.3 40.9  0.6031 0.2409 0.2056 0.1187  w  15.6 23.3 42.5 21.8  2.1 3.4 1.3 2.3  63  (m K/kW-min) 2  0.2900 0.0713 0.1619 0.0514  Table 25. Results for slack wax M C T - 1 0 at 20% by wt. using sand-blasted stainless steel and Re= 9357±877.Cloud Point? 2 7 . 8 ° C , > =11.7±0.8°C,. u=1.6 m/s, V = l . l m/s t  U°c)  K (m  *c (min.) 2  K/kW)  w  Uncertainty (%)  (m  2  K/kW-min)  31.3  0.8027  9.3  11.7  0.0863  33.6  0.4572  1.1  20.2  0.4011  37.1  0.3645  12.8  11.6  0.0285  40.2  0.2664  •7:8;  11.2  0.0342  /v\v-  Table 26. Results for slack wax M C T - 1 0 at 2 0 % by wt. using n-C18 silane-coated chrome-plated stainless steel and Re=9391±940. Cloud Point=27.8PC,  r =12.8±0.5 0 C , 6  u=1.6m/s, V „ = I 1 nVs  T {°C) b  ' •:  *  c  (min.)  Uncertainty  (m K/kW)  (%)  2  KI*. (m  2  K/kW-min)  31.5  0.4854  20.9  19.4  0.0232  33.5  0.3180  4.5  16.6  0.0707  36.9  0.2098  5.7  20.6  0.0368  41.0  0.0640  12.5  60.6  0.0051  3.0 n  " 4  zo A  1 0  1  0.5 A  0.0-j—i—r—i—i—•—i • I—'—I—T—I—7—I— —T— 0 20 40 60 80 100 120 140 160 1  Time (min)  Fig. 16a. of'R  f  vs. time for slack wax M C T - 1 0 at 20 % by wt.using stainless steel.  Re=8391, r = 28.9 °C, Cloud Point=27.8°C. b  2.0 1.81.61.4 1.2-1  0.8  CO**!  'o o o  or 0.6 0.4  0.2H 0.0-£ 0  -I—I • I  20  40  '—I—<—1—1—1— —I— —1—•>—I— 1  60  80  100  r  120  140  Time (min)  160  -.;  Fig. 16b. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. f  Re=8722, 5= 31.2 °C, Cloud Point=27.8°C. 20'  1.5'  1.0  E  0.5 A  0.0-{ 1—I 0 20  1  1  '1  I • I • i - l • I r—1 40 60 80 . 100 120 140 160 Time (min) .  Fig. 16c. Rf ys. time for slack wax • MCT-10.at 20 % by wt.using stainless steel. Re=9372, T = 34.0 °C, Cloud Point=27.8°C. b  65  1.H  1.0  0.5  0.0 } • | i i — T — I • i — • — i — • ,. i . •. i—•—r—> 0 20 40 60 80 100 120 140 160 Time (min)  Fig. 16d. R/ vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=984i,5= 38.1 °C, Cloud Point=27.8°C.  2-0-,  1.SH  10H  0.5 A  o.o-f 0  —•—J—> 1 • 1 • 1 20  40  I r~l • I  1  60Time 80 (min) 100 120 140- 160  Fig. 16e. R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. f  Re=10115, 5=40.6 °C, Cloud Point=27.8°C.  66  ^  "  67  • • O +  1.6H  Uncoated stainless steel tube Chrome-plated stainless steel tube Sand-blasted stainless steel tube n-C18 silane-coated chrome-plated stainless steel tube  1.4J  1.2-J  1.CH  2 CNI  0.8H  E "Q:  o.6-  0.4-  0.2-•  0.0  —i—«—i—>—i—•—i—•—r~  28  30  32  34 T  B  36 °  (  C  —\  38  1  1  40  1  1  42  )  Fig. 18. Results for MCT-10 slack wax at 20% by wt. and Re =9363 + 277 for different surfaces.  68  7.2.3 Effect of Surface Conditions Figure 15a shows that the general ranking of tubes from the best to the worst in terms of increasing Rf is both Heresite coated stainless steel tubes < n-C18 silane coated stainless steel < n-C18 silane-coated chrome-plated stainless steel < chrome-plated stainless steel < uncoated stainless steel <sand-blasted stainless steel. It can also be seen that the two Heresite-coated tubes show a lower asymptotic fouling resistance compared to the others at all Reynolds numbers tested. These results agree with prior studies, in which it has been shown that plastic coatings give a lower wax deposit (lessen and Howell, 1958), and it can be recalled that Jorda (1966) has attributed this phenomenon to the general smoothness of plastics. Jorda has argued that smooth plastics do not harbor wax crystals as easily as a rough tube. Evidence of poor adhesion of wax is described in the next section where sliding of wax was observed to occur on the chrome-plated stainless steel, n-C 18 silane-coated chrome-plated stainless steel tube and the n-C18 silane-coated stainless steel tube, indicating that they are very smooth. Both silane-coated tubes have shown a lower fouling resistance compared to the uncoated stainless steel, the sand-blasted stainless steel and the chrome-plated stainless steel tubes.  Because the plastic coatings will increase the overall thermal resistance, it is useful to compare surfaces according to their total thermal resistance, i.e. original plus fouling resistance. Data are listed in Tables 15-21 and shown plotted versus Reynolds number in Figure 19. On this basis the Heresite coated tubes again proved superior, the Heresite Si 57 E (shiny) outclassing the Heresite P-400/L-66 (dull) slightly; and the silane coated tubes next best. The chrome plated tube was essentially no better than the standard and the sand-blasted stainless tube, although the chrome-plated stainless steel has a lower asymptotic fouling resistance compared to both the stainless steel and the sand-blasted stainless steel tubes (Fig. 15a). This phenomenon conforms to the traditional reasoning  69  that the higher the thermal resistance, the lower the heat transfer, which brings about a lower wax deposit.  Considering only the roughness factor (in brackets), the chrome-plated stainless steel tube (0.5p.m) has a lower Rf compared to the uncoated stainless steel (2.5u.m), which again has a lower Rf at lower Re when compared to the sand-blasted stainless steel tube (5.0|im). It does not follow, however, that a lower wax deposit is necessarily obtained by using a smooth surface, as wax deposit is a function of several factors. The Heresites were said to have enamel-like finish surfaces according to manufacturer's brochure (Heresite Protective Coatings, Inc.), but no roughness figures were given.  Wax fouling is also a function of the material type inasmuch as some materials can form a weak hydrogen bond with the paraffin wax, which could enhance the wax deposit. It was shown in the literature survey that materials like tetra-fluoroethylene (Jorda, 1966) which have an ultra-smooth surface show an extreme adhesion to wax deposit, which is evidence that there might be some sort of bond between this type of surface and wax. A micro study of the type of adhesion which occurs between wax deposit and surface has yet to be done. However, in summary, wax deposition must be a function of thermal resistance of the surface material, its roughness and its intrinsic properties.  Four tests have been carried out to compare the different surfaces as a function of bulk temperature of the wax-kerosene (Fig. 18). The uncoated stainless steel and the sandblasted stainless steel tubes show a higher wax deposit compared to the chrome-plated stainless steel and the n-C18 silane-coated chrome-plated stainless steel tubes. This is exactly the same hierarchy as shown by Fig. 15a for asymptotic fouling resistance vs. Re, and the same explanations can be applied.  70  • o +  2.62.4-  Uncoated stainless steel tube Chrome-plated stainless steel tube Sand-blasted stainless steel tube n-C18 silane-coated chrome-plated stainless steel tube  o  Heresite Si 57 E coated stainless steel tube (shiny) Heresite P-400/L-66 coated stainless steel tube (dull) n-C18 silane-coated stainless steel tube.  A  o  2.2  5  2.0 -]  ^  ^  1.8H  +  3  1.6-1 o  1.4  II  o 1.2 H  1.0  .A  0.8 0.6 6000  T  8000  —I  1  10000  1  12000  T  14000  1 16000  Re Fig. 19. Graph for slack wax MCT-10 at 20 % by wt. and 4 =31.3±0.2 (J tor ditterent surfaces. 71  7.2.4 Effect of wax concentration The effects of wax concentration on the fouling resistance were also studied for both types of wax. Fig. 20a-d shows R vs. time data on the stainless steel tube for slack f  wax at concentrations from 5 to 20 % . A large increase in wax deposition with concentration is noted. At the highest wax concentration of 20 %, deposition was extremely heavy. Similar trends were apparent for the refined wax, although the amount of wax deposited was markedly higher. Tables 27 and 28 summarize the data. Figures 21 and 22 show strongly non-linear effects of concentration on R* . At low concentrations there is f  little increase in R* ; however above about 15 % concentration for refined wax, and above f  10 % concentration for slack wax, R* increases sharply. Doubling the concentration from f  10 % to 20 % results in about a 13-14 fold increase in R* for both refined and slack wax. f  Table 27 for refined wax shows no consistent trend of 0 with concentration, but for C  slack wax MCT-10, it can be seen in Table 18 that there is an increase in 0 with C  7  increasing wax concentration. Increased concentration of the wax-kerosene solution will increase the number of particles available for deposition on the surface as the driving force in Eq. (4) (the concentration difference) increases. From Fig. 23, a plot of R* vs. f  T - T , as the concentration increases at a constant bulk temperature and flowrate of the b  c  wax-kerosene, T - T decreases and therefore the cloud point temperature will move away b  c  from the tube surface, which leads to increased wax deposition.  An increase of initial fouling rate, R}/0 , with concentration for refined wax has C  been observed (Table 27), which shows that the attachment rate for this wax is higher when the wax concentration driving force is higher. The slack wax MCT-10 (Table 28) showed smaller initial fouling rates compared to the refined wax at 10-20 wt. % concentrations, which indicates that slack wax displays lower adhesion to the stainless steel tube (Tables 27 and 28). In general, slack wax has shown smaller fouling resistances than the refined wax, even when its concentration has been higher.  72  Table 27. Results for refined wax using stainless steel at Re=10664±1902 and ^ - 3 2 . 5 ±  %-%  &c (min.) Uncertainty  Gone. (%by weight)  (m  (%)  (m K/kW) 2  (°C)  2  K/kW-min)  20  36.0 15.1 25.3 33.0  79.6  0.5400 1.2700 2.8000 17.1200  5 TO  15.3  V  0.0068 0.4379 0.5091 1.1190  17.0 .. . : 11.4 6.9 3.5  ;  '-y^.  Table 28. Results for slack wax MCT-10 using stainless steel at Re= 10003±1760 and  -..  • 510 15 20  •-.  %-x  Uncertainty :  Cone. (%) by weight  (m K/kW) 2  (min.)  (m , 2  (%)  i-  CQ  K/kW.min) 0.0774 0.0799 0.4899 : 1.1080  r  0.0387 0.0055 0.0360 0.0412  43.6 57.5 13.1 15.5  2.0 14.6 13.6 26.9  14.0 8.0 5.9 : ' 1.5  ;  :  0.5  CM  oo -{> 0  T—i—i—•. i 20 40 60  1  i 80  1  i 100  1  i—'—r— 120 140  1  r— 160  Time (min) Fig. 20a. R vs. time for slack wax MCT-10 at 5 % by wt.using stainless steel: Re=11185, f  7; =29.2 °C, Cloud Point=15.0°C.  73  0.6 4  =2 0.4 E, or 0.2  o.o -!•  50  100 Time (min)  150  200  Fig. 20b. R vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. f  Re=10714, 5=29.2 °C, Cloud Point=21.1°C. 2.0  n  1.8. 1.6 1.4, 1.2 |;1:0H 0.8 H 0.6 :0:4 0.2 .0.0^  -r 40: -  20  i  1  60  i  80  — I — > — i — ' — i — ' — l —  100  120  140 160  Time (min)  Fig 20c. R vs. time for slack wax MCT-10 at 15 % by wt.using stainless steel. f  Re=9569, 5=29.2 °C, Cloud Point=23.3°C.  74'  2.0 n 1:8 1.6 1.41.2-  § CM  ,v°°  1.0  o  0 o  „° ,0.  • .  c  ° o :  E —  0.8-|  DU 0.60.40.2 0.0 -{  0  i  i,, i—r—}—i—'—i—•—i— —i— —i—•—i—• 1  20  40  60  80  100  1  120  . Time (min)  140  160  •  Fig. 20d, R vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel f  Re=8545, 5=29.2 °C, Cloud Point=27.8°C.  75  20  n  15H  5H  OH A—I—r—|—.—|—i—r—i—\—i—|—i—i—i—|—i—|—•—|  4  6  8  10  12  14  16  Concentration (wt. %)  18  20  22  Fig. 21. Results for refined wax on uncoated stainless steel tube. Re=10664 and T =32.50C. b  76  i— —i— —i— —i 1  4  1  1  6  1  8  i  1  i  1  i  1  —i— —r —i 1  - 1  10 12 14 16 18 20 22  Concentration (wt. %)  Fig. 22. Results for slack wax MCT-10 on uncoated stainless steel tube. Re= 10003 and 5=29.2°C.  77  1.2-.  1.0 H  0.8  H  0.6  H  0.4  H  0.2  H  5  CM  o.o H 1 — « — i — r — | — . — I — i — | — i — | — i — r ~ 0  2  4  6  8  10  12  14  T -T (°C) b  c  x  Fig 23. Graph of R* vs. T - T for slack wax MCT-10 on uncoated stainless steel tube. f  Re= 10003 and  b  c  T =29.2°C. b  78  7.2.5. Removal and Sliding of Fouling Deposit The glass section on the double pipe heat exchanger shown in Fig. 5 permits the fouling process to be critically observed. Removal was not observed at the micro level, but relatively large chunks (max. 5 mm size) of both wax types were seen to be removed by the flowing fluid, resulting in small patches of free exposed surface. This phenomenon appeared to happen randomly approximately after 60 minutes from startup until the end of an experiment for some of the tubes. The patches were randomly located. These observations are supported by Bott and Gudmundsson (1977b), who found that wax deposition reaches an asymptotic value that fluctuates randomly around a mean constant value. Table 29 summarizes observations on deposit motion for the various tubes tested.  Sliding of wax chunks was also observed along the chrome-plated stainless steel, the rt-C18 silane-coated chrome-plated stainless steel, and the n-C18 silane-coated stainless steel tubes. Values of sliding velocity measured for the chrome-plated stainless steel tube are shown below in Table 30. The sliding velocity (which refers to velocity of wax chunks along the tube) was measured manually through the glass section on the heat exchanger by using a ruler and timing a particular wax chunk movement from one marked point to the next. For the other two tubes, the sliding velocity was difficult to measure as the chunks were removed after a short distance of movement. The phenomena of sliding and wax chunk removal were also reported by other authors (Hunt, 1962; Jorda, 1966). It would be expected that the sliding velocity would increase with increasing liquid velocity, as the shear stress on the layer is increasing. The results, however, do not show a clearcut trend. An improved technique for measurement of sliding velocity might reveal a more consistent trend.  79  Table 29. Summary of removal and sliding of fouling deposit. Sliding  Wax removal/bare patches  Type of tube  observed  Uncoated stainless steel Chrome-plated stainless steel Sand-blasted stainless steel n-C18 silane-coated chrome-plated stainless steel Heresite Si 57 E coated stainless steel (shiny) Heresite P-400/L-66 coated stainless steel (dull) n-C18 silane-coated stainless steel  Yes Very Small Patches  No Yes  No Yes  No Yes (but removed immediately)  No  No  No  No  Yes  Yes (but removed immediately)  Table 30. Sliding velocity for chrome-plated stainless steel tube using slack wax MCT-10 at 20% by wt. T = 31.3±0.1°C ,Cloud Point=27.8 ° C , f =7.6±0.4°C, V = l . l m/s b  6  w  Re  u(m/s)  Sliding velocity (m/s)  6586 9224 9208 11015 13156 14428  1.17 1.64 1.64 1.96 2:35 2.57  0.68 0.74 0.70 0.64 1.00 0.75  7.2.6. Uncertainty Fouling resistance was determined from Eq. (20) as the small difference between two reciprocal values of the heat transfer coefficients, which are nearly equal large terms. Therefore precision is required in the experimental measurements to get satisfactory R results with little scatter. The major objective of uncertainty analysis is to f  identify those variables that have the greatest effect on the precision of the calculated result. Because of the scatter observed in early experiments the flowrate of water was adjusted to a lower value so that its temperature increase could be larger. Also, the  80  temperature measurement instruments were changed to higher precision thermocouples, and the water side thermocouples were arranged in such a way that the temperature rise was recorded directly.  It can be inferred that uncertainty is mainly affected by the cooling water side temperature rise, the thermocouple resolution, the magnitude of the fouling resistance, the initial overall heat transfer coefficient, and the cooling water mass flowrate fluctuation. A higher cooling water temperature rise, more precise thermocouple resolution, higher fouling resistance, higher overall heat transfer coefficient and lower fluctuation of cooling water mass flowrate from the set value will generally reduce the uncertainty.  There is no particularly set acceptable uncertainty level, but determination of uncertainty is useful to indicate how one can redesign the equipment or change the operational parameters in such a way as to improve precision. Crittenden et al. (1992) state that for the majority of their measurements the maximum error in R  f  was in the  order of 20%. However, this value is for a shell and tube industrial heat exchanger and higher values would be expected for the present laboratory equipment because of the smaller temperature changes. The average uncertainties as indicated in Tables 14-29 which were calculated using Eq. (41) are acceptable, although there are sometimes high uncertainties at lower values of asymptotic fouling resistance. The high uncertainty occurs due to lower R* , but nevertheless a consistent trend of R* with Re and bulk temperature f  f  of wax-kerosene has been shown. As the water side flowrate is fixed, and the thermocouple resolution is also constant, it appears that the only variable in determining Q that could be improved is the cooling water side mass flowrate fluctuation. This w  fluctuation occurs as other users draw water from the same building water main, or turn the water flow off and on. This action changes the pressure and water flowrate in the cooling water line. 81  7.2.6. Prior work at U B C Prior work was done by Guohong Zhang (1992) with refined wax in kerosene on the same equipment as shown in Fig. 5. These were preliminary test results, and the present work has been done with improved temperature measurements. Using a 10% refined wax in kerosene at about 30 °C bulk temperature, it was shown that R* remains f  constant while the time constant decreases with increasing Re, which implies that at higher surface temperatures weaker deposits are formed. The effects of bulk temperature from 25 to 48°C for 10% refined wax was also detennined. His results show that R* decreases f  with increasing bulk temperature and that the time constant does not show any trend for this series. The effect of concentrations of 5, 10, 15, and 20 % by wt of refined wax was also determined. The results show that both R* and the time constant first increase and f  then decrease with increasing wax concentration. Although this prior work had been done without improving the temperature measuring system, it provided a useful guide to the expected results. The range of values of these experiments agree with the present results, but the trends shown for R* vs. Re and concentration are not the same. The trends of R* f  f  vs. T , 6 vs. Re and 0 vs. concentration agree with the present results. 0 vs. T does not b  C  C  C  show any consistent trend for both sets of experiments.  82  b  Chapter 8 8. Conclusions One of the ultimate objectives of fouling research is to minimize deposition in industrial equipment. This research was undertaken to understand the role of process variables and tube wall materials on refinery chillers where the process of separation of wax from the rest of petroleum occurs by cooling. Two waxes were used-refined wax and slack wax MCT-10. Seven tubes with differing surfaces were tested. The following conclusions were drawn:  1. The wax-kerosene mixtures for both refined and slack wax MCT-10 were found to be Newtonian at the invetigated concentrations of 5 %, 10 %, 15 %, and 20 %. The cloud point measured for both waxes was found to be a function of concentration. The bulk temperature of the inlet wax-kerosene mixture was maintained above the cloud point.  2. The wax fouling showed a fouling resistance which increased with time to reach a fluctuating asymptotic value. In many cases, wax chunk removal leaving a bare patch was observed after approximately an hour. Also, sliding of wax along the tube was observed on the chrome-plated stainless steel, the n-C18 silane coated chrome-plated stainless steel and the n-C18 silane coated stainless steel tubes, although the sliding velocity was difficult to measure in the latter two tubes. These observations lead to the conclusion that there is less attachment between the wax and the surface of the tube for these cases, indicating that the surface is smooth enough not to harbor wax crystals from the flowing fluid. Smooth surfaces coupled with a low adhesion to wax could be good candidates for equipment to avoid wax fouling.  83  3. Graphs of asymptotic fouling resistance versus Reynolds number for all tubes and both waxes showed a decrease in R* as flow velocity increased. The decrease was non-linear f  and was fitted by using a polynomial of degree two. The plot of R* vs. Re for refined wax f  decreased sharply, and then almost assumed a constant value, showing that increased flow velocity does not decrease fouling by a large factor once past a critical velocity. For slack wax, the sand-blasted stainless steel, the chrome-plated stainless steel, the n-C18 silane coated chrome-plated stainless steel and the n-C18 silane coated stainless steel tubes showed a sharp decrease and then also leveled off towards a constant value at high Re. The uncoated stainless steel and the two Heresite coated tubes showed a strong decrease with Re without any tendency to level off. These results appear logical, since the probability of getting planes of weakness among the deposited particles increases as deposit thickness increases, and the increase of flow velocity increases the shear stress on the deposit.  4. For both waxes, the asymptotic fouling resistance decreased non-linearly with increasing bulk temperature of the wax-kerosene mixture. The data points were fitted with a polynomial equation of degree 2. There was a sharp decrease in R* with increasing f  temperature near the cloud point and then it slowly leveled off with increasing temperature for refined wax. For slack wax, a stronger decrease was observed at all bulk temperatures for the following four tubes: stainless steel, chrome-plated stainless steel, sand-blasted stainless steel and n-C18 silane-coated chrome-plated stainless steel.  5. In the range of Reynolds number employed (6418-14642), the asymptotic fouling resistance decreased among tubes tested in the following order: sand-blasted stainless steel, uncoated stainless steel, chrome-plated stainless steel, n-C18 silane-coated chromeplated stainless steel, n-C18 silane coated stainless steel tube, and the two Heresite-coated tubes. The decreasing order in terms of the asymptotic fouling resistance vs. the bulk 84  temperature was sand-blasted stainless steel, uncoated stainless steel, chrome-plated stainless steel, and n-C18 silane-coated chrome-plated stainless steel, which thus shows the same hierarchy as R* against Re. f  6. Roughness (bracketed values) seems to play an important role in wax fouling. It was shown that the chrome-plated tube (0.5 pm) had a lower R* compared to the uncoated f  stainless steel (2.5 pm), which had again a lower value of R* compared to the sandf  blasted stainless steel tube (5.0 pm) for a part of the Re range employed. It was reported in the Heresite Protective Company brochure that the two Heresite-coated tubes have enamel-like smooth surfaces, and both were found to have the lowest wax deposit. This indicates that a lower roughness decreases wax deposit.  7. For both waxes the asymptotic fouling resistance increased with concentration of wax in the wax-kerosene mixture on stainless steel. There was a small increase at low concentration and then a sharp increase at the higher concentrations. The slack wax shows less wax deposit as compared to refined wax at all concentrations.  8. Trends of the time constant, 0 , in the Kern-Seaton equation with process variables C  were often poorly defined. According to Kern and Seaton (1959), the time constant is inversely proportional to the shear stress and, according to Taborek et al. (1972), it is proportional to the deposit strength. In most cases, the time constant showed little trend with Re, bulk temperature or concentration. But it was noted that the time constant decreased with increasing Re for the refined wax, indicating that the wax shows less firm attachment with increasing Re. The slack wax MCT-10 tested on stainless steel also showed a decrease of time constant with increasing bulk temperature of the wax-kerosene mixture. In addition, the time constant showed an increase with concentration for the slack  85  wax MCT-10 using stainless steel, but showed a high value with refined wax using stainless steel both at the lowest and the highest concentrations.  9. The thinnest MCT-10 slack wax deposits were observed on the two Heresite-coated stainless steel tubes, the performance of which were comparable. In practical situations, it may be difficult to affect the temperature or concentration of a solution, but the flowrate can easily be affected by installing a pump or an agitator. A lower wax deposit can therefore be obtained by operating a heat exchanger at increased flow velocity or turbulence, and using a smooth surface which has a low affinity for wax.  86  Nomenclature  A  = inner surface area of inner tube, m  A  = outer surface area of inner tube, m  A  = cross-sectional area of orifice, m  B  - constant in Eq. (5)  C  = constant in Eq. (11)  C  = bulk concentration, kg/m  or  2  2  2  3  C  = discharge coefficient of orifice  C  = specific heat capacity of wax-kerosene, kJ/kg K  C  = specific heat capacity of water, kJ/kg K  d  = interface concentration, kg/m  C  3  = hydraulic diameter of the annulus where wax-kerosene flows, m  d  h  D  = shear rate, 1/s  g  = gravitational acceleration, m/s  h  = the level difference between the high and low side of manometer,  h.  = inner heat transfer coefficient, kW/m K  h  = outer heat transfer coefficient, kW/m K  2  2  2  o  '  k  = thermal conductivity of wax deposit, kW/m K  k  - turbulent mass transfer coefficient, m/s  f  m  - mass of deposit per unit area, kg/m  m  = mass of asymptotic wax deposit per unit area, kg/m  m m  d  = mass flow rate, kg/s = deposition flux, kg/s.m  rh  r  = removal flux, kg/s.m  Q  = heat gained by cooling water, kW  w  2  2  2  R,, = deposit bond resistance 87  2  R  = fouling resistance at a given time, m K/kW  Rf  = asymptotic fouling resistance, m K/kW  2  f  2  Rfi = calculated experimental fouling resistance at the time 0., m K/kW 2  IL, ~ thermal resistance of the wall, m K/kW 2  pdu k  h  Re = wax-kerosene Reynolds No.= r,  = inlet cooling water temperature, °C  t  2  = outlet cooling water temperature, °C  t  b  = average bulk temperature of water, °C  T  = inlet temperature of wax-kerosene, °C  T  = outlet temperature of wax-kerosene, °C  }  2  T  b  T  c  = average bulk temperature of wax-kerosene, °C = cloud point temperature of wax-kerosene mixture, °C  T  = initial surface temperature of tube, °C  At  = temperature rise of cooling water, °C  s  At = log mean temperature difference, °C u  = velocity of wax-kerosene mixture, m/s  u* U  = friction velocity, m/s = initial overall heat transfer coefficient based on A., kW/m K 2  o  r  U  = instantaneous overall heat transfer coefficient based on A, kW/m K  V  = volumetric flowrate of wax-kerosene mixture, m /s  2  3  V  - velocity of water, m/s  V  = volumetric flowrate of water, m /s  w  3  w  x P  = thickness of wax deposit, m = orifice diameter / pipe diameter = 2/24.84=0.4831  0  = time, min  0„  = time constant, min  88  8.  = time from experimental data, min = viscosity of wax-kerosene, Pa.s  H p  = viscosity of water, Pa.s  w  = density of wax deposit, kg/m  f  PH  Z  p  =  density of mercury, kg/m  3  3  k  = density of wax-kerosene, kg/m  p  w  = density of water, kg/m  x,  = shear stress, N/m  \\f = deposit strength  2  3  3  References: Armenski, E.A. et. al, Izv Vyssh Ucheb Zaved, Neft Gas, 14, 71, (1971). Bland, W. F. and Davidson, R. L . , "Petroleum Processing Hanbook", McGraw-Hill, Inc., pp. 11-51- 11-54, (1967). Bott, T.R.. and Gudmundsson, J.S., "Deposition of Fouling Wax from Flowing Systems", Institute of Petroleum, BP 77-007, (1977a). Bott, T.R. and Gudmundsson, J.S., "Deposition of Paraffin Wax from Kerosene in Cooled Heat Exchanger Tubes", Can. J. Chem. Eng., 55, 381, (1977b). Gudmundsson, J. S., Particulate Fouling, in "Fouling of Heat Transfer Equipment", eds. E. F. C. Somerscales and J. G. Knudsen, 357-387, Hemisphere, Washington, D . C , (1981). Brod, M , Deane, B . C , and Rossi, F., "Field Experience with the Use of Additives in the Pipeline Transportation of Waxy Crudes", J. Inst. Pet., 57, No. 554, 110, (1971). Cleaver, J.W. and Yates, B., "The Effect of Reentrainment on Particle Deposition", Chem. Eng. Sci., 31,47-151,(1976). Cleaver, J.W. and Yates, B.. " A Sublayer Model for the Deposition of Particles from Turbulent Flow", Chem. Eng. Sci, 30, 983-992, (1975). Crittenden, B.D., Kolaczkowski, S.T. and Downey, I.L., "Fouling of Crude Oil Preheat Exchangers", Trans IChemE, 70, Part A, 555-557, (1992). Dinkelacker, A., "Play Tornado-Like Vortices a Role in the Generation of Flow Noise?" Reprinted from Mechanics of Sound Generation in Flows, ed. E.-A. Muller, I U T A M / I C A / A I A A Symposium, Max-Planck-Institut fur Stromungsforschung, Gottingen, B R D , Springer-Verlag, Berlin, (1979). Eaton, P.E. and Weeter, G. Y . , "Paraffin Deposition in Flow Lines", Tretolite Division, presented at 16th Nat. Heat Transfer conf, Paper 76-CSME/CSChE-22, St. Louis, (1976). Epstein, N „ "Thinking about Heat Transfer", Heat Transfer Engineering, 4, N o . l , 43-53, (1983). Epstein, N . , "Fouling of Heat Exchanger Surfaces", presented at GVC.VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen, 1.1-1.4, Munchen, Germany, (1990).  90  Frendenlund, J. H . , Pedersen, K . S., Ronningsen, H . P., " A Thermodynamic Model for Predictions of Wax formation in Crude Oils", AIChE Journal, 34, No. 12, 1937-1942, (1988). Hansen, G . Arthur, "Fluid Mechanics", John Wiley & Sons, Inc., N . Y . , (1967), pp. 438440. Holder, G.A. and Winkler, J., "Wax Crystalization from Distillate Fuels", Journal of Institute Petroleum, 51, No. 499, 228, (1965). Hunt, E . B . , "Laboratory Study of Paraffin Deposition", Petroleum Transactions, 12591265, (Nov. 1962). Jessen, F.W.and Howell, J.N., "Effect of Flowrate on Paraffin Accumulation in Plastic, Steel and Coated Pipe", Petroleum Transactions, ALME, 213, 80-84, (1958). Jorda, R . M . , "Paraffin Deposition and Prevention in Oil Wells", J. Pet. Tech., 18, 16051612, (Dec. 1966). Kern, D.Q. and Seaton, R.E., " A Theoretical Analysis of Thermal Surface Fouling", British Chemical Engineering, 4, No. 5, 258-262, (1959) Majeed, A., Bringedal, B., Overa, S., "Model Calculates Wax Deposition for N . Sea Oils", Oil and Gas Journal, 88, No. 25, 63-69, (1990). Patton, C C . and Casad, B . M . , "Paraffin Deposition from Refined Wax-Solvent Systems", Soc. Pet. Engineers Journal, 10, No. 1, 17-24, (March 1970). Patton, C C , and Jessen, F . W . , " The Effect of Petroleum Residua on Paraffin Deposition from a Heptane-Refined Wax System", Soc. Pet. Engineers Journal, 5, No. 1, 333, (1965). Svendsen, J.A., "Mathematical Modeling of Wax Deposition in Oil Pipeline Systems", AIChE Journal, 39, No.8., 1377-1387, (1993). Weast, Robert C , Astle, Melvin J., Beyer, William H . , "Handbook of Physics and Chemistry", 68 th ed., C R C Press, Inc., Boca Raton, Florida, pp. D-171-172, F-10, F-39, (1987-1988). Taborek, J., Aoki, T., Ritter, R.B. and Palen, J.W., Knudsen, J.G., "Predictive Methods for Fouling Behavior", Chemical Engineering Progress, 68, No. 7, 69-74, (1972). Taborek, J„ Aoki T, Ritter, R.B. and Palen, J.W.,"Fouling: The Major Unresolved Problem in Heat Transfer", Chemical Engineering Progress, 68, No.2, 59-63, (1972). Toronov, V.P., Tatar Neft Nauch-Issled Inst., 13, 207, (1969).  91  Watkinson, A.P.and Epstein, N . , "Gas oil Fouling in a Sensible Heat Exchanger", Chem. Eng. Prog. Symp. Ser., 65, N o . 92, 84-90, (1969). Zhang, G., "Investigation of Paraffin Wax Fouling", report on work done at U B C , 45 pages, (1992).  92  Appendix A Rotameter Calibration The calibration curve and its equation for cooling water flow is: Flow Rate (U.S. gal/min.)= 0.275 + 0.05 S + 1 * 10" where S is the scale of the rotameter reading in %. See Fig. 24.  Fig. 24. Calibration curve of rotameter  93  4  S  2  (43)  Appendix B Calibration equations for thermocouples: No. 2 thermocouple (wax-kerosene mixture inlet) T = -0.21064 + 17.53609F -0.88371P~ + 0.3139F" -0.0499IV* 2  x  2  3  2  2  No. 3 Thermocouple (wax-kerosene mixture outlet) T = -0.0963 + 17.05522F3 - 0.2259F3 - 0.02855p3 + 0.00832^ 2  3  2  No. 4 Thermocouple(cooling water inlet) t = -0.32759+ 17.68791F -0.98792F + 0.3553F -0.05466F" 2  x  4  3  4  4  4 4  No. 5 Thermocouple (cooling water outlet) t = -0.33693 +17.6865 \V - 0.9769^/ + 0.35688F - 0.0561IV* 3  2  5  5  No. Thermocouple (differential temperature reading for water side) At = (t -t,) = -0.00088 +16.79067AF" 2  where V  i = 2 3 4 5  is thermoelectric voltage in mV and T is temperature in °C  94  Appendix C Computer Program C Purpose C C This program fits data into a non-linear equation(Kern-Seaton) C finds the asymptotic value of fouling resistance and time constant. C C Argument C C M Number of data C T K J Inlet temperature of mixture C T K O Outlet temperature of water C TWI Inlet temperature of cooling water C TWO Outlet temperature of cooling water C R H O Densities C l=mixture C 2=water C CP Specific heat capacities C l=mixture C 2=water C VIC viscosities C l=mixture C 2=water C V Mixture flowrate C FL Water flowrate C D E L P Pressure drop across orifice C D E L T Log-mean temperature difference C QW Heat gain by water C QK Heat loss by mixture C R E W Reynolds number of water side C R E H Reynolds number of mixture side C U(I) Overall heat transfer coefficient C RF Fouling resistance C T Time C Dl Inner diameter of inner tube C DO Outer diameter of inner tube C D Inner diameter of outer tube C WT Resolution of thermocouple C C C C C  CD Discharge coefficient W Length of tube S U M U Uncertainty B2 Orifice diameter/pipe diameter A O R Area of orifice P R O G R A M PROJEC IMPLICIT D O U B L E PRECISION (A-H.O-Z) E X T E R N A L F,RHO,CP,VIC D I M E N S I O N X(2),DX(2),A(2,3),TKI(300),TXO(300),TWI(300),TWO(300) *,TW(300),TK(300),UW(300),UK(3()0) RFW(300),RFK(300),W(300),TR(3(W )  95  *,DT(300),TI(300) C O M M O N RF(30O),T(300),M D A T A 01,02,03,04,05/3.785411D-3,.275D0,.05D0,1.D-4,60.D0/ D A T A CD,B2,AOR,RHOM,RHOW,G/.62D0,.4831D0,1.13D-4 * ,13.6D0,1.D0,9.8D0/ D A T A N,EPS,WT,W,DM/2,1.D-4,.008D0,.72D0,.01D0/ D A T A DI,DO,D/9.957D-3,12.446D-3.25.4D-3/ C Files for data input and output OPEN(UNTr=4,r^E=Vax49.dat') OPEN(UNIT=7,FILE= c:\f77\out49.dat') 0PEN(UNIT=8,FILE='TEMP.DAr) M=76 ,  C Bulk concentration in % C=20 C Manometer reading across orifice in inches Z=8.8 Z=2.53D-2*Z C Rotameter reading in % S=20 D O 20 I=1,M  READ(4,10) T(jO,TKI(jO,TKO(jO,TWT©,TWO(jO,DT(r) TI© >  10 FORMAT(1X,F6.0,4F7.4,2F7.4) 20 C O N T I N U E C Converting the m V to C DO30I=l,M TKI(I)=TKI(I)+TI(I) TKI(J0=-O.21O64+17.536O9*TJ^(J0-O.88371*TKI(I)**2+O.3139 *  *ra©**3-0.04991*TKI(I)**4 TKO(I)=TKO(I)+TI(I) TKO(I)=-O.0963+17.05522*TKO(T)-0.22591*TKO(I)**2-O.02855  *  *TKO(I)**3-K).00832*TKO(I)**4 TWI(I)=-TWI(I)+TI(I) j^(l)=-0.32759+17.68791*TWI(J^.98792*T^  * *TWI(I)**3-0.05466*TWI(I)**4 TWO(I)=-TWO(I)+TI(I) TWO©=-0.33693+17.68651*TWO(r)-0.9769*TWO(I)**2+0.35688 *  *TWO(I)**3-0.05611*TWO(I)**4 DT(I)=-0.00088+16.79067*DT(I)  WRrTE(8,300) I,TWO(I)-TWI(I) 300 F0RMAT(1X,I8,F8.2) 30 C O N T I N U E  96  C Outer and inner heat exchange area of tube. PI=4.D0*DATAN(1.D0) AI=PI*DI*W AO=PI*DO*W C Initializes the final fouling resistance X ( l ) and time consatnt X(2) X(1)=.7D0 X(2)=10D0 X(2)=l/X(2) SUMW=0.D0 SUMK=0.D0 SUMD=O.DO SUMQ=O.D0 TAVW=0.D0 TAVK=O.DO C Cooling water flowrate F L = 01*(02+03*S+04*S**2)/05 DELP=1000.D0*G*Z*(RHOM-RHOW) C Finds bulk temperature and average temp, of fluid D O 401=1,M Wm=(TWO(I)+TWI(l))/2 TK(I)=(TKO(r)+TKI(I))/2 TAVW=TAVW+TW(I) TAVK=TAVK+TK(l) 40  CONTINUE  C Flowrates, velocities, densities and viscosities are evaluated at C the average temperature for Re. TAVW=TAVW/M TAVK=TAVK/M V=CD*AOR*SQRT(2*DELP/(RHO(TAVK,l)*(l-B2**4))) VW=FL/(PI/4*DI**2) VK=V/(PI/4*(D**2-DO**2)) C Finds the Reynolds number for both sides REW=RHO(TAW,2)*W*DJ7VIC(C,TAVW,2) R E K = R H O ( T A V K , 1)* V K * . 0 1 2 9 5 4 D 0 m C ( C , T A V K , 1) C Writes the results into file WRrTE(7,50) "Bulk concentration (%) 50  WRITE(7,60) 'Mixture Re 60  ',C  F0RMAT(1X,A26,F4.1) ',REK  FORMAT(1X,A26,F6.0)  97  WRrTE(7,70) WateRe \REW 70 FORMAT(1X,A26,F6.0) WRTTE(7,80) 'Water average Temp.( C) ', T A V W WRrTE(7,80) M . average Temp. ( C) ', T A V K 80 FORMAT(lX,A26,F6.2) WRTTE(7,80)' WRTTE(7,90) Time\Touling Res. , QW(kW)^ EQ(%)• WRrTE(7,90) '(min)', '(m K/kW) W.side' 90 FORMAT(1X,A15,A15,A15,A10) ,  ,  ,  ,  C Determines the heat gain and loss. C Also, the uncertainity is found by the following loop. D O 120 I=1,M QW=FL*RHO(TW(0,2)*CP(TW©,2)*DT(I) SUMQ=SUMCH-QW V=CD*AOR*SQRT(2*Dr^/(RHO(TK(I),l)*(l-B2**4))) QK=V*RHO(TK(I), 1)*CP(TK(I), l)*(TKI(I)-TKO(I)) EQ=(QK-QW)/QK* 100 DELH=TKI(I)-TWO(I) DELC=TWO(I)-TWI(I) DELL=TKO(I)-TWI(I) BH=DELH/DELL E=DLOG(BH) DELT=(DELH-DELL)/E C For Crittenden WN=DELH-DELL YN=WN/DELH ZN=WN/DELL PRINT*,'jVr,DM UD=DM+2*WT/DELC+l/WN*(PABS(ZN/LOG(BH)-l)*WT+DABS(l-YN^ *+DABS(YN/DLOG(BH)-l)*WT+DABS(l-ZN/DLOG(BH))*WT)  C Finds the overall heat transfer coefficient C Based on water side UW(I)=QW/(DELT*AI) C Based on mixture side UK(I)=QK/(DELT*AO) C The initial overall heat transfer coefficient belongs to the C clean tube. C Fouling resistance is 0 at time 0. JT(I.EQ1)THEN  UCN=UD PRTNT*, UCN ,UCN ,  ,  UCW=UW(1) UCK=UK(1)  98  CPW0=CP(TK(I),2) RHWO=RHO(TK(I),2) CPKO=CP(TK(I),l) RHK0=RH0(TK(1),1)  RFW(1)=0.D0 RFK(1)=0.D0 ELSE C Subsequent fouling res. at time T is calculated. RFW(J>(1/UW(J>1/UCW*CPWO/^^  100  W ^ m = l / U K © - l / U C K * C P K O / C P ( T K © , l)*RHKO/RHO(TK(T), 1) IF ((RFWmXE.O).OR.(RFK(I).LE.O)) T H E N WRTrE(6,100)' Fouling resistance zero or negative' F0RMAT(1X,A35) ENDIF  C The uncertainity for Crittenden UNCD=(UD/UWm+UCN/UCVO/RFW(I) C C C  The uncertainity for the individual is added up and the average is calculated. For Crittenden SUMD=UNCD+SUMD ENDIF IF (I.EQ.l) T H E N  UNCD=0 ENDIF WRrrE(7,110) T © , R F W ( I ) , Q W , E Q 110 FORMAT(1X,F15.1,F15.4,F15.3,F10.2) 120 CONTINUE C Finds the average uncertainity % C For Crittenden SUMD=100*SUMD/(M-1) C Finds the average heat transferred on the water side QAVW=SUMQ/M C Loop to find the surface temperature of the outer side C of tube.  400  TC=0 TF=TAVW H=1057*(1.352+0.02*TF)*VW**0.8/DI**0.2 TWSI=TF+QAVW* 1000/(H*PI*DI* W) PRrNT*,'***',TWSI AAV=(DI+DO)/2*PI DELX=(DO-Di)/2  99  COND=(0.0135*TWSI+8)*1.73 TWSO=QAVW* 1000*DELX/(COND* A A V * W)+TWSI TF=(TWSI+TAVW)/2 IF (DABS(TWSO-TC).GT.0.01)  THEN  TC=TWSO G O T O 400 ENDIF PRTNT*, WSO ,TWSO ,  ,  C Loop to find the parameters for water side.  130  140  WRTTE(7,130)' WRrTE(7,130) 'Water side' FORMAT(1X,A40) D O 140 I=1,M RF(T)=RFW(I) CONTINUE  C Determines the fitted parameters to an accuracy of EPS. D O 190 ITER=1,50 DJTMAX=0.D0 C A L L COEFF(F,N,2,3,X,A) C A L L GAUSS(A,N,2,3,DX,RNORM,IERROR) IF (TERROR.EQ.2) T H E N WRITE(6,170) ' Zero entry in matrix' 170 FORMAT(1X,A20) STOP E N D IF D O 180 I=1,N X(1)=X(I)+DX(I) DJTMAX=DMAX1(DJTMAX,DABS(DX(I)))  180  CONTINUE  PRTNT*;8',DrFMAX,DX(l),DX(2) PRTNT*,X(1),X(2) IF (PIFMAX.LE.EPS) T H E N PRTNT*,'DONE' G O T O 200 ENDIF 190 CONTINUE 200 WRITE(7,210) To.Res.',Time const.(min) ,'Unc(BDC)%' S. Temp' 210 FORMAT(1X,A15,A20,A15,A15) ,  220  )  WRTTE(7,220) ITER,X(l),l/X(2),SUMD,TWSO F O R M A T ( l X , I 4 , F l 1.4,F20.2,F15.2,F15.2) END  C C C C  Purpose The subroutine is to find the argument of the matrix by finite difference method.  100  ,  c C C C C  Argument X(J) Parameters to be fitted A(I,J) Matrix of coefficients  S U B R O U T I N E COEFF(F,N,NDR,NDC,X,A) IMPLICIT D O U B L E PRECISION (A-ILO-Z) D I M E N S I O N X(N),A(NDR,NDC),DELX(10) NP=N+1 D O 10 I=1,N DELX(I)=1.D-6*X(1) 10 CONTINUE DO30I=l,N D O 20 J=1,NP IF (J.NE.NP) T H E N X(J)=X(J)+DELX(J) FUP=F(LN,X) X(J)=X(J)-2.D0*DELX(J) FDOWN=F(LN,X) X(J)=X(J)+DELX(J) A(I,n=(FUP-FDOWN)/(2.D0*DELX(J)) ELSE A(LNP)=-F(LN,X) ENDIF 20 CONTINUE 30 CONTINUE RETURN END C C C C C C C C C C C C C C C C C C  Purpose Uses Gauss Jordan elimination with partial pivot selection to solve simultaneous linear equation of form [A]*{X}={C}. Argument A Augumented coefficient matrix. N Number of equtions to be solved. N D R First(row) dimension of A in calling program. N D C Second(column) dimension of A in calling program. E R R O R Error flag =1 Succesful Gauss elimination. =2 Zero diagonal entry after pivot selection. R N O R M If IERROR= 1, measure size of residual error. If IERROR=2, RNORM=0 X Solution vector.  C S U B R O U T I N E GAUSS(A,N,NDR,NDC,X,RNORM,IERROR) IMPLICIT D O U B L E PRECISION (A-ILO-Z) D I M E N S I O N A(2,3),X(N),B(50,51)^(50) NM=N-1  101  NP=N+1 C Sets up working matix. D O 20 I=1,N D O 10 J=1,NP 10 20  B(I,J)=A(I,J) CONTINUE CONTINUE  C Carry out elimination process N - l times to determine the main C diagonal entry. D O 110K=1,NM KP=K+1 C Find for each row the column containing the largest coefficient. D O 40 I=K,N BIG2=ABS(B(I,K))  nWOT=K  30  D O 30 J=KP,N AB2=ABS(B(I,J)) IF (AB2.GT.BIG2)THEN BIG2=AB2 n>IVOT=J ENDIF CONTINUE  C  For each row divide the first coefficient by the largest coefficient  C  in that row to find S(I).  S(I)=B(I,K)/Ba,IPrVOT) 40  CONTINUE  C Find the row having the largest S(I) represented by IPIVOT. BIG =ABS(S(K)) IPlVOT=K D O 50 I=KP,N AB=ABS(S(K)) IF (AB.GT.BIG) T H E N BIG=AB  n>rvoT=i 50  ENDIF CONTINUE  C If JTIVOT.NE.K then interchange row K and MVOT. IF (JTIVOT.NE.K) T H E N D O 60 J=K,NP TEMP=B(TPIVOT,J)  B(TPrVOT J)=B(K J) )  )  B(K,J)=TEMP  102  60  CONTINUE E N D IF  C Checks for zero entry in the main diagonal. IF (B(K,K).EQ.0) T H E N IERROR=2 ENDIF C Eliminate B(I,K) from rows K P through N  70 80  D O 80 I=KP,N QUOT=B(I,K)/B(K,K) B(LK)=0 D O 70 J=KP,NP Ba,J>Ba,J)-QUOT*B(K,J) CONTINUE CONTINUE  C Eliminates B(I,KP) from K down to 1. D O 100 I=K, 1,-1 QT=B(I,KP)/B(KP,KP) D O 90 J=KP,NP Ba,J)=Ba,J)-QT*B(KP,J) 90 CONTINUE 100 CONTINUE 110 CONTINUE C Checks last diagonal element for zero entry. B(N,N)=0 C causes an abnormal entry return with IERROR=2. IF (B(N,N).EQ.0) T H E N IERROR=2 ENDIF C Finds out the solution vector by dividing the r.h.s. coefficient C to the main diagonal entry for each column. D O 120 I=1,N X(I)=B(LNP)/B(T,r> 120 CONTINUE C Calculates norm of the residual vector, C-A*X C Normal return with EBRROR=l RSQ=0 D O 140 I=1,N SUM=0 D O 130 J=1,N SUM=SUM+A(I,J)*X(J) 130 CONTINUE 140  R S Q = R S Q K A(I,NP)-SUM) * * 2 CONTINUE  103  RNORM=SQRT(RSQ) IERR0R=1 RETURN END  C Purpose C Finds the sum for regression of Kern-Seaton equation from C  T=OtoM  C C Arguments C X ( l ) Asymptotic fouling resistance. C  X(2) Time constant. D O U B L E PRECISION F U N C T I O N F(I,N,X) IMPLICIT D O U B L E PRECISION (A-H.O-Z) D I M E N S I O N X(2) C O M M O N RF(300),T(300),M G O T O (10,20),I SUM=0.D0 D O 30 K=1,M SUM=SIM+(RF(K)-X(1)*(1-DEXP(-T(K)*X(2))))*  10  *  (1-DEXP(-T(K)*X(2))) CONTINUE F=SUM RETURN 20 SUM=0.D0 D O 40 K=1,M SUM=SUM+(RF(K)-X(1)*(1-DEXP(-T(K)*X(2))))* * X(1)*T(K)*DEXP(-T(K)*X(2)) 40 CONTINUE F=SUM RETURN END 30  C Pupose C C  Function determines the density at a given temperature for  C  both mixture and water.  C C Argument C C  T  C  K  C  Teperature =1 mixture =2 water  D O U B L E PRECISION F U N C T I O N RHOfT.K) IMPLICIT D O U B L E PRECISION (A-ILO-Z) G O T O (10,20),K 10 RHO=816.25-.74892*T RETURN 20 RHO=(999.83952+16.9451768*T-7.9870401D-3*T**2-46.170461D-6 * *T**3+105.56302D-9*T**4-280.54253D-12*T**5)/(1+16.87985D-3*T) RETURN  104  END C Purpose C C  Function determines the specific heat capacity of mixture  C  and water.  C C Argument C C T Temperaure C K =1 mixture C =2 water D O U B L E PRECISION F U N C T I O N CP(T,K) IMPLICIT D O U B L E PRECISION (A-ILO-Z) G O T O (10,20),K 10 CP=1.18143+ .012246T RETURN 20 CP=4.21765-3.74987D-3*T+1.49921D-4*T**2-3.35545D-6*T**3+ * 4.27292D-8*T**4-2.30244D-10*T**5 RETURN END C Purpose C C Function determines viscosities of mixture and water C C Argument C C T Temperature C K =1 mixture C =2 water C D O U B L E PRECISION F U N C T I O N VIC(C,T,K) IMPLICIT D O U B L E PRECISION (A-H.O-Z) G O T O (10 20),K 10 IF (C.EQ.5) T H E N Al=4.16D-6 B1=13676.D0 E L S E I F (C.EQ.10) T H E N Al=3.80D-6 B1=14160.D0 E L S E I F (C.EQ. 15) T H E N Al=1.86D-7 B1=21993.D0 E L S E I F (C.EQ.20) T H E N Al=5.92D-7 B1=18820.D0 ENDIF ;  20  VTC=A1 * E X P ( B 1/8.314/(273.15+T)) RETURN IF (T.LE.20) T H E N VTC=1301/(998.333+8.1855*(T-20)+.00585*(20-T)**2)-1.30233 VTC=10**VIC*l.D-3  105  E L S E I F (T.LE. 100) T H E N VIC=(1.3272*(20-T)-.001053*(T-20)**2)/(T+105) VIC=10**(VIC*1.002)*lD-3 ENDIF RETURN END  106  Appendix D Experimental data. The following Table shows the mn number listed in the appendix, the file number and name in a diskette, tube type, wax type used and the overall initial heat transfer coefficient for each run. The following abbreviation is used: SS = Stainless steel Table 31. Lists of run number, disk numbr, tube type, wax type and U„ Run. No.  Disk No.  Tube Type  Wax Type  U„(kW/m K)  u(m/s)  T„(°C)  1  out7.dat  SS  Refined  0.4644  1.2  11.3  0.5082  1.6  13.3 12.9  2 3  l  outl5.dat  n  n  out5.dat  tt  tt  0.5145  2.1  M  0.5796  2.4  14.2  H  0.6538  2.7  15.8  0.7478  1.2  15.0 18.0  4  out6.dat  II  5  out9.dat  n  6  out35.dat  M  7  out31.dat  H  n  0.9130  1.6  8  out32.dat  H  H  1.1533  1.9  19.2  9  out34.dat  tt  tl  1.1238  2.2  17.9  10  out36.dat  it  It  11  out42.dat  Slack Wax  Chrome-plated SS  1.2197  2.6  17.5  II  0.5681  1.2  12.7  It  12  out46.dat  M  0.7493  1.6  14.5  13  out47.dat  H  tt  0.7438  1.6  14.4  14  out43.dat  II  H  0.9248  2.0  15.8  15  out44.dat  tt  II  1.1182  2.4  17.3  16  out45.dat  tt  tl  1.2108  2.6  18.4  17  out50.dat  tt  0.8802  16.3  out49.dat  H  H  0.9074  1.2 1.6  out51.dat  It  H  1.3004  2.0  19.1  20  out52.dat  II  It  1.3680  2.3  19.7  21  out53.dat  tt  II  1.6324  2.6  21.2  22  out58.dat  tl  0.7842  1.2  18.8  23  out57.dat  n  n  0.7936  1.6  18.6  M  1.2069  2.0  21.3  1.4296  2.3  22.2  18 19  Sand-blasted SS  n-C18 silane chrome-plated SS  16.9  24  out59.dat  it  25  out60.dat  tt  n  26  out61.dat  tt  II  1.0777  2.6  23.5  27  out66.dat  H  0.9458  1.2  22.1  28  out65.dat  tt  tl  1.0973  1.6  21.9  out67.dat  H  tt  1.3992  2.0  24.8  30  out68.dat  II  H  1.5088  2.3  26.0  31  out69.dat  tt  n  1.5120  2.5  26.7  29  Heresite Si 57 E S S  107  Run. No.  Disk No.  Tube Type  U„(kW/m K)  u(m/s)  T„(°C)  tl  0.7841  1.2  20.5  Wax Type  32  out71.dat  33  out70.dat  ll  tt  1.0745  1.6  22.3  out75.dat  II  tt  1.1595  1.6  23.5  out72.dat  tl  tt  1.1701  2.0  24.7  36  out73.dat  tt  II  1.2517  2.3  25.5  37  out74.dat  It  II  1.2651  2.6  22.8  38  out77.dat  II  1.2  18.7  39  out76.dat  II  ll  0.8673 1.0150  1.6  20.3  40  out78.dat  ll  tt  1.2427  2.0  21.4  out79.dat  II  tt  1.3433  2.2  22.2  42  out80.dat  II  II  1.4645  2.5  22.8  43  outl0.dat  SS  0.3485  1.6  10.8  44 Same as run 2  outl5.dat  II  M  0.5082  1.6  13.3  45  outll.dat  ll  n  0.5261  1.6  14.9  46  outl2.dat  tl  n  0.5926  1.6  16.5  47  outl4.dat  It  II  0.6975  1.6  18.7  48  out40.dat  It  0.7123  1.6  11.9  49 Same as run 7  out31.dat  II  •I  0.9130  1.6  12.7  out37.dat  H  tt  1.0341  1.6  19.5  51  out38.dat  II  tt  1.1141  1.6  22.7  52  out39.dat  II  »  1.3886  1.6  24.2  53  out41.dat  tt  tt  1.1767  1.6  24.2  tt  0.7493  1.6  15.4  it  0.8818  1.6  18.7  1.2727  1.6  25.3  n  1.3512  1.6  28.8  n  34 35  41  50  54 Same as run 12 out46.dat  Heresite P-400/L-66 SS  2  n-C18 silane SS  Refined wax  Slack wax  Chrome-plated SS  55  out48.dat  tt  56  out81.dat  it  57  out82.dat  0.9074  1.6  16.9  59  out54.dat  II  it  1.0620  1.6  20.2  60  out55.dat  tl  tt  1.2528  1.6  23.9  out56.dat  ll  tt  1.3476  1.6  26.9  0.7936  1.6  18.6  58 Same as run 18 out49.dat  61  62 Same as run 23 out57.dat  Sand-blasted SS  II  n-C18 silane chrome plated SS  63  out62.dat  it  ti  1.0952  1.6  22.8  it  1.3638  1.6  27.1  tt  1.3564  1.6  31.5  0.5512  1.6  13.6  0.4994  1.6  11.2  64  out63.dat  II  65  out64.dat  II  66  out3.dat  SS  67  out4.dat  II  it  outl6.dat  II  H  0.2944  1.6  11.5  outl8.dat  II  tt  0.1699  1.6  10.4  70  out27.dat  II  1.4638  1.6  16.6  71  out28.dat  tl  tt  1.3223  1.6  16.0  72  out29.dat  tt  tt  1.1979  1.6  15.5  73  out30.dat  tt  M  0.7437  1.6  14.8  68 69  Refined wax  Slack wax  108  Sample Calculations The following sample calculation was done for slack wax M C T - 1 0 at 20 % by using stainless steel. Re = 8722. The calculation has been done at time = 0 and time = 2 min. The file is denoted by Run 7. The reading from the data logger (or as stored in a diskette file) is: V = 0.6195 mv  V , = 0.6585 mv  V = -0.4060 mv V =-0.3485 mv A V = 0.0610 m v V = 1.2145 mv 4  5  The actual voltage is calculated by adding the reference voltage V to V , V , V , , V , 2  3  i.e., V = 1.8340 mv  V , = 1.8730 mv  2  V =-0.8085 mv V=-0.8660 mv A V = 0.0610 mv 4  Using the calibration equations in Appendix B T = 31.52 °C, T = 30.97°C, t,= 13.49°C, t,= 14.45°C, At = 1.02 °C 2  The pipe diameters are: D = 25.400 mm, D, = 9.957 mm, D = 12.446 mm o  The distance between the inlet and outlet of the flow line is = 0.72 m.  Wax-kerosene flow rate : Manual reading from the mercury manometer is Ah = 9 inches Conversion to SI Ah= 0.0253*9 = 0.228 m AP = pg Ah =  1000(13.6-1)9.81.0.228  = 28182.2 Pa The average wax-kerosene temperature for the whole run is T  =31.22°C •v&k  p = 816.25-0.7489T . = 792.9 kg/m  5  C = 0.62  109  A  ==*DV¥=fl0.012V4=0.0001131m  1  or  p = 12/24.84 = 0.4831 V =  CA J  I  2  AP  \p>(l-P ) 4  V= 0.000607 mVs The velocity of wax-kerosene mixture  V  ~  (n/4)(D -D J  U  2  2  = 1.58 m/s  Water flow rate: The Rotameter reading was S = 20 % for all runs. Using the calibration equation H o w Rate (U.S. gal/min.)= 0.275 + 0.05 S + mO"  4  S  2  = 3.78541.IO" (0.275 + 0.05 S + 1 M 0 " 3  V  w  4  S )/60 mVs 2  = 8.296X10 mVs 5  The velocity of water:  v.-  *~  (n/4)D  2  i  =1.1 m/s  Heat gained by water: The bulk temperature of water is t. =-^-±^-=13.97 °C 2 C^=4.21765-3.74987.10- / +1.49921.10 r;-3.35545.10^ 3  t  M  r;+4.27292.10V;-2.30244.10-'V^  = 4.1879 kJ/kg°C _ (999.83952+16.945176f„ -7.98704010''/; -46.17046110^/; +105.5630210^^ - 280.54253.10"// P  "  1 +16.879850. IO" /, 3  110  = 999.37 kg/m  3  = 8.296X10' X999.37X4.1879X1.02 = 0.355 k W A, = rcDL = 0.0225 m  2  A = 7tD L = 0.0282 m o  0  l  The log-mean temperature difference  =17.27°C  = 0.9136 k W / m K J  Overall heat transfer coefficient at time = 2 min.: V = 0.6195 mv V = 0.6585 mv V = -0.4060 mv V = -0.3485 mv AV= 0.0610 mv V= 1.2145 mv 2  3  4  5  The same calculation done above can be used to get the temperature in °C and the results are T =31.26 °C, T =30.74 °C, t =12.63 °C, t =13.46 °C, At=0.89 °C Heat gained by water: (the volume flow rate of water is constant throughout the experiment) p = 999.37 kg/m w  3  C , = 4.1879 kJ/kg°C  a.=Kp.c^t = 0.309 k W Ar = 17.95 °C ta  U =  ®"  = 0.7651 k W / m K J  111  From previous calculation  U„ =0.9130 k W / m ' K The fouling resistance at time = 2 min. is  '  4{u  u,  = 0.2662 m K / k W J  Re of wax-kerosene mixture: The density and viscosity are evaluated at the average bulk temperature T  = 31.22 °C  = 8722  Re of water: The density and viscosity are calculated at the average bulk temperature of water for the run T  =12.27 °C •vg,w  **• = 8648  112  Run 1 Bulk concentration (%) 10.0 Mixture Re 9093. Water Re 18344. Water average Temp.(°C) 9.40 M . average Temp. ( ° C ) 32.59 Q at 0=0 = 0.392 k W w  Time Fouling Res. (m K/kW) (min) 2  Time Fouling Res. (m K/kW) (min] 2  0  0.0000  92  2.2196  1  0.2561  93  2.2265  2  0.4490  94  1.8213  3  95  1.8436  4 5  0.5095 1.1698 1.0993  1.8622 1.7220  6  1.3197  96 97 98  7  1.7163  8  2.6964 2.7093  1.8020  99 100  9  1.5293  101  2.1699  10  1.4995  102  2.2193  11  1.8804  103  2.1997  12  1.9004  104  2.1671  13  1.9441  14  1.0008  105 106  2.1801 2.1807  15  1.9138  107  2.2088  16 17  1.9380  108  2.2391  1.9806  1.7668  18  1.9461 1.9786  109 110  19  2.1562  111  1.7631 1.7781  21  1.6339 1.6053  112 113  1.4500 2.2045  22 23  1.6254  114  2.2153  2.0284  115  1.2036  24  2.0495  116  2.2196  25  1.6500  117  2.1910  26  2.5202  118  2.1954  27  2.0039  119  2.1959  28  2.5703  120  2.2240  29  2.5787  121  1.7874  30  2.5495  122  2.2149  31  2.5776  123  2.2280  32  2.5973  124  1.4745  33  3.2498  125  1.4909  34  3.2347  126  1.8583  35  3.2559  127  1.8827  36 37  3.3044 2.5740  128 129  2.1967 2.7146  38  2.0885  130  2.7328  39  2.6624  131  2.7907  40  2.6575  132  2.2080  41  2.1031  133  2.2149  42  2.1083  134  1.8151  43  2.1537  135  2.1665  44  1.7385  136  2.7750  45  3.3329  137  2.7959  46  2.5744  138  2.2102  20  113  47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91  139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180  2.6195 4.8699 2.6545 2.6185 2.0780 2.6500 2.1272 2.6699 2.1558 2.6970 2.6500 2.6720 2.1410 2.1389 2.6600 2.1293 1.7526 2.0076 2.0315 2.0549 2.1028 2.1328 1.7317 1.7593 1.7630 1.7398 1.1763 1.7618 1.7225 2.1520 2.1486 1.7593 2.1991 1.7630 1.7990 2.1829 2.1850 2.1649 1.7457 2.1770 2.1942 2.1440 2.7092 2.7272 2.7631  R*(mKlkW) 2.1890  6c(min)  1.1865 2.2692 2.3019 1.5156 2.2299 2.2406 2.2582 2.3068 1.8147 2.2670 2.2758 2.2846 2.2430 2.2516 1.8073 2.2867 1.8469 2.2451 2.2015 2.2384 2.2408 1.8319 1.8545 1.5257 2.2670 2.2495 1.8300 2.2802 2.2911 2.2516 1.8241 1.8431 2.3024 1.8488 2.3068 1.8488 1.8317 1.8393 1.8431 2.8925 2.3021 1.8187  Unc(B.D. Crittenden)% 8.88  13.65  114  Run 2 Bulk concentration (%) Mixture Re Wate Re Water average Temp.( °C) M . average Temp. ( °C)  10.0 11414. 18807. 10.27 32.38  = 0.451 k W  0.316=0  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0702 1 0.1180 2 0.2458 3 0.4585 4 0.4917 5 0.7193 6 0.8924 7 0.7585 8 0.8923 9 0.7474 10 0.6291 11 0.6341 12 0.7722 13 0.7873 14 0.9312 15 0.7612 16 17 0.9273 0.9392 18 0.7828 19 0.6557 20 0.6611 21 0.7888 22 0.8868 23 0.8828 24 0.8828 25 0.8933 26 0.9132 27 0.9224 28 0.7678 29 0.9330 30 1.1131 31 32 0.9238 0.9290 33 0.9236 34 1.1160 35 0.9251 36 0.9317 37 0.9383 38 0.9408 39 0.9487 40 0.9566 41 0.9700 42 0.9737 43 0.8253 44 0.8254 45 0.6976 46 2  Time (min] 86 87 88 89 90 . 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132  Fouling Res. (m K/kW) 0.8589 0.8357 1.1355 1.1463 0.9487 0.9581 0.9535 1.1750 0.9875 0.8260 0.9738 0.9809 0.9701 1.1776 0.9755 0.8150 0.9845 0.8332 0.8394 0.8370 0.8491 0.8552 0.8565 0.7214 0.7218 0.8735 0.7307 0.9524 0.9217 1.1200 0.9283 0.7738 0.9511 0.9591 0.9628 0.9722 0.8117 0.8214 0.8274 0.6922 0.8407 0.5873 0.5924 0.8577 0.6017 0.6023 0.6064 2  115  47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85  0.9345 1.1058 1.3505 1.1213 0.9415 0.9308 0.9348 1.1361 0.7887 0.9493 0.9535 0.9588 0.9668 0.8103 0.9872 0.8249 1.0032 0.9832 0.0475 0.8065 0.8101 0.9805 0.8188 0.8541 1.0015 0.8419 0.8346 0.8297 0.9698 0.9631 0.9728 0.9711 0.9791 0.8247 1.0023 0.6969 0.6973 0.8528 0.8528  RArnKlkW)  0.8896  133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 9  C  (min)  5.45  0.6105 0.6146 0.6849 0.9546 0.7923 0.9532 0.9708 0.9788 0.9855 0.9961 0.8359 0.8420 0.8286 1.1296 1.1065 1.3642 0.9200 1.1302 0.9495 0.9588 0.9599 0.6639 0.9742 0.8191 0.8288 0.8348 0.8408 0.8469 0.7155 0.7200 0.8698 0.6109 0.7292 0.7366 0.6201 0.7466 0.7488 0.7522 0.7909 1.1073 1.1141 0.9203 1.1183 0.9388 0.9508 0.9615 0.9708  Unc(BDC)%  30.00  Run 3 Bulk concentration (%) 10.0 Mixture Re 14812. WateRe 18018. Water average Temp.(°C) 8.78 M . average Temp. (°C) 32.58 0 . at G=0 = 0.573 k W Time Fouling Res. (m K/kW) (min) 0.0000 0 0.2802 1 0.3303 2 0.2985 3 0.3851 4 0.3885 5 0.3996 6 0.4047 7 0.4830 8 0.4779 9 0.6905 10 0.6926 11 0.5828 12 0.5892 13 0.5867 14 0.4887 15 0.4875 16 0.5896 17 0.4954 18 0.4973 19 0.5004 20 0.5935 21 22 0.4991 0.4898 23 0.4960 24 0.4153 25 0.4198 26 0.4053 27 0.0922 28 0.4809 29 0.3985 30 0.4827 31 0.4836 32 0.4846 33 34 0.4855 0.4864 35 0.4026 36 37 0.4026 0.1451 38 0.4043 39 0.4878 40 0.4878 41 0.4878 42 0.4896 43 0.3312 44 0.4896 45 0.4955 46 2  Time (min] 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136  Fouling Res (m K/kW) 0.5066 0.5076 0.5085 0.6057 0.4215 0.5135 0.5154 0.6143 0.7328 0.6200 0.6210 0.6220 0.6220 0.6277 0.5209 0.6259 0.6259 0.6259 0.4309 0.6242 0.6242 0.5264 0.6242 0.5264 0.5264 0.6299 0.6249 0.6163 0.6210 0.6200 0.6143 0.6163 0.6200 0.6143 0.6163 0.6163 0.6182 0.6220 0.7370 0.6240 0.6287 0.6297 0.5260 0.6317 0.6317 0.5297 0.6317 2  117  47  0.4924  137  0.6337  48  0.4111  138  0.5330  49  0.4982  139  0.4392  50  0.4084  140  0.4392  51  0.4951  141  0.4355  52  0.3360  142  0.5264  53  0.4026  143  0.4363  54  0.3992  144  0.5223  55  0.4855  145  0.5232  56  0.4846  146  0.4363  57  0.4885  147  0.5264  58  148  0.4363  59  0.5879 0.4904  149  0.5273  60  0.4913  150  0.5283  61  0.5918  151  0.5255  62  0.4922  152  0.5980  63  0.5974  0.5893  64  0.5021  153 154  65  0.2086  155  0.5043  66  156  67  0.5089 0.5089  0.5131 0.5168  68  0.6106  157 158  69  0.5149  159  0.5140  70  0.5158  160  0.5191  71  0.4238  161  0.5167  72  0.5177  162  0.5209  73  0.5126  163  0.4329  74  0.5144  164  0.4337  75  0.4301  165  0.5237  76  0.5144  166  0.5246  77  0.5144  167  0.5246  78  0.4301  168  0.5246  79  0.5154  169  0.5246  80  0.4309  170  0.4392  81  0.4318  171  0.4392  82  0.4318  172  0.1185  83  0.4318  173  0.4372  84  0.4318  174  0.5241  85  0.4249  175  0.4900  86  0.5103  176  0.5167  87  0.4189  177  0.5200  88  0.6037  89  0.5034  R*(m 2K/kW) 0.5122  0c(min) 2.47  0.4951  0.5195  /  Unc(BDC)% 22.48  118  Run 4 10.0 Bulk concentration (%) 17332. Mixture Re 163. Wate Re 9.25 Water average Temp.(°C) 32.71 M . average Temp. ( °C) C^ate^ =0.616 k W  Time Fouling Res. (min) (m K/kW) 2  Time Fouling Res. (min) (m K/kW) 2  0  0.0000  92  0.2833  1  0.0378  93  0.2763  2  0.1421  94  0.3333  3  0.2049  95  0.3333  4  0.1705  0.3348  5  0.2702  96 97  6  0.4420  98  0.2798  7 8  0.4083 0.2998  99  0.3372  9  0.3723  100 101  0.2303 0.3387  10  0.2959  102  0.3387  11  0.5019  103  0.2798  12  0.5100  104  0.3320  13  0.4372  105  0.2745  14  0.5188  106  0.3348  15  0.5379  107  0.3313  16  0.4620  108  0.2236  17  0.5439  109  0.2763  18  0.4653  110  0.2763  19  0.4628  111  0.2738  20  0.4670  112  0.3328  21  0.3412  113  0.2745  22  0.3379  114  0.2727  23  0.4080  115  0.2745  24  0.3452  116  0.2752  25  0.3419  117  0.3342  26  0.4073  118  0.2791  27  0.4653  119  0.2748  28  0.4603  120  0.3385  29  0.5375  121  0.3385  30  0.4553  122  0.2830  31  0.4528  123  0.2830  32  0.4578  124  0.2812  33  0.3899  125  0.2812  34  0.4653  126  0.3420  35  0.3333  127  0.2851  36 37  0.4033  128  0.2833  0.2862  38  0.4104  129 130  0.2802 0.3303  0.2777  39  0.4127  131  0.2703  40  0.3526  132  0.3266  41  0.4017  0.2685  42  0.4696  133 134  43  0.2203  135  0.2706  44  0.3994  136  0.3283  45  0.4779  137  0.2720  46  0.4080  138  0.2717  0.3253  119  47  0.4150  139  0.2749  48  0.4662  140  0.2749  49  0.4621  141  0.3313  50  0.4688  142  0.2738  51  0.4739  143  0.2720  52 53 54  0.3414 0.4102 0.4149  144 145 146  0.2220 0.2727 0.2713  55  0.4204  147  0.2727  56  0.3571  148  0.0896  57 58 59  0.3039  149  0.3981 0.4622  150 151  0.1756 0.3322 0.2791  60  0.5462  152  0.2805  61  0.4672  153  0.1784  62  0.4007  154  0.2812  63  0.3386  155  0.2830  64  0.3459  156  0.2837  65  0.4172  157  0.2819  66  0.3520  158  67  0.3537  159  0.2819 0.2320  68  0.4205  160  0.2855  69  0.2912  161  0.2844  70  0.2884  162  0.2826  71  0.3412 0.3388  163 164  0.2320  0.3338  165  0.2869 0.2310  74  0.3984  166  0.2303  75  0.3284  167  0.2303  76  168 169  0.2320  77  0.3289 0.3252  78  0.3194  170  0.2819  79  0.3826  171  0.2303  80  0.4520  172  0.2303  81  0.3154  173  0.2819  82  0.3778  174  0.2801  83  0.3787  175  0.2801  84  0.3857  176  0.2819  85  0.3889  177  0.2826  86  0.3284  178  0.1796  87  0.3915  179  0.2819  88  0.3318  180  0.2819  89  0.3340  90  0.2777  91  0.2805  72 73  RArnKlkW) 0.3363  9 (min) C  2.55  0.2320  Unc(BDC)% 27.50  120  Run 5 Bulk concentration (%) 10.0 Mixture Re 19053. Water Re 18590. Water average Temp.(°C) 9.86 M . average Temp. ( ° C ) 32.68 Q„ at 6=0 = 0.733 k W Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0811 1 0.1272 2 0.1364 3 0.2118 4 0.1804 5 0.2206 6 0.2206 7 0.2596 8 0.3025 9 0.2996 10 0.2523 11 0.2563 12 0.2591 13 0.2576 14 0.2589 15 0.2137 16 17 0.2163 0.2150 18 0.1768 19 0.1750 20 0.2561 21 0.2562 22 0.2137 23 0.2137 24 0.2588 25 0.2162 26 0.2162 27 0.2175 28 0.1762 29 0.2143 30 0.2174 31 0.2174 32 0.2131 33 0.2517 34 0.1301 35 0.2982 36 0.2075 37 0.3001 38 0.3015 39 0.3028 40 0.3035 41 0.3582 42 0.3085 43 0.3610 44 0.1402 45 0.2522 46 2  Time Fouling Res. (min) (m K/kW) 0.2094 . 90 0.2087 91 0.2119 92 0.1733 93 0.2575 94 0.2150 95 0.1750 96 0.1396 97 0.1762 98 0.2193 99 0.2180 100 0.2206 101 0.2193 102 0.2618 103 104 0.2205 0.0788 105 0.2645 106 0.1827 107 0.2057 108 0.1608 109 0.2014 110 0.2452 111 0.2912 112 0.2082 113 0.2524 114 0.3025 115 0.2106 116 0.2556 117 0.0744 118 0.2169 119 120 0.2131 0.2181 121 0.2130 122 0.2162 123 0.2634 124 0.2219 125 0.2225 126 0.2212 127 0.2224 128 0.0532 129 0.2250 130 0.2256 131 0.2230 132 0.1768 133 0.1709 134 0.2094 . 135 0.2094 136 2  121  47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173  0.2025 0.2450 0.2456 0.2462 0.2088 0.2113 0.2556 0.2150 0.2595 0.2188 0.2493 0.2375 0.2408 0.2064 0.2565 0.2943 0.2454 0.2454 0.2945 0.2966 0.2948 0.2491 0.2524 0.2536 0.2549 0.0705 0.2554 0.3064 0.2156 0.2553 0.2137 0.3060 0.3060 0.2613 0.2994 0.2885 0.3380 0.3380 0.2885 0.2045 0.2051 0.2057 0.2075  R(rnKlkW) 0.2249  0  C  (min) 2.12  0.1709 0.2119 0.2131 0.1697 0.1709 0.2093 0.2087 0.1697 0.2106 0.2118 0.2093 0.1709 0.2118 0.2149 0.2149 0.1757 0.1397 0.1762 0.2167 0.1774 0.1757 0.1763 0.1774 0.1751 0.1727 0.1727 0.2062 0.2043 0.2474 0.2487 0.2068 0.2068 0.2486 0.2080 0.1709 0.2105 0.2118  Unc(BDC)% 27.91  122  Run  6  Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C) Q  w  at 9=0  20.0 6645. 7906. 9.10 31.87  = 0.347 k W Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.6206 0.5618 4 6 0.6027 0.6083 8 10 0.6315 12 0.6615 14 0.6996 16 0.7194 0.7600 18 0.8083 20 22 0.7979 0.7704 24 26 0.7954 28 0.8345 30 0.8074 0.7936 32 34 0.7951 36 0.8917 0.7753 38 40 0.8054 0.9212 42 44 0.8882 0.9136 46 0.8240 48 0.8682 50 52 0.9680 0.9999 54 0.9219 56 58 0.9233 0.7557 60 0.8967 62 64 0.9561 66 0.9302 68 0.9664 70 0.9679 0.9876 72 0.9640 74 76 1.0092 78 0.9271 0.8981 80 82 0.9153 1.0198 84 2  RAtnKlkW) 0.9293  0 (min) C  8.02  Fouling Res. (m K/kW) 0.9223 0.9899 0.9834 0.9727 0.6458 1.0091 1.0020 1.0616 1.0275 1.0238 1.0120 1.0560 0.9215 0.9065 0.9992 0.8623 0.9879 0.6927 0.9944 0.9915 1.0207 1.0351 1.1040 1.0518 1.0292 1.0035 0.9117 0.7287 0.7957 0.8974 1.0092 1.0183 1.0111 2  Unc(BDC)% 11.94  123  Run 7 Bulk concentration (%) 20.0 Mixture Re 8722. Water Re 8648. Water average Temp.( °C) 12.27 M . average Temp. ( °C) 31.22 CLate=0 = 0.355 k W Time Fouling Res (min) (m K/kW) 86 0.8185 88 0.8731 0.8564 90 0.8849 92 94 0.8912 0.8568 96 0.8316 98 0.6608 100 0.6642 102 0.7943 104 0.8302 106 0.8464 108 110 0.8203 0.8778 112 114 0.7902 0.8602 116 0.8188 118 0.9036 120 122 0.7931 0.8251 124 0.7703 126 0.7856 128 130 0.9006 0.7397 132 134 0.8636 136 0.7902 138 0.8840 140 0.8399 142 0.8006 144 0.8020 146 0.8418 0.8248 148 150 0.8127  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.2683 4 0.5102 6 0.5203 0.5012 8 10 0.5061 0.5413 12 0.5649 14 16 0.5765 0.6564 18 0.6415 20 0.6015 22 24 0.6428 0.6916 26 0.7168 28 30 0.7059 0.7482 32 0.7691 34 36 0.7675 38 0.7414 40 0.7848 0.7731 42 44 0.8001 0.7427 46 0.8363 48 0.8114 50 52 0.7789 54 0.8166 56 0.8027 58 0.8455 60 0.8916 0.8900 62 64 0.8244 66 0.7896 0.8275 68 70 0.8531 72 0.8475 0.9177 74 76 0.9368 0.9232 78 80 0.8615 0.9121 82 84 0.8311  2  2  R*(m 2K/kW) 0.8244  0c(min) 10.77  Unc(BDC)% 11.39  124  Run 8 Bulk concentration (%) 20.0 Mixture Re 10615. Water Re 8706. Water average Temp.( °C) 12.51 M . average Temp. ( ° C ) 31.30 Q,, at 0=0 = 0.444 k W Time Fouling Res. (m K/kW) (min) 86 0.7276 0.7053 88 90 0.7644 0.7974 92 0.7656 94 0.7538 96 0.7409 98 0.6855 100 0.8194 102 104 0.6910 106 0.7536 0.7737 108 0.7427 110 0.7779 112 114 0.7826 0.8416 116 0.7699 118 120 0.8853 0.8177 122 124 0.8813 0.8489 126 0.7773 128 130 0.7905 0.6784 132 134 0.8399 0.8374 136 0.8671 138 0.7980 140 0.8168 142 0.8661 144 0.8107 146 148 0.7857 150 0.8621  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.3622 2 4 0.3402 0.4229 6 0.4533 8 10 0.4669 12 0.4660 14 0.5202 16 0.5122 0.5441 18 20 0.5389 0.5847 22 24 0.5713 0.6170 26 0.6622 28 30 0.6939 0.6761 32 34 0.6962 0.7142 36 38 0.7306 0.7396 40 42 0.7772 44 0.7681 46 0.7638 48 0.7780 0.7570 50 52 0.8583 0.7938 54 56 0.7371 0.7844 58 60 0.8673 62 0.7821 64 0.8639 0.8574 66 0.8135 68 70 0.7955 0.8086 72 74 0.7935 76 0.7982 78 0.8489 80 0.7953 82 0.7579 84 0.8065  2  2  RArnKlkW) 0.7926  0 (min) C  13.21  Unc(BDC)% 8.89  125  Run 9 Bulk concentration (%) 20.0 Mixture Re 12184. Water Re 8103. Water average Temp.( °C) 9.96 M . average Temp. ( °C) 31.16 Q , at 9=0 =0.452 k W Time Fouling Res. (m K/kW) (min) 0.7645 86 0.6151 88 90 0.7091 0.7571 92 0.7543 94 0.6615 96 0.7036 98 100 0.7130 0.8062 102 0.6967 104 0.7254 106 0.6530 108 0.7117 110 0.7282 112 0.6691 114 0.6092 116 118 0.6729 0.6777 120 0.8016 122 0.8154 124 0.7269 126 0.7825 128 0.6676 130 0.8419 132 0.8974 134 136 0.8715 0.8241 138 0.7821 140 142 0.6475 0.6871 144 0.6108 146 148 0.6477 0.6675 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.2961 0.3281 4 0.3394 6 0.3789 8 0.4138 10 0.4301 12 0.3866 14 0.4198 16 0.4952 18 0.4904 20 22 0.4573 0.4944 24 0.5156 26 0.5462 28 0.5387 30 0.5473 32 34 0.5322 0.6014 36 0.5208 38 0.5463 40 0.6192 42 0.6017 44 0.5673 46 0.5809 48 0.6561 50 0.7042 52 0.7044 54 56 0.6295 58 0.8028 0.7300 60 0.7062 62 0.7040 64 0.7196 66 0.7406 68 0.7245 70 0.7072 72 0.7084 74 0.8759 76 0.7100 78 0.7372 80 0.7063 82 84 0.8423  2  2  R*{rnKlkW) 0.7244  6  C  (min) 18.09  Unc(BDC)% 9.21  126  Run 10 Bulk concentration (%)  20.0  Mixture Re  14430.  Water Re  7685.  Water average Temp.( °C)  8.13  M . average Temp. ( ° C ) Q at9=0  31.33  = 0.522 k W  w  Time  Fouling Res.  (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  (m K/kW) 0.0000 0.2904 0.3469 0.3856 0.4020 0.4830 0.4874 0.5071 0.4671 0.4984 0.5450 0.5138 0.5417 0.5061 0.5575 0.5260 0.5842 0.5421 0.5895 0.6010 0.5933 0.6780 0.6367 0.7312 0.6619 0.7166 0.6726 0.6908 0.6541 0.7259 0.6696 0.6582 0.6485 0.6888 0.6457 0.7713 0.7068 0.6666 0.7547 0.6655 0.7676 0.8343 0.6846  Time (min)  2  RArnKlkW) 0.6668  86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  B  c  (min) 10.34  Fouling Res. (m K/kW) 0.6502 0.6458 0.7001 0.6940 0.6075 0.7266 0.7221 0.6833 0.7064 0.7650 0.7171 0.5147 0.7602 0.6587 0.6025 0.6262 0.6907 0.6608 0.6662 0.5923 0.6947 0.6763 0.5609 0.6550 0.7447 0.6772 0.5808 0.7250 0.6024 0.4911 0.6404 0.7185 0.7072 2  Unc(BDC)% 7.99  127  Run 11 Bulk concentration (%)  20.0  Mixture Re Water Re  6586. 7474.  Water average Temp.( °C) M . average Temp. ( °C)  7.20 31.32  = 0.289 k W  Q.ate-0  Time Fouling Res. (min] (m K/kW)  Time Fouling Res. (min) (m K/kW)  2  2  86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  0.0000 0.5410 0.7250 0.7019 0.7522 0.7626 0.8757 0.8910 0.8524 0.9283 0.8100 0.9110 0.8191 0.9388 0.8597 0.9759 0.7736 1.2896 1.0417 1.0816 1.0629 0.9107 1.0762 0.9751 1.0087 0.7359 0.8249 0.8263 0.8642 0.8966 0.7726 0.8906 0.7511 0.8640 0.8780 0.8612 0.7999 0.8208 0.9067 0.9050 0.8747 0.7554 0.7042  0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  R*(m K/kW) 2  0.8238  0 (min) c  2.07  0.6666 0.5462 0.6401 0.8349 0.7242 0.6603 0.6826 0.5674 0.7945 0.6493 0.7654 0.7626 0.6971 0.8677 0.7664 0.6399 0.6799 0.7637 0.7706 0.7877 0.8238 0.7476 0.7984 0.6544 0.9873 0.7909 0.8075 0.8315 0.8869 0.7237 0.9006 0.7026 0.8685  Unc(BDC)%  17.80  128  Run 12 Bulk concentration (%)  20.0  Mixture Re  9224.  Water Re  7511.  Water average Temp.( °C)  7.36  M . average Temp. ( ° C ) CL at 8=0  31.34  = 0.338 kw  Time  Fouling Res.  (min)  (m K/kW)  Time  Fouling Res.  (min)  2  (m  2  0  0.0000  86  0.5615  2  0.4187  88  0.6161  4  0.5065  90  0.5854  6  0.4510  92  0.4546  8  0.6059  94  0.6359  10  0.6654  96  0.5154  12  0.626  98  0.6135  14  0.6019  100  0.6116  16 18  0.6172 0.6124  102 104  0.2521 0.5746  20  0.7411 0.6628  106 108  0.5373 0.7396  22 24  0.7318  110  0.5611  26  0.6682  112  0.7292  28  0.7473  114  0.4921  30  0.7076  116  0.5552  32  0.7562  118  0.6752  34  0.6447  120  0.6174  36  0.6787  122  0.554  38  0.7263  124  0.6421  40  0.6761  126  0.5323  42  0.6775  128  0.375  44  130  0.5585  46  0.567 0.717  132  0.4836  48  0.6105  134  0.4985  50  0.6263  136  0.555  52  0.6126  138  0.609  54  0.5844  140  0.541  56  0.6503  142  0.6394  58  0.5699  144  0.6152  60  0.5778  146  0.656  62  0.4968  148  0.5153  64  0.7304  150  0.6409  66  0.5732  68  0.603  70  0.588  72  0.6293  74  0.593  76  0.5247  78  0.4529  80  0.6818  82  0.542  84  0.6733 RAtnKlkW) 0.6031  0  C  (min) 2.08  K/kW)  Unc(BDC)% 15.14  129  Run 13 Bulk concentration (%) 20.0 Mixture Re 9208. Water Re 7494. Water average Temp.( °C) 7.29 M . average Temp. ( ° C ) 31.24 Q at 6=0 = 0.374 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (m K/kW) (min) 0.0000 0 2 0.3749 4 0.4131 6 0.5793 8 0.5843 10 0.6339 0.6817 12 14 0.7225 0.5321 16 18 0.5747 20 0.5302 0.5697 22 0.5760 24 26 0.5855 28 0.6781 30 0.5665 0.5674 32 34 0.6315 0.7590 36 0.5830 38 40 0.6367 0.5829 42 44 0.6127 46 0.5546 48 0.6185 0.6706 50 0.6307 52 0.5816 54 0.6495 56 0.4924 58 0.6267 60 0.6174 62 64 0.6039 66 0.6357 0.3178 68 0.5383 70 0.5348 72 0.5981 74 0.4994 76 0.5318 78 0.4934 80 0.5998 82 0.4869 84 2  R*(jnKlkW) 0.5814  0  C  (min) 2.16  Fouling Res. (m K/kW) 0.5837 0.6151 0.5309 0.5945 0.6114 0.5698 0.6064 0.5282 0.6010 0.6335 0.5921 0.6368 0.5529 0.4512 0.5692 0.5977 0.6182 0.5516 0.5392 0.6182 0.6030 0.5362 0.5429 0.5897 0.5975 0.5527 0.5737 0.5624 0.6163 0.5891 0.4776 0.5409 0.5798 2  Unc(BDC)% 15.55  130  Run 14 (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) Q . at 9=0  20.0 11015. 7597. 7.75 31.29  = 0.408 K W Time (min) 86 88 90 92 94 96 98 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.4471 2 4 0.6013 6 0.5177 8 0.4849 0.5546 10 12 0.5935 0.5710 14 18 0.5879 0.5688 20 0.6027 22 24 0.5674 26 0.6972 0.5253 28 0.5863 30 0.6373 32 34 0.6078 36 0.6341 0.6015 38 0.5583 40 0.6162 42 44 0.5351 0.6144 46 0.6335 48 50 0.6388 52 0.6033 54 0.5911 0.5709 56 58 0.6201 0.5980 60 0.6306 62 0.5935 64 0.6144 66 0.5792 68 70 0.6221 0.6424 72 74 0.6280 76 0.5864 0.5953 78 0.6074 80 82 0.5900 0.5210 84 2  R (rnKlkW) f  0.5941  0  C  (min) 1.42  Fouling Res. (m K/kW) 0.5774 0.6229 0.6407 0.5105 0.4801 0.6043 0.6308 0.5923 0.5966 0.5956 0.5803 0.5952 0.5337 0.6103 0.6258 0.6138 0.6229 0.5866 0.6180 0.5701 0.5425 0.5816 0.5613 0.5863 0.6186 0.6215 0.5921 0.6362 0.5965 0.7184 0.5892 0.5741 2  Unc(BDC)% 11.59  131  Run IS Bulk concentration (%) Mixture Re Water Re Water average Temp.(°C) M . average Temp. (°C) CL at 9=0  20.0 13156. 7604. 7.78 31.25  = 0.482 k W  Time Fouling Res. (min) (m K/kW) 0.5628 86 0.4769 88 0.5180 90 0.5022 92 0.5577 94 0.5611 96 0.5824 98 0.5643 100 0.5359 102 0.5881 104 0.4950 106 0.5644 108 0.5487 110 0.4830 112 0.5322 114 0.5775 116 0.4866 118 0.5415 120 0.5357 122 0.5348 124 0.4840 126 0.5614 128 0.5020 130 0.5532 132 134 0.5141 0.5659 136 0.8016 138 0.5908 140 0.5197 142 144 • 0.5004 0.4877 146 0.5000 148 0.5000 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.4232 2 4 0.4887 6 0.4618 0.4186 8 0.5109 10 0.4778 12 0.5208 14 16 0.4983 18 0.5635 20 0.5223 22 0.5258 24 0.3444 0.5101 26 0.5133 28 0.5039 30 0.5487 32 0.5187 34 0.5389 36 38 0.3859 40 0.5103 42 0.4830 0.5070 44 0.4984 46 0.5314 48 0.5600 50 0.5597 52 54 0.4613 56 0.5275 0.5393 58 0.4729 60 0.5418 62 0.5629 64 0.4839 66 68 0.5554 0.5146 70 0.5189 72 0.5128 74 0.5367 76 0.5254 78 0.5317 80 0.5308 82 0.5808 84  2  2  RAtnKlkW) 0.5240  6  C  (min) 1.34  Unc(BDC)% 9.80  132  R u n 16 Bulk concentration (%)  20.0  Mixture Re  14428.  Water Re  7700.  Water average Temp. ( ° C )  8.20  M . average Temp. ( ° C ) Q„ate=o  31.32  = 0.545 k W  Time  Fouling Res.  (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  (m K/kW) 0.0000 0.3175 0.2162 0.2603 0.3090 0.3691 0.3410 0.4723 0.4813 0.3504 0.5087 0.4509 0.4370 0.4795 0.4725 0.4483 0.5029 0.5026 0.5190 0.4649 0.4882 0.5187 0.5075 0.5192 0.5110 0.4655 0.4161 0.4533 0.5491 0.4987 0.5640 0.4699 0.4217 0.4737 0.5695  Time (min)  2  86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Fouling Res. (m K/kW) 0.4492 0.4448 0.5544 0.4117 0.5079 0.5171 0.4658 0.4923 0.4581 0.4694 0.4457 0.6174 0.5133 0.5298 0.5039 0.2992 0.4705 0.5081 0.4957 0.4627 0.4444 0.4896 0.4997 0.5230 0.5117 2  0.4373 0.6130 0.4738 0.4470 0.4983 0.5126 0.4559 0.5634  0.4992. 0.4871 0.3995 0.4052 0.4979 0.4217 0.4527 0.3335  RArnKlkW) 0.4817  9  C  (min) 6.43  Unc(BDC)% 9.65  133  R u n 17 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C )  20.0 6418. 8417. 11.30  30.99  = 0.276 kW  Q ate=0 w  Time Fouling Res (min) (m K/kW) 1.2402 86 88 1.3519 90 1.3141 92 1.1302 94 1.3962 96 1.2329 1.1463 98 100 1.2379 1.0870 102 1.3661 104 1.1579 106 108 1.2232 1.2276 110 112 1.1293 1.2733 114 116 1.3402 1.3344 118 1.3738 120 1.3768 122 124 1.3925 1.3430 126 128 1.4537 130 1.3039 1.4411 132 1.2064 134 1.1258 136 138 1.2462 1.4278 140 1.2682 142 1.3149 144 1.1974 146 1.2940 148 150 1.3310  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.7368 0.7330 4 6 0.8910 0.8752 8 0.8510 10 1.0074 12 1.0384 14 16 0.9941 18 0.9146 20 1.1254 1.1056 22 24 1.0644 1.0661 26 28 1.1344 1.0454 30 1.2791 32 34 1.2305 1.3763 36 38 1.3749 40 1.2981 42 1.2393 1.2419 44 46 0.9473 1.1412 48 50 1.1599 1.0287 52 1.2030 54 56 0.9810 58 1.1594 1.1379 60 62 1.1208 64 1.1643 1.0404 66 1.0216 68 70 1.1013 1.2017 72 74 1.2250 76 1.3102 1.2291 78 80 1.1832 1.2366 82 1.2001 84 1.2402 86  2  2  RArnKlkW) 1.2187  6  C  (min) 5.88  Unc(BDC)% 10.14  134  Run 18 Bulk concentration (%) 20.0 Mixture Re 8734. Water Re 8233. Water average Temp.( °C) 10.51 M . average Temp. ( ° C ) 31.30 0^9=0 = 0.361 k W Time Fouling Res. (min) (m K/kW) 0.8754 86 0.8168 88 0.7215 90 0.8259 92 0.7910 94 0.8161 96 0.7642 98 0.7946 100 102 0.7725 0.8036 104 0.6893 106 0.9088 108 0.7963 110 0.8420 112 0.7689 114 0.8214 116 0.8150 118 0.7601 120 0.8495 122 0.7747 124 0.8464 126 0.7769 128 0.7618 130 0.8208 132 0.7945 134 0.8197 136 0.8431 138 0.8644 140 0.7647 142 0.8330 144 0.8170 146 0.9015 148 0.8146 150  Time Fouling Res. (m K/kW) (min) 0.0000 0 0.3787 2 0.4663 4 6 0.5853 0.6480 8 10 0.5519 0.1141 12 0.1540 14 0.7583 16 0.7310 18 20 0.6911 0.8869 22 0.7078 24 0.7691 26 0.8021 28 30 0.8599 0.7385 32 0.8156 34 0.8093 36 0.8024 38 0.7604 40 0.7634 42 0.7914 44 0.7986 46 0.9238 48 0.7672 50 0.8512 52 0.7816 54 0.7844 56 0.8123 58 0.7570 60 0.8492 62 64 0.6426 0.9419 66 0.8492 68 0.7762 70 0.8103 72 0.8023 74 0.7619 76 0.7674 78 0.7397 80 0.7390 82 0.7510 84  2  2  R*(m 2K/kW) 0.8027  0  C  (min) 9.30  Unc(BDC)% 11.66  135  Run 19 Bulk concentration (%)  20.0  Mixture Re  11340.  Water Re  8463.  Water average Temp.( °C)  11.49  M . average Temp. (°C)  31.37  at 9=0  = 0.460 k W  Time  Fouling Res.  (min)  (m K/kW)  Time (min)  2  Fouling Res. (m  2  0.7974  2  0.0000 0.4138  86 88  4  0.4247  90  0.7428  6  0.4603  92  0.8092  8 10  0.5597 0.5687  94 96  0.6901 1.3474  12 14  0.5327  98  0.7553  0.1459  100  0.7389  16  0.6147  102  0.8125  18  0.6568  104  0.7639  20  0.7093  106  0.7057  22  0.6795  108  0.7615  24  0.6662  110  0.7554  26  0.6920  28 30  0.7538  112 114  0.7765 0.7667  0.7659 0.7419  116 118  0.7256 0.7423  0.7604 0.7188  120  0.7271  36  122  0.7736  38  0.7654  124  0.7689  40  0.7286  126  0.8019  42  0.7363  128  0.8033  44  0.7129  130  0.7701  46  0.7530  132  0.6996  48  0.7347  134  0.7849  50  0.7397  136  0.8425  52  0.7106  138  0.7676  54  0.6776  140  0.7623  56  0.7054  142  0.8045  58  0.7442  144  0.8237  60  0.6191  146  0.8181  62  0.7101  148  0.7903  64  0.7367  150  0.7671  66  0.7466  68  0.7615  70  0.7799  72  0.7699  74  0.7203  76  0.7386  78  0.7292  80  0.7674  82  0.7391  84  0.7650  0  32 34  R*(m K/kW) 2  0.7614  0 (min) c  8.89  K/kW)  0.7292  Unc(BDC)% 7.62  136  Run 20 Bulk concentration (%)  20.0  Mixture Re  12732.  Water Re  8461.  Water average Temp.( ° C )  11.48  M . average Temp. ( ° C )  31.13  at 9=0  = 0.468 k W  Time  Fouling Res.  (min)  (m K/kW)  Time  Fouling Res.  (min)  0  0.0000  86  (m K/kW) 0.6607  2  0.3060  88  0.6788  4  0.3350  90  0.7044  6  92  0.6717  8  0.4359 0.4320  94  0.6544  10  0.5048  96  0.6621  12  0.5429  98  0.6821  14  0.5226  100  0.6602  16  0.5211  102  0.7283  18  0.5960  104  0.7050  20  0.5242  106  0.7214  22 24  0.5560  108 110  0.7106  112  0.7013  2  2  0.7261  26  0.5911 0.5788  28  0.5486  114  0.7418  30  0.5905  116  0.7292  32  0.5880  118  0.7295  34  120  0.7072  36 38  0.6159 0.6108 0.6572  122 124  0.7076 0.7130  40  0.6093  126  0.7294  42  0.6210  128  0.6908  44  0.6085  130  0.7082  46  0.6161  48  0.6009  50  0.6292  52  0.6167  54  0.6410  56  0.5716  58  0.6343  60  0.6128  62  0.6477  64  0.6568  66  0.6727  68  0.6746  70  0.6612  72  0.6711  74  0.6838  76  0.6678  78  0.6327  80  0.7181  82  0.6630  84  0.6379  R*(m K/kW) 2  0.6609  0  C  (min) 7.61  Unc(BDC)% 7.72  137  R u n 21  20.0 Bulk concentration (%) 14440. Mixture Re 8579. Water Re 11.98 Water average Temp.( °C) 31.37 M . average Temp. (°C) CL at 6=0 = 0.480 kW Time Fouling Res. (min) (m K/kW) 86 0.6279 88 0.6302 0.6304 90 0.5727 92 94 0.6231 96 0.6121 0.6188 98 0.5815 100 0.5792 102 0.6043 104 0.6196 106 0.6050 108 0.6176 110 0.6053 112 0.6267 114 0.6512 116 0.5680 118 0.6291 120 0.6381 122 0.6352 124 0.6120 126 0.6247 128 0.6354 130 132 0.6151 0.5984 134 136 0.6362 138 0.6181 0.6432 140 0.6248 142 0.6253 144 0.6165 146 0.6421 148 0.4387 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.2516 2 4 0.3352 0.3122 6 0.4343 8 0.4739 10 0.5145 12 0.5060 14 0.4963 16 0.4205 18 20 0.5125 0.5629 22 0.5389 24 0.5185 26 0.5544 28 30 0.5590 0.5756 32 0.5626 34 0.5852 36 38 0.5809 0.5638 40 0.5334 42 0.5942 44 0.6179 46 0.5605 48 0.5986 50 0.6209 52 0.5998 54 0.6222 56 0.5929 58 0.5689 60 0.5909 62 0.6047 64 0.6143 66 0.6024 68 70 0.6255 0.6325 72 0.6131 74 0.6130 76 0.6116 78 0.6197 80 0.6149 82 84 0.6039  2  2  R*(m 2K/kW)  0.6016  0c.(min) 7.33  Unc(BDC)% 6.70  138  R u n 22 Bulk concentration (%)  20.0  Mixture Re  6629.  WateRe  9019.  Water average Temp.( °C)  13.81  M . average Temp. ( ° C )  31.42  Q  w  at G=0  = 0.282 k W  Time  Fouling Res.  (min)  (m K/kW) 0.0000  0  Time (min)  2  Fouling Res. (m  2  86  0.8029  2  0.3475  88  0.8473  4  0.4359  90  0.8697  6  0.4613  92  0.8291  8  0.5619  94  0.7654  10  0.4985  96  0.6451  12 14 16  0.5420  0.7441  18  0.6134  98 100 102 104  20  0.5258  106  0.6940  22  0.6899  108  0.8370  24 26  0.6498 0.6650  110 112  0.5948 0.7193  28  0.7290  114  0.8528  30  0.6137  116  0.7679  32  0.6037  118  0.8709  34  0.6145  120  0.8273  36  0.7101  122  0.4462  38  0.4537  124  0.7520  40  0.7457  126  0.6709  42  0.7144  128  0.8355  44  0.7132  130  0.7767  46  0.7170  132  0.7902  48  0.7436  134  0.7608  50  0.7115  136  0.7526  52  0.7864  138  0.6345  54  0.7999  140  0.9283  56  0.7107  142  0.8609  58  0.7439  144  0.6751  60  0.6635  146  0.8218  62  0.7380  148  0.9892  64  0.7806  150  0.8494  66  0.7191  68  0.7170  70  0.7972  72  0.4289  74  0.6391  76  0.7570  78  0.7506  80  0.8206  82  0.5838  0.5340 0.6696  K/kW)  0.7655 0.9005 0.8554  0.7768  84  R*(m K/kW) 2  0.7407  0  C  (min) 7.92  Unc(BDC)% 15.93  139  Run  23  Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. (°C) CL at 9=0  20.0 8773. 8702. 12.50 31.50  = 0.303 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.0885 4 0.1721 -0.0591 6 0.1744 8 0.2343 10 0.2563 12 0.3249 14 16 0.346 0.3496 18 20 0.3378 0.3127 22 24 0.2665 0.3982 26 28 0.3211 30 0.4268 0.4101 32 0.3557 34 0.3891 36 38 0.3582 0.3950 40 0.3565 42 0.4294 44 46 0.2981 0.3850 48 50 0.3700 0.4694 52 0.4469 54 0.4760 56 0.4587 58 0.3946 60 0.4883 62 0.4790 64 66 0.3721 0.4675 68 0.4489 70 0.4065 72 0.4603 74 0.4124 76 0.4672 78 0.4788 80 0.5168 82 0.5301 84 2  RArnKlkW) 0.4854  d  c  (min) 20.86  Fouling Res. (m K/kW) 0.5665 0.6014 0.4520 0.3084 0.2458 0.3591 0.4825 0.6111 0.5565 0.5664 0.5606 0.6091 0.4572 0.4509 0.4914 0.4907 0.4367 0.5132 0.5873 0.5410 0.4272 0.5838 0.5334 0.3656 0.4837 0.4990 0.4936 0.5371 0.4832 2  Unc(BDC)% 19.35  140  Run 24 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. (°C) C^ate^ = 0.399 k W  20.0 11314. 8977. 13.64 31.35  Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.2395 0.2759 4 6 0.3030 8 0.4661 10 0.4087 0.4034 12 0.4062 14 16 0.4090 18 0.4370 0.4194 20 0.3993 22 0.4055 24 26 0.4781 0.5589 28 30 0.4325 0.4744 32 0.4220 34 0.4304 36 0.4499 38 0.5307 40 0.5546 42 44 0.4563 0.4258 46 0.5152 48 50 0.4264 52 0.4339 0.4542 54 0.4963 56 0.4915 58 0.4565 60 0.4015 62 64 0.4556 66 0.3870 68 0.2969 70 0.4124 0.5105 72 74 0.4991 0.4358 76 78 0.5222 80 0.4549 0.5597 82 0.4852 84 2  R (inKlkW) f  0.4605  Bjmin) 4.15  Fouling Res. (m K/kW) 0.5180 0.5359 0.4130 0.4436 0.4452 0.4685 0.5383 0.3881 0.5179 0.4572 0.4719 0.4902 0.5823 0.3661 0.5608 0.5146 0.4405 0.4618 0.4663 0.4182 0.4085 0.4678 0.3637 0.4812 0.4402 0.4199 0.3997 0.5000 0.4945 0.4410 0.4710 0.4751 0.4817 2  Unc(BDC)% 11.53  141  R u n 25 Bulk concentration (%) Mixture Re Water Re Water average Temp.(°C) M . average Temp. ( °C)  = 0.416 kW  CLate=0 Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  20.0 12888. 9002. 13.74 31.26  Fouling Res. (m K/kW) 0.0000 0.1549 0.2589 0.2994 0.2940 0.3517 0.3774 0.4316 0.4250 0.4083 0.3889 0.4550 0.4195 0.4930 0.4602 0.4213 0.4011 0.3859 0.4377 0.3596 0.4759 0.4697 0.5196 0.4235 0.5875 0.4055 0.4323 0.5151 0.4692 0.4261 0.4875 0.4693 0.4531 0.4509 0.4809 0.4484 0.4558 0.4294 0.4528 0.4458 0.5065 0.3811 0.5052  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138  2  R (rnKlkW) f  0.4572  ft. (min) 6.26  Fouling Res. (m K/kW) 0.4681 0.3878 0.4120 0.4384 0.4294 0.3457 0.5222 0.4540 0.4972 0.4912 0.4312 0.4634 0.4573 0.4854 0.4000 0.4633 0.5296 0.4628 0.5393 0.4480 0.4414 0.5350 0.4326 0.4878 0.4567 0.5205 0.4562 2  Unc(BDC)% 9.55  142  R u n 26 Bulk concentration (%) 20.0 Mixture Re 14642. Water Re 9110. Water average Temp.( °C) 14.18 M . average Temp. ( ° C ) 31.16 Q at 6=0 = 0.503 k W Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.1749 2 4 0.2096 0.3161 6 0.2949 8 0.2939 10 0.3332 12 0.2969 14 0.3141 16 0.2755 18 0.3764 20 0.3843 22 0.3470 24 0.3352 26 0.3486 28 30 0.3475 0.4023 32 0.4034 34 0.3453 36 0.3354 38 0.4880 40 0.4001 42 0.4169 44 0.4564 46 0.4010 48 0.3958 50 0.4505 52 0.4290 54 0.3577 56 0.3714 58 0.4295 60 0.4532 62 0.4431 64 0.4784 66 0.4621 68 0.4573 70 0.4158 72 0.4498 74 0.5476 76 0.4339 78 0.4361 80 0.5133 82 0.444 84 2  R*(rnK/kW) 0.4527  0  C  (min) 12.06  Fouling Res. (m K/kW) 0.4064 0.4871 0.4891 0.4446 0.4134 0.4209 0.4675 0.4525 0.4268 0.4674 0.4833 0.4865 0.4206 0.4372 0.3785 0.4024 0.4268 0.5013 0.4463 0.4810 0.5354 0.5561 0.5730 0.4552 0.4757 " 0.4772 0.4829 0.5105 0.5042 0.4790 0.4636 0.5042 0.4620 2  Unc(BDC)% 8.13  143  Run 27 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. (°C) 0. at 9=0 = 0.285 k W  20.0 6567. 9663. 13.43 31.60  Time Fouling Res. (min) (m K/kW) 0.5688 86 0.4979 88 0.5015 90 0.4079 92 0.4826 94 0.5726 96 0.4991 98 0.5525 100 0.5998 102 0.5592 104 0.5905 106 0.2157 108 0.6144 110 0.5718 112 0.7986 114 0.6555 116 0.6347 118 0.4880 120 0.6327 122 124 0.6318 0.6271 126 0.4584 128 0.5523 130 0.4555 132 0.4074 134 0.4433 136 0.3259 138 0.6103 140 0.4764 142 0.6489 144 0.6723 146 0.5493 148 0.6392 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.3162 2 4 0.2911 0.2763 6 0.4337 8 0.3532 10 0.4294 12 14 0.4582 16 0.4719 0.4852 18 0.4930 20 0.5416 22 24 0.5067 0.3515 26 28 0.3272 0.2352 30 0.2214 32 0.2746 34 0.4771 36 0.4645 38 40 0.3953 0.4040 42 0.3430 44 0.2590 46 0.2498 48 50 0.2051 0.1610 52 54 0.0506 56 0.4549 0.3519 58 0.4025 60 0.3400 62 0.2969 64 66 0.2678 0.1081 68 0.1697 70 0.3982 72 0.4013 74 0.2638 76 78 0.4238 0.4591 80 0.4308 82 0.3974 84  2  2  R*(m 2K/kW) 0.4406  dc (min) 3.15  Unc(BDC)% 20.99  144  R u n 28 Bulk concentration (%)  20.0  Mixture Re  8819.  Water Re  9326.  Water average Temp.( °C)  12.06  M . average Temp. ( ° C )  31.29  Q at0=O  = 0.355 k W  w  Time  Fouling Res.  (min)  (m K/kW)  Time (min)  2  Fouling Res (m  2  0  0.0000  86  0.2688  2  0.1466  88  0.3187  4  0.2167  90  0.1590  6  0.2610  92  0.1523  8  0.2622  94  0.4185  10  0.3151  96  0.3352  12  0.2628  98  0.3660  14  0.5789  100  0.3952  16 18  0.3678 0.5704  102  0.3596  104  0.1952  20  0.4241  106  0.3602  22 24  0.4566 0.4512  108 110  0.3060 0.3830  26  0.4798  112  0.3301  28  114  0.4159  30  0.3267 0.6292  116  0.3541  32  0.4557  118  0.3380  34  0.4727  120  0.3765  36  0.6264  122  0.3769  38  0.4884  124  0.3929  40  0.3597  126  0.3949  42  0.3412  128  0.4155  44  0.4936  130  0.4759  46  0.3842  132  0.3616  48  0.3407  134  0.3872  50  0.3225  136  0.3715  52  138  0.3561  54  0.4763 0.4678  140  0.4266  56  0.4866  58  0.5396  60  0.5069  62  0.4916  64  0.4786  66  0.5044  68  0.2074  70  0.4524  72  0.4342  74  0.4688  76  0.5032  78  0.3991  80  0.4650  82  0.3711  84  0.4859  RArnKlkW) 0.4056  0  C  (min) 4.98  K/kW)  Unc(BDC)% 15.82  145  R u n 29  Bulk concentration (%) 20.0 Mixture Re 11215. Water Re 9760. Water average Temp.( °C) 13.82 M . average Temp. ( °C) 31.23 Q . at 9=0 = 0.407 k W Time FoulingRes. (min) (m K/kW) 0.1203 86 0.1288 88 0.2402 90 0.2225 92 0.2699 94 0.2548 96 0.2491 98 100 0.2370 102 0.2482 0.2662 104 0.2207 106 0.1944 108 110 0.2285 0.2293 112 114 0.2352 0.2358 116 0.2343 118 120 0.2633 122 0.2494 0.2574 124 0.2038 126 0.2492 128 130 0.1915 0.2194 132 0.2386 134  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.1593 4 0.1796 0.2071 6 0.2107 8 0.1711 10 0.2661 12 14 0.2262 0.1884 16 0.1825 18 0.1500 20 0.2205 22 24 0.2086 0.2636 26 0.1935 28 0.2060 30 0.2665 32 0.2309 34 36 0.2118 0.1754 38 0.1633 40 0.1293 42 0.2585 44 0.2305 46 0.2710 48 50 0.2211 0.2588 52 0.2387 54 0.2749 56 0.2755 58 0.2347 60 0.2213 62 0.2406 64 0.2510 66 0.2650 68 0.2532 70 0.1973 72 . 0.2550 74 0.3227 76 0.2518 78 0.2346 80 0.2117 82 0.1571 84  2  2  R* (m 2K  IkW)  0.2263  6  C  (min) 2.09  Unc(BDC)% 18.19  146  Run 30  Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) CLate=0 = 0.351 k W  20.0 12697. 9836. 14.12 31.33  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.0876 2 0.1046 4 0.1279 6 0.1083 8 0.1389 10 0.1678 12 0.1760 14 0.1891 16 0.1566 18 0.1333 20 0.1848 22 0.2283 24 0.1557 26 0.1820 28 0.1690 30 0.1827 32 34 0.0592 0.1758 36 0.2066 38 0.1915 40 0.1673 42 0.1261 44 0.1420 46 0.1196 48 0.1239 50 0.1338 52 0.1189 54 0.2153 56 0.1735 58 60 0.1315 0.1813 62 0.0487 64 0.0677 66 0.1705 68 0.1505 70 0.1911 72 0.1629 74 0.1639 76 0.2097 78 0.1561 80 0.2187 82 0.1685 84 2  f  R  *  (rnKlkW)  0.1534  Fouling Res. (m K/kW) 0.1658 0.1886 0.1736 0.0755 0.1841 0.1601 0.1461 0.1244 0.1155 0.1192 0.0908 0.1044 0.1081 0.2080 0.1622 0.1426 0.1676 0.1732 0.1835 0.0656 0.1681 0.1493 0.2147 0.1951 0.1510 0.1895 0.1677 0.1826 0.0525 0.2025  t)  Unc(BDC)%  32  24.13  2  147  Run 31 (%) 20.0 Mixture Re 14207. Water Re 9834. Water average Temp.( °C) 14.11 M . average Temp. ( ° C ) 31.21 CL at 9=0 = 0.401 k W Time Fouling Res. (m K/kW) (min) 0.0944 86 88 0.0996 0.0900 90 0.0743 92 0.0815 94 0.0693 96 0.0608 98 0.0579 100 0.0476 102 0.0562 104 0.0354 106 0.1081 108 0.0982 110 0.0823 112 0.0761 114 0.0943 116 0.0873 118 120 0.0712 0.0861 122  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0130 2 4 0.0306 6 0.0502 0.0498 8 0.0637 10 0.0702 12 0.0457 14 16 0.0335 0.0597 18 0.0534 20 22 0.0702 0.0592 24 0.0738 26 0.0470 28 0.0568 30 0.0463 32 0.0412 34 0.0396 36 0.0473 38 0.0317 40 0.1014 42 0.0711 44 0.0646 46 0.0727 48 0.0788 50 0.0776 52 0.0597 54 0.0771 56 0.0418 58 60 0.0651 0.0707 62 0.0404 64 0.0495 66 0.0177 68 70 0.0995 0.1084 72 0.0487 74 0.0758 76 78 0.0835 0.0897 80 0.0604 82 0.0835 84  2  2  R*(_rnKlkW) 0.0700  9  C  (min) 9.37  Unc(BDC)% 55.60  148  Run  32  Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) Q . at 6=0  20.0 6616. 9545. 12.95 31.20  = 0.244 k W Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (m K/kW) (min) 0 0.0000 0.2265 2 0.3475 4 0.3996 6 0.3684 8 0.4716 10 0.4100 12 0.4354 14 0.5458 16 0.4220 18 20 0.5099 0.4834 22 0.5289 24 0.4995 26 28 0.5436 0.6256 30 0.4238 32 0.3371 34 0.1973 36 0.5762 38 0.4595 40 0.5600 42 0.3644 44 46 0.4969 0.5836 48 0.5342 50 0.5685 52 0.6504 54 0.6014 56 0.6009 58 0.6592 60 0.6111 62 0.7299 64 0.5976 66 0.3170 68 70 0.3541 0.5841 72 0.6459 74 0.5620 76 0.6466 78 0.7928 80 0.5644 82 0.6195 84 2  RJinKlkW) 0.5552  9 (min) c  6.37  Fouling Res. (m K/kW) 0.6337 0.4634 0.2779 0.2412 0.5125 0.6167 0.4253 0.6543 0.6265 0.5559 0.4212 0.5247 0.6854 0.7058 0.6392 0.5590 0.6846 0.6084 0.3935 0.6086 0.5832 0.6617 0.4696 0.6697 0.4717 0.6218 0.5973 0.5996 0.6811 0.6223 0.6710 0.6257 0.6641 2  Unc(BDC)% 21.08  149  R u n 33 Bulk concentration (%)  20.0  Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C) Q . at 9=0 = 0.340 k W  8803. 9542. 12.94 31.32  Time Fouling Res. (min) (m K/kW) 86 0.2429 0.1884 88 0.1589 90 0.1266 92 94 0.1221 0.1094 96 0.2386 98 0.3763 100 102 0.4341 104 0.4191 0.3598 106 108 0.4482 110 0.5052 112 0.4549 0.3389 114 116 0.2762 0.3772 118 0.4591 120 0.4563 122 0.4277 124 0.4461 126 0.3283 128 0.6556 130 0.3992 132 0.3470 134 136 0.3953 0.4270 138 0.3949 140 0.3980 142 0.4356 144 146 0.3921 0.4339 148 0.4070 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.2713 2 4 0.2972 0.3908 6 0.2528 8 0.3693 10 0.4107 12 14 0.4271 16 0.3473 0.4548 18 20 0.4550 0.3821 22 0.3469 24 0.4308 26 28 0.3887 0.4575 30 0.4446 32 0.4526 34 0.4230 36 0.4494 38 0.2923 40 0.3522 42 0.4560 44 0.3756 46 48 0.2933 0.4151 50 0.4168 52 0.4379 54 0.4559 56 0.3712 58 0.3183 60 0.2345 62 0.4071 64 0.3652 66 0.4169 68 0.4786 70 0.4930 72 0.3927 74 0.4429 76 0.4264 78 0.4133 80 0.3503 82 0.2764 84  2  2  Rf(tnKlkW) 0.3804  0c(min) 2.04  Unc(BDC)% 17.22  150  R u n 34 20.0 Bulk concentration (%) 8765. Mixture Re 9646. Water Re 13.36 Water average Temp.( °C) 31.30 M . average Temp. ( ° C ) Q at 9=0 = 0.349 k W w  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.2433 2 0.2875 4 0.3586 6 0.3324 8 10 0.2954 0.2648 12 0.3382 14 0.3049 16 0.3456 18 0.3454 20 0.3651 22 0:3842 24 0.3587 26 0.4117 28 0.3685 30 0.3349 32 0.3843 34 0.3766 36 0.4205 38 40 0.4810 0.4803 42 0.3222 44 0.2811 46 0.2513 48 0.3358 50 0.3976 52 0.3945 54 56 0.3976 0.3703 58 0.4149 60 0.3866 62 64 0.3711 0.4264 66 0.3545 68 0.3995 70 0.3703 72 74 0.3429 0.3261 76 0.2785 78 0.3157 80 0.4702 82 84 0.3003 2  R*(m 2K/kW) 0.3671  0 (min) C  2.30  Fouling Res. (m K/kW) 0.5446 0.4971 0.3993 0.4264 0.4121 0.3947 0.3927 0.4636 0.4032 0.3828 0.1586 0.3905 0.3796 0.4202 0.3800 0.2838 0.2902 0.3751 0.3830 0.3876 0.1574 0.4100 0.3659 0.3599 0.3839 0.4223 0.1438 0.3518 0.418 0.4001 0.3547 0.3423 0.4088 2  Unc(BDC)% 16.34  151  Run  35  Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C) Q . at 9=0 = 0.375 k W  20.0 11042. 9534. 12.91 31.00  Time Fouling Res. (min) (m K/kW) 0.1537 86 0.1843 88 0.2110 90 0.1738 92 0.2150 94 96 0.1680 98 0.2013 0.0490 100 0.2650 102 104 0.3012 106 0.3583 108 0.3884 110 0.1596 0.2118 112 114 0.1588 116 0.2227 118 0.2081 0.1176 120 0.2161 122 124 0.2497 126 0.2018 0.1641 128 130 0.2118 132 0.2259 134 0.2246 0.1324 136 138 0.1952 0.1602 140 0.1645 142 0.2102 144 0.1615 146 0.2176 148 0.1684 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.1263 2 4 0.1329 6 0.1131 0.1784 8 10 0.1740 12 0.1507 14 0.1877 16 0.1588 18 0.1956 20 0.1796 0.2000 22 24 0.1984 0.2054 26 28 0.1432 0.2215 30 0.2139 32 0.1904 34 0.1696 36 0.2043 38 40 0.2432 0.2387 42 0.1924 44 46 0.1897 48 0.2066 50 0.2257 0.1851 52 54 0.1633 56 0.1088 58 0.0972 0.0917 60 62 0.0759 64 0.2060 66 0.2072 68 0.0350 70 0.2106 0.2025 72 0.1813 74 0.2037 76 78 0.2275 0.2645 80 82 0.1952 84 0.1481  2  2  R*(m 2KlkW) 0.1912  0  C  (min) 3.71  Unc(BDC)% 28.18  152  Run  36  Bulk concentration (%) 20.0 Mixture Re 12674. Water Re 9683. Water average Temp.( °C) 13.51 M. average Temp. (°C) 31.21 Q at 9=0 = 0.375 kW w  Time Fouling Res. (min) (m K/kW) 86 0.1316 0.1264 88 90 0.0986 92 0.1303 94 0.0529 96 0.1453 98 0.1472 0.1521 100 0.1217 102 104 0.1616 0.1608 106 108 0.1846 110 0.1992 0.1243 112 114 0.1655 0.0547 116 118 0.1373 120 0.1655 0.1395 122 124 0.1587 126 0.1368 128 0.148 0.1482 130 0.0977 132 0.0050 134 136 0.1504 140 0.1229 142 0.1683 0.1335 144  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.0501 4 0.0616 0.0670 6 8 0.1036 10 0.0532 12 0.1083 14 0.0607 16 0.1361 18 0.1076 20 0.1548 22 0.0492 24 0.1164 0.2134 26 28 0.1662 30 0.1249 32 0.0917 34 0.1393 36 0.1716 0.1367 38 0.1024 40 42 0.0913 44 0.0758 0.0937 46 0.0785 48 50 0.1462 52 0.1480 54 0.1421 56 0.1318 58 0.1226 60 0.1228 62 0.1390 64 0.0381 0.1200 66 68 0.0987 0.1020 70 0.1154 72 0.1495 74 76 0.1077 78 0.1450. 80 0.1673 0.1409 82 84 0.1363  2  2  Rf(m 2K/kW)  0.1288  6. (min) 7.91  Unc(BDC)% 47.23  153  Run  37  B u l k concentration (%) 20.0 Mixture Re 14432. Water R e 9741. Water average Temp.( °C) 13.74 M . average T e m p . ( ° C ) 31.37 Q , at 0=0 = 0.387 k W Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  F o u l i n g Res. (m K/kW) 0.0000 0.0388 0.0511 0.0120 0.0176 0.0555 0.0734 0.0113 0.0404 0.0540 0.0747 0.0418 0.0217 0.1048 0.0651 0.0964 0.0107 0.0578 0.0514 0.0647 0.0621 0.0011 0.0257 0.0233 0.0260 0.0629 0.0746 0.0503 0.0354 0.0496 0.0551 0.0737 0.1085 0.0359 0.0718 0.0266 0.0036 0.0356 0.0520 0.0370 0.0145 0.0338 0.0591  Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  2  R*(m K/kW) 2  0.0520  Ojmin) 4.89  F o u l i n g Res ( m K/kW) 0.0252 0.0157 0.0379 0.0425 0.0278 0.0535 0.0745 0.0357 0.0145 0.0310 0.1215 0.1151 0.1161 0.0574 0.0741 0.0587 0.0643 0.0163 0.0139 0.0173 0.0402 0.0616 0.0807 0.0361 0.0330 0.0526 0.0615 0.0918 0.0598 0.0938 0.0663 0.0994 0.0619 2  Unc(BDC)% 155.10  154  Run 38 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) Q  at 9=0  Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  20.0 6631. 8854. 13.13 31.50  = 0.352 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142  Fouling Res. (m K/kW) 0.0000 0.2317 0.6261 0.6537 0.5720 0.3310 0.6281 0.5892 0.7603 0.4491 0.7182 0.7597 0.6997 0.5711 0.7489 0.4098 0.7279 0.7327 0.7346 0.7198 0.7042 0.6970 0.7932 0.7706 0.5212 0.6601 0.8312 0.8003 0.7637 0.7260 0.6401 0.6316 0.5949 0.6166 0.7889 0.8246 0.7342 0.7214 0.6820 0.6711 0.6790 0.7630 0.6672 2  R*(m K/kW)  0 (min)  0.7016  4.4  2  c  Fouling Res. (m K/kW) 0.8311 0.7017 0.7820 0.7330 0.8423 0.7666 0.7373 0.3893 0.7353 0.8007 0.6865 0.6482 0.6168 0.6451 0.3167 0.7581 0.8067 0.8038 0.7151 0.7537 0.7835 0.8169 0.8007 0.8407 0.8306 0.8270 0.8217 0.7287 0.8451 2  Unc(BDC)% 14.36  155  R u n 39 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) Q . at 6=0 = 0.376 k W  20.0 8734. 8939. 13.48 31.39  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.2007 4 0.3766 6 0.3223 8 0.3315 10 0.2939 12 0.3130 14 0.3146 16 0.2570 18 0.3072 20 0.3393 22 0.3797 24 0.5373 0.3377 26 0.3068 28 30 0.3755 0.3258 32 34 0.3648 36 0.3649 38 0.3778 40 0.1419 42 0.3665 44 0.3952 46 0.3274 48 0.3491 50 0.5104 52 0.4136 54 0.3553 56 0.3949 58 0.4338 60 0.3768 62 0.3064 64 0.4053 66 0.4248 0.7120 68 70 0.1724 72 0.4852 74 0.4343 76 0.2763 0.5120 78 80 0.5312 82 0.4396 84 0.3276 2  R*(m K/kW) 2  0.4639  0 (i c  in) 4.19  Fouling Res. (m K/kW) 0.4883 0.4574 0.5231 0.5403 0.4829 0.5747 0.5214 0.5276 0.4647 0.5244 0.5473 0.5220 0.5223 0.4932 0.5014 0.4481 0.5827 0.5447 0.4172 0.5695 0.6982 0.4108 0.4627 0.4998 0.5165 0.5439 0.4606 0.4965 0.4868 2  Unc(BDC)% 15.65  156  R u n 40 Bulk concentration (%) Mixture Re Water Re Water average Temp.(°C) M . average Temp. ( ° C ) CL at 9=0 = 0.407 k W  20.0 11084. 8890. 13.28 31.67  Time Fouling Res. (min) (m K/kW) 86 0.4700 88 0.3625 0.3879 90 0.4138 92 94 0.3677 0.4442 96 0.4164 98 0.4668 100 102 0.4715 104 0.4626 106 0.4596 108 0.4211 110 0.4545 112 0.4856 114 0.5136 116 0.5130 0.3704 118 120 0.4197 0.4041 122 124 0.4766 0.4714 126 128 0.4695 130 0.4375 132 0.4155 0.5379 134 136 0.4987 138 0.4051 140 0.5077 0.5440 142 144 0.4115 146 0.4869 148 0.4338 150 0.5441  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.1677 2 4 0.1953 6 0.3341 0.2534 8 10 0.3154 12 0.3005 14 0.3579 16 0.3129 18 0.3809 20 0.3572 0.2744 22 24 0.4030 0.4040 26 0.3387 28 30 0.4448 32 0.3804 34 0.4169 36 0.1982 0.4698 38 40 0.4414 0.4914 42 0.5315 44 46 0.4972 48 0.4677 0.3601 50 0.4839 52 54 0.3935 56 0.4441 58 0.5406 60 0.5308 62 0.4737 0.4538 64 66 0.4601 68 0.4674 70 0.5572 72 0.4919 74 0.4246 76 0.3653 0.3912 78 0.4164 80 82 0.4031 0.5020 84  2  2  R*(tnKlkW) 0.4496  0 (r, c  n) i.02  Unc(BDC)% 11.45  157  Run 41 20.0  B u l k concentration (%) Mixture Re  12672.  Water R e  8835. 13.05 31.42  Water average Temp.( °C) M . average T e m p . ( °C)  O^ate^ Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  = 0.507 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146  F o u l i n g Res. (m K/kW) 0.0000 0.2221 0.2191 0.2576 0.2915 0.3131 0.3651 0.3722 0.3722 0.3601 0.3886 0.4288 0.4113 0.3733 0.3343 0.2844 0.3058 0.4121 0.3938 0.3670 0.3474 0.1505 0.2605 0.2194 0.2117 0.1765 0.3974 0.4322 0.3355 0.3108 0.2375 0.2124 0.1935 0.2308 0.2474 0.4586 0.4976 0.4433 0.3549 0.3867 0.4900 0.4449 0.3637 2  RAinKlkW)  0.3753  0 (min) C  4.19  F o u l i n g Res. (m K/kW) 0.3223 0.2667 0.2442 0.2342 0.2149 0.1849 0.4455 0.6018 0.5686 0.4926 0.4473 0.4020 0.5427 0.5823 0.4086 0.5696 0.5043 0.4152 0.3523 0.3146 0.2593 0.3561 0.4669 0.3936 0.4068 0.4606 0.3967 0.5380 0.4696 0.4838 0.5972 2  Unc(BDC)%  11.63  158  Run 42 Bulk concentration (%) Mixture Re Water Re Water average Temp.(°C) M . average Temp. ( °C) CLate=0  20.0 14147. 8796. 12.89 31.69  = 0.506 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0396 2 0.1226 4 0.2560 6 0.2606 8 10 0.3147 12 0.3362 0.3117 14 16 0.2921 0.2868 18 20 0.2652 0.2871 22 0.4870 24 26 0.4381 28 0.3727 0.3676 30 0.2921 32 34 0.2973 36 0.1144 0.2296 38 0.1854 40 0.2209 42 0.1820 44 0.4967 46 0.5871 48 0.5083 50 0.2431 52 0.4663 54 0.5356 56 58 0.3807 60 0.3403 0.3213 62 64 0.2977 0.2657 66 68 0.2251 70 0.2073 0.2268 72 0.2085 74 76 0.1533 0.5086 78 0.5370 80 0.4160 82 0.1752 84 2  R*(rnK/kW) 0.3574  9  C  (min) 6.87  Fouling Res. (m K/kW) 0.4428 0.4499 0.3169 0.4353 0.5734 0.4729 0.4020 0.3566 0.2900 0.2708 0.3151 0.4336 0.4704 0.3519 0.3039 0.4981 0.3954 0.4030 0.4445 0.3339 0.3839 0.3832 0.3946 0.4865 0.3812 0.3191 0.2625 0.2588 0.2865 0.3160 0.3470 0.4028 0.4824 2  Unc(BDC)% 8.96  159  Run  43  B u l k concentration (%) 10.0 Mixture Re 10766. Water Re 18408. Water average Temp.( °C) 9.52 M . average T e m p . ( ° C ) 28.69 Q at 6=0 - 0.308 k W w  Time (min) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  F o u l i n g Res. (m K/kW) 0.0000 0.4666 0.6087 0.9077 0.9697 1.0823 1.8591 1.8838 1.9524 2.0081 2.9451 1.5067 2.8579 2.8815 4.3914 2.9306 4.5517 4.5615 4.6052 3.0640 3.0821 3.0857 3.1454 3.1125 2.1856 3.1693 3.2012 2.2498 2.2125 2.2532 2.3307 2.3523 1.7356 2.2398 2.2691 3.1571 3.1836 3.2480 3.2562 2.3354 2.3998 2.3974 2.4533 1.8053 1.3710 1.8491 1.4009 2  Time (min) 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136  F o u l i n g Res. ( m K/kW) 3.4701 2.4135 2.4378 3.4898 2.3922 3.4505 3.5038 3.4544 3.4701 3.4858 3.5015 1.7538 3.5408 3.4151 3.4190 2.4377 3.4898 3.4898 2.4469 2.4561 2.4683 3.5871 3.6069 2.5020 1.8168 2.4986 3.3410 5.2145 3.4269 2.3922 3.3993 3.3648 5.0867 9.3581 9.4056 5.1758 5.3424 3.3710 2.3142 3.4112 3.4269 3.4544 2.4074 2.4287 2.4198 3.5072 1.7909 2  160  47  3.3047  137  1.7851  48  3.3124  138  1.8023  49  3.3394  139  1.8355  50  3.2589  140  1.8504  51  3.2815  141  1.3767  52  5.0172  142  1.0370  53  5.0119  143  1.8663  54  5.0065  144  1.4195  55  5.0065  145  1.0745  56  3.2321  146  2.2659  57  3.2359  147  3.3482  58 59  3.2473 3.2550  148 149  2.2824 2.3436  60  5.0546  150  2.3040  61  5.0653  151  5.2581  62  3.2704  152  3.2616  63  3.2741  153  3.2139  64  2.2808  154  5.1145  65 66  3.2971  155  9.1783  156  67  3.3085 3.3162  68  3.3200  157 158  9.3369 4.9543 9.4837  69  3.3277  159  9.4442  70 71  1.6666 2.3254  9.3646 9.0751 4.8364  72  3.3973  160 161 163  73  2.3603  164  9.3677  74  2.3633  165  5.1367  75  3.3620  166  5.2382  76  2.3433  167  5.0000  78  2.2914  169  8.9073  79  3.2198  170  9.2865  80  4.9530  171  5.3146  81  3.1761  172  5.6296  82  3.2101  173  5.4721  83  1.1705  174  2.3709  84  3.2397  175  2.3983  85  2.2704  176  3.4998  86  3.2359  177  3.4799  87  3.3047  178  3.4151  88  5.2547  179  3.4482  89  2.3739  180  3.3954  R*(rnKlkW) 3.6474  0  C  (min) 12.01  Unc(BDC)% 21.00  161  Run 45 10.0 B u l k concentration (%) 12150. Mixture Re 18687. Water Re 10.04 Water average Temp.( °C) 36.44 M . average T e m p . (°C) Q . at 9=0 = 0.610 k W Time (min) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  F o u l i n g Res. (m K/kW) 0.0000 0.0269 0.2306 0.1569 0.2685 0.3401 0.2788 0.2277 0.2274 0.4267 0.3625 0.3669 0.3726 0.4367 0.4359 0.4374 0.4381 0.3735 0.3714 0.3749 0.3096 0.3751 0.4522 0.5349 0.3824 0.3853 0.5390 0.5398 0.3884 0.3270 0.4663 0.4719 0.3345 0.4545 0.4443 0.5401 0.5493 0.5537 0.5573 0.6357 0.6331 0.5386 0.4616 0.6397 0.5489 0.4664 0.5443 0.4672 2  Time (min) 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137  F o u l i n g Res. ( m K/kW) 0.5554 0.4641 0.5467 0.5467 0.5484 0.5501 0.4697 0.6500 0.6518 0.4777 0.4793 0.4793 0.5667 0.5675 0.4849 0.4849 0.5717 0.6695 0.4138 0.4864 0.5760 0.4920 0.3490 0.4896 0.4904 0.5737 0.4176 0.4184 0.4943 0.4943 0.4266 0.2889 0.4070 0.4763 0.4025 0.2746 0.3346 0.4033 0.4048 0.2796 0.2803 0.4071 0.3446 0.2844 0.2857 0.4123 0.4168 0.3522 2  162  48  0.4711  138  0.2904  49  0.3984  139  0.3531  50  0.4727  140  0.4213  51 52  0.5581 0.4791  141 142  0.4251 0.2931  53  0.5606  143  0.2927  54  0.4029  144  0.3574  55  0.5587  145  0.4258  56  0.4790  146  57 58  0.4806 0.3390  147 148  0.2972 0.2954  59 60  0.4059  149 150  0.4289  151  0.3006  0.4251 0.3006  61  0.5648 0.4854  62  0.1791  152  0.3623  63  0.4791  153  0.4319  64  0.5482  154  0.3037  65  0.5476  155  0.3044  66  0.4641  156  0.4334  67  0.3915  0.4371  68  0.6392  157 158  69  0.5501  159  0.1999  70  0.4688  160  0.5757  71  0.2185  0.4819  72  0.5560  161 162  73  0.6532  163  0.4869  74  0.5639  164  0.4852  75  0.4027  165  0.5743  76 77  0.4759  166  0.6729  0.6613  167  0.4183  78  0.5698  168  0.4175  79  0.4080  169  0.5811  80  0.4872 0.5704  170 171  0.5845 0.4963  0.5611 0.5510  172  0.4971  83  173  0.5020  84  0.4705  174  0.5020  85  0.6442  175  0.3593  86  0.5537  176  0.3600  87  0.5526  177  0.5068  88  0.5543  178  0.5043  89  0.6487  179  0.3628  180  0.4319  81 82  R*f{rnKlkW) 0.4632  Ojmin) 6.55  0.3033  0.4836  Unc(BDC)% 27.27  163  Run 46 Bulk concentration (%) 10.0 Mixture Re 12814. Water Re 18685. Water average Temp.( °C) 10.04 M . average Temp. ( ° C ) 39.98 at G=o = 0.725 k W Time Fouling Res. (min) (m K/kW) 2  Time Fouling Res. (min) (m K/kW) 2  0  0.0000  90  1  0.0972  91  0.3725 0.4250  2  0.1040 0.1291  92  0.3725  93  0.1656  94  0.3725 0.3702  3 4 5  0.2070  95  0.3225  6  0.2523  96  0.3199  7  0.2998  97  0.3682  8  0.3044  98  0.3676  9  0.2746  99  0.3676  10  0.1650  100  0.2751  11  0.2859  101  0.3191  12  102  13  0.3836 0.3900  103  0.3166 0.3166  14  0.3980  104  0.3643  15  0.4604  105  0.3643  16  0.4091 0.4138  106  0.3171 0.3177  0.4178  107 108  19  0.4209  109  0.3177  20  0.3236  110  0.3177  21  0.4943  111  0.3682  22  0.3242  112  0.3197  23  0.3311  113  0.3658  24  0.3454  114  0.3163  25  0.3536  115  0.1267  26  0.3582  116  0.2714  27  0.3144  117  0.3141  28  0.3166  118  0.3617  29  0.2764  119  0.3129  30  0.2767  120  0.3129  31  0.3118  121  0.3129  32  0.3446  122  0.3104  33  0.3887  123  0.2692  34  0.3962  124  0.3579  35  0.3498  125  0.3579  36  0.3051  126  0.3124  37  0.3495  127  0.3590  38  0.4000  128  0.3633  39  0.4000  129  0.3639  40  0.3994  130  0.4155  41  0.3988  131  0.4161  42  0.3487  132  0.3639  43  0.3992  133  0.3623  44  0.2577  134  0.3639  45  0.3996  135  0.3629  46  0.3478  136  0.3623  17 18  0.3177  164  47  0.3467  137  0.4144  48  0.2998  138  0.3623  49 50  0.1146  139  0.3629  0.3434  140  0.3152  51 52  0.3455 0.3470  141  0.3152  142  0.3623  53 54  0.3464  0.3152  0.2965  143 144  55  0.3964  145  0.3158  56  0.3982  146  0.3608  57  0.3497  147  0.3138  58  0.3043  0.3132  59 60  0.4019 0.3544  148 149 150  0.3118  61  0.3555  151  0.3118  62  0.3576  152  0.2688  63  0.3588  153  0.3118  64  0.3606  154  0.3593  65  0.4109  155  66  0.3639  156  0.3129 0.3604  67  0.3629  157  0.3135  68  0.4729  158  0.3135  69  0.3668  159  0.3155  70  0.4169  160  0.3160  71  0.3180  161  0.3166  72  0.4204  162  0.2727  73  0.3692  163  0.3191  74  0.3670  164  0.2757  75  0.3676  165  0.3191  76  0.3202  166  0.3191  77  0.3661  167  0.3191  78  0.3682 0.3838  168  0.2346 0.2334  0.3158  0.2701  0.3862  169 170  81  0.3962  171  0.3183  82  0.3596  172  0.3639  83  0.4177  173  0.3188  84  0.3222  174  0.3163  85  0.3707  175  0.3188  86  0.3713  176  0.3188  87  0.3698  177  0.3666  88  0.3725  178  0.3188  179  0.2754  180  0.2749  79 80  R*(rnKlkW) 0.3435  0  C  (min) 4.41  0.3177  Unc(BDC)% 18.56  165  Run 4 7 Bulk concentration (%)  10.0  Mixture Re 13629. Water R e 18838. Water average Temp.( ° C ) 10.32 M . average T e m p . ( ° C ) 44.18 at 6=0 = 0.715 k W Time (min) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  F o u l i n g Res. (m K/kW) 0.0000 0.0757 0.0985 0.1716 0.1993 0.2107 0.1704 0.1328 0.2139 0.2178 0.3474 0.1966 0.2251 0.1762 0.1807 0.2075 0.2369 0.2402 0.1916 0.2158 0.2154 0.2154 0.2428 0.2719 0.2710 0.2728 0.2186 0.2736 0.2753 0.2757 0.2473 0.2481 0.2448 0.2736 0.2444 0.2444 0.2453 0.2465 0.2461 0.2481 0.2775 0.2784 0.2498 0.2797 0.2511 0.2523 0.2531 0.2540 2  Time (min) 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157  F o u l i n g Res. (m K/kW) 0.2824 0.2537 0.2238 0.2238 0.3468 0.2820 0.3135 0.2541 0.2541 0.2549 0.3150 0.3158 0.3163 0.2558 0.3186 0.2872 0.2578 0.3181 0.2881 0.3200 0.2885 0.2604 0.2894 0.2616 0.2599 0.2907 0.2327 0.3229 0.2650 0.2359 0.2937 0.2645 0.2654 0.2616 0.2899 0.2891 0.3177 0.2868 0.3560 0.3560 0.2953 0.2660 0.3299 0.2966 0.2992 0.2970 0.3249 . 0.3574 2  166  48  0.2557  158  0.3240  49  0.2565  159  0.3573  50  0.2866  160  0.3230  72  0.2810  161  0.3593  73  0.3466  162  0.3571  74  0.2549  163  0.3596  75  0.2540  164  0.4366  76  0.3135  165  0.3605  77 78  0.3121 0.3126  166 167  0.3605 0.4371  79  0.3150  168  0.4381  80 81  0.2842 0.2846  169  0.4005  82  0.2841  170 171  0.4010 0.3998  83  0.3162  172  0.4383  84  0.3171  173  0.4022  85  0.2885  174  0.4022  86  0.3153  175  0.4031  87  0.2806  176  0.3996  88  0.2802  177  0.4381  89  0.2798  178  0.3625  90  0.2528  179  0.3620  91  0.3118  92  0.2802  180 181  0.2953 0.3979  93  0.2806  182  0.3967  94  0.2810  183  0.3603  95  0.2810  184  0.4381  96  0.2828  97  0.2540  185 186  0.3612 0.3993  98  0.3162  187  0.3612  99  0.2845  188  0.3637  100  0.2544  189  0.3653  101  0.3152  190  0.3296  102  0.3162  191  0.3671  103  0.2858  192  0.3665  104  0.2849  105  0.2582  106  0.2318  107  0.2318  108  0.2561  109  0.2536  RArnKlkW) 0.3070  0  C  (min) 11.07  Unc(BDC)% 14.17  167  R u n 48 Bulk concentration (%) 20.0 Mixture Re 8391. Water Re 7448. Water average Temp. ( ° C ) 7.09 M . average Temp. ( ° C ) 28.90 Q„ at 9=0 = 0.280 k W Time Fouling Res. (min) (m K/kW) 1.4243 86 1.7618 88 1.7698 90 1.1881 92 1.3581 94 1.4355 96 1.5660 98 1.5026 100 1.7027 102 1.5624 104 1.6876 106 1.4712 108 1.4997 110 1.5568 112 1.5717 114 1.5851 116 1.5969 118 1.5644 120 1.6815 122 1.3907 124 1.5730 126 1.8154 128 1.6576 130 1.6981 132 1.6835 134 1.7773 136 1.5672 138 140 1.5389 1.4224 142 1.6571 144 1.6043 146 1.6159 148 1.6002 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.5910 2 4 0.7963 0.9453 6 0.7367 8 1.0500 10 1.0107 12 14 0.9813 0.8728 16 1.0527 18 1.0900 20 0.9658 22 1.1653 24 1.2739 26 1.1227 28 1.0688 30 1.2877 32 1.1686 34 1.1030 36 1.1932 38 40 1.4985 1.1867 42 1.2988 44 1.2177 46 1.2790 48 1.1491 50 1.2791 52 1.4070 54 1.2910 56 1.3549 58 1.6184 60 1.4312 62 1.6457 64 1.5942 66 1.4517 68 70 1.3269 1.3587 72 1.4895 74 1.4238 76 1.5168 78 1.5505 80 1.5135 82 1.5039 84  2  2  RArnKlkW) 1.5241  6  C  (min) 16.17  Unc(BDC)% 11.01  168  Run  50  Bulk concentration (%) 20.0 Mixture Re 9372. Water Re 7788. Water average Temp.( °C) 8.59 M . average Temp. ( °C) 34.98 CLatO^ = 0.539 k W Time Fouling Res. (m K/kW) (min) 0.3728 86 0.3913 88 0.3922 90 0.3630 92 0.2911 94 0.4132 96 0.4057 98 0.3122 100 0.4389 102 0.4690 104 0.4010 106 0.3571 108 0.3225 110 0.3715 112 0.3207 114 0.3245 116 0.3632 118 0.3601 120 0.3432 122 0.3326 124 0.3094 126 0.3866 128 0.3753 130 0.3862 132 0.3340 134 0.2709 136 0.3427 138 0.3565 140 0.3722 142 0.3533 144 0.3388 146 0.3547 148 0.4124 150  Time Fouling Res. (m K/kW) (min) 0.0000 0 0.1761 2 0.2386 4 0.2881 6 0.2791 8 0.2911 10 0.2549 12 0.3063 14 0.3654 16 0.3668 18 0.3781 20 0.3847 22 0.3750 24 0.4073 26 0.4161 28 0.4017 30 0.4498 32 0.3808 34 0.3756 36 0.3598 38 0.4245 40 0.4041 42 44 0.4161 0.3865 46 0.4040 48 0.3979 50 0.3887 52 0.4012 54 0.4386 56 0.4148 58 0.3982 60 0.3959 62 0.4260 64 0.3926 66 0.3869 68 70 0.3391 0.3766 72 0.3453 74 0.4395 76 0.3656 78 0.4436 80 0.4116 82 0.4136 84  2  2  RAtnKlkW) 0.3788  6  C  (min) 5.21  Unc(BDC)% 13.07  169  R u n 51 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( ° C ) Q at 9=0 = 0.703  20.0 9841. 7762. 8.48 38.08 kW Time Fouling Res. (min] (m K/kW)  Time Fouling Res. (min) (m K/kW)  2  2  0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  0.0000 0.1303 0.1205 0.2437 0.205 0.2185 0.2165 0.2673 0.2501 0.2549 0.2235 0.2117 0.2382 0.2455 0.2461 0.2371 0.1298 0.2332 0.2258 0.2708 0.2547 0.2522 0.2393 0.2310 0.2415 0.1987 0.2322 0.2027 0.2321 0.1991 0.2472 0.2688 0.2409 0.2396 0.2175 0.2693 0.2431 0.2060 0.2205 0.1954 0.2331 0.2273 RArnKlkW) 0.2205  0 (min) C  2.74  0.2058 0.2302 0.2205 0.2114 0.2166 0.2433 0.2205 0.2370 0.2322 0.2204 0.2246 0.2385 0.2286 0.2245 0.2264 0.2404 0.1696 0.1759 0.1881 0.2112 0.2173 0.2423 0.1714 0.2147 0.2157 0.1901 0.2252 0.2094 0.2134 0.1940 0.2134 0.2102 0.2129  Unc(BDC)% 16.67  170  Run 52  Bulk concentration (%) 20.0 Mixture Re 10115. Water Re 7625. Water average Temp.(°C) 7.87 M . average Temp. (°C) 40.59 Q . at 0=0 = 0.768 k W Time Fouling Res. (min) (m K/kW) 86 0.3884 0.3928 88 0.3981 90 0.4427 92 0.3756 94 0.3699 96 0.3757 98 0.3754 100 0.3511 102 0.2920 104 106 0.4213 108 0.4078 110 0.4325 0.4263 112 0.3690 114 116 0.3829 118 0.3748 120 0.3565 0.3626 122 0.4012 124 126 0.3892 0.3121 128 130 0.3744 0.3638 132 0.3673 134 0.3798 136 0.3702 138 140 0.3533 0.3668 142 0.3580 144 0.3008 146 0.3622 148 0.3328 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.2160 2 0.2860 4 6 0.4237 8 0.4031 10 0.3822 12 0.4336 0.4068 14 16 0.4126 18 0.4214 0.4228 20 22 0.4032 24 0.4246 0.4396 26 28 0.3822 0.4282 30 0.3907 32 34 0.4338 36 0.4170 0.4370 38 0.4160 40 0.3870 42 44 0.4103 0.3911 46 0.4530 48 50 0.4388 0.4014 52 54 0.4016 0.3996 56 0.4060 58 0.3913 60 0.4031 62 0.3818 64 66 0.4008 68 0.4393 0.4058 70 0.3668 72 74 0.3743 0.3720 76 0.3858 78 80 0.3761 0.4128 82 0.3736 84  2  2  R*f(tnKlkW)  0.3916  djmin)  2.29  Unc(BDC)%  7.88  171  R u n 53 20.0 Bulk concentration (%) 10140. Mixture Re 7687. Water Re 8.14 Water average Temp.( °C) 40.75 M . average Temp. ( ° C ) Q at 9=0 = 0. l k W w  Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Fouling Res. (m K/kW) 0.0000 0.2040 0.2304 0.2538 0.2422 0.2484 0.2260 0.2349 0.2137 0.2247 0.1908 0.2450 0.2556 0.2389 0.2554 0.2408 0.2523 0.2306 0.2009 0.2711 0.2107 0.2222 0.2458 0.2331 0.2854 0.2478 0.2486 0.2281 0.2136 0.2343 0.2401 0.2423 0.2450 0.2091 0.2343 0.2301 0.2496 0.2606 0.2245 0.2407 0.2302 0.2369 0.2251 2  R*(rnKlkW) 0.2359  9c(min, 0.'  Fouling Res. (m K/kW) 0.2727 0.2553 0.0913 0.1912 0.2414 0.2527 0.2231 0.2085 0.2251 0.2214 0.2417 0.2349 0.2385 0.2517 0.2861 0.2464 0.2602 0.2292 0.2452 0.2624 0.2245 0.2219 0.2554 0.2183 0.2369 0.2383 0.1824 0.2508 0.2348 0.2333 0.2150 0.2844 0.2817 2  Unc(BDC)% 14.06  172  Run 55  Bulk concentration (%) 20.0 9513. Mixture Re 7472. Water Re 7.19 Water average Temp.( °C) 35.92 M . average Temp. ( ° C ) Q at9=0 = 0.519 k W w  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.1038 4 0.2043 6 0.2049 8 0.2242 0.2012 10 0.1586 12 14 0.2165 16 0.2415 18 0.2204 20 0.2102 0.2366 22 0.2064 24 0.0930 26 0.2337 28 30 0.2061 32 0.2055 34 0.1909 0.1867 36 38 0.2428 40 0.2591 0.2455 42 44 0.2068 46 0.2572 48 0.0798 0.2606 50 52 0.3210 0.2651 54 0.3297 56 0.2354 58 0.2304 60 0.1820 62 0.2442 64 66 0.2690 0.2444 68 0.2234 70 0.2474 72 0.2317 74 76 0.2388 0.2501 78 80 0.2375 82 0.3393 84 0.3006 2  R*(rnKlkW) 0.2409  6 (min) C  3.38  Fouling (m 0.2738 0.2382 0.2481 0.2210 0.1734 0.2415 0.2416 0.2798 0.2542 0.2342 0.2527 0.2595 0.2502 0.2789 0.2604 0.2936 0.3010 0.2939 0.2747 0.2411 0.2321 0.2140 0.2352 0.2342 0.2410 0.2483 0.2967 0.2921 0.2343 0.2192 0.2193 0.2323 0.2796 2  Unc(BDC)% 23.03  173  Run  56  20.0 Bulk concentration (%) 9616. Mixture Re 8542. Water Re 11.82 Water average Temp.( C) 37.32 M . average Temp. ( C ) Q at 9=0 = 0.647 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.1566 2 0.2040 4 6 0.2204 8 0.2402 10 0.2010 12 0.2340 0.2666 14 0.2424 16 0.2197 18 0.2198 20 22 0.0651 0.1588 24 26 0.1837 0.2605 28 30 0.2603 32 0.2592 0.2390 34 0.2389 36 0.2165 38 0.2192 40 42 0.2028 44 0.1917 46 0.1695 0.2800 48 50 0.3123 0.2644 52 54 0.2579 0.2312 56" 0.2550 58 0.2260 60 62 0.2051 64 0.1993 0.2277 66 0.2530 68 70 0.2556 72 0.2167 74 0.2173 0.1110 76 0.1610 78 80 0.1982 0.1716 82 0.1609 84 2  R*(m 2K/kW) 0.2056  6c(min) 1.27  Foulin (m 0.1355 0.1516 0.1673 0.1386 0.2503 0.2893 0.2413 0.2109 0.1935 0.1860 0.1994 0.1884 0.1734 0.1573 0.1774 0.1467 0.1493 0.1261 0.0579 0.2739 0.2665 0.2478 0.2176 0.2384 0.2366 0.2361 0.2460 0.2531 0.0007 0.2171 0.2245 2  Unc(BDC)% 42.46  174  Run 57 20.0 Bulk concentration (%) 10163. Mixture Re 8577. Water Re 11.97 Water average Temp.( C) 40.90 M . average Temp. ( C ) Q at 9=0 =0.816 k W w  Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.0540 4 0.0876 0.1477 6 0.1345 8 10 0.0853 12 0.1385 14 0.1273 16 0.1292 0.1444 18 0.1684 20 0.1324 22 24 0.1365 0.1351 26 0.1829 28 30 0.1993 32 0.1725 34 0.2113 36 0.1792 0.0418 38 40 0.1807 42 0.1826 44 0.1443 0.1324 46 0.1286 48 50 0.1165 52 0.1395 54 0.1426 0.1291 56 58 0.1352 60 0.1220 62 0.1117 64 0.1741 66 0.1758 0.0341 68 70 0.1481 0.1117 72 0.1434 74 76 0.1210 0.1188 78 0.1266 80 82 0.1153 84 0.1071 2  R*(m K/kW) 2  0.1187  9  C  (min) 2.31  Fouling Res. (m K/kW) 0.1184 0.1262 0.0980 0.1078 0.0949 0.0821 0.1057 0.0779 0.1412 0.1452 0.1536 0.1145 0.1468 0.1401 0.1465 0.1244 0.1252 0.1132 0.1150 0.1321 0.1040 0.1208 0.1217 0.1385 0.1067 0.1414 0.1378 0.1441 0.1207 0.1213 0.1314 0.1580 0.1336 2  Unc(BDC)% 21.10  175  Run 59 Bulk concentration (%) Mixture Re Water Re  20.0 9060. 8478.  Water average Temp.( C) M . average Temp. ( C) 0.816=0 = 0.489 k W  Time Fouling Res. (min) (m K/kW) 0.5576 86 0.4584 88 0.4641 90 0.5339 92 94 0.5685 0.5212 96 0.4959 98 100 0.4869 0.6139 102 104 0.5114 0.5482 106 0.3622 108 0.4526 110 0.4141 112 0.5955 114 0.4292 116 118 0.5666 0.5492 120 0.6008 122 124 0.5824 0.5439 126 0.5422 ' 128 0.0700 130 0.5372 132 0.5751 134 0.6082 136 0.5514 138 0.4998 140  Time Fouling Res. (min) (m K/kW) 0 0.0000 0.4047 2 0.3847 4 0.4104 6 0.3811 8 0.3716 10 12 0.4111 14 0.3182 0.3439 16 0.3217 18 0.4286 20 0.3976 22 0.4018 24 26 0.4505 0.3660 28 0.3904 30 0.3702 32 0.4147 34 36 0.4123 0.4420 38 40 0.4781 0.2152 42 0.4189 44 0.4130 46 0.3768 48 0.5064 50 0.4973 52 0.4145 54 0.4899 56 0.4629 58 0.5046 60 0.2791 62 0.2596 64 0.4848 66 0.5618 68 0.2910 70 0.5372 72 0.5512 74 0.5198 76 0.5203 78 0.4621 80 0.5260 82 0.4760 84  2  2  RArnKlkW) 0.4572  11.55 33.56  9  C  (min) 1.14  Unc(BDC)% 20.21  176  Run 60 20.0 Bulk concentration (%) 9583. Mixture Re 8635. Water Re 12.21 Water average Temp.( C) 37.11 M . average Temp. ( C ) CL at 6=0 = 0.585 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.1075 2 0.1442 4 0.2120 6 0.1883 8 0.2382 10 0.2254 12 0.2749 14 0.2632 16 0.2999 18 0.2941 20 0.2215 22 0.2748 24 0.3207 26 0.2928 28 0.2760 30 0.2521 32 0.3373 34 0.3867 36 0.3269 38 0.3314 40 0.3048 42 0.3398 44 0.3031 46 0.3514 48 0.3421 50 0.3083 '52 0.3368 54 0.3717 56 0.3385 58 0.3640 60 0.3776 62 0.3373 64 0.3721 66 0.3586 68 0.3366 70 0.3608 72 0.4209 74 0.3265 76 0.3280 78 0.3672 80 0.3909 82 0.3744 84 2  RAtnKlkW) 0.3645  0 (min) C  12.82  Foulinj (m 0.3654 0.3688 0.3149 0.3675 0.3638 0.3107 0.3726 0.4059 0.3802 0.3454 0.3513 0.3618 0.3735 0.3890 0.4318 0.3663 0.3292 0.3589 0.3649 0.3629 0.3888 0.3710 0.4104 0.4046 0.3467 0.3892 0.3758 0.3798 0.4057 0.4176 0.3910 0.3713 0.4013 2  Unc(BDC)% 11.65  177  Run 61 Bulk concentration (%) 20.0 Mixture Re 10049. Water Re 8697. Water average Temp.( C) 12.47 M . average Temp. ( C) 40.17 Q . at 9=0 = 0.751 k W Time Fouling Res. (min) (m K/kW) 86 0.2818 0.2887 88 90 0.2893 0.2729 92 0.2999 94 96 0.2773 98 0.2810 0.2761 100 0.2958 102 0.2896 104 0.3104 106 108 0.2815 110 0.2770 0.2911 112 114 0.2645 0.3020 116 118 0.2985 120 0.2805 0.2680 122 0.0580 124 126 0.2780 128 0.2883 130 0.2732 0.2810 132 0.2700 134 0.3267 136 0.2812 138 0.2679 140 0.2961 142 0.2914 144 0.2763 146 0.2458 148 0.2652 150  Time Fouling Res. (min) ( m K / k W ) 0.0000 0 0.1327 2 0.1373 4 0.1883 6 0.1994 8 0.1223 10 0.1883 12 0.2154 14 0.2258 16 0.2217 18 20 0.2216 0.2245 22 0.3464 24 0.2424 26 0.2534 28 0.2497 30 0.2118 32 0.2204 34 0.2175 36 38 0.2381 0.2585 40 0.2189 42 0.2379 44 0.2583 46 0.2605 48 0.2613 50 0.2494 52 0.2726 54 0.2692 56 0.2638 58 0.2723 60 0.2649 62 0.2388 64 66 0.2613 68 0.2525 0.2813 70 0.2804 72 0.2570 74 0.2931 76 0.2953 78 0.2918 80 0.2647 82 84 0.2769  2  2  RArnKlkW) 0.2664  0 (min) C  7.79  Unc(BDC)% 11.14  178  Run  63  B u l k concentration Mixture Re Water Re  20.0 9054. 9288. 12.91 33.52  (%)  Water average Temp.( C ) M . average T e m p . ( C ) CL at 9=0 Time (min) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84  = 0.422 k W Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146 148 150  F o u l i n g Res. (m K/kW) 0.0000 0.2092 0.2234 0.2361 0.2262 0.2481 0.2609 0.2851 0.2897 0.2478 0.2730 0.2669 0.3683 0.2973 0.2724 0.2921 0.2668 0.3164 0.2658 0.2387 0.3241 0.2897 0.2900 0.2495 0.3001 0.2721 0.2793 0.2954 0.2742 0.2619 0.3084 0.2652 0.2771 0.2770 0.2547 0.3078 0.2321 0.2792 0.3032 0.3762 0.4356 0.3983 0.4211 2  R*(tnKlkW) 0.3180  0c(min 4.  F o u l i n g Res. ( m K/kW) 0.2669 0.2799 0.3267 0.3548 0.3641 0.3249 0.4037 0.3947 0.3092 0.2802 0.4029 0.4361 0.4602 0.3846 0.3927 0.2882 0.2752 0.3046 0.3045 0.2238 0.2983 0.3159 0.3943 0.4272 0.4541 0.4759 0.3094 0.3746 0.3591 0.2949 0.1824 0.3654 0.2595 2  Unc(BDC)% 16.61  179  Run 64 Bulk concentration (%) Mixture Re Water Re Water average Temp.( C) M . average Temp. ( C ) Q at 6=0 = 0.506 k W  20.0 9555. 9460. 12.61 36.92  Time Fouling Res. (min) (m K/kW) 0.2612 86 88 0.2179 0.2259 90 0.1910 92 94 0.1964 96 0.2271 0.1814 98 0.1797 100 0.1885 102 104 0.2452 106 0.2047 108 0.1856 110 0.2459 0.1421 112 114 0.2312 0.2537 116 0.0906 118 0.1388 120 122 0.2275 0.2267 124 0.1384 126 0.2301 128 130 0.2450 0.2008 132  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.0723 4 0.1383 0.0159 6 0.2059 8 0.1919 10 0.2024 12 14 0.2034 16 0.1875 0.2036 18 20 0.1981 0.2276 22 24 0.2109 26 0.2340 0.2144 28 30 0.2658 32 0.2072 0.0918 34 36 0.1612 38 0.1322 40 0.2221 42 0.2115 0.2220 44 46 0.2359 48 0.1922 0.1960 50 0.2141 52 0.2152 54 0.2292 56 58 0.2170 0.2633 60 0.2208 62 64 0.2436 66 0.2576 0.2700 68 0.2617 70 0.2159 72 0.2294 74 76 0.2031 0.1651 78 80 0.1677 0.2273 82 84 0.2235  2  2  RJrnKlkW) 0.2098  6  C  (min) 5.73  Unc(BDC)% 20.62  180  Run 65 Bulk concentration (%) 20.0 Mixture Re 10183. Water Re 9872. Water average Temp.( C) 13.26 M . average Temp. ( C ) 41.03 0,018=0 = 0.511 k W Time Fouling Res. (min) (m K/kW) 0.0679 86 0.0468 88 0.0255 90 0.0924 92 0.0857 94 0.0752 96 0.0263 98 0.0454 100 0.0515 102 0.0406 104 0.0349 106 0.0342 108 110 0.0911 0.0526 112 0.0615 114 0.0617 116 0.0451 118 0.0157 120 0.1036 122 0.0921 124 0.1298 126 0.0944 128 0.1045 130 0.0897 132  Time Fouling Res. (min) (m K/kW) 0.0000 0 2 0.0115 0.0092 4 0.0138 6 0.0073 8 0.0320 10 0.0134 12 0.0469 14 0.0477 16 0.0444 18 0.0515 20 0.0746 22 0.0648 24 26 0.0531 0.0649 28 0.0453 30 0.0690 32 0.0628 34 0.0657 36 0.0803 38 0.0208 40 0.1161 42 0.1172 44 0.0981 46 0.1247 48 0.1339 50 0.0596 52 0.0523 54 0.0859 56 0.0807 58 0.0655 60 0.0558 62 0.0565 64 66 0.0405 0.0265' 68 0.0198 70 0.0467 72 0.0121 74 0.0386 76 0.0597 78 0.0690 80 0.0026 82 84 0.0875  2  2  RArnKlkW) 0.0640  6  C  (min) 12.51  Unc(BDC)% 60.64  181  R u n 66 5.0 Bulk concentration (%) 11942. Mixture Re 17980. Water Re 8.71 Water average Temp.( C) 32.57 M . average Temp. ( C) Q . at 9=0 = 0.415 Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0537 1 0.0646 2 0.0855 3 0.2220 4 0.1957 5 0.2030 6 7 0.2125 8 0.1552 0.2139 9 10 0.3424 0.0459 11 0.1351 11 0.2437 13 0.2432 14 0.3089 15 0.2034 16 17 0.3244 0.3275 18 19 0.2177 0.4804 20 0.3417 21 0.2734 22 0.3227 23 0.2076 24 0.2063 25 0.2638 26 0.2645 27 28 0.2689 0.2703 29 0.2190 30 0.2766 31 0.2781 32 0.2795 33 0.2824 34 0.3447 35 0.2840 36 0.0686 37 0.0252 38 0.3126 39 0.2535 40 0.3156 41 42 0.3143 0.3211 43 0.3286 44 0.4024 45 46 0.3355 2  Time Fouling Res. (m K/kW) (min) 0.3855 90 0.3217 91 0.2680 92 0.3268 93 94 0.3355 0.4738 95 0.5219 96 0.5072 97 0.5158 98 0.5193 99 100 0.5215 101 0.4458 0.4458 102 0.4456 103 0.4532 104 0.4644 105 0.3927 106 0.2156 107 0.4005 108 0.4785 109 0.4042 110 0.3994 111 0.4815 112 0.4823 113 0.4839 114 0.4502 115 0.5044 116 0.4230 117 0.5956 118 0.3569 119 120 0.5162 0.5241 121 0.5294 122 0.3113 123 0.4611 124 0.2729 125 0.3950 126 0.3399 127 0.5659 128 0.6075 129 0.5034 130 0.5900 131 0.5039 132 0.5109 133 0.4424 134 0.4490 135 0.4521 136 2  182  47  0.3423  137  0.3866  48  0.3454  138  0.5457  49  0.2315  139  0.3999  50  0.2329  140  0.4705  51  0.3546  141  0.3253  52  0.3569  142  0.3990  53  0.2379  143  0.4716  54  0.2967  144  0.7633  55 56  0.3638 0.3523  145 146  0.6557 0.4123  57  0.2819  147  0.5756  58 59  0.3415 0.3431  0.4436 0.5846  60  0.3492  148 149 150  61  0.4230  151  0.5837  62  0.3631  152  0.4165  63  0.3646  153  0.5051  64  0.3653  154  0.4314  65  155  0.5171  66  0.3064 0.3746  156  0.5250  67  0.3123  157  0.1998  68  0.3792  158  0.3834  69  0.3855  159  0.3215  70  0.3239  160  0.3943  71  0.268  161  0.3296  72  0.3304  162  0.4741  73  0.3939  163  0.5808  74  0.4179  164  0.6629  75  0.4737  165  0.6609  76  0.4703  166  0.668  77  0.4709  167  0.6742  78  0.4016  168  79 80  0.4129 0.425  169 170  0.9511 0.6955  81  0.1779  171  0.7158  82  0.3757  172  0.6231  83  0.3947  173  0.6182  84  0.4824  174  0.6337  85  0.3438  175  0.6403  86  0.3576  176  0.6459  87  0.3630  177  0.6480  88  0.3754  89  0.3123  RAtnKlkW) 0.5368  0  C  (min) 79.60  0.4923  0.6016  Unc(BDC)% 35.99  183  R u n 67  Bulk concentration (%) 10.0 Mixture Re 11428. Water Re 17827. 8.42 Water average Temp.( C) 32.46 M . average Temp. (C) Q at 6=0 = 0.448 kW Time Fouling Res. (min) (m K/kW) 0 0.0000 1 0.1148 2 0.4597 3 0.5181 4 0.9055 5 1.0652 6 1.0965 7 1.1144 8 1.1506 9 0.975 10 1.2037 11 1.1289 12 1.5169 13 2.1637 14 2.6787 15 3.7632 16 3.8769 17 4.036 18 3.0749 19 1.9706 20 1.1497 21 1.2134 22 0.8910 23 0.9127 24 1.1085 25 0.8744 26 1.1738 27 1.4238 28 1.7968 29 1.2801 30 0.9366 31 1.0432 32 0.8840 33 1.5301 34 1.2988 35 1.3160 0.9340 36 37 1.7418 38 2.7991 39 1.2304 40 1.2864 41 1.1137 42 0.9298 43 1.3290 44 1.0913 1.0900 45 0.7917 46  Time Fouling Res. (min] (m K/kW) 90 0.9493 91 0.9325 1.3345 92 1.1199 93 94 1.0653 95 1.2695 96 0.8923 97 1.2945 0.9310 98 99 0.9512 100 0.9736 0.9926 101 1.1003 102 103 1.7710 104 2.7675 2.2302 105 1.5204 106 107 1.5477 108 1.3175 0.9359 109 110 1.1499 0.9887 111 112 0.8433 113 1.5833 1.3138 114 115 1.5732 1.5996 116 1.1257 117 1.3718 118 0.9876 119 120 1.6006 1.3158 121 122 1.3377 1.1247 123;. 1.1394 1241.1638 125 1.6722 126 127 1.4041 128 1.0008 0.8537 129 1.0224 130 1.1314 131 1.8427 132 1.4973 133 1.5099 134 1.8860 135 1.9106 136 2  2  i  184  47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  0.6788 0.6244 1.5084 0.9112 1.0963 0.6706 1.0795 0.8946 1.5328 1.0793 1.3082 1.0354 1.8297 1.2590 0.8896 0.9131 0.9225 0.9151 1.2963 1.2825 1.2834 1.2602 1.2668 1.0587 .1:2682 1.2762 1.0652 1.0757 1.5264 1.2682 1.0704 1.2820 1.0743 1.0848 1.2935 0.9159 0.9171 1.0911 1.1017 1.1124 1.0955 0.9298 1.1147  R*(m 2K/kW) 1.2719  137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177  0c(min) 2.89  1.3261 1.3336 1.1465 1.6491 1.1574 1.3997 1.6508 1.1473 0.9624 1.1638 1.3835 0.8234 0.8311 0.9996 1.1399 1.1278 1.1372 1.3615 0.8207 0.9912 1.0033 1.2050 1.0238 1.1691 0.6712 1.3792 1.1617 0.9863 1.1871 0.8324 1.0021 0.9425 1.1007 1.1047 0.9364 1.1355 0.9680 0.9814 1.1865 0.8508 1.3435  Unc(BDC)% 15.07  185  Run  68  15.0 B u l k concentration (%) 10195. Mixture Re 18695. Water R e 10.06 Water average Temp.( C ) 32.49 M . average T e m p . ( C ) Q at 9=0 = 0.300 k W Time (min) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  F o u l i n g Res. (m K/kW) 0.0000 0.3328 0.5510 0.5977 0.8991 0.9206 0.9383 0.9608 1.3666 1.3960 1.4395 1.8498 1.8742 1.8996 0.9907 1.9733 2.0319 2.8777 2.1085 2.1443 2.1749 1.6285 2.2606 2.8008 2.743 4.0884 2.7943 2.8360 2.8841 2.9322 2.9834 2.1512 2.1822 1.6115 2.9037 2.8326 4.2239 2.8810 2.9230 2.9682 2.1392 3.0927 2.2290 1.6449 2.2174 2.1846 2.9977 2  Time (min) 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 • 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136  F o u l i n g Res. ( m K/kW) 3.2422 2.3186 1.7064 1.7356 2.4129 2.4102 2.3374 1.6759 3.2732 3.2557 3.2828 1.2649 1.6647 4.6109 7.7140 3.1573 2.2269 3.1750 3.2625 3.3064 1.7199 1.7277 1.7737 2.3294 2.3240 1.6974 2.3591 2.3672 3.3208 2.3401 3.3630 2.3645 3.1914 3.2257 3.2566 4.9554 2.3591 2.3646 1.7358 2.3837 2.2006 3.1192 3.1433 2.2070 2.2799 2.3073 2.3129 2  186  47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89  137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179  2.9943 3.0175 3.0571 3.0967 3.1264 3.1522 3.1388 3.2018 3.2186 3.2253 2.3001 2.3295 2.3298 2.3565 2.2948 1.6295 3.1180 7.5226 7.4824 7.5361 4.5918 4.6634 4.7260 3.2490 2.2970 2.3051 4.9046 3.2760 3.2625 3.2794 3.3165 3.3651 2.3509 2.3374 3.3379 2.3428 1.6398 0.8562 2.2916 3.2220 3.1848 2.2613 3.1949  R*(m K/klV) 2  2.7913  0 (i nin) c  I .51  1.71548 1.7426 1.7896 1.8170 0.9938 1.0091 1.3800 1.0312 1.0481 0.7727 1.0854 2.2163 4.5536 3.0528 4.6321 4.7788 3.2156 2.2878 1.6756 2.3730 2.4143 1.7736 1.7248 2.3620 2.4149 2.4225 1.7782 1.3193 1.8394 3.3067 3.2928 2.3235 3.3264 2.3730 2.4088 2.3785 3.2840 4.9599 5.0108 3.3447 2.3998 2.3974 2.4083  Unc(BDC)%  25.29  187  Run 69 Bulk concentration (%) 20.0 Mixture Re 9089. Water Re 18622. Water average Temp.( C) 9.92 M . average Temp. ( C) 32.39 Q . at 9=0 = 0.502 k W Time (min) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 42 43 44 45 46 47 48 49 50  Fouling Res. (m K/kW) 0.0000 0.6930 2.3525 4.9826 2.7740 3.0367 5.8166 6.3371 6.3307 6.3307 6.6772 3.4662 14.6704 15.3872 15.5039 6.5651 16.0695 6.7084 6.7754 16.1230 16.9078 6.9179 16.5213 16.5626 15.9089 16.5626 16.4934 17.2331 16.6318 16.5902 17.2331 15.9892 16.7837 16.7837 7.09290 17.5472 17.7326 7.3763 16.7147 17.2902 17.2902 17.2617 17.8336 17.9665 18.1587 17.5045 17.5045 2  Time (min) 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 73 74 77 85 94 99 100 101 102 103 106 109 110 111 117 118 119 120 122 127 128 129 130 131 132 138 170 171 172 173  Fouling Res. (m K/kW) 7.4835 7.4978 7.4835 7.5478 7.4531 19.3502 7.5257 7.6350 18.8928 18.8161 7.6276 19.6836 19.5248 19.5565 19.4930 19.6518 19.6518 18.9234 7.5258 19.6836 7.6663 22.4439 21.0500 20.9510 21.1159 21.3302 20.4560 20.5880 19.8267 18.9386 18.2178 18.4394 18.2771 7.3094 19.0152 19.0152 18.9231 18.9537 19.0304 19.2292 7.5907 18.6784 20.3026 21.6542 21.5685 22.5811 21.6372 2  188  51  17.0903  176  21.8778  52  7.2761  178  22.5633  53  7.3476  179  21.7916  54  7.4191  R*(tnKlkW) 17.1193  dc  (min)  Unc(BDC)% 15.25  32.99  189  Run 70 Bulk concentration (%) 5.0 Mixture Re 11185. WateRe 9344. , Water average Temp.( C) 15.14 M . average Temp. ( C) 29.02 Q at 9=0 = 0.439 k W w  Time (min) 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 128 130 132 134 136 138 140 142 144 146 148 150  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.0594 4 0.0619 6 0.0587 8 0.0681 10 0.0817 12 0.0845 14 0.0834 16 0.0878 18 0.0889 20 0.0750 0.0726 22 24 0.0821 26 0.0705 28 0.0728 30 0.0873 0.0813 32 34 0.0772 0.0727 36 38 0.0396 40 0.0760 0.0816 42 0.0818 44 0.0786 46 48 0.0742 50 0.0742 52 0.0701 0.0898 54 56 0.0840 0.0876 58 0.0804 60 62 0.0911 64 0.0616 0.1030 66 0.0802 68 70 0.0860 0.0581 72 74 0.0587 76 0.0971 0.0711 78 0.0797 82 84 0.0835 2  Rf{mKlkW) 0.0774  0c(min) 1.99  Fouling Res. (m K/kW) 0.0959 0.0967 0.0857 0.0973 0.0783 0.0771 0.0636 0.0660 0.0842 0.0686 0.0650 0.0652 0.0669 0.0637 0.0586 0.0908 0.0794 0.0747 0.0901 0.0800 0.0779 0.0852 0.0684 0.0743 0.0592 0.0906. 0.0794 0.0751 0.0692 0.0862 0.0667 0.0729 2  Unc(BDC)% 43.56  190  Run  71  Bulk concentration (%) 10.0 Mixture Re 10714. Water Re 9262. Water average Temp.( C) 14.81 M . average Temp. ( C) 29.08 Q at 9=0 = 0.416 k W Time (min] 86 88 90 92 94 96 98 100 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132 152 154 156 158 160 162 164 166 168  Time Fouling Res. (min) (m K/kW) 0.0000 0 0.0508 2 0.0543 4 0.0517 6 0.0678 8 0.0573 10 0.0396 12 0.0548 14 0.0639 16 0.0578 18 0.0551 20 0.0610 22 0.0703 24 0.0084 26 0.0577 28 0.0692 30 0.0683 32 0.0915 34 0.0204 36 38 0.0923 0.0508 40 42 0.0729 44 0.0946 0.0574 46 48 0.0486 0.0474 50 0.0683 52 0.0695 54 0.0601 56 0.0724 58 0.0816 60 0.0706 62 64 0.0651 0.0914 66 0.0826 68 0.0635 70 0.1114 72 0.0776 74 0.0864 76 0.0663 78 80 0.0755 0.0629 82 0.0449 84 2  RArnKlkW) 0.0799  0  C  (min) 13.62  Fouling Res. (m K/kW) 0.0644 0.0855 0.0741 0.0712 0.0674 0.0885 0.0763 0.0845 0.0834 0.0841 0.0794 0.0875 0.1000 0.0763 0.0969 0.0963 0.0893 0.0850 0.0968 0.0843 0.1029 0.0828 0.0867 0.0862 0.0934 0.1037 0.0561 0.0941 0.0847 0.1172 0.0617 0.0743 0.0938 2  Unc(BDC)% 57.45  191  Run 72 Bulk concentration (%) 15.0 Mixture Re 9569. Water Re 9018. Water average Temp.( C) 13.80 M . average Temp. ( C ) 29.24 CL at 9=0 = 0.364 k W Time Fouling Res. (min) (m K/kW) 0 0.0000 0.2776 2 4 0.2370 6 0.2157 8 0.2997 0.3144 10 0.3085 12 14 0.3084 16 0.3423 0.3490 18 0.3665 20 0.3837 22 24 0.4079 26 0.3780 0.3971 28 0.4162 30 0.3990 32 34 0.4105 0.4194 36 38 0.4217 0.4354 40 0.4396 42 44 0.2138 0.3940 46 0.4720 48 50 0.4293 52 0.4663 54 0.4725 56 0.4650 58 0.4629 0.4601 60 62 0.4359 0.4252 64 0.4777 66 0.4507 68 0.4857 70 0.4876 72 74 0.5164 76 0.4869 0.5135 78 0.4835 80 0.5706 82 0.5398 84  Time Fouling Res. (min) (m K/kW) 0.4989 86 0.4640 88 90 0.4692 0.5005 92 94 0.5442 96 0.5721 0.4882 98 100 0.4303 0.5028 102 104 0.4480 106 0.5602 108 0.5066 0.4563 110 0.4820 112 114 0.5424 116 0.4079 118 0.5746 120 0.5187 0.5274 122 124 0.6135 0.5233 126 0.6838 128 130 0.4487 0.5107 132 0.5271 134 0.5289 136 138 0.4795 140 0.5058 0.5133 142 0.4803 144 0.4873 146 148 0.3886 0.5446 150  2  RjtrnKlkW) 0.4899  2  0 (min) C  13.62  Unc(BDC)% 13.06  192  Run  73  Bulk concentration (%) Mixture Re Water Re Water average Temp.( C) M . average Temp. (C) Q . at 9=0 = 0.265 kW  Time Fouling Res. (min) (m K/kW) 86 1.0446 88 1.0454 1.0078 90 1.0852 92 94 1.0644 96 1.0288 98 1.0782 1.2041 100 102 1.0552 104 1.0891 1.1399 106 108 1.0892 110 1.1891 112 1.0822 114 1.2008 116 1.2186 118 1.2354 120 1.2057 122 1.1966 124 1.2036 126 1.1875 128 1.1771 130 1.1202 1.1053 132 134 1.0912 136 1.1378 138 1.1053 0.9872 140 142 1.1022 144 1.0480 146 1.1268 148 1.1855  Time Fouling Res. (min) (m K/kW) 0 0.0000 2 0.3669 4 0.4297 6 0.5662 8 0.5522 10 0.5533 0.6390 12 14 0.6291 16 0.6580 18 0.5780 20 0.6094 22 0.6223 24 0.5917 26 0.5932 28 0.6897 30 0.7214 32 0.8319 34 0.7189 36 0.6966 38 0.7611 40 0.7535 42 0.7407 44 0.8456 46 0.7897 48 0.7604 50 0.9654 0.9929 52 54 0.9518 56 0.9822 58 0.9247 60 0.9574 0.9986 62 64 0.8534 66 0.9208 68 0.9785 70 0.8852 72 0.9736 74 0.8344 76 1.0150 78 1.0170 80 1.1302 82 0.9811 84 0.9837  2  2  R*(m K/kW) 2  1.1080  20.0 8545. 8765. 12.76 29.28  6 (min, c  26.!  Unc(BDC)% 15.48  193  

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