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

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W A X D E P O S I T I O N F R O M K E R O S E N E ONTO C O O L E D S U R F A C E S By Michael Abraha Ghedamu B . A . S c , Addis Ababa University, 1989 A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR THE 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 UNIVERSITY OF BRITISH C O L U M B I A May 1995 Cc), Michael Abraha Ghedamu , 1 9 9 5 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbia Vancouver, Canada DE-6 (2/88) 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 wax-kerosene, 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 ASTM 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*f and 9C from the resistance vs. time experimental data. The wax deposit showed a decrease in R*f with increasing Re, with increasing Tb and with decreasing concentration. Similar results were found by Bott and Gudmundsson (1977b). From the plots of R*f vs. Re, the hierarchy in increasing R*f was found to be: Heresite-coated stainless steel (dull and shiny) < 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. A similar hierarchy with four of the seven tubes was shown with respect to R*f vs. Tb. That 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 21 Table 2. Summary of literature review of vs. wax-solvent velocity, Tb and 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. Tb =32.6±0.2°C, Cloud Point= 21.1 °C , tb =9.5+0.5 °C, Vw=2.5 m/s 53 Table 15. Results for slack wax MCT-10 at 20% by wt. using stainless steel. Tb =31.4±0.3 °C, Cloud Point= 27.8 °C , f 6=10.4±1.5°C, V w = l . l m/s 53 Table 16. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel. Tb = 31.3+0.1°C ,CloudPoint=27.8 °C, / f c=7.6±0.4°C, V w = l . l m/s....54 Table 17. Results for slack wax MCT-10 at 20% by wt. using sand-blasted stainless steel. Tb = 31.2+0.1 °C, Cloud Point= 27.8°C, f6=11.4±0.6 °C, V w = l . l m/s 54 Table 18. Results for slack wax MCT-10 at 20% by wt. using n-C18 silane-coated chrome- plated stainless steel. Tb =31.3+0.1 °C, Cloud Point=27.8°C , tb=13.6± 0.7°C, V w = l . l m/s 54 vii 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 , / 6=13.5±0.9 °C, V w = 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, f6=13.2±0.4 oc, V w = l . l m/s 55 Table 21. Results for slack wax MCT-10 at 20% by wt. using monolayer n-C18 silane coated stainless steel. Tb =31.5+0.1 °C, Cloud Point=27.8 °C , f 6=13.2+0.2°C, V w = l . l m/s 55 Table 22. Results for refined wax at 10% by wt. using stainless steel and wax-kerosene atRe=12155. Cloud Point=27.8 °C , fb=10.0+0.3 °C, V w = l . l m/s 63 Table 23. Results for slack wax MCT-10 at 20% by wt. using stainless steel at Re=9074. Cloud Point=27.8 °C , f 6=7.9±0.5°C, V w = l . l m/s 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 , f6=9.6±1.5 °C, V w = l . l m/s 63 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 6=11.7±0.8°C, V w = l . l m/s 64 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 6=12.8±0.5°C, V w = l . l m/s 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 , / 6=9.3±0.5°C, Vw=2.5 m/s 73 Table 28. Results for slack wax MCT-10 using stainless steel at Re= 10003 and Tb =29.2 ±0.1 °C , Cloud Point=27.8 <>C , f6=13.9±0.9 °C, V w = l . l m/s 73 Table. 29. Summary of removal and sliding of wax deposit 80 Table. 30. Sliding velocity for chrome-plated stainless steel tube using slack wax MCT-10 at 20% by wt. Tb = 31.3±0.1°C , Cloud Point=27.8 °C , 4=7.6±0.4°C, V w = l . l m/s 80 Table 31. Lists of run number, disk number, tube type, wax type and U 0 107 viii 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 39 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. GC chromatogram for refined wax 43 Fig. 10. GC chromatogram for slack MCT-10 wax 44 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. Rf vs. time for slack wax MCT-10 at 10 % by wt. using stainless steel. Re = 8722, 7^=31.4 °C, Cloud Point = 27.8°C 56 Fig. 13 c. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=10615, 5=31.4 °C, Cloud Point=27.8°C 57 ix Fig. 13d. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=12184, 5=31.4 °C, Cloud Point=27.8°C 57 Fig. 13e. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. 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*f vs. Re for MCT-10 slack wax, 20% by wt at 5=31.3+0.2 °C for different surfaces 60 Fig. 15b. Result of Log (R*f) vs. Log (Re) for MCT-10 slack wax, 20 % by wt at 5= 31.3+0.2 °C for different surfaces 61 Fig. 16a. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=9430, 5= 28.9 °C, Cloud Point=27.8°C 64 Fig. 16b. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=9430, 5 = 31.2 °C,Cloud Point=27.8°C 65 Fig. 16c. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=9430, 5= 34.0 °C,Cloud Point=27.8°C 65 Fig. 16d. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=9430,5 = 38.1 °C,Cloud Point=27.8°C 66 Fig. 16e. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. 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*f 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 Fig. 20a. Rf vs. time for slack wax MCT-10 at 5 % by wt.using stainless steel. Re=10003, 5 =29.2 °C, Cloud Point=27.8°C 73 Fig. 20b. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=10003, T„ =29.2 °C, Cloud Point=27.8°C 74 Fig. 20c Rf vs. time for slack wax MCT-10 at 15 % by wt.using stainless steel. Re=10003, 7^=29.2 °C, Cloud Point=27.8°C 74 Fig. 20d. Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. 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 Tb=29.2°C 77 Fig. 23. Graph of R^ vs. Tb-Tc 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. My 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 C h a p t e r 1 1. Introduction Petroleum waxes are broadly defined as waxes which naturally occur in the various fractions o f crude petroleum. Some crudes contain little or no wax, whereas others are so waxy that they are semisolid at r oom temperature. There are three main types o f petroleum waxes: paraffin waxes, microcrystalline waxes, and petrolatum. Paraffin waxes are mainly composed o f straight-chain molecules with a small number o f branched chains and crystallize in large, well formed, distinct crystals o f plate and needle types. Typical ly paraffin waxes contain 18-56 carbon atoms. Microcrystal l ine waxes have molecules o f 40-50 carbon atoms and crystals formed are small and indistinct. This type o f wax contains more branched hydrocarbons compared to paraffin. Petrolatum contains both solid and liquid hydrocarbons. W a x is recovered as a product from some refineries. The separation o f wax from a paraffin distillate is made possible by the fact that the solubility o f wax in the distillate decreases with decreasing temperature. The petroleum stream is first chilled in heat exchangers to a low temperature to solidify the wax, which is then removed from the heat transfer surface by scraping. The chilling may be accompanied by incremental dilution as in the DILCHILL process where a petroleum stream is diluted by a solvent such as propane, which is a good solvent for oil but a poor one for wax, and then chilled. The scraped wax is recovered usually by a vacuum 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, +- + RW +^Rfi + (1) u f° h0 4 4 h Here Rfo and Rfi refer to the thermal resistance of the fouling deposit on the 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 Rf values does not guarantee longer operating 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 Rf=—-— (2) where U 0 is the overall heat transfer coefficient at time zero. Rf can also be written as for a small thickness x with respect to diameter. Many researchers have studied fouling problems based on measurement of Rf, 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 Cs. Assuming turbulent flow, m d = k t ( C b - C . ) (4) where kt is a turbulent mass transport coefficient. The surface integration step is then given by m d = k r C : (4a) where kr is the surface integration constant and n the order of the integration step. 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 xs. The fact that removal increases with increasing 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 . Bmx s — = m d - m r = m d '- (6) d9 \y 7 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 (8) m r m d 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 9C can be interpreted as the average residence time of an 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 md . By putting 9- 9C in Eq.(7), m works out to be 0.632m*, so that 9C is also the actual time required to achieve 63.2% of the asymptotic fouling resistance. 6C can 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 9C in order to determine a reliable value of R*f. Since m =md9c and 9C oc 1/r, <X1/M? in turbulent flow, it follows that even if md is directly proportional to w„, as would be the case under conditions of turbulent mass transfer control at high values of Sc, m* and hence R*f would still decrease as the velocity increases. This generalization 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 c with fluid velocity 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 9C can reasonably be 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. By reference to Eq. (8 ), it is reasonable to generalize the criterion to be fulfilled by any deposit as '.<('.L (9) or, since 0cac(y//TS)<X(y//ul), 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 i f 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 = "L_ (13) t=0 &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 l l 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 WAP. 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. No 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 Tb and concentration. 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 r ; - Cloud point T c = 23 °C j _ Average bulk temp. T b = 28°C i ^ - 1 5 0 — Time t = 15 min. ! T J -Q r i i 1 1 i i i i i i i i i i 1 1 i i i i 0 0-05 0-10 0-15 0-2( W—Flowra te (kg/s) 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. Al l 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 a t l 0 6 ° 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 phenol-formaldehyde (roughness <2u), epoxy-phenolic ( <5|_i) and polyurethane (<3u.) have shown less deposit compared to surfaces covered by mill scale (30-40u). Tetra-fluoroethylene 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 36 34 32 30 28 *C 100.4 96.8 93.2 89.6 86.0 82.4 ' F COLD 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 = 38*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 10-percent 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 T A B L E t — E F F E C T OF 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 = 4 ° C Stirring Rate = 300 rpm Preparat ion Deposit Wt. (mg) 6 hours Percent Change Deposit Wt. (mg) 16 hour s P ercent Change Polished 86.6 — 1 19.0 — 240-Grit 90.0 -f 3.9 1 13.5 - 4.6 50-Grit 90.3 + 4.3 103.2 - 13.3 Coating X 59.8 -30.9 81.9 -31.2 Coating Y 55.3 -36.7 74.4 -37.5 Coating Y* 60.4 -30.2 84.5 -29.0 Coating Z 78.3 -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*f vs. wax-solvent velocity, Tb and concentration effects. lessen and Howell Jorda Toronov Patton and Cassad Eaton and Weeter Bott and Gudmundss-on Velocity Effects Not studied * * ± * Temperature Effects Not studied * Not studied Not studied ± * Concentrat-ion Not studied Not studied Not studied Not studied Not studied + 21 + when indicated variable increases , R^- increases. * when indicated variable increases, R*f decreases. ± when indicated variable increases, both an increase and decrease in R*f are observed. 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*f decreases with increasing velocity. Bott and Gudmundsson indicate that R*f decreases as Tb increases, but little was reported 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 P-400/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 " No 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 wax-kerosene 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: M, = h(phg-Pw)g Cd, the discharge coefficient, was determined by calibration (Zhang, 1992) over the Re-range studied and was found to be 0.62 (confirmed at Reynolds No. of (14) where 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. Al l thermocouples were calibrated in the range 0°C to 60°C . The temperature-electrical 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 (ASTM 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 wax-kerosene 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 s). In this case the viscosity is defined by the 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. %) = 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) Al l display instruments in the test rig are turned on. A particular temperature display ^ weight _+10Q wax weight + kerosene weight 33 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. Cone (% by wt.) Refined wax MCT-10 MCT-30 5 15.6 15.0 31.1 10 21.1 21.1 36.7 15 25.6 23.3 40.0 20 28.9 27.8 42.2 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. Al l 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 Shear 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 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 S h e a r R a t e ( 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] 15.6 25.0 30.0 35.0 40.0 u.rPa.sl.10-3 1.30 0.89 0.82 0.76 0.78 Table 5: Viscosity runs for refined wax at 10% by wt. in kerosene. T[0C1 21.1 25.0 30.0 35.0 40.0 p. [Pa.s].10-3 1.02 1.26 1.00 0.87 0.80 Table 6: Viscosity runs for refined wax at 15 % by wt. in kerosene. T [ °C] 25.6 30.0 35.0 40.0 p |Ta.sl.lO- 3 1.25 1.10 0.93 0.82 Table 7: Viscosity runs for refined wax at 20 % by wt. in kerosene. Tr °c i 28.9 35.0 40.0 u[Pa.s].10-3 1.10 1.00 0.80 Table 8: Viscosity runs for slack wax MCT-10 at 5 % by wt. in kerosene. T [ °C] 15.0 20.0 25.0 30.0 35.0 40.0 p[Pa.s].10-3 1.37 1.03 1.03 0.90 0.90 0.81 Table 9: Viscosity runs for slack wax MCT-10 at 10 % by wt. in kerosene. T T O 21.1 25.0 30.0 35.0 40.0 45.0 uTPa.sl.10-3 1.27 1.14 1.07 0.95 0.87 0.81 40 Table 10: Viscosity runs for slack wax MCT-10 at 15 % by wt. in kerosene. T P C I 23.3 30.0 35.0 40.0 45.0 u.rPa.sl.10-3 1.40 1.10 0.98 0.84 0.78 Table 11: Viscosity runs for slack wax MCT-10 at 20 % by wt. in kerosene. T r°ci 27.8 35.0 40.0 45.0 nlTa.sl.10- 3 1.04 0.91 0.81 0.80 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/m3) 280 54253 x 10"nf5 p„ = (999.83952 +16.945176f4 -7.9870401 x IO"3** -46.170461 x IO"**3 + 105.56302 x \Qr*t* for 0 °C <tb < 20 °C Viscosity of water (Pa.s) l o g 1 0 /U0 3 -1301 998.333 + 8.1855(ffc - 20) + 0.00575(ffc -20) 2 — 1.30233 tb i n O C Heat capacity of water (kJ/kg °C) =4.21765-3.74987 x 10-3rt +1.49921 x IO"4** -3.35545x 1CT\3 +4.27292x IO"8:,4 - 2.30244 xlO"10/,5 where The density and heat capacity of the wax-kerosene mixtures were experimentally measured 41 by Zhang (1992) using refined wax. The results are as follows. Density (kg/m3): pk = 816.25 - 0.748927;, Tb in °C 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 wax-kerosene solutions were measured from about 25 to 80 °C. Heat capacity (kJ/kg °C): C M = 1.18143 + 0.0122467; , where Tb = 2L±£ jb in °C The effect of wax on the wax-kerosene specific heat capacity was minimal, so the above equation was used for all concentrations. Viscosity: juk=aexp KRT» , T b i n K . 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. %) 5 10 15 20 a 1.83x10-* 7.58X10" 6 1.27xl0-7 1.65xl0-7 b 15525 12147 22830 22171 Table 13: Viscosity Coefficients a and b for MCT-10 Slack Wax. Wax concentration (wt %) 5 10 15 20 a 4.16X10" 6 3.80x10-* 1.86xl0-7 5.92xl0-7 b 13676 14160 21993 18820 42 0 CO C\2 01 O (J U o pn >^ N 9 Oi ol 5)-N J3 6 0 <^ z 1 y ft (A ! £ z -J o x V < < in o h o in •rt o UJ I— Ul < — I — in —i— o in o ro —r~ in o CVJ in — T — o in o Fig. 9. GC chromatogram for refined wax. 43 o PQ < C/l u o to - J o UJ 5 0 ^ Q 0 UJ '—. o k o O 5 5; C O o If) 10 o h o CD S?0 LZ «-• « =3F £3 0 I ' 1 • 1 1 1 <~—i • r— •H o cn co I D in UJ •rt < _n o m o o m OJ Fig. 10. G C chromatogram of slack wax MCT-10. 44 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 w = m C p w ( t 2 - t 1 ) (16) or by using the directly measured At (the differential temperature rise) for accuracy Q w = m C p w A t (17) Equation (17) was preferred since the measurement of A/ was more accurate than that of (t2 - / , ) . Because of uncertainties in the heat capacity for the wax-kerosene mixture the heat 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 0 8 ) 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 0 is the clean overall coefficient at 0=0. The Reynolds number of wax-kerosene solution was calculated as Re = (21) where dh is the hydraulic diameter for the annulus, and u is the actual velocity in the annulus. 6.2. Data Fitting and Determination of Parameters From the fouling tests, it was found that most plots of R*f vs. 9 followed asymptotic behaviour, i.e. the deposit was built up at a falling rate and eventually reached a constant value. Even without constancy of md and the other assumptions underlying Eq. (6), this type of behaviour can be represented by the well known Kern-Seaton equation Eq. (7), which can be rewritten as 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*f and 6C. Given a set of data points (0t,Rfi), where i=l,....N, the values of Rf=RU\-e«<) (22) where Rf = m , and was calculated via Equation (20). Pfkf R*f and 6C were calculated to minimize the sum, (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 Rf is dependent upon the errors in the calculated values of both U n and U . For the function Rf=Rf(U0,U) cRf cRf dR,=-^-dU0+—^dU (24) (25) If the errors in U 0 and U are 5 U 0 and 8U respectively, and are small relative to U 0 and U , then the error induced in Rf is given by: cRf cRf f d U ° cU (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 0 and 8U to be positive, SRf = cRf su0 + 5U W0 (27) FromEq. (20), u2 4 (28) (29) Thus 47 SRf = (30) {Ul 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 [^(r.-O-te-O] Thus neglecting errors in the calculation of A j , (31) 5U 32* a2 + cU c57I (32) Hence u Qw w\ InX — 1 1 — InX a2 + InX ST2 (33) where W = (T]-t2)-(T2-tl) Y = Z = T 2 - t w {Tx-t2) W (34) (35) (36) (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 tx and t2, 3 2 * dm dm + 3Q, a, 3 2 . a2 dt, (38) or and 5QW = C^-t^Sm+mC^St, + AWC^<* 2 8QW Sm + 8tt+a2 Qw ™ (t2-t,) The uncertainty as a percentage can be written by modifiying Eq. (30) SRf ' 1 5UQ 1 5U^ JJ0 u0+u u) A\Rf :100% 5UAJ is given by combining Eq. (40) and (33), i.e. 5U _bm 5t,+a2 | 1 \ U ~ m + (t2-t,) +W[ InX -iax + 1-InX \St2 + InX -w,+ (39) (40) (41) 1-InX ,< 5 r u ( 4 2 ) SU/U0 can be calculated from the corresponding values at time 0=0, the mass flowrate, 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 res i s t ances ,^ /^ , 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 Rf. A slightly smaller maximum would have been reported if the above calculation were based on a single measurement of tx-t2 or Af. 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. f » •° « » « . • 1-8 IS — 1-2' 5 1-0-o - 4 H AO Time (min) 110 160 46 80 Time (min) I2P 160 Fig. 11. Result for slack wax at 20% by wt Fig on chrome-plated stainless steel tube, Re=9224 and Tb =31.2 °C. i L =0.6031(1-e"") . 12. Result for slack wax at 20% by wt. on chrome-plated stainless steel tube, Re=9208 and 7^=31.2 °C. Rf =0.5814(1- <T") 5 0 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 9C . Table 16 lists results for R*f and 0C. For the two experiments, Rf* =0.592 m 2 K/kW and the total range of Rf was 0.022 m 2 K/kW, which is less than 4 % of the mean. The time 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 Rf versus time plots and the corresponding fitted curves. It is apparent that at lower velocity, the Rf values are larger. Table 15 shows that as the Reynolds number is roughly doubled from 6645 to 14,430, the R*f value decreases by a factor of 1.5. For refined wax at 10 % by weight, the above trend with Reynolds number was similar for the same tube and in this case the time constant, 0c, also decreases as Re increases, i.e. the fouling resistance takes less time to reach 63 % of R*f at higher flow velocities, as seen in Table 14. Figure 14 shows the Reynolds No. effect on R*f for the refined wax runs. Rf 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*f with velocity was evident, but the 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*f drops markedly over the same range of Re. Fig. 15b shows a plot of log (Rf) vs. log (Re) for the data of Fig. 15a. The uncoated stainless steel (slope=-0.42), chrome-plated 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*f with velocity may be the increased shear 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*f/9C versus Re are widely scattered, this parameter tends to 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*FJ9C, 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. Tb =32.6+0.2°C, Cloud Point= 21.1 °C , ffc=9.5±0.5 <>C, Vw=2.5 m/s. Re K (m 2 K/kW) 0c (min.) Uncertainty (%) KI*. (m2 K/kW-min) 7093 2.1890 8.9 13.7 0.2460 11414 0.8896 5.5 30.0 0.1617 14812 0.5122 2.5 22.5 0.2049 17332 0.3363 2.6 27.5 0.1293 19053 0.2249 2.1 27.9 0.1071 Table 15. Results for slack wax MCT-10 at 20% by wt. using stainless steel. Tb =31.4±0.3 °C, Cloud Point= 27.8 °C , r 6=10.4±1.5°C, V w = l . l m/s. Re K (m 2 K/kW) Qc (min.) Uncertainty (%) (m2 K/kW-min) Rf.»< = llu°+Rj (m 2 K/kW) 6645 0.9293 8.0 11.9 0.1162 2.2666 8722 0.8244 10.8 11.4 0.0765 1.9197 10615 0.7926 13.2 8.9 0.0600 1.6597 12184 0.7244 18.1 9.2 0.0400 1.6142 14430 0.6668 10.3 7.8 0.0645 1.4867 53 Table 16. Results for slack wax MCT-10 at 20% by wt. using chrome-plated stainless steel. Tb = 31.3±0.1°C ,Cloud Point=27.8 °C , r t=7.6±0.4 oC, V w = l . l m/s. Re (m 2 K/kW) 9C (min.) Uncertainty (%) (m 2 K/kW-min) K.^^+R) (m 2 K/kW) 6586 0.8238 2.1 17.8 0.3980 2.5841 9224 0.6031 2.1 15.4 0.2900 1.9377 9208 0.5814 2.2 15.6 0.4184 1.9258 11015 0.5941 1.4 11.6 0.3910 1.6754 13156 0.5240 1.3 9.8 0.0749 1.4183 14428 0.4817 6.4 9.6 0.2692 1.3076 Table 17. Results for slack wax MCT-10 at 20% by wt. using sand-blasted stainless steel. Tb = 31.2±0.1 °C, Cloud Point= 27.8°C , / f c=11.4±0.6 °C, V w = l . l m/s. Re K (m 2 K/kW) &c (min.) Uncertainty (%) (m 2 K/kW-min) R* =\/U0+R) f, tot 1 ° J (m2K7kW) 6418 1.2187 5.9 10.1 0.2066 2.3548 8734 0.8227 9.3 11.7 0.0863 1.9047 11340 0.7614 8.9 7.6 0.0856 1.5304 12732 0.6609 7.6 7.7 0.0870 1.3919 14440 0.6016 7.3 6.7 0.0824 1.2142 Table 18. Results for slack wax MCT-10 at 20% by wt. using n-C18 silane-coated chrome- plated stainless steel. Tb =31.3±0.1 °C, Cloud Point=27.80C , r6=13.6+0.7OCj Re K (m2 K/kW) ®c (min.) Uncertainty (%) (m2 K/kW-min) (m2 K/kW) 6629 0.7407 7.9 15.9 0.0938 2.0159 8773 0.4854 20.9 19.4 0.0232 1.7455 11314 0.4605 4.1 11.5 0.1123 1.2891 12888 0.4572 6.3 9.6 0.0726 1.1567 14642 0.4527 12.1 8.1 0.0374 1.0383 54 Table 19. Results for slack wax MCT-10 at 20% by wt using Heresite Si 57 E coated stainless steel. Tb =31.3±0.2 °C, Cloud Point=27.8 <>C, fft=13.5±0.9 QC, V w =l . l m/s. Re (m2K/kW) 9C (min.) Uncertainty (%) (m2 K/kW-min) Rf.<o< = llU°+R*f (m2 K/kW) 6567 0.4406 3.2 21.0 0.1377 1.4979 8819 0.4056 5.0 15.8 0.0811 1.3169 11215 0.2263 2.1 18.2 0.1078 0.9410 12697 0.1534 3.2 24.1 0.0479 0.8162 14207 0.0700 9.4 55.6 0.0074 0.7314 Table 20: Results for slack wax MCT-10 at 20% by wt. using Heresite P-400/L-66 coated stainless steel. Tb= 31.2+0.1 °C, Cloud Point=27.8°C, f6=13.2±0.4 °C, V w =l . l m/s. Re K 9C (min.) Uncertainty (m2 K/kW) (m2K/kW) (%) (m2 K/kW-min) 6616 0.5552 6.4 21.1 0.0868 1.8305 8803 0.3804 2.0 17.2 0.1902 1.3111 8765 0.3671 2.3 16.3 0.0517 1.2295 11042 0.1912 3.7 28.2 0.0163 1.0458 12674 0.1288 7.9 47.2 0.0106 0.9277 14432 0.0520 4.9 155.1 0.1596 0.8425 Table 21. Results for slack wax MCT-10 at 20% by wt. using monolayer n-C18 silane coated stainless steel. Tb =31.5+0.1 °C, Cloud Point=27.8 °C , f6=13.2± 0.2°C, V w =l . l m/s. Re K (m2 K/kW) 9C (min.) Uncertainty (%) (m2K7kW.min) K.«>< = l/U<>+Rf (m2 K/kW) 6631 0.7016 4.4 14.4 0.1595 1.8546 8734 0.4639 14.2 15.7 0.0327 1.4491 11084 0.4496 10.0 11.5 0.0450 1.2543 12672 0.3753 4.2 11.6 0.0894 1.1197 14147 0.3574 6.9 9.0 0.0518 1.0402 55 2.0-1 1.8-1.6-1.4-1.2-20 40 60 80 100 120 140 160 Time (min) Fig. 13 a. Rf vs. time for slack wax MCT-10 at 20 % by wt. using stainless steel. Re = 6645, Tb =31.4 °C, Cloud Point = 27.8°C. 2.0-1 1.8-1.6-1.4-> 1.2-K/kV 1.0-CM E 0.8-OC • 0.6-0.4-0.2-0.0-0 20 40 60 80 100 120 140 160 Time (min) Fig . 13b. Rf vs. time for slack wax M C T - 1 0 at 20 % by wt. using stainless steel. R e = 8722, 7^=31.4 °C, C l oud Point = 27.8°C. 56 2.0-, 1.8-1.6-1.4-1.2-K/kV 1.0-eg E 0.8-DC • 0.6-0.4-0.2-0.0-0 20 40 60 80 100 120 140 160 Time (min) Fig. 13 c. Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=10615, 7^=31.4 °C, Cloud Point=27.8°C. 1.8-1.6-1.4-1.2-Time (min) Fig. 13d. Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=12184, 7^=31.4 °C, Cloud Point=27.8°C. 57 2 0 n 1.8-1.6 1.4 H 1.2 2 CM E of 1.0 H 0.8 ° o ° o o i—i—1—i—•—i—'—i—'—i—'—i—'—i—'—i— 0 20 40 60 80 100 120 140 160 Time (min) Fig. 13e. Rf 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. 58 59 1.4-1 t . 2 H 1.0 H 2 CM E K a: 0.8 ^ 0.6 0.4 0.2 • Uncoated stainless steel tube • Chrome-plated stainless steel tube O Sand-blasted stainless steel tube '+ n-C18 silane-coated chrome-plated stainless steel tube * 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 A 0.0 - | 1 1 1 1 • 1 1 1 ' I 6000 8000 10000 12000 14000 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 o Sand-blasted stainless steel + n-C18 silane-coated chrome-plated stainless steel * Heresite Si 57 E coated stainless steel (shiny) A Heresite P-40G7L-66 coated stainless steel (dull) O n-C18 silane-coated stainless steel ------o. N A —I 1 1 1 \ i —i 1 1 3.8 3.9 4.0 4.1 4.2 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 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 Rf versus time curves for the case of slack wax. The trends 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 2 K/kW, whereas in Fig. 16d at 7^=38.1 °C, R*f =0.22 m 2 K/kW. Fig 17. and Fig. 18 show the trends of R*f with Tb .The most significant drop in R*f occurs between the data near the cloud point and those at some 5 °C higher, where R*f has decreased by almost an order of magnitude. While R*f decreased sharply with increasing bulk temperature for all cases, the time constant did not show any consistent trend. Near the cloud point, 9C values tended to be high, and usually decreased with increasing temperature. In Table 23, for slack wax fouling on the stainless steel tube, a consistent drop in 9C with increasing temperature is observed, whereas in other cases (Table 22 and Table 26) there appears to be an increase in 0e at the highest temperatures. The initial fouling rate, R*fJ9c, for refined wax at 10 % on stainless steel showed a decrease with bulk temperature (Table 22). The principal explanation for a decrease in R*f with increasing Tb is that the higher the value of Tb, the smaller the zone of the hydrocarbon flow which is between the cloud 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 , ffe=10.0±0.3 °C, u=1.6 m/s, Vw=2.5 m/s. T„(°C) (m 2 K/kW) Qc (min.) Uncertainty (%) (m 2 K/kW-min) 28.7 3.6474 12.0 21.0 0.3040 32.4 0.8896 5.5 30.0 0.1617 36.4 0.4632 6.6 27.3 0.0702 40.0 0.3435 4.4 18.6 0.0781 44.2 0.3070 111 14.2 0.0277 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 , fft=7.9±0.5QC, u= 1.6 m/s, V w = l . l m/s. U°c) K (m 2 K/kW) 0C (min.) Uncertainty (%) (m 2 K/kW-min) 28.9 1.5241 16.2 11.0 0.0943 31.2 0.8244 10.8 11.1 0.0765 34.0 0.3788 5.2 13.1 0.0727 38.1 0.2205 2.7 16.7 0.0832 40.6 0.3916 2.3 7.9 0.1733 40.8 0.2359 1.0 14.1 0.2359 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 f t=9.6±1.5 °C, u=1.6 m/s, V w = l . 1 m/s Tbrc) K (m2 K/kW) 9C (min.) Uncertainty (%) (m2 K/kW-min) 31.2 0.6031 2.1 15.6 0.2900 35.9 0.2409 3.4 23.3 0.0713 37.3 0.2056 1.3 42.5 0.1619 40.9 0.1187 2.3 21.8 0.0514 63 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? 27.8°C, > t=11.7±0.8°C,. u=1.6 m/s, V w = l . l m/s U°c) K *c (min.) Uncertainty (m 2 K/kW) (%) (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; / v \ v - 11.2 0.0342 Table 26. Results for slack wax M C T - 1 0 at 20% by wt. using n-C18 silane-coated chrome-plated stainless steel and Re=9391±940. Cloud Point=27.8PC, r6=12.8±0.5 0C, u=1.6m/s, V „ = I 1 nVs Tb{°C) ' •: * c (min.) Uncertainty KI*. (m 2K/kW) (%) (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—1—T— 0 20 40 60 80 100 120 140 160 Time (min) Fig. 16a. of'Rf vs. time for slack wax MCT -10 at 20 % by wt.using stainless steel. Re=8391, rb= 28.9 °C, Cloud Point=27.8°C. 2.0 1.8-1.6-1.4 1.2-1 or 0.8 0.6 0.4 0.2H CO**! ' o o o 0.0-£ -I—I • I '—I—<—1—1—1—1—I—r—1—•>—I— 0 20 40 60 80 100 120 140 160 Time (min) -.; Fig. 16b. Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=8722, 5= 31.2 °C, Cloud Point=27.8°C. 20' 1.5' 1.0 E 0.5 A 0.0-{ 1—I 1 I • I • 1 i - l • I r—1 ' 1 0 20 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, Tb = 34.0 °C, Cloud Point=27.8°C. 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 —•—J—> 1 • 1 • 1 1 I r~l • I 0 20 40 60 80 100 120 140- 160 Time (min) Fig. 16e. Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel. Re=10115, 5=40.6 °C, Cloud Point=27.8°C. ^ " 66 67 2 CNI 1.6H 1.4J 1.2-J 1.CH 0.8H E "Q: o . 6 -0 .4-0.2-0.0 • Uncoated stainless steel tube • Chrome-plated stainless steel tube O Sand-blasted stainless steel tube + n-C18 silane-coated chrome-plated stainless steel tube -• — i — « — i — > — i — • — i — • — r ~ 28 30 32 34 36 T B ( ° C ) —\ 1 1 1 1 38 40 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 sand-blasted 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 2.6-2.4-2.2 5 2.0 -] ^ 1.8H ^ 1.6-1 + o 3 1.4 II o 1.2 H 1.0 0.8 0.6 o • o + A o Uncoated stainless steel tube Chrome-plated stainless steel tube Sand-blasted stainless steel tube n-C18 silane-coated chrome-plated stainless steel tube 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 T 6000 8000 — I 1 1 10000 12000 Re T 1 14000 16000 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 Rf vs. time data on the stainless steel tube for slack 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*f. At low concentrations there is little increase in R*f ; however above about 15 % concentration for refined wax, and above 10 % concentration for slack wax, R*f increases sharply. Doubling the concentration from 10 % to 20 % results in about a 13-14 fold increase in R*f for both refined and slack wax. Table 27 for refined wax shows no consistent trend of 0C with concentration, but for slack wax MCT-10, it can be seen in Table 18 that there is an increase in 0 with 7 C 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*f vs. Tb - Tc, as the concentration increases at a constant bulk temperature and flowrate of the wax-kerosene, Tb - Tc decreases and therefore the cloud point temperature will move away from the tube surface, which leads to increased wax deposition. An increase of initial fouling rate, R}/0C, with concentration for refined wax has 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 ± Gone. (%by weight) (m 2 K/kW) &c (min.) Uncertainty (%) (m 2 K/kW-min) %-% (°C) 5 0.5400 79.6 36.0 0.0068 17.0 ; TO 1.2700 15.1 0.4379 .. . : 11.4 '-y^ . 2.8000 25.3 V 0.5091 6.9 20 17.1200 15.3 33.0 1.1190 3.5 Table 28. Results for slack wax MCT-10 using stainless steel at Re= 10003±1760 and Cone. (%) by weight -.. •-. i-(m 2 K/kW) (min.) Uncertainty : (%) (m 2 , K/kW.min) %-x CQ • 5- r 0.0774 2.0 43.6 0.0387 14.0 10 0.0799 14.6 57.5 0.0055 8.0 15 0.4899 : 13.6 13.1 0.0360 5.9 : : '; 20 1.1080 26.9 15.5 0.0412 1.5 0.5 CM oo -{> T — i — i — • . i 1 i 1 i 1 i—'—r—1 r— 0 20 40 60 80 100 120 140 160 Time (min) Fig. 20a. Rf vs. time for slack wax MCT-10 at 5 % by wt.using stainless steel: Re=11185, 7; =29.2 °C, Cloud Point=15.0°C. 73 0.6 4 =2 0.4 E, or 0.2 o.o -!• 50 100 150 200 Time (min) Fig. 20b. Rf vs. time for slack wax MCT-10 at 10 % by wt.using stainless steel. Re=10714, 5=29.2 °C, Cloud Point=21.1°C. 2.0 n 1.8. 1.6 1.4, 1.2 | ; 1 : 0 H 0.8 H 0.6 :0:4 0.2 .0.0^ 20 - r -40: i 1 i 60 80 — I — > — i — ' — i — ' — l — 100 120 140 160 Time (min) Fig 20c. Rf vs. time for slack wax MCT-10 at 15 % by wt.using stainless steel. Re=9569, 5=29.2 °C, Cloud Point=23.3°C. 74' 2.0 n 1:8 1.6 1.4-1.2-§ 1.0 CM • . E — 0.8-| DU 0.6-0.4-0.2 ,v°°c o 0 o „ ° ° ,0. o : 0.0 -{ i i , , i—r—}—i—'—i—•—i—1—i—1—i—•—i—• 0 20 40 60 80 100 120 140 160 . Time (min) • Fig. 20d, Rf vs. time for slack wax MCT-10 at 20 % by wt.using stainless steel 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 18 20 22 Concentration (wt. %) Fig. 21. Results for refined wax on uncoated stainless steel tube. Re=10664 and Tb =32.50C. 76 i—1—i—1—i—1—i 1 i 1 i 1 i 1 —i— 1 — r - 1 — i 4 6 8 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 5 0 . 6 H CM 0 . 4 H 0 . 2 H o.o H 0 1 — « — i — r — | — . — I — i — | — i — | — i — r ~ 2 4 6 8 1 0 1 2 1 4 T -T (°C) b c x Fig 23. Graph of R*f vs. Tb - Tc for slack wax MCT-10 on uncoated stainless steel tube. Re= 10003 and Tb=29.2°C. 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. Type of tube Wax removal/bare patches observed Sliding Uncoated stainless steel Yes No Chrome-plated stainless steel Very Small Patches Yes Sand-blasted stainless steel No No n-C18 silane-coated chrome-plated stainless steel Yes Yes (but removed immediately) Heresite Si 57 E coated stainless steel (shiny) No No Heresite P-400/L-66 coated stainless steel (dull) No No n-C18 silane-coated stainless steel Yes Yes (but removed immediately) Table 30. Sliding velocity for chrome-plated stainless steel tube using slack wax MCT-10 at 20% by wt. Tb = 31.3±0.1°C ,Cloud Point=27.8 °C , f 6=7.6±0.4°C, V w = l . l m/s Re u(m/s) Sliding velocity (m/s) 6586 1.17 0.68 9224 1.64 0.74 9208 1.64 0.70 11015 1.96 0.64 13156 2:35 1.00 14428 2.57 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 Rf results with little scatter. The major objective of uncertainty analysis is to 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 Rf 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*f , but nevertheless a consistent trend of R*f with Re and bulk temperature 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 Qw that could be improved is the cooling water side mass flowrate fluctuation. This 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*f remains 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*f decreases 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*f and the time constant first increase and 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*f vs. Re and concentration are not the same. The trends of R*f vs. Tb, 6C vs. Re and 0C vs. concentration agree with the present results. 0C vs. Tb does not show any consistent trend for both sets of experiments. 82 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*f as flow velocity increased. The decrease was non-linear and was fitted by using a polynomial of degree two. The plot of R*f vs. Re for refined wax 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*f with increasing 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 chrome-plated 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*f against Re. 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*f compared to the uncoated stainless steel (2.5 pm), which had again a lower value of R*f compared to the sand-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, 0C, in the Kern-Seaton equation with process variables 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 2 A = outer surface area of inner tube, m 2 Aor = cross-sectional area of orifice, m 2 B - constant in Eq. (5) C = constant in Eq. (11) C = bulk concentration, kg/m3 Cd = discharge coefficient of orifice C = specific heat capacity of wax-kerosene, kJ/kg K C = specific heat capacity of water, kJ/kg K C = interface concentration, kg/m3 dh = hydraulic diameter of the annulus where wax-kerosene flows, m D = shear rate, 1/s g = gravitational acceleration, m/s2 h = the level difference between the high and low side of manometer, h. = inner heat transfer coefficient, kW/m 2 K h = outer heat transfer coefficient, kW/m 2 K o ' k = thermal conductivity of wax deposit, kW/m K kf - turbulent mass transfer coefficient, m/s m - mass of deposit per unit area, kg/m2 m = mass of asymptotic wax deposit per unit area, kg/m2 m = mass flow rate, kg/s md = deposition flux, kg/s.m2 rhr = removal flux, kg/s.m2 Q w = heat gained by cooling water, kW R,, = deposit bond resistance 87 Rf = fouling resistance at a given time, m 2 K/kW Rf = asymptotic fouling resistance, m 2 K/kW Rfi = calculated experimental fouling resistance at the time 0., m 2 K/kW IL, ~ thermal resistance of the wall, m 2 K/kW pkdhu Re = wax-kerosene Reynolds No.= r, = inlet cooling water temperature, °C t2 = outlet cooling water temperature, °C tb = average bulk temperature of water, °C T} = inlet temperature of wax-kerosene, °C T2 = outlet temperature of wax-kerosene, °C Tb = average bulk temperature of wax-kerosene, °C Tc = cloud point temperature of wax-kerosene mixture, °C Ts = initial surface temperature of tube, °C At = temperature rise of cooling water, °C At = log mean temperature difference, °C u = velocity of wax-kerosene mixture, m/s u* = friction velocity, m/s U = initial overall heat transfer coefficient based on A., kW/m 2 K o r U = instantaneous overall heat transfer coefficient based on A, kW/m 2 K V = volumetric flowrate of wax-kerosene mixture, m3/s Vw - velocity of water, m/s Vw = volumetric flowrate of water, m3/s x = thickness of wax deposit, m P = 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 w = viscosity of water, Pa.s p f = density of wax deposit, kg/m3 PHZ = density of mercury, kg/m3 p k = density of wax-kerosene, kg/m3 pw = density of water, kg/m3 x, = shear stress, N /m 2 \\f = deposit strength 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, IUTAM/ICA/AIAA Symposium, Max-Planck-Institut fur Stromungsforschung, Gottingen, BRD, 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. 438-440. 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, 1259-1265, (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, 1605-1612, (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., CRC 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, No. 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"4 S 2 (43) where S is the scale of the rotameter reading in %. See Fig. 24. Fig. 24. Calibration curve of rotameter 93 Appendix B Calibration equations for thermocouples: No. 2 thermocouple (wax-kerosene mixture inlet) Tx = -0.21064 + 17.53609F2 -0.88371P~22 + 0.3139F"23 -0.0499IV* No. 3 Thermocouple (wax-kerosene mixture outlet) T2 = -0.0963 + 17.05522F3 - 0.2259F32 - 0.02855p33 + 0.00832^ No. 4 Thermocouple(cooling water inlet) tx = -0.32759+ 17.68791F4 -0.98792F 4 2 + 0.3553F43 -0.05466F"44 No. 5 Thermocouple (cooling water outlet) t2 = -0.33693 +17.6865 \V5 - 0.9769^/ + 0.35688F53 - 0.0561IV* No. Thermocouple (differential temperature reading for water side) At = (t2-t,) = -0.00088 +16.79067AF" 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 TKJ 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 RHO 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 F L 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 Q K 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 D l 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 CD Discharge coefficient C W Length of tube C SUMU Uncertainty C B2 Orifice diameter/pipe diameter C AOR Area of orifice PROGRAM 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 DIMENSION 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 CONTINUE C Converting the mV to C D O 3 0 I = l , M TKI ( I )=TKI ( I )+TI ( I ) TKI(J0=-O.21O64+17.536O9*TJ^(J0-O.88371*TKI(I)**2+O.3139 * * r a © * * 3 - 0 . 0 4 9 9 1 * T K I ( I ) * * 4 T K O ( I ) = T K O ( I ) + T I ( I ) T K O ( I ) = - O . 0 9 6 3 + 1 7 . 0 5 5 2 2 * T K O ( T ) - 0 . 2 2 5 9 1 * T K O ( I ) * * 2 - O . 0 2 8 5 5 * * T K O ( I ) * * 3 - K ) . 0 0 8 3 2 * T K O ( I ) * * 4 TWI( I )=-TWI( I )+TI ( I ) j ^ ( l ) = - 0 . 3 2 7 5 9 + 1 7 . 6 8 7 9 1 * T W I ( J ^ . 9 8 7 9 2 * T ^ * * T W I ( I ) * * 3 - 0 . 0 5 4 6 6 * T W I ( I ) * * 4 T W O ( I ) = - T W O ( I ) + T I ( I ) T W O © = - 0 . 3 3 6 9 3 + 1 7 . 6 8 6 5 1 * T W O ( r ) - 0 . 9 7 6 9 * T W O ( I ) * * 2 + 0 . 3 5 6 8 8 * * T W O ( I ) * * 3 - 0 . 0 5 6 1 1 * T W O ( 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 CONTINUE 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 FL= 01*(02+03*S+04*S**2)/05 DELP=1000.D0*G*Z*(RHOM-RHOW) C Finds bulk temperature and average temp, of fluid DO 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 / (P I/4*DI**2) VK=V / (PI/4*(D**2 -DO**2)) C Finds the Reynolds number for both sides R E W = R H O ( T A W , 2 ) * W * D J 7 V I C ( C , T A V W , 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 (%) ',C 50 F0RMAT(1X,A26,F4.1) WRITE(7,60) 'Mixture Re ' ,REK 60 FORMAT ( 1 X ,A26,F6 . 0 ) 9 7 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. J T ( I . E Q 1 ) T H E N 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 E L S E C Subsequent fouling res. at time T is calculated. R F W ( J > ( 1 / U W ( J > 1 / U C W * C P W O / ^ ^ 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' 100 F0RMAT(1X,A35) E N D I F C The uncertainity for Crittenden UNCD=(UD/UWm+UCN/UCVO/RFW(I) C The uncertainity for the individual is added up and the average C is calculated. C For Crittenden SUMD=UNCD+SUMD E N D I F IF (I.EQ.l) T H E N UNCD=0 E N D I F WRrrE(7,110) T©,RFW(I),QW,EQ 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. TC=0 TF=TAVW 400 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) T H E N TC=TWSO GO T O 400 E N D I F PRTNT*, ,WSO ,,TWSO C Loop to find the parameters for water side. WRTTE(7,130)' WRrTE(7,130) 'Water side' 130 FORMAT(1X,A40) D O 140 I=1,M RF(T)=RFW(I) 140 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) D J T M A X = D M A X 1 ( D J T M A X , D A B S ( D X ( 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' GO T O 200 E N D I F 190 CONTINUE 200 WRITE(7,210) To.Res.',Time const.(min) ,,'Unc(BDC)%' ) ,S. Temp' 210 FORMAT(1X,A15,A20,A15,A15) WRTTE(7,220) ITER,X(l),l/X(2),SUMD,TWSO 220 FORMAT(lX,I4,Fl 1.4,F20.2,F15.2,F15.2) END C Purpose C C The subroutine is to find the argument of the matrix by C finite difference method. 100 c C Argument C C X(J) Parameters to be fitted C A(I,J) Matrix of coefficients SUBROUTINE COEFF(F,N,NDR,NDC,X,A) IMPLICIT D O U B L E PRECISION (A-ILO-Z) DIMENSION 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)) E L S E A(LNP)=-F(LN,X) E N D I F 20 CONTINUE 30 CONTINUE R E T U R N END C C Purpose C C Uses Gauss Jordan elimination with partial pivot selection C to solve simultaneous linear equation of form [A]*{X}={C}. C C Argument C C A Augumented coefficient matrix. C N Number of equtions to be solved. C NDR First(row) dimension of A in calling program. C N D C Second(column) dimension of A in calling program. C E R R O R Error flag C =1 Succesful Gauss elimination. C =2 Zero diagonal entry after pivot selection. C RNORM If IERROR= 1, measure size of residual error. C If IERROR=2, RNORM=0 C X Solution vector. C SUBROUTINE GAUSS(A,N,NDR,NDC,X,RNORM,IERROR) IMPLICIT D O U B L E PRECISION (A-ILO-Z) DIMENSION 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 B(I,J)=A(I,J) 10 CONTINUE 20 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 D O 30 J=KP,N AB2=ABS(B(I,J)) IF (AB2.GT.BIG2)THEN BIG2=AB2 n>IVOT=J E N D I F 30 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 DO 50 I=KP,N AB=ABS(S(K)) IF (AB.GT.BIG) T H E N BIG=AB n>rvoT=i E N D I F 50 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 E N D I F C Eliminate B(I,K) from rows K P through N 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) 70 CONTINUE 80 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 E N D I F 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 RSQ=RSQK A(I,NP)-SUM) * * 2 140 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 FUNCTION F(I,N,X) IMPLICIT D O U B L E PRECISION (A-H.O-Z) DIMENSION X(2) C O M M O N RF(300),T(300),M GO T O (10,20),I 10 SUM=0.D0 D O 30 K=1,M SUM=SIM+(RF(K)-X(1)*(1-DEXP(-T(K)*X(2))))* * (1-DEXP(-T(K)*X(2))) 30 CONTINUE F=SUM RETURN 20 SUM=0.D0 DO 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 C Pupose C C Function determines the density at a given temperature for C both mixture and water. C C Argument C C T Teperature C K =1 mixture C =2 water D O U B L E PRECISION FUNCTION RHOfT.K) IMPLICIT DOUBL E PRECISION (A-ILO-Z) GO 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 FUNCTION CP(T,K) IMPLICIT D O U B L E PRECISION (A-ILO-Z) GO 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 R E T U R N E N D 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 FUNCTION VIC(C,T,K) IMPLICIT D O U B L E PRECISION (A-H.O-Z) GO T O (10;20),K 10 IF (C.EQ.5) T H E N Al=4.16D-6 B1=13676.D0 ELSEIF (C.EQ.10) T H E N Al=3.80D-6 B1=14160.D0 ELSEIF (C.EQ. 15) T H E N Al=1.86D-7 B1=21993.D0 ELSEIF (C.EQ.20) T H E N Al=5.92D-7 B1=18820.D0 ENDIF VTC=A1 *EXP(B 1/8.314/(273.15+T)) RETURN 20 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 ELSEIF (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 E N D I F RETURN E N D 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 lK) u(m/s) T„(°C) 1 out7.dat SS Refined 0.4644 1.2 11.3 2 outl5.dat n n 0.5082 1.6 13.3 3 out5.dat tt tt 0.5145 2.1 12.9 4 out6.dat II M 0.5796 2.4 14.2 5 out9.dat n H 0.6538 2.7 15.8 6 out35.dat M Slack Wax 0.7478 1.2 15.0 7 out31.dat H n 0.9130 1.6 18.0 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 1.2197 2.6 17.5 11 out42.dat Chrome-plated SS II 0.5681 1.2 12.7 12 out46.dat M It 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 Sand-blasted SS tt 0.8802 1.2 16.3 18 out49.dat H H 0.9074 1.6 16.9 19 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 n-C18 silane chrome-plated SS tl 0.7842 1.2 18.8 23 out57.dat n n 0.7936 1.6 18.6 24 out59.dat it M 1.2069 2.0 21.3 25 out60.dat tt n 1.4296 2.3 22.2 26 out61.dat tt II 1.0777 2.6 23.5 27 out66.dat Heresite Si 57 E S S H 0.9458 1.2 22.1 28 out65.dat tt tl 1.0973 1.6 21.9 29 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 26.7 107 Run. No. Disk No. Tube Type Wax Type U„(kW/m 2K) u(m/s) T„(°C) 32 out71.dat Heresite P-400/L-66 SS tl 0.7841 1.2 20.5 33 out70.dat ll tt 1.0745 1.6 22.3 34 out75.dat II tt 1.1595 1.6 23.5 35 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 n-C18 silane SS II 0.8673 1.2 18.7 39 out76.dat II ll 1.0150 1.6 20.3 40 out78.dat ll tt 1.2427 2.0 21.4 41 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 Refined wax 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 Slack wax 0.7123 1.6 11.9 49 Same as run 7 out31.dat II •I 0.9130 1.6 12.7 50 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 54 Same as run 12 out46.dat Chrome-plated SS tt 0.7493 1.6 15.4 55 out48.dat tt it 0.8818 1.6 18.7 56 out81.dat it 1.2727 1.6 25.3 57 out82.dat n 1.3512 1.6 28.8 58 Same as run 18 out49.dat Sand-blasted SS n 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 61 out56.dat ll tt 1.3476 1.6 26.9 62 Same as run 23 out57.dat n-C18 silane chrome plated SS II 0.7936 1.6 18.6 63 out62.dat it ti 1.0952 1.6 22.8 64 out63.dat II it 1.3638 1.6 27.1 65 out64.dat II tt 1.3564 1.6 31.5 66 out3.dat SS Refined wax 0.5512 1.6 13.6 67 out4.dat II it 0.4994 1.6 11.2 68 outl6.dat II H 0.2944 1.6 11.5 69 outl8.dat II tt 0.1699 1.6 10.4 70 out27.dat II Slack wax 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 14.8 108 Sample Calculations The following sample calculation was done for slack wax MCT-10 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 4 = -0.4060 mv V5=-0.3485 mv A V = 0.0610 m v V = 1.2145 mv The actual voltage is calculated by adding the reference voltage V to V 2 , V 3 , V , , V, i.e., V 2 = 1.8340 mv V,= 1.8730 mv V 4 =-0.8085 mv V=-0.8660 mv A V = 0.0610 mv Using the calibration equations in Appendix B T = 31.52 °C, T 2 = 30.97°C, t,= 13.49°C, t,= 14.45°C, At = 1.02 °C The pipe diameters are: D = 25.400 mm, D, = 9.957 mm, D o = 12.446 mm 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/m5 C = 0.62 109 A ==*DV¥=fl0.012V4=0.0001131m1 or p = 12/24.84 = 0.4831 I 2 AP V = CJA \p>(l-P4) V= 0.000607 mVs The velocity of wax-kerosene mixture V U~ (n/4)(D2-D2J = 1.58 m/s Water flow rate: The Rotameter reading was S = 20 % for all runs. Using the calibration equation How Rate (U.S. gal/min.)= 0.275 + 0.05 S + mO"4 S 2 = 3.78541.IO"3 (0.275 + 0.05 S + 1M0" 4 S2)/60 mVs Vw = 8.296X105 mVs The velocity of water: v.- *~ (n/4)D2i =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- 3/ t+1.49921.10Mr;-3.35545.10^ 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/m3 = 8.296X10' X999.37X4.1879X1.02 = 0.355 kW A, = rcDL = 0.0225 m 2 A0 = 7tDoL = 0.0282 m l The log-mean temperature difference =17.27°C = 0.9136 kW/m JK Overall heat transfer coefficient at time = 2 min.: V 2= 0.6195 mv V 3= 0.6585 mv V 4= -0.4060 mv V 5= -0.3485 mv AV= 0.0610 mv V= 1.2145 mv 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 w = 999.37 kg/m3 C , = 4.1879 kJ/kg°C a.=Kp.c^t = 0.309 kW Ar t a= 17.95 °C U = ®" = 0.7651 kW/m JK 111 From previous calculation U„ =0.9130 kW/m'K The fouling resistance at time = 2 min. is ' 4{u u, = 0.2662 m JK/kW 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 w at 0=0 = 0.392 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m2 K/kW) 0 0.0000 92 2.2196 1 0.2561 93 2.2265 2 0.4490 94 1.8213 3 0.5095 95 1.8436 4 1.1698 96 1.8622 5 1.0993 97 1.7220 6 1.3197 98 2.6964 7 1.7163 99 2.7093 8 1.8020 100 2.1562 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 105 2.1801 14 1.0008 106 2.1807 15 1.9138 107 2.2088 16 1.9380 108 2.2391 17 1.9806 109 1.7668 18 1.9461 110 1.7631 19 1.9786 111 1.7781 20 1.6339 112 1.4500 21 1.6053 113 2.2045 22 1.6254 114 2.2153 23 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 3.3044 128 2.1967 37 2.5740 129 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 113 47 2.6195 139 1.1865 48 4.8699 140 2.2692 49 2.6545 141 2.3019 50 2.6185 142 1.5156 51 2.0780 143 2.2299 52 2.6500 144 2.2406 53 2.1272 145 2.2582 54 2.6699 146 2.3068 55 2.1558 147 1.8147 56 2.6970 148 2.2670 57 2.6500 149 2.2758 58 2.6720 150 2.2846 59 2.1410 151 2.2430 60 2.1389 152 2.2516 61 2.6600 153 1.8073 62 2.1293 154 2.2867 63 1.7526 155 1.8469 64 2.0076 156 2.2451 65 2.0315 157 2.2015 66 2.0549 158 2.2384 67 2.1028 159 2.2408 68 2.1328 160 1.8319 69 1.7317 161 1.8545 70 1.7593 162 1.5257 71 1.7630 163 2.2670 72 1.7398 164 2.2495 73 1.1763 165 1.8300 74 1.7618 166 2.2802 75 1.7225 167 2.2911 76 2.1520 168 2.2516 77 2.1486 169 1.8241 78 1.7593 170 1.8431 79 2.1991 171 2.3024 80 1.7630 172 1.8488 81 1.7990 173 2.3068 82 2.1829 174 1.8488 83 2.1850 175 1.8317 84 2.1649 176 1.8393 85 1.7457 177 1.8431 86 2.1770 178 2.8925 87 2.1942 179 2.3021 88 2.1440 180 1.8187 89 2.7092 90 2.7272 91 2.7631 R*(mKlkW) 6c(min) Unc(B.D. Crittenden)% 2.1890 8.88 13.65 114 Run 2 Bulk concentration (%) Mixture Re Wate Re Water average Temp.( °C) M . average Temp. ( °C) 0.316=0 = 0.451 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 1 0.0702 2 0.1180 3 0.2458 4 0.4585 5 0.4917 6 0.7193 7 0.8924 8 0.7585 9 0.8923 10 0.7474 11 0.6291 12 0.6341 13 0.7722 14 0.7873 15 0.9312 16 0.7612 17 0.9273 18 0.9392 19 0.7828 20 0.6557 21 0.6611 22 0.7888 23 0.8868 24 0.8828 25 0.8828 26 0.8933 27 0.9132 28 0.9224 29 0.7678 30 0.9330 31 1.1131 32 0.9238 33 0.9290 34 0.9236 35 1.1160 36 0.9251 37 0.9317 38 0.9383 39 0.9408 40 0.9487 41 0.9566 42 0.9700 43 0.9737 44 0.8253 45 0.8254 46 0.6976 10.0 11414. 18807. 10.27 32.38 Time Fouling Res. (min] (m 2 K/kW) 86 0.8589 87 0.8357 88 1.1355 89 1.1463 90 . 0.9487 91 0.9581 92 0.9535 93 1.1750 94 0.9875 95 0.8260 96 0.9738 97 0.9809 98 0.9701 99 1.1776 100 0.9755 101 0.8150 102 0.9845 103 0.8332 104 0.8394 105 0.8370 106 0.8491 107 0.8552 108 0.8565 109 0.7214 110 0.7218 111 0.8735 112 0.7307 113 0.9524 114 0.9217 115 1.1200 116 0.9283 117 0.7738 118 0.9511 119 0.9591 120 0.9628 121 0.9722 122 0.8117 123 0.8214 124 0.8274 125 0.6922 126 0.8407 127 0.5873 128 0.5924 129 0.8577 130 0.6017 131 0.6023 132 0.6064 115 47 0.9345 133 0.6105 48 1.1058 134 0.6146 49 1.3505 135 0.6849 50 1.1213 136 0.9546 51 0.9415 137 0.7923 52 0.9308 138 0.9532 53 0.9348 139 0.9708 54 1.1361 140 0.9788 55 0.7887 141 0.9855 56 0.9493 142 0.9961 57 0.9535 143 0.8359 58 0.9588 144 0.8420 59 0.9668 145 0.8286 60 0.8103 146 1.1296 61 0.9872 147 1.1065 62 0.8249 148 1.3642 63 1.0032 149 0.9200 64 0.9832 150 1.1302 65 0.0475 151 0.9495 66 0.8065 152 0.9588 67 0.8101 153 0.9599 68 0.9805 154 0.6639 69 0.8188 155 0.9742 70 0.8541 156 0.8191 71 1.0015 157 0.8288 72 0.8419 158 0.8348 73 0.8346 159 0.8408 74 0.8297 160 0.8469 75 0.9698 161 0.7155 76 0.9631 162 0.7200 77 0.9728 163 0.8698 78 0.9711 164 0.6109 79 0.9791 165 0.7292 80 0.8247 166 0.7366 81 1.0023 167 0.6201 82 0.6969 168 0.7466 83 0.6973 169 0.7488 84 0.8528 170 0.7522 85 0.8528 171 0.7909 172 1.1073 173 1.1141 174 0.9203 175 1.1183 176 0.9388 177 0.9508 178 0.9615 179 0.9708 RArnKlkW) 9C (min) Unc(BDC)% 0.8896 5.45 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 kW Time Fouling Res. Time Fouling Res (min) (m 2K/kW) (min] (m2 K/kW) 0 0.0000 90 0.5066 1 0.2802 91 0.5076 2 0.3303 92 0.5085 3 0.2985 93 0.6057 4 0.3851 94 0.4215 5 0.3885 95 0.5135 6 0.3996 96 0.5154 7 0.4047 97 0.6143 8 0.4830 98 0.7328 9 0.4779 99 0.6200 10 0.6905 100 0.6210 11 0.6926 101 0.6220 12 0.5828 102 0.6220 13 0.5892 103 0.6277 14 0.5867 104 0.5209 15 0.4887 105 0.6259 16 0.4875 106 0.6259 17 0.5896 107 0.6259 18 0.4954 108 0.4309 19 0.4973 109 0.6242 20 0.5004 110 0.6242 21 0.5935 111 0.5264 22 0.4991 112 0.6242 23 0.4898 113 0.5264 24 0.4960 114 0.5264 25 0.4153 115 0.6299 26 0.4198 116 0.6249 27 0.4053 117 0.6163 28 0.0922 118 0.6210 29 0.4809 119 0.6200 30 0.3985 120 0.6143 31 0.4827 121 0.6163 32 0.4836 122 0.6200 33 0.4846 123 0.6143 34 0.4855 124 0.6163 35 0.4864 125 0.6163 36 0.4026 126 0.6182 37 0.4026 127 0.6220 38 0.1451 128 0.7370 39 0.4043 129 0.6240 40 0.4878 130 0.6287 41 0.4878 131 0.6297 42 0.4878 132 0.5260 43 0.4896 133 0.6317 44 0.3312 134 0.6317 45 0.4896 135 0.5297 46 0.4955 136 0.6317 117 4 7 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 0.5879 148 0.4363 59 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 153 0.5893 64 0.5021 154 0.4951 65 0.2086 155 0.5043 66 0.5089 156 0.5131 67 0.5089 157 0.5168 68 0.6106 158 0.5195 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) 0c(min) U n c ( B D C ) % 0 . 5 1 2 2 2 . 4 7 2 2 . 4 8 118 Run 4 Bulk concentration (%) Mixture Re Wate Re Water average Temp.(°C) M . average Temp. ( °C) C ^ a t e ^ =0.616 kW Time Fouling Res. (min) (m2 K/kW) 0 0.0000 1 0.0378 2 0.1421 3 0.2049 4 0.1705 5 0.2702 6 0.4420 7 0.4083 8 0.2998 9 0.3723 10 0.2959 11 0.5019 12 0.5100 13 0.4372 14 0.5188 15 0.5379 16 0.4620 17 0.5439 18 0.4653 19 0.4628 20 0.4670 21 0.3412 22 0.3379 23 0.4080 24 0.3452 25 0.3419 26 0.4073 27 0.4653 28 0.4603 29 0.5375 30 0.4553 31 0.4528 32 0.4578 33 0.3899 34 0.4653 35 0.3333 36 0.4033 37 0.2862 38 0.4104 39 0.4127 40 0.3526 41 0.4017 42 0.4696 43 0.2203 44 0.3994 45 0.4779 46 0.4080 10.0 17332. 163. 9.25 32.71 Time Fouling Res. (min) (m 2 K/kW) 92 0.2833 93 0.2763 94 0.3333 95 0.3333 96 0.3348 97 0.2777 98 0.2798 99 0.3372 100 0.2303 101 0.3387 102 0.3387 103 0.2798 104 0.3320 105 0.2745 106 0.3348 107 0.3313 108 0.2236 109 0.2763 110 0.2763 111 0.2738 112 0.3328 113 0.2745 114 0.2727 115 0.2745 116 0.2752 117 0.3342 118 0.2791 119 0.2748 120 0.3385 121 0.3385 122 0.2830 123 0.2830 124 0.2812 125 0.2812 126 0.3420 127 0.2851 128 0.2833 129 0.2802 130 0.3303 131 0.2703 132 0.3266 133 0.2685 134 0.3253 135 0.2706 136 0.3283 137 0.2720 138 0.2717 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 0.3414 144 0.2220 53 0.4102 145 0.2727 54 0.4149 146 0.2713 55 0.4204 147 0.2727 56 0.3571 148 0.0896 57 0.3039 149 0.1756 58 0.3981 150 0.3322 59 0.4622 151 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 0.2819 67 0.3537 159 0.2320 68 0.4205 160 0.2855 69 0.2912 161 0.2844 70 0.2884 162 0.2826 71 0.3412 163 0.2320 72 0.3388 164 0.2869 73 0.3338 165 0.2310 74 0.3984 166 0.2303 75 0.3284 167 0.2303 76 0.3289 168 0.2320 77 0.3252 169 0.2320 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 RArnKlkW) 9C (min) Unc(BDC)% 0.3363 2.55 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 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 1 0.0811 2 0.1272 3 0.1364 4 0.2118 5 0.1804 6 0.2206 7 0.2206 8 0.2596 9 0.3025 10 0.2996 11 0.2523 12 0.2563 13 0.2591 14 0.2576 15 0.2589 16 0.2137 17 0.2163 18 0.2150 19 0.1768 20 0.1750 21 0.2561 22 0.2562 23 0.2137 24 0.2137 25 0.2588 26 0.2162 27 0.2162 28 0.2175 29 0.1762 30 0.2143 31 0.2174 32 0.2174 33 0.2131 34 0.2517 35 0.1301 36 0.2982 37 0.2075 38 0.3001 39 0.3015 40 0.3028 41 0.3035 42 0.3582 43 0.3085 44 0.3610 45 0.1402 46 0.2522 Time Fouling Res. (min) (m2 K/kW) 90 0.2094 . 91 0.2087 92 0.2119 93 0.1733 94 0.2575 95 0.2150 96 0.1750 97 0.1396 98 0.1762 99 0.2193 100 0.2180 101 0.2206 102 0.2193 103 0.2618 104 0.2205 105 0.0788 106 0.2645 107 0.1827 108 0.2057 109 0.1608 110 0.2014 111 0.2452 112 0.2912 113 0.2082 114 0.2524 115 0.3025 116 0.2106 117 0.2556 118 0.0744 119 0.2169 120 0.2131 121 0.2181 122 0.2130 123 0.2162 124 0.2634 125 0.2219 126 0.2225 127 0.2212 128 0.2224 129 0.0532 130 0.2250 131 0.2256 132 0.2230 133 0.1768 134 0.1709 135 0.2094 . 136 0.2094 121 47 0.2025 137 0.1709 48 0.2450 138 0.2119 49 0.2456 139 0.2131 50 0.2462 140 0.1697 51 0.2088 141 0.1709 52 0.2113 142 0.2093 53 0.2556 143 0.2087 54 0.2150 144 0.1697 55 0.2595 145 0.2106 56 0.2188 146 0.2118 57 0.2493 147 0.2093 58 0.2375 148 0.1709 59 0.2408 149 0.2118 60 0.2064 150 0.2149 61 0.2565 151 0.2149 62 0.2943 152 0.1757 63 0.2454 153 0.1397 64 0.2454 154 0.1762 65 0.2945 155 0.2167 66 0.2966 156 0.1774 67 0.2948 157 0.1757 68 0.2491 158 0.1763 69 0.2524 159 0.1774 70 0.2536 160 0.1751 71 0.2549 161 0.1727 72 0.0705 162 0.1727 73 0.2554 163 0.2062 74 0.3064 164 0.2043 75 0.2156 165 0.2474 76 0.2553 166 0.2487 77 0.2137 167 0.2068 78 0.3060 168 0.2068 79 0.3060 169 0.2486 80 0.2613 170 0.2080 81 0.2994 171 0.1709 82 0.2885 172 0.2105 83 0.3380 173 0.2118 84 0.3380 85 0.2885 86 0.2045 87 88 0.2051 0.2057 89 0.2075 R(rnKlkW) 0C (min) Unc(BDC)% 0.2249 2.12 27.91 122 Run 6 Bulk concentration (%) 20.0 Mixture Re 6645. Water Re 7906. Water average Temp.( °C) 9.10 M . average Temp. ( °C) 31.87 Q w at 9=0 = 0.347 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m2 K/kW) 0 0.0000 86 0.9223 2 0.6206 88 0.9899 4 0.5618 90 0.9834 6 0.6027 92 0.9727 8 0.6083 94 0.6458 10 0.6315 96 1.0091 12 0.6615 98 1.0020 14 0.6996 100 1.0616 16 0.7194 102 1.0275 18 0.7600 104 1.0238 20 0.8083 106 1.0120 22 0.7979 108 1.0560 24 0.7704 110 0.9215 26 0.7954 112 0.9065 28 0.8345 114 0.9992 30 0.8074 116 0.8623 32 0.7936 118 0.9879 34 0.7951 120 0.6927 36 0.8917 122 0.9944 38 0.7753 124 0.9915 40 0.8054 126 1.0207 42 0.9212 128 1.0351 44 0.8882 130 1.1040 46 0.9136 132 1.0518 48 0.8240 134 1.0292 50 0.8682 136 1.0035 52 0.9680 138 0.9117 54 0.9999 140 0.7287 56 0.9219 142 0.7957 58 0.9233 144 0.8974 60 0.7557 146 1.0092 62 0.8967 148 1.0183 64 0.9561 150 1.0111 66 0.9302 68 0.9664 70 0.9679 72 0.9876 74 0.9640 76 1.0092 78 0.9271 80 0.8981 82 0.9153 84 1.0198 RAtnKlkW) 0C (min) Unc(BDC)% 0.9293 8.02 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 kW Time Fouling Res. Time Fouling Res (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.8185 2 0.2683 88 0.8731 4 0.5102 90 0.8564 6 0.5203 92 0.8849 8 0.5012 94 0.8912 10 0.5061 96 0.8568 12 0.5413 98 0.8316 14 0.5649 100 0.6608 16 0.5765 102 0.6642 18 0.6564 104 0.7943 20 0.6415 106 0.8302 22 0.6015 108 0.8464 24 0.6428 110 0.8203 26 0.6916 112 0.8778 28 0.7168 114 0.7902 30 0.7059 116 0.8602 32 0.7482 118 0.8188 34 0.7691 120 0.9036 36 0.7675 122 0.7931 38 0.7414 124 0.8251 40 0.7848 126 0.7703 42 0.7731 128 0.7856 44 0.8001 130 0.9006 46 0.7427 132 0.7397 48 0.8363 134 0.8636 50 0.8114 136 0.7902 52 0.7789 138 0.8840 54 0.8166 140 0.8399 56 0.8027 142 0.8006 58 0.8455 144 0.8020 60 0.8916 146 0.8418 62 0.8900 148 0.8248 64 0.8244 150 0.8127 66 0.7896 68 0.8275 70 0.8531 72 0.8475 74 0.9177 76 0.9368 78 0.9232 80 0.8615 82 0.9121 84 0.8311 R*(m 2K/kW) 0c(min) Unc(BDC)% 0.8244 10.77 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.7276 2 0.3622 88 0.7053 4 0.3402 90 0.7644 6 0.4229 92 0.7974 8 0.4533 94 0.7656 10 0.4669 96 0.7538 12 0.4660 98 0.7409 14 0.5202 100 0.6855 16 0.5122 102 0.8194 18 0.5441 104 0.6910 20 0.5389 106 0.7536 22 0.5847 108 0.7737 24 0.5713 110 0.7427 26 0.6170 112 0.7779 28 0.6622 114 0.7826 30 0.6939 116 0.8416 32 0.6761 118 0.7699 34 0.6962 120 0.8853 36 0.7142 122 0.8177 38 0.7306 124 0.8813 40 0.7396 126 0.8489 42 0.7772 128 0.7773 44 0.7681 130 0.7905 46 0.7638 132 0.6784 48 0.7780 134 0.8399 50 0.7570 136 0.8374 52 0.8583 138 0.8671 54 0.7938 140 0.7980 56 0.7371 142 0.8168 58 0.7844 144 0.8661 60 0.8673 146 0.8107 62 0.7821 148 0.7857 64 0.8639 150 0.8621 66 0.8574 68 0.8135 70 0.7955 72 0.8086 74 0.7935 76 0.7982 78 0.8489 80 0.7953 82 0.7579 84 0.8065 RArnKlkW) 0C (min) Unc(BDC)% 0.7926 13.21 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.7645 2 0.2961 88 0.6151 4 0.3281 90 0.7091 6 0.3394 92 0.7571 8 0.3789 94 0.7543 10 0.4138 96 0.6615 12 0.4301 98 0.7036 14 0.3866 100 0.7130 16 0.4198 102 0.8062 18 0.4952 104 0.6967 20 0.4904 106 0.7254 22 0.4573 108 0.6530 24 0.4944 110 0.7117 26 0.5156 112 0.7282 28 0.5462 114 0.6691 30 0.5387 116 0.6092 32 0.5473 118 0.6729 34 0.5322 120 0.6777 36 0.6014 122 0.8016 38 0.5208 124 0.8154 40 0.5463 126 0.7269 42 0.6192 128 0.7825 44 0.6017 130 0.6676 46 0.5673 132 0.8419 48 0.5809 134 0.8974 50 0.6561 136 0.8715 52 0.7042 138 0.8241 54 0.7044 140 0.7821 56 0.6295 142 0.6475 58 0.8028 144 0.6871 60 0.7300 146 0.6108 62 0.7062 148 0.6477 64 0.7040 150 0.6675 66 0.7196 68 0.7406 70 0.7245 72 0.7072 74 0.7084 76 0.8759 78 0.7100 80 0.7372 82 0.7063 84 0.8423 R*{rnKlkW) 6C (min) Unc(BDC)% 0.7244 18.09 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 ) 31.33 Q w at9=0 = 0.522 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.6502 2 0.2904 88 0.6458 4 0.3469 90 0.7001 6 0.3856 92 0.6940 8 0.4020 94 0.6075 10 0.4830 96 0.7266 12 0.4874 98 0.7221 14 0.5071 100 0.6833 16 0.4671 102 0.7064 18 0.4984 104 0.7650 20 0.5450 106 0.7171 2 2 0.5138 108 0.5147 24 0.5417 110 0.7602 26 0.5061 112 0.6587 28 0.5575 114 0.6025 30 0.5260 116 0.6262 32 0.5842 118 0.6907 34 0.5421 120 0.6608 36 0.5895 122 0.6662 38 0.6010 124 0.5923 40 0.5933 126 0.6947 42 0.6780 128 0.6763 44 0.6367 130 0.5609 46 0.7312 132 0.6550 48 0.6619 134 0.7447 50 0.7166 136 0.6772 52 0.6726 138 0.5808 54 0.6908 140 0.7250 56 0.6541 142 0.6024 58 0.7259 144 0.4911 60 0.6696 146 0.6404 62 0.6582 148 0.7185 64 0.6485 150 0.7072 66 0.6888 68 0.6457 70 0.7713 72 0.7068 74 0.6666 76 0.7547 78 0.6655 80 0.7676 82 0.8343 84 0.6846 RArnKlkW) Bc (min) Unc(BDC)% 0.6668 10.34 7 .99 127 Run 11 Bulk concentration (%) 20.0 Mixture Re 6586. Water Re 7474. Water average Temp.( °C) 7.20 M . average Temp. ( °C) 31.32 Q.ate-0 = 0.289 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m 2 K/kW) 0 0.0000 86 0.6666 2 0.5410 88 0.5462 4 0.7250 90 0.6401 6 0.7019 92 0.8349 8 0.7522 94 0.7242 10 0.7626 96 0.6603 12 0.8757 98 0.6826 14 0.8910 100 0.5674 16 0.8524 102 0.7945 18 0.9283 104 0.6493 20 0.8100 106 0.7654 22 0.9110 108 0.7626 24 0.8191 110 0.6971 26 0.9388 112 0.8677 28 0.8597 114 0.7664 30 0.9759 116 0.6399 32 0.7736 118 0.6799 34 1.2896 120 0.7637 36 1.0417 122 0.7706 38 1.0816 124 0.7877 40 1.0629 126 0.8238 42 0.9107 128 0.7476 44 1.0762 130 0.7984 46 0.9751 132 0.6544 48 1.0087 134 0.9873 50 0.7359 136 0.7909 52 0.8249 138 0.8075 54 0.8263 140 0.8315 56 0.8642 142 0.8869 58 0.8966 144 0.7237 60 0.7726 146 0.9006 62 0.8906 148 0.7026 64 0.7511 150 0.8685 66 0.8640 68 0.8780 70 0.8612 72 0.7999 74 0.8208 76 0.9067 78 0.9050 80 0.8747 82 0.7554 84 0.7042 R*(m2K/kW) 0c(min) Unc(BDC)% 0.8238 2.07 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 ) 31.34 CL at 8=0 = 0.338 kw Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 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 0.6172 102 0.2521 18 0.6124 104 0.5746 20 0.7411 106 0.5373 22 0.6628 108 0.7396 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 0.567 130 0.5585 46 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) 0C (min) Unc(BDC)% 0.6031 2.08 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.5837 2 0.3749 88 0.6151 4 0.4131 90 0.5309 6 0.5793 92 0.5945 8 0.5843 94 0.6114 10 0.6339 96 0.5698 12 0.6817 98 0.6064 14 0.7225 100 0.5282 16 0.5321 102 0.6010 18 0.5747 104 0.6335 20 0.5302 106 0.5921 22 0.5697 108 0.6368 24 0.5760 110 0.5529 26 0.5855 112 0.4512 28 0.6781 114 0.5692 30 0.5665 116 0.5977 32 0.5674 118 0.6182 34 0.6315 120 0.5516 36 0.7590 122 0.5392 38 0.5830 124 0.6182 40 0.6367 126 0.6030 42 0.5829 128 0.5362 44 0.6127 130 0.5429 46 0.5546 132 0.5897 48 0.6185 134 0.5975 50 0.6706 136 0.5527 52 0.6307 138 0.5737 54 0.5816 140 0.5624 56 0.6495 142 0.6163 58 0.4924 144 0.5891 60 0.6267 146 0.4776 62 0.6174 148 0.5409 64 0.6039 150 0.5798 66 0.6357 68 0.3178 70 0.5383 72 0.5348 74 0.5981 76 0.4994 78 0.5318 80 0.4934 82 0.5998 84 0.4869 R*(jnKlkW) 0C (min) Unc(BDC)% 0.5814 2.16 15.55 130 Run 14 (%) 20.0 Mixture Re 11015. Water Re 7597. Water average Temp.( °C) 7.75 M . average Temp. ( °C ) 31.29 Q . at 9=0 = 0.408 K W Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.5774 2 0.4471 88 0.6229 4 0.6013 90 0.6407 6 0.5177 92 0.5105 8 0.4849 94 0.4801 10 0.5546 96 0.6043 12 0.5935 98 0.6308 14 0.5710 102 0.5923 18 0.5879 104 0.5966 20 0.5688 106 0.5956 22 0.6027 108 0.5803 24 0.5674 110 0.5952 26 0.6972 112 0.5337 28 0.5253 114 0.6103 30 0.5863 116 0.6258 32 0.6373 118 0.6138 34 0.6078 120 0.6229 36 0.6341 122 0.5866 38 0.6015 124 0.6180 40 0.5583 126 0.5701 42 0.6162 128 0.5425 44 0.5351 130 0.5816 46 0.6144 132 0.5613 48 0.6335 134 0.5863 50 0.6388 136 0.6186 52 0.6033 138 0.6215 54 0.5911 140 0.5921 56 0.5709 142 0.6362 58 0.6201 144 0.5965 60 0.5980 146 0.7184 62 0.6306 148 0.5892 64 0.5935 150 0.5741 66 0.6144 68 0.5792 70 0.6221 72 0.6424 74 0.6280 76 0.5864 78 0.5953 80 0.6074 82 0.5900 84 0.5210 Rf(rnKlkW) 0C (min) Unc(BDC)% 0.5941 1.42 11.59 131 Run IS Bulk concentration (%) 20.0 Mixture Re 13156. Water Re 7604. Water average Temp.(°C) 7.78 M . average Temp. (°C) 31.25 CL at 9=0 = 0.482 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.5628 2 0.4232 88 0.4769 4 0.4887 90 0.5180 6 0.4618 92 0.5022 8 0.4186 94 0.5577 10 0.5109 96 0.5611 12 0.4778 98 0.5824 14 0.5208 100 0.5643 16 0.4983 102 0.5359 18 0.5635 104 0.5881 20 0.5223 106 0.4950 22 0.5258 108 0.5644 24 0.3444 110 0.5487 26 0.5101 112 0.4830 28 0.5133 114 0.5322 30 0.5039 116 0.5775 32 0.5487 118 0.4866 34 0.5187 120 0.5415 36 0.5389 122 0.5357 38 0.3859 124 0.5348 40 0.5103 126 0.4840 42 0.4830 128 0.5614 44 0.5070 130 0.5020 46 0.4984 132 0.5532 48 0.5314 134 0.5141 50 0.5600 136 0.5659 52 0.5597 138 0.8016 54 0.4613 140 0.5908 56 0.5275 142 0.5197 58 0.5393 144 • 0.5004 60 0.4729 146 0.4877 62 0.5418 148 0.5000 64 0.5629 150 0.5000 66 0.4839 68 0.5554 70 0.5146 72 0.5189 74 0.5128 76 0.5367 78 0.5254 80 0.5317 82 0.5308 84 0.5808 RAtnKlkW) 6C (min) Unc(BDC)% 0.5240 1.34 9.80 132 Run 16 Bulk concentration (%) 20.0 Mixture Re 14428. Water Re 7700. Water average Temp. ( °C ) 8.20 M . average Temp. ( °C ) 31.32 Q„ate=o = 0.545 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.4492 2 0.3175 88 0.4448 4 0.2162 90 0.5544 6 0.2603 92 0.4117 8 0.3090 94 0.5079 10 0.3691 96 0.5171 12 0.3410 98 0.4658 14 0.4723 100 0.4923 16 0.4813 102 0.4581 18 0.3504 104 0.4694 20 0.5087 106 0.4457 22 0.4509 108 0.6174 24 0.4370 110 0.5133 26 0.4795 112 0.5298 28 0.4725 114 0.5039 30 0.4483 116 0.2992 32 0.5029 118 0.4705 34 0.5026 120 0.5081 36 0.5190 122 0.4957 38 0.4649 124 0.4627 40 0.4882 126 0.4444 42 0.5187 128 0.4896 44 0.5075 130 0.4997 46 0.5192 132 0.5230 48 0.5110 134 0.5117 50 0.4655 136 0.4373 52 0.4161 138 0.6130 54 0.4533 140 0.4738 56 0.5491 142 0.4470 58 0.4987 144 0.4983 60 0.5640 146 0.5126 62 0.4699 148 0.4559 64 0.4217 150 0.5634 66 0.4737 68 0.5695 70 0.4992. 72 0.4871 74 0.3995 76 0.4052 78 0.4979 80 0.4217 82 0.4527 84 0.3335 RArnKlkW) 9C (min) Unc(BDC)% 0.4817 6.43 9.65 133 Run 17 Bulk concentration (%) 20.0 Mixture Re 6418. Water Re 8417. Water average Temp.( °C) 11.30 M. average Temp. ( °C ) 30.99 Qwate=0 = 0.276 kW Time Fouling Res. Time Fouling Res (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 1.2402 2 0.7368 88 1.3519 4 0.7330 90 1.3141 6 0.8910 92 1.1302 8 0.8752 94 1.3962 10 0.8510 96 1.2329 12 1.0074 98 1.1463 14 1.0384 100 1.2379 16 0.9941 102 1.0870 18 0.9146 104 1.3661 20 1.1254 106 1.1579 22 1.1056 108 1.2232 24 1.0644 110 1.2276 26 1.0661 112 1.1293 28 1.1344 114 1.2733 30 1.0454 116 1.3402 32 1.2791 118 1.3344 34 1.2305 120 1.3738 36 1.3763 122 1.3768 38 1.3749 124 1.3925 40 1.2981 126 1.3430 42 1.2393 128 1.4537 44 1.2419 130 1.3039 46 0.9473 132 1.4411 48 1.1412 134 1.2064 50 1.1599 136 1.1258 52 1.0287 138 1.2462 54 1.2030 140 1.4278 56 0.9810 142 1.2682 58 1.1594 144 1.3149 60 1.1379 146 1.1974 62 1.1208 148 1.2940 64 1.1643 150 1.3310 66 1.0404 68 1.0216 70 1.1013 72 1.2017 74 1.2250 76 1.3102 78 1.2291 80 1.1832 82 1.2366 84 1.2001 86 1.2402 RArnKlkW) 6C (min) Unc(BDC)% 1.2187 5.88 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.8754 2 0.3787 88 0.8168 4 0.4663 90 0.7215 6 0.5853 92 0.8259 8 0.6480 94 0.7910 10 0.5519 96 0.8161 12 0.1141 98 0.7642 14 0.1540 100 0.7946 16 0.7583 102 0.7725 18 0.7310 104 0.8036 20 0.6911 106 0.6893 22 0.8869 108 0.9088 24 0.7078 110 0.7963 26 0.7691 112 0.8420 28 0.8021 114 0.7689 30 0.8599 116 0.8214 32 0.7385 118 0.8150 34 0.8156 120 0.7601 36 0.8093 122 0.8495 38 0.8024 124 0.7747 40 0.7604 126 0.8464 42 0.7634 128 0.7769 44 0.7914 130 0.7618 46 0.7986 132 0.8208 48 0.9238 134 0.7945 50 0.7672 136 0.8197 52 0.8512 138 0.8431 54 0.7816 140 0.8644 56 0.7844 142 0.7647 58 0.8123 144 0.8330 60 0.7570 146 0.8170 62 0.8492 148 0.9015 64 0.6426 150 0.8146 66 0.9419 68 0.8492 70 0.7762 72 0.8103 74 0.8023 76 0.7619 78 0.7674 80 0.7397 82 0.7390 84 0.7510 R*(m 2K/kW) 0C (min) Unc(BDC)% 0.8027 9.30 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.7974 2 0.4138 88 0.7292 4 0.4247 90 0.7428 6 0.4603 92 0.8092 8 0.5597 94 0.6901 10 0.5687 96 1.3474 12 0.5327 98 0.7553 14 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 112 0.7765 28 0.7538 114 0.7667 30 0.7659 116 0.7256 32 0.7419 118 0.7423 34 0.7604 120 0.7271 36 0.7188 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 R*(m2K/kW) 0c(min) Unc(BDC)% 0.7614 8.89 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.6607 2 0.3060 88 0.6788 4 0.3350 90 0.7044 6 0.4359 92 0.6717 8 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 0.5560 108 0.7106 24 0.5911 110 0.7261 26 0.5788 112 0.7013 28 0.5486 114 0.7418 30 0.5905 116 0.7292 32 0.5880 118 0.7295 34 0.6159 120 0.7072 36 0.6108 122 0.7076 38 0.6572 124 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*(m2K/kW) 0C (min) Unc(BDC)% 0.6609 7.61 7.72 137 Run 21 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M. average Temp. (°C) CL at 6=0 = 0.480 kW Time Fouling Res. (min) (m2 K/kW) 0 0.0000 2 0.2516 4 0.3352 6 0.3122 8 0.4343 10 0.4739 12 0.5145 14 0.5060 16 0.4963 18 0.4205 20 0.5125 22 0.5629 24 0.5389 26 0.5185 28 0.5544 30 0.5590 32 0.5756 34 0.5626 36 0.5852 38 0.5809 40 0.5638 42 0.5334 44 0.5942 46 0.6179 48 0.5605 50 0.5986 52 0.6209 54 0.5998 56 0.6222 58 0.5929 60 0.5689 62 0.5909 64 0.6047 66 0.6143 68 0.6024 70 0.6255 72 0.6325 74 0.6131 76 0.6130 78 0.6116 80 0.6197 82 0.6149 84 0.6039 R*(m 2K/kW) 0.6016 20.0 14440. 8579. 11.98 31.37 Time Fouling Res. (min) (m2 K/kW) 86 0.6279 88 0.6302 90 0.6304 92 0.5727 94 0.6231 96 0.6121 98 0.6188 100 0.5815 102 0.5792 104 0.6043 106 0.6196 108 0.6050 110 0.6176 112 0.6053 114 0.6267 116 0.6512 118 0.5680 120 0.6291 122 0.6381 124 0.6352 126 0.6120 128 0.6247 130 0.6354 132 0.6151 134 0.5984 136 0.6362 138 0.6181 140 0.6432 142 0.6248 144 0.6253 146 0.6165 148 0.6421 150 0.4387 0c.(min) Unc(BDC)% 7.33 6.70 138 Run 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 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 0.5420 98 0.7441 14 0.5340 100 0.7655 16 0.6696 102 0.9005 18 0.6134 104 0.8554 20 0.5258 106 0.6940 22 0.6899 108 0.8370 24 0.6498 110 0.5948 26 0.6650 112 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 84 0.7768 R*(m2K/kW) 0C (min) Unc(BDC)% 0.7407 7.92 15.93 139 R u n 23 Bulk concentration (%) 20.0 Mixture Re 8773. Water Re 8702. Water average Temp.( °C) 12.50 M . average Temp. (°C) 31.50 CL at 9=0 = 0.303 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.5665 2 0.0885 88 0.6014 4 0.1721 90 0.4520 6 -0.0591 92 0.3084 8 0.1744 94 0.2458 10 0.2343 96 0.3591 12 0.2563 98 0.4825 14 0.3249 100 0.6111 16 0.346 102 0.5565 18 0.3496 104 0.5664 20 0.3378 106 0.5606 22 0.3127 108 0.6091 24 0.2665 110 0.4572 26 0.3982 112 0.4509 28 0.3211 114 0.4914 30 0.4268 116 0.4907 32 0.4101 118 0.4367 34 0.3557 120 0.5132 36 0.3891 122 0.5873 38 0.3582 124 0.5410 40 0.3950 126 0.4272 42 0.3565 128 0.5838 44 0.4294 130 0.5334 46 0.2981 132 0.3656 48 0.3850 134 0.4837 50 0.3700 136 0.4990 52 0.4694 138 0.4936 54 0.4469 140 0.5371 56 0.4760 142 0.4832 58 0.4587 60 0.3946 62 0.4883 64 0.4790 66 0.3721 68 0.4675 70 0.4489 72 0.4065 74 0.4603 76 0.4124 78 0.4672 80 0.4788 82 0.5168 84 0.5301 RArnKlkW) dc (min) Unc(BDC)% 0.4854 20.86 19.35 140 Run 24 Bulk concentration (%) 20.0 Mixture Re 11314. Water Re 8977. Water average Temp.( °C) 13.64 M. average Temp. (°C) 31.35 C^ate^ = 0.399 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m 2 K/kW) 0 0.0000 86 0.5180 2 0.2395 88 0.5359 4 0.2759 90 0.4130 6 0.3030 92 0.4436 8 0.4661 94 0.4452 10 0.4087 96 0.4685 12 0.4034 98 0.5383 14 0.4062 100 0.3881 16 0.4090 102 0.5179 18 0.4370 104 0.4572 20 0.4194 106 0.4719 22 0.3993 108 0.4902 24 0.4055 110 0.5823 26 0.4781 112 0.3661 28 0.5589 114 0.5608 30 0.4325 116 0.5146 32 0.4744 118 0.4405 34 0.4220 120 0.4618 36 0.4304 122 0.4663 38 0.4499 124 0.4182 40 0.5307 126 0.4085 42 0.5546 128 0.4678 44 0.4563 130 0.3637 46 0.4258 132 0.4812 48 0.5152 134 0.4402 50 0.4264 136 0.4199 52 0.4339 138 0.3997 54 0.4542 140 0.5000 56 0.4963 142 0.4945 58 0.4915 144 0.4410 60 0.4565 146 0.4710 62 0.4015 148 0.4751 64 0.4556 150 0.4817 66 0.3870 68 0.2969 70 0.4124 72 0.5105 74 0.4991 76 0.4358 78 0.5222 80 0.4549 82 0.5597 84 0.4852 Rf(inKlkW) Bjmin) Unc(BDC)% 0.4605 4.15 11.53 141 Run 25 Bulk concentration (%) 20.0 Mixture Re 12888. Water Re 9002. Water average Temp.(°C) 13.74 M . average Temp. ( °C) 31.26 CLate=0 = 0.416 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.4681 2 0.1549 88 0.3878 4 0.2589 90 0.4120 6 0.2994 92 0.4384 8 0.2940 94 0.4294 10 0.3517 96 0.3457 12 0.3774 98 0.5222 14 0.4316 100 0.4540 16 0.4250 102 0.4972 18 0.4083 104 0.4912 20 0.3889 106 0.4312 22 0.4550 108 0.4634 24 0.4195 110 0.4573 26 0.4930 112 0.4854 28 0.4602 114 0.4000 30 0.4213 116 0.4633 32 0.4011 118 0.5296 34 0.3859 120 0.4628 36 0.4377 122 0.5393 38 0.3596 124 0.4480 40 0.4759 126 0.4414 42 0.4697 128 0.5350 44 0.5196 130 0.4326 46 0.4235 132 0.4878 48 0.5875 134 0.4567 50 0.4055 136 0.5205 52 0.4323 138 0.4562 54 0.5151 56 0.4692 58 0.4261 60 0.4875 62 0.4693 64 0.4531 66 0.4509 68 0.4809 70 0.4484 72 0.4558 74 0.4294 76 0.4528 78 0.4458 80 0.5065 82 0.3811 84 0.5052 Rf(rnKlkW) 0.4572 ft. (min) 6.26 Unc(BDC)% 9.55 142 Run 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m2 K/kW) 0 0.0000 86 0.4064 2 0.1749 88 0.4871 4 0.2096 90 0.4891 6 0.3161 92 0.4446 8 0.2949 94 0.4134 10 0.2939 96 0.4209 12 0.3332 98 0.4675 14 0.2969 100 0.4525 16 0.3141 102 0.4268 18 0.2755 104 0.4674 20 0.3764 106 0.4833 22 0.3843 108 0.4865 24 0.3470 110 0.4206 26 0.3352 112 0.4372 28 0.3486 114 0.3785 30 0.3475 116 0.4024 32 0.4023 118 0.4268 34 0.4034 120 0.5013 36 0.3453 122 0.4463 38 0.3354 124 0.4810 40 0.4880 126 0.5354 42 0.4001 128 0.5561 44 0.4169 130 0.5730 46 0.4564 132 0.4552 48 0.4010 134 0.4757 " 50 0.3958 136 0.4772 52 0.4505 138 0.4829 54 0.4290 140 0.5105 56 0.3577 142 0.5042 58 0.3714 144 0.4790 60 0.4295 146 0.4636 62 0.4532 148 0.5042 64 0.4431 150 0.4620 66 0.4784 68 0.4621 70 0.4573 72 0.4158 74 0.4498 76 0.5476 78 0.4339 80 0.4361 82 0.5133 84 0.444 R*(rnK/kW) 0C (min) Unc(BDC)% 0.4527 12.06 8.13 143 Run 27 Bulk concentration (%) 20.0 Mixture Re 6567. Water Re 9663. Water average Temp.( °C) 13.43 M . average Temp. (°C) 31.60 0. at 9=0 = 0.285 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.5688 2 0.3162 88 0.4979 4 0.2911 90 0.5015 6 0.2763 92 0.4079 8 0.4337 94 0.4826 10 0.3532 96 0.5726 12 0.4294 98 0.4991 14 0.4582 100 0.5525 16 0.4719 102 0.5998 18 0.4852 104 0.5592 20 0.4930 106 0.5905 22 0.5416 108 0.2157 24 0.5067 110 0.6144 26 0.3515 112 0.5718 28 0.3272 114 0.7986 30 0.2352 116 0.6555 32 0.2214 118 0.6347 34 0.2746 120 0.4880 36 0.4771 122 0.6327 38 0.4645 124 0.6318 40 0.3953 126 0.6271 42 0.4040 128 0.4584 44 0.3430 130 0.5523 46 0.2590 132 0.4555 48 0.2498 134 0.4074 50 0.2051 136 0.4433 52 0.1610 138 0.3259 54 0.0506 140 0.6103 56 0.4549 142 0.4764 58 0.3519 144 0.6489 60 0.4025 146 0.6723 62 0.3400 148 0.5493 64 0.2969 150 0.6392 66 0.2678 68 0.1081 70 0.1697 72 0.3982 74 0.4013 76 0.2638 78 0.4238 80 0.4591 82 0.4308 84 0.3974 R*(m 2K/kW) 0.4406 dc (min) Unc(BDC)% 3.15 20.99 144 Run 28 Bulk concentration (%) 20.0 Mixture Re 8819. Water Re 9326. Water average Temp.( °C) 12.06 M. average Temp. ( °C ) 31.29 Q wat0=O = 0.355 kW Time Fouling Res. Time Fouling Res (min) (m 2K/kW) (min) (m 2 K/kW) 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 0.3678 102 0.3596 18 0.5704 104 0.1952 20 0.4241 106 0.3602 22 0.4566 108 0.3060 24 0.4512 110 0.3830 26 0.4798 112 0.3301 28 0.3267 114 0.4159 30 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 0.4763 138 0.3561 54 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) 0C (min) Unc(BDC)% 0.4056 4.98 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 kW Time Fouling Res. Time FoulingRes. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.1203 2 0.1593 88 0.1288 4 0.1796 90 0.2402 6 0.2071 92 0.2225 8 0.2107 94 0.2699 10 0.1711 96 0.2548 12 0.2661 98 0.2491 14 0.2262 100 0.2370 16 0.1884 102 0.2482 18 0.1825 104 0.2662 20 0.1500 106 0.2207 22 0.2205 108 0.1944 24 0.2086 110 0.2285 26 0.2636 112 0.2293 28 0.1935 114 0.2352 30 0.2060 116 0.2358 32 0.2665 118 0.2343 34 0.2309 120 0.2633 36 0.2118 122 0.2494 38 0.1754 124 0.2574 40 0.1633 126 0.2038 42 0.1293 128 0.2492 44 0.2585 130 0.1915 46 0.2305 132 0.2194 48 0.2710 134 0.2386 50 0.2211 52 0.2588 54 0.2387 56 0.2749 58 0.2755 60 0.2347 62 0.2213 64 0.2406 66 0.2510 68 0.2650 70 0.2532 72 . 0.1973 74 0.2550 76 0.3227 78 0.2518 80 0.2346 82 0.2117 84 0.1571 R* (m 2K IkW) 6C (min) Unc(BDC)% 0.2263 2.09 18.19 146 Run 30 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C) CLate=0 = 0.351 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 2 0.0876 4 0.1046 6 0.1279 8 0.1083 10 0.1389 12 0.1678 14 0.1760 16 0.1891 18 0.1566 20 0.1333 22 0.1848 24 0.2283 26 0.1557 28 0.1820 30 0.1690 32 0.1827 34 0.0592 36 0.1758 38 0.2066 40 0.1915 42 0.1673 44 0.1261 46 0.1420 48 0.1196 50 0.1239 52 0.1338 54 0.1189 56 0.2153 58 0.1735 60 0.1315 62 0.1813 64 0.0487 66 0.0677 68 0.1705 70 0.1505 72 0.1911 74 0.1629 76 0.1639 78 0.2097 80 0.1561 82 0.2187 84 0.1685 * Rf (rnKlkW) 0.1534 20.0 12697. 9836. 14.12 31.33 Time Fouling Res. (min) (m 2 K/kW) 86 0.1658 88 0.1886 90 0.1736 92 0.0755 94 0.1841 96 0.1601 98 0.1461 100 0.1244 102 0.1155 104 0.1192 106 0.0908 108 0.1044 110 0.1081 112 0.2080 114 0.1622 116 0.1426 118 0.1676 120 0.1732 122 0.1835 124 0.0656 126 0.1681 128 0.1493 130 0.2147 132 0.1951 134 0.1510 136 0.1895 138 0.1677 140 0.1826 142 0.0525 144 0.2025 t) Unc(BDC)% 32 24.13 147 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.0944 2 0.0130 88 0.0996 4 0.0306 90 0.0900 6 0.0502 92 0.0743 8 0.0498 94 0.0815 10 0.0637 96 0.0693 12 0.0702 98 0.0608 14 0.0457 100 0.0579 16 0.0335 102 0.0476 18 0.0597 104 0.0562 20 0.0534 106 0.0354 22 0.0702 108 0.1081 24 0.0592 110 0.0982 26 0.0738 112 0.0823 28 0.0470 114 0.0761 30 0.0568 116 0.0943 32 0.0463 118 0.0873 34 0.0412 120 0.0712 36 0.0396 122 0.0861 38 0.0473 40 0.0317 42 0.1014 44 0.0711 46 0.0646 48 0.0727 50 0.0788 52 0.0776 54 0.0597 56 0.0771 58 0.0418 60 0.0651 62 0.0707 64 0.0404 66 0.0495 68 0.0177 70 0.0995 72 0.1084 74 0.0487 76 0.0758 78 0.0835 80 0.0897 82 0.0604 84 0.0835 R*(_rnKlkW) 9C (min) Unc(BDC)% 0.0700 9.37 55.60 148 Run 32 Bulk concentration (%) 20.0 Mixture Re 6616. Water Re 9545. Water average Temp.( °C) 12.95 M . average Temp. ( °C ) 31.20 Q . at 6=0 = 0.244 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m2 K/kW) 0 0.0000 86 0.6337 2 0.2265 88 0.4634 4 0.3475 90 0.2779 6 0.3996 92 0.2412 8 0.3684 94 0.5125 10 0.4716 96 0.6167 12 0.4100 98 0.4253 14 0.4354 100 0.6543 16 0.5458 102 0.6265 18 0.4220 104 0.5559 20 0.5099 106 0.4212 22 0.4834 108 0.5247 24 0.5289 110 0.6854 26 0.4995 112 0.7058 28 0.5436 114 0.6392 30 0.6256 116 0.5590 32 0.4238 118 0.6846 34 0.3371 120 0.6084 36 0.1973 122 0.3935 38 0.5762 124 0.6086 40 0.4595 126 0.5832 42 0.5600 128 0.6617 44 0.3644 130 0.4696 46 0.4969 132 0.6697 48 0.5836 134 0.4717 50 0.5342 136 0.6218 52 0.5685 138 0.5973 54 0.6504 140 0.5996 56 0.6014 142 0.6811 58 0.6009 144 0.6223 60 0.6592 146 0.6710 62 0.6111 148 0.6257 64 0.7299 150 0.6641 66 0.5976 68 0.3170 70 0.3541 72 0.5841 74 0.6459 76 0.5620 78 0.6466 80 0.7928 82 0.5644 84 0.6195 RJinKlkW) 9c(min) Unc(BDC)% 0.5552 6.37 21.08 149 Run 33 Bulk concentration (%) 20.0 Mixture Re 8803. Water Re 9542. Water average Temp.( °C) 12.94 M . average Temp. ( °C) 31.32 Q . at 9=0 = 0.340 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.2429 2 0.2713 88 0.1884 4 0.2972 90 0.1589 6 0.3908 92 0.1266 8 0.2528 94 0.1221 10 0.3693 96 0.1094 12 0.4107 98 0.2386 14 0.4271 100 0.3763 16 0.3473 102 0.4341 18 0.4548 104 0.4191 20 0.4550 106 0.3598 22 0.3821 108 0.4482 24 0.3469 110 0.5052 26 0.4308 112 0.4549 28 0.3887 114 0.3389 30 0.4575 116 0.2762 32 0.4446 118 0.3772 34 0.4526 120 0.4591 36 0.4230 122 0.4563 38 0.4494 124 0.4277 40 0.2923 126 0.4461 42 0.3522 128 0.3283 44 0.4560 130 0.6556 46 0.3756 132 0.3992 48 0.2933 134 0.3470 50 0.4151 136 0.3953 52 0.4168 138 0.4270 54 0.4379 140 0.3949 56 0.4559 142 0.3980 58 0.3712 144 0.4356 60 0.3183 146 0.3921 62 0.2345 148 0.4339 64 0.4071 150 0.4070 66 0.3652 68 0.4169 70 0.4786 72 0.4930 74 0.3927 76 0.4429 78 0.4264 80 0.4133 82 0.3503 84 0.2764 Rf(tnKlkW) 0c(min) Unc(BDC)% 0.3804 2.04 17.22 150 Run 34 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C ) Q w at 9=0 = 0.349 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 2 0.2433 4 0.2875 6 0.3586 8 0.3324 10 0.2954 12 0.2648 14 0.3382 16 0.3049 18 0.3456 20 0.3454 22 0.3651 24 0:3842 26 0.3587 28 0.4117 30 0.3685 32 0.3349 34 0.3843 36 0.3766 38 0.4205 40 0.4810 42 0.4803 44 0.3222 46 0.2811 48 0.2513 50 0.3358 52 0.3976 54 0.3945 56 0.3976 58 0.3703 60 0.4149 62 0.3866 64 0.3711 66 0.4264 68 0.3545 70 0.3995 72 0.3703 74 0.3429 76 0.3261 78 0.2785 80 0.3157 82 0.4702 84 0.3003 R*(m 2K/kW) 0C 0.3671 20.0 8765. 9646. 13.36 31.30 Time Fouling Res. (min) (m 2 K/kW) 86 0.5446 88 0.4971 90 0.3993 92 0.4264 94 0.4121 96 0.3947 98 0.3927 100 0.4636 102 0.4032 104 0.3828 106 0.1586 108 0.3905 110 0.3796 112 0.4202 114 0.3800 116 0.2838 118 0.2902 120 0.3751 122 0.3830 124 0.3876 126 0.1574 128 0.4100 130 0.3659 132 0.3599 134 0.3839 136 0.4223 138 0.1438 140 0.3518 142 0.418 144 0.4001 146 0.3547 148 0.3423 150 0.4088 (min) Unc(BDC)% 2.30 16.34 151 Run 35 Bulk concentration (%) 20.0 Mixture Re 11042. Water Re 9534. Water average Temp.( °C) 12.91 M . average Temp. ( °C) 31.00 Q . at 9=0 = 0.375 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.1537 2 0.1263 88 0.1843 4 0.1329 90 0.2110 6 0.1131 92 0.1738 8 0.1784 94 0.2150 10 0.1740 96 0.1680 12 0.1507 98 0.2013 14 0.1877 100 0.0490 16 0.1588 102 0.2650 18 0.1956 104 0.3012 20 0.1796 106 0.3583 22 0.2000 108 0.3884 24 0.1984 110 0.1596 26 0.2054 112 0.2118 28 0.1432 114 0.1588 30 0.2215 116 0.2227 32 0.2139 118 0.2081 34 0.1904 120 0.1176 36 0.1696 122 0.2161 38 0.2043 124 0.2497 40 0.2432 126 0.2018 42 0.2387 128 0.1641 44 0.1924 130 0.2118 46 0.1897 132 0.2259 48 0.2066 134 0.2246 50 0.2257 136 0.1324 52 0.1851 138 0.1952 54 0.1633 140 0.1602 56 0.1088 142 0.1645 58 0.0972 144 0.2102 60 0.0917 146 0.1615 62 0.0759 148 0.2176 64 0.2060 150 0.1684 66 0.2072 68 0.0350 70 0.2106 72 0.2025 74 0.1813 76 0.2037 78 0.2275 80 0.2645 82 0.1952 84 0.1481 R*(m 2KlkW) 0C (min) Unc(BDC)% 0.1912 3.71 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 w at 9=0 = 0.375 kW Time Fouling Res. Time Fouling Res. (min) (m2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.1316 2 0.0501 88 0.1264 4 0.0616 90 0.0986 6 0.0670 92 0.1303 8 0.1036 94 0.0529 10 0.0532 96 0.1453 12 0.1083 98 0.1472 14 0.0607 100 0.1521 16 0.1361 102 0.1217 18 0.1076 104 0.1616 20 0.1548 106 0.1608 22 0.0492 108 0.1846 24 0.1164 110 0.1992 26 0.2134 112 0.1243 28 0.1662 114 0.1655 30 0.1249 116 0.0547 32 0.0917 118 0.1373 34 0.1393 120 0.1655 36 0.1716 122 0.1395 38 0.1367 124 0.1587 40 0.1024 126 0.1368 42 0.0913 128 0.148 44 0.0758 130 0.1482 46 0.0937 132 0.0977 48 0.0785 134 0.0050 50 0.1462 136 0.1504 52 0.1480 140 0.1229 54 0.1421 142 0.1683 56 0.1318 144 0.1335 58 0.1226 60 0.1228 62 0.1390 64 0.0381 66 0.1200 68 0.0987 70 0.1020 72 0.1154 74 0.1495 76 0.1077 78 0.1450. 80 0.1673 82 0.1409 84 0.1363 Rf(m 2K/kW) 0.1288 6. (min) 7.91 Unc(BDC)% 47.23 153 Run 37 B u l k concentration (%) 20.0 M ix ture Re 14432. Water Re 9741. Water average Temp.( °C) 13.74 M . average Temp. ( ° C ) 31.37 Q , at 0=0 = 0.387 k W T ime Fou l ing Res. T ime Fou l ing Res (min) ( m 2 K / k W ) (min] ( m 2 K/kW) 0 0.0000 86 0.0252 2 0.0388 88 0.0157 4 0.0511 90 0.0379 6 0.0120 92 0.0425 8 0.0176 94 0.0278 10 0.0555 96 0.0535 12 0.0734 98 0.0745 14 0.0113 100 0.0357 16 0.0404 102 0.0145 18 0.0540 104 0.0310 20 0.0747 106 0.1215 22 0.0418 108 0.1151 24 0.0217 110 0.1161 26 0.1048 112 0.0574 28 0.0651 114 0.0741 30 0.0964 116 0.0587 32 0.0107 118 0.0643 34 0.0578 120 0.0163 36 0.0514 122 0.0139 38 0.0647 124 0.0173 40 0.0621 126 0.0402 42 0.0011 128 0.0616 44 0.0257 130 0.0807 46 0.0233 132 0.0361 48 0.0260 134 0.0330 50 0.0629 136 0.0526 52 0.0746 138 0.0615 54 0.0503 140 0.0918 56 0.0354 142 0.0598 58 0.0496 144 0.0938 60 0.0551 146 0.0663 62 0.0737 148 0.0994 64 0.1085 150 0.0619 66 0.0359 68 0.0718 70 0.0266 72 0.0036 74 0.0356 76 0.0520 78 0.0370 80 0.0145 82 0.0338 84 0.0591 R*(m2K/kW) Ojmin) U n c ( B D C ) % 0.0520 4.89 155.10 154 Run 38 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C ) Q at 9=0 = 0.352 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 2 0.2317 4 0.6261 6 0.6537 8 0.5720 10 0.3310 12 0.6281 14 0.5892 16 0.7603 18 0.4491 20 0.7182 22 0.7597 24 0.6997 26 0.5711 28 0.7489 30 0.4098 32 0.7279 34 0.7327 36 0.7346 38 0.7198 40 0.7042 42 0.6970 44 0.7932 46 0.7706 48 0.5212 50 0.6601 52 0.8312 54 0.8003 56 0.7637 58 0.7260 60 0.6401 62 0.6316 64 0.5949 66 0.6166 68 0.7889 70 0.8246 72 0.7342 74 0.7214 76 0.6820 78 0.6711 80 0.6790 82 0.7630 84 0.6672 R*(m2K/kW) 0c (min) 0.7016 4.4 20.0 6631. 8854. 13.13 31.50 Time Fouling Res. (min) (m 2 K/kW) 86 0.8311 88 0.7017 90 0.7820 92 0.7330 94 0.8423 96 0.7666 98 0.7373 100 0.3893 102 0.7353 104 0.8007 106 0.6865 108 0.6482 110 0.6168 112 0.6451 114 0.3167 116 0.7581 118 0.8067 120 0.8038 122 0.7151 124 0.7537 126 0.7835 128 0.8169 130 0.8007 132 0.8407 134 0.8306 136 0.8270 138 0.8217 140 0.7287 142 0.8451 Unc(BDC)% 14.36 155 Run 39 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C ) Q . at 6=0 = 0.376 kW Time Fouling Res. (min) (m 2K/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 26 0.3377 28 0.3068 30 0.3755 32 0.3258 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 68 0.7120 70 0.1724 72 0.4852 74 0.4343 76 0.2763 78 0.5120 80 0.5312 82 0.4396 84 0.3276 R*(m2K/kW) 0c(i 0.4639 20.0 8734. 8939. 13.48 31.39 Time Fouling Res. (min) (m 2 K/kW) 86 0.4883 88 0.4574 90 0.5231 92 0.5403 94 0.4829 96 0.5747 98 0.5214 100 0.5276 102 0.4647 104 0.5244 106 0.5473 108 0.5220 110 0.5223 112 0.4932 114 0.5014 116 0.4481 118 0.5827 120 0.5447 122 0.4172 124 0.5695 126 0.6982 128 0.4108 130 0.4627 132 0.4998 134 0.5165 136 0.5439 138 0.4606 140 0.4965 142 0.4868 in) Unc(BDC)% 4.19 15.65 156 Run 40 Bulk concentration (%) Mixture Re Water Re Water average Temp.(°C) M . average Temp. ( °C ) CL at 9=0 = 0.407 kW Time Fouling Res. (min) (m 2K/kW) 0 0.0000 2 0.1677 4 0.1953 6 0.3341 8 0.2534 10 0.3154 12 0.3005 14 0.3579 16 0.3129 18 0.3809 20 0.3572 22 0.2744 24 0.4030 26 0.4040 28 0.3387 30 0.4448 32 0.3804 34 0.4169 36 0.1982 38 0.4698 40 0.4414 42 0.4914 44 0.5315 46 0.4972 48 0.4677 50 0.3601 52 0.4839 54 0.3935 56 0.4441 58 0.5406 60 0.5308 62 0.4737 64 0.4538 66 0.4601 68 0.4674 70 0.5572 72 0.4919 74 0.4246 76 0.3653 78 0.3912 80 0.4164 82 0.4031 84 0.5020 R*(tnKlkW) 0c(r, 0.4496 20.0 11084. 8890. 13.28 31.67 Time Fouling Res. (min) (m 2 K/kW) 86 0.4700 88 0.3625 90 0.3879 92 0.4138 94 0.3677 96 0.4442 98 0.4164 100 0.4668 102 0.4715 104 0.4626 106 0.4596 108 0.4211 110 0.4545 112 0.4856 114 0.5136 116 0.5130 118 0.3704 120 0.4197 122 0.4041 124 0.4766 126 0.4714 128 0.4695 130 0.4375 132 0.4155 134 0.5379 136 0.4987 138 0.4051 140 0.5077 142 0.5440 144 0.4115 146 0.4869 148 0.4338 150 0.5441 n) Unc(BDC)% i.02 11.45 157 Run 41 B u l k concentration (%) 20.0 Mixture Re 12672. Water Re 8835. Water average Temp.( °C) 13.05 M . average Temp. ( °C) 31.42 O^ate^ = 0.507 k W T ime Fou l ing Res. T ime Fou l ing Res. (min) ( m 2 K / k W ) (min) ( m 2 K/kW) 0 0.0000 86 0.3223 2 0.2221 88 0.2667 4 0.2191 90 0.2442 6 0.2576 92 0.2342 8 0.2915 94 0.2149 10 0.3131 96 0.1849 12 0.3651 98 0.4455 14 0.3722 100 0.6018 16 0.3722 102 0.5686 18 0.3601 104 0.4926 20 0.3886 106 0.4473 22 0.4288 108 0.4020 24 0.4113 110 0.5427 26 0.3733 112 0.5823 28 0.3343 114 0.4086 30 0.2844 116 0.5696 32 0.3058 118 0.5043 34 0.4121 120 0.4152 36 0.3938 122 0.3523 38 0.3670 124 0.3146 40 0.3474 126 0.2593 42 0.1505 128 0.3561 44 0.2605 130 0.4669 46 0.2194 132 0.3936 48 0.2117 134 0.4068 50 0.1765 136 0.4606 52 0.3974 138 0.3967 54 0.4322 140 0.5380 56 0.3355 142 0.4696 58 0.3108 144 0.4838 60 0.2375 146 0.5972 62 0.2124 64 0.1935 66 0.2308 68 0.2474 70 0.4586 72 0.4976 74 0.4433 76 0.3549 78 0.3867 80 0.4900 82 0.4449 84 0.3637 RAinKlkW) 0C 0.3753 (min) 4.19 U n c ( B D C ) % 11.63 158 Run 42 Bulk concentration (%) 20.0 Mixture Re 14147. Water Re 8796. Water average Temp.(°C) 12.89 M . average Temp. ( °C) 31.69 CLate=0 = 0.506 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.4428 2 0.0396 88 0.4499 4 0.1226 90 0.3169 6 0.2560 92 0.4353 8 0.2606 94 0.5734 10 0.3147 96 0.4729 12 0.3362 98 0.4020 14 0.3117 100 0.3566 16 0.2921 102 0.2900 18 0.2868 104 0.2708 20 0.2652 106 0.3151 22 0.2871 108 0.4336 24 0.4870 110 0.4704 26 0.4381 112 0.3519 28 0.3727 114 0.3039 30 0.3676 116 0.4981 32 0.2921 118 0.3954 34 0.2973 120 0.4030 36 0.1144 122 0.4445 38 0.2296 124 0.3339 40 0.1854 126 0.3839 42 0.2209 128 0.3832 44 0.1820 130 0.3946 46 0.4967 132 0.4865 48 0.5871 134 0.3812 50 0.5083 136 0.3191 52 0.2431 138 0.2625 54 0.4663 140 0.2588 56 0.5356 142 0.2865 58 0.3807 144 0.3160 60 0.3403 146 0.3470 62 0.3213 148 0.4028 64 0.2977 150 0.4824 66 0.2657 68 0.2251 70 0.2073 72 0.2268 74 0.2085 76 0.1533 78 0.5086 80 0.5370 82 0.4160 84 0.1752 R*(rnK/kW) 9C (min) Unc(BDC)% 0.3574 6.87 8.96 159 Run 43 B u l k concentration (%) 10.0 M ix ture Re 10766. Water Re 18408. Water average Temp.( °C) 9.52 M . average Temp. ( ° C ) 28.69 Q w at 6=0 - 0.308 k W T ime Fou l ing Res. (min) ( m 2 K / k W ) 0 0.0000 1 0.4666 2 0.6087 3 0.9077 4 0.9697 5 1.0823 6 1.8591 7 1.8838 8 1.9524 9 2.0081 10 2.9451 11 1.5067 12 2.8579 13 2.8815 14 4.3914 15 2.9306 16 4.5517 17 4.5615 18 4.6052 19 3.0640 20 3.0821 21 3.0857 22 3.1454 23 3.1125 24 2.1856 25 3.1693 26 3.2012 27 2.2498 28 2.2125 29 2.2532 30 2.3307 31 2.3523 32 1.7356 33 2.2398 34 2.2691 35 3.1571 36 3.1836 37 3.2480 38 3.2562 39 2.3354 40 2.3998 41 2.3974 42 2.4533 43 1.8053 44 1.3710 45 1.8491 46 1.4009 T ime Fou l ing Res. (min) ( m 2 K/kW) 90 3.4701 91 2.4135 92 2.4378 93 3.4898 94 2.3922 95 3.4505 96 3.5038 97 3.4544 98 3.4701 99 3.4858 100 3.5015 101 1.7538 102 3.5408 103 3.4151 104 3.4190 105 2.4377 106 3.4898 107 3.4898 108 2.4469 109 2.4561 110 2.4683 111 3.5871 112 3.6069 113 2.5020 114 1.8168 115 2.4986 116 3.3410 117 5.2145 118 3.4269 119 2.3922 120 3.3993 121 3.3648 122 5.0867 123 9.3581 124 9.4056 125 5.1758 126 5.3424 127 3.3710 128 2.3142 129 3.4112 130 3.4269 131 3.4544 132 2.4074 133 2.4287 134 2.4198 135 3.5072 136 1.7909 160 4 7 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 3.2473 148 2.2824 59 3.2550 149 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 3.2971 155 9.1783 66 3.3085 156 9.3369 67 3.3162 157 4.9543 68 3.3200 158 9.4837 69 3.3277 159 9.4442 70 1.6666 160 9.3646 71 2.3254 161 9.0751 72 3.3973 163 4.8364 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) 0C (min) Unc(BDC)% 3.6474 12.01 21.00 161 Run 45 B u l k concentration (%) M ix ture Re Water Re Water average Temp.( °C) M . average Temp. (°C) Q . at 9=0 = 0.610 k W T ime Fou l ing Res. (min) ( m 2 K / k W ) 0 0.0000 1 0.0269 2 0.2306 3 0.1569 4 0.2685 5 0.3401 6 0.2788 7 0.2277 8 0.2274 9 0.4267 10 0.3625 11 0.3669 12 0.3726 13 0.4367 14 0.4359 15 0.4374 16 0.4381 17 0.3735 18 0.3714 19 0.3749 20 0.3096 21 0.3751 22 0.4522 23 0.5349 24 0.3824 25 0.3853 26 0.5390 27 0.5398 28 0.3884 29 0.3270 30 0.4663 31 0.4719 32 0.3345 33 0.4545 34 0.4443 35 0.5401 36 0.5493 37 0.5537 38 0.5573 39 0.6357 40 0.6331 41 0.5386 42 0.4616 43 0.6397 44 0.5489 45 0.4664 46 0.5443 47 0.4672 10.0 12150. 18687. 10.04 36.44 T ime Fou l ing Res. (min) ( m 2 K/kW) 90 0.5554 91 0.4641 92 0.5467 93 0.5467 94 0.5484 95 0.5501 96 0.4697 97 0.6500 98 0.6518 99 0.4777 100 0.4793 101 0.4793 102 0.5667 103 0.5675 104 0.4849 105 0.4849 106 0.5717 107 0.6695 108 0.4138 109 0.4864 110 0.5760 111 0.4920 112 0.3490 113 0.4896 114 0.4904 115 0.5737 116 0.4176 117 0.4184 118 0.4943 119 0.4943 120 0.4266 121 0.2889 122 0.4070 123 0.4763 124 0.4025 125 0.2746 126 0.3346 127 0.4033 128 0.4048 129 0.2796 130 0.2803 131 0.4071 132 0.3446 133 0.2844 134 0.2857 135 0.4123 136 0.4168 137 0.3522 162 48 0.4711 138 0.2904 49 0.3984 139 0.3531 50 0.4727 140 0.4213 51 0.5581 141 0.4251 52 0.4791 142 0.2931 53 0.5606 143 0.2927 54 0.4029 144 0.3574 55 0.5587 145 0.4258 56 0.4790 146 0.2972 57 0.4806 147 0.2954 58 0.3390 148 0.4251 59 0.4059 149 0.4289 60 0.5648 150 0.3006 61 0.4854 151 0.3006 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 157 0.4371 68 0.6392 158 0.3033 69 0.5501 159 0.1999 70 0.4688 160 0.5757 71 0.2185 161 0.4819 72 0.5560 162 0.4836 73 0.6532 163 0.4869 74 0.5639 164 0.4852 75 0.4027 165 0.5743 76 0.4759 166 0.6729 77 0.6613 167 0.4183 78 0.5698 168 0.4175 79 0.4080 169 0.5811 80 0.4872 170 0.5845 81 0.5704 171 0.4963 82 0.5611 172 0.4971 83 0.5510 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 R*f{rnKlkW) Ojmin) U n c ( B D C ) % 0 . 4 6 3 2 6 .55 2 7 . 2 7 163 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 kW Time Fouling Res. (min) (m 2 K/kW) 0 0.0000 1 0.0972 2 0.1040 3 0.1291 4 0.1656 5 0.2070 6 0.2523 7 0.2998 8 0.3044 9 0.2746 10 0.1650 11 0.2859 12 0.3836 13 0.3900 14 0.3980 15 0.4604 16 0.4091 17 0.4138 18 0.4178 19 0.4209 20 0.3236 21 0.4943 22 0.3242 23 0.3311 24 0.3454 25 0.3536 26 0.3582 2 7 0.3144 28 0.3166 29 0.2764 30 0.2767 31 0.3118 32 0.3446 33 0.3887 34 0.3962 35 0.3498 36 0.3051 37 0.3495 38 0.4000 39 0.4000 40 0.3994 41 0.3988 42 0.3487 43 0.3992 44 0.2577 45 0.3996 46 0.3478 Time Fouling Res. (min) (m2 K/kW) 90 0.3725 91 0.4250 92 0.3725 93 0.3725 94 0.3702 95 0.3225 96 0.3199 97 0.3682 98 0.3676 99 0.3676 100 0.2751 101 0.3191 102 0.3166 103 0.3166 104 0.3643 105 0.3643 106 0.3171 107 0.3177 108 0.3177 109 0.3177 110 0.3177 111 0.3682 112 0.3197 113 0.3658 114 0.3163 115 0.1267 116 0.2714 117 0.3141 118 0.3617 119 0.3129 120 0.3129 121 0.3129 122 0.3104 123 0.2692 124 0.3579 125 0.3579 126 0.3124 127 0.3590 128 0.3633 129 0.3639 130 0.4155 131 0.4161 132 0.3639 133 0.3623 134 0.3639 135 0.3629 136 0.3623 164 47 0.3467 137 0.4144 48 0.2998 138 0.3623 49 0.1146 139 0.3629 50 0.3434 140 0.3152 51 0.3455 141 0.3152 52 0.3470 142 0.3623 53 0.3464 143 0.3152 54 0.2965 144 0.3158 55 0.3964 145 0.3158 56 0.3982 146 0.3608 57 0.3497 147 0.3138 58 0.3043 148 0.3132 59 0.4019 149 0.2701 60 0.3544 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 0.3129 66 0.3639 156 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 168 0.2346 79 0.3838 169 0.2334 80 0.3862 170 0.3177 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 R*(rnKlkW) 0C (min) Unc(BDC)% 0.3435 4.41 18.56 165 Run 4 7 Bulk concentration (%) 10.0 Mix ture Re 13629. Water Re 18838. Water average Temp.( °C) 10.32 M . average Temp. ( °C) 44.18 at 6=0 = 0.715 k W T ime Fou l ing Res. T ime Fou l ing Res. (min) ( m 2 K / k W ) (min) (m 2 K/kW) 0 0.0000 110 0.2824 1 0.0757 111 0.2537 2 0.0985 112 0.2238 3 0.1716 113 0.2238 4 0.1993 114 0.3468 5 0.2107 115 0.2820 6 0.1704 116 0.3135 7 0.1328 117 0.2541 8 0.2139 118 0.2541 9 0.2178 119 0.2549 10 0.3474 120 0.3150 11 0.1966 121 0.3158 12 0.2251 122 0.3163 13 0.1762 123 0.2558 14 0.1807 124 0.3186 15 0.2075 125 0.2872 16 0.2369 126 0.2578 17 0.2402 127 0.3181 18 0.1916 128 0.2881 19 0.2158 129 0.3200 20 0.2154 130 0.2885 21 0.2154 131 0.2604 22 0.2428 132 0.2894 23 0.2719 133 0.2616 24 0.2710 134 0.2599 25 0.2728 135 0.2907 26 0.2186 136 0.2327 27 0.2736 137 0.3229 28 0.2753 138 0.2650 29 0.2757 139 0.2359 30 0.2473 140 0.2937 31 0.2481 141 0.2645 32 0.2448 142 0.2654 33 0.2736 143 0.2616 34 0.2444 144 0.2899 35 0.2444 145 0.2891 36 0.2453 146 0.3177 37 0.2465 147 0.2868 38 0.2461 148 0.3560 39 0.2481 149 0.3560 40 0.2775 150 0.2953 41 0.2784 151 0.2660 42 0.2498 152 0.3299 43 0.2797 153 0.2966 44 0.2511 154 0.2992 45 0.2523 155 0.2970 46 0.2531 156 0.3249 . 47 0.2540 157 0.3574 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 0.3121 166 0.3605 78 0.3126 167 0.4371 79 0.3150 168 0.4381 80 0.2842 169 0.4005 81 0.2846 170 0.4010 82 0.2841 171 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 180 0.2953 92 0.2802 181 0.3979 93 0.2806 182 0.3967 94 0.2810 183 0.3603 95 0.2810 184 0.4381 96 0.2828 185 0.3612 97 0.2540 186 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) 0C (min) Unc(BDC)% 0.3070 11.07 14.17 167 Run 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 1.4243 2 0.5910 88 1.7618 4 0.7963 90 1.7698 6 0.9453 92 1.1881 8 0.7367 94 1.3581 10 1.0500 96 1.4355 12 1.0107 98 1.5660 14 0.9813 100 1.5026 16 0.8728 102 1.7027 18 1.0527 104 1.5624 20 1.0900 106 1.6876 22 0.9658 108 1.4712 24 1.1653 110 1.4997 26 1.2739 112 1.5568 28 1.1227 114 1.5717 30 1.0688 116 1.5851 32 1.2877 118 1.5969 34 1.1686 120 1.5644 36 1.1030 122 1.6815 38 1.1932 124 1.3907 40 1.4985 126 1.5730 42 1.1867 128 1.8154 44 1.2988 130 1.6576 46 1.2177 132 1.6981 48 1.2790 134 1.6835 50 1.1491 136 1.7773 52 1.2791 138 1.5672 54 1.4070 140 1.5389 56 1.2910 142 1.4224 58 1.3549 144 1.6571 60 1.6184 146 1.6043 62 1.4312 148 1.6159 64 1.6457 150 1.6002 66 1.5942 68 1.4517 70 1.3269 72 1.3587 74 1.4895 76 1.4238 78 1.5168 80 1.5505 82 1.5135 84 1.5039 RArnKlkW) 6C (min) Unc(BDC)% 1.5241 16.17 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 C L a t O ^ = 0.539 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.3728 2 0.1761 88 0.3913 4 0.2386 90 0.3922 6 0.2881 92 0.3630 8 0.2791 94 0.2911 10 0.2911 96 0.4132 12 0.2549 98 0.4057 14 0.3063 100 0.3122 16 0.3654 102 0.4389 18 0.3668 104 0.4690 20 0.3781 106 0.4010 22 0.3847 108 0.3571 24 0.3750 110 0.3225 26 0.4073 112 0.3715 28 0.4161 114 0.3207 30 0.4017 116 0.3245 32 0.4498 118 0.3632 34 0.3808 120 0.3601 36 0.3756 122 0.3432 38 0.3598 124 0.3326 40 0.4245 126 0.3094 42 0.4041 128 0.3866 44 0.4161 130 0.3753 46 0.3865 132 0.3862 48 0.4040 134 0.3340 50 0.3979 136 0.2709 52 0.3887 138 0.3427 54 0.4012 140 0.3565 56 0.4386 142 0.3722 58 0.4148 144 0.3533 60 0.3982 146 0.3388 62 0.3959 148 0.3547 64 0.4260 150 0.4124 66 0.3926 68 0.3869 70 0.3391 72 0.3766 74 0.3453 76 0.4395 78 0.3656 80 0.4436 82 0.4116 84 0.4136 RAtnKlkW) 6C (min) Unc(BDC)% 0.3788 5.21 13.07 169 Run 51 Bulk concentration (%) 20.0 Mixture Re 9841. Water Re 7762. Water average Temp.( °C) 8.48 M. average Temp. ( °C ) 38.08 Q at 9=0 = 0.703 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m 2 K/kW) 0 0.0000 86 0.2058 2 0.1303 88 0.2302 4 0.1205 90 0.2205 6 0.2437 92 0.2114 8 0.205 94 0.2166 10 0.2185 96 0.2433 12 0.2165 98 0.2205 14 0.2673 100 0.2370 16 0.2501 102 0.2322 18 0.2549 104 0.2204 20 0.2235 106 0.2246 22 0.2117 108 0.2385 24 0.2382 110 0.2286 26 0.2455 112 0.2245 28 0.2461 114 0.2264 30 0.2371 116 0.2404 32 0.1298 118 0.1696 34 0.2332 120 0.1759 36 0.2258 122 0.1881 40 0.2708 124 0.2112 42 0.2547 126 0.2173 44 0.2522 128 0.2423 46 0.2393 130 0.1714 48 0.2310 132 0.2147 50 0.2415 134 0.2157 52 0.1987 136 0.1901 54 0.2322 138 0.2252 56 0.2027 140 0.2094 58 0.2321 142 0.2134 60 0.1991 144 0.1940 62 0.2472 146 0.2134 64 0.2688 148 0.2102 66 0.2409 150 0.2129 68 0.2396 70 0.2175 72 0.2693 74 0.2431 76 0.2060 78 0.2205 80 0.1954 82 0.2331 84 0.2273 RArnKlkW) 0C (min) Unc(BDC)% 0.2205 2.74 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. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.3884 2 0.2160 88 0.3928 4 0.2860 90 0.3981 6 0.4237 92 0.4427 8 0.4031 94 0.3756 10 0.3822 96 0.3699 12 0.4336 98 0.3757 14 0.4068 100 0.3754 16 0.4126 102 0.3511 18 0.4214 104 0.2920 20 0.4228 106 0.4213 22 0.4032 108 0.4078 24 0.4246 110 0.4325 26 0.4396 112 0.4263 28 0.3822 114 0.3690 30 0.4282 116 0.3829 32 0.3907 118 0.3748 34 0.4338 120 0.3565 36 0.4170 122 0.3626 38 0.4370 124 0.4012 40 0.4160 126 0.3892 42 0.3870 128 0.3121 44 0.4103 130 0.3744 46 0.3911 132 0.3638 48 0.4530 134 0.3673 50 0.4388 136 0.3798 52 0.4014 138 0.3702 54 0.4016 140 0.3533 56 0.3996 142 0.3668 58 0.4060 144 0.3580 60 0.3913 146 0.3008 62 0.4031 148 0.3622 64 0.3818 150 0.3328 66 0.4008 68 0.4393 70 0.4058 72 0.3668 74 0.3743 76 0.3720 78 0.3858 80 0.3761 82 0.4128 84 0.3736 R*f(tnKlkW) djmin) Unc(BDC)% 0.3916 2.29 7.88 171 Run 53 Bulk concentration (%) Mixture Re Water Re Water average Temp.( °C) M . average Temp. ( °C ) Q w at 9=0 = 0. Time Fouling Res. (min) (m 2K/kW) 0 0.0000 2 0.2040 4 0.2304 6 0.2538 8 0.2422 10 0.2484 12 0.2260 14 0.2349 16 0.2137 18 0.2247 20 0.1908 22 0.2450 24 0.2556 26 0.2389 28 0.2554 30 0.2408 32 0.2523 34 0.2306 36 0.2009 38 0.2711 40 0.2107 42 0.2222 44 0.2458 46 0.2331 48 0.2854 50 0.2478 52 0.2486 54 0.2281 56 0.2136 58 0.2343 60 0.2401 62 0.2423 64 0.2450 66 0.2091 68 0.2343 70 0.2301 72 0.2496 74 0.2606 76 0.2245 78 0.2407 80 0.2302 82 0.2369 84 0.2251 R*(rnKlkW) 9c(min, 0.2359 0.' 20.0 10140. 7687. 8.14 40.75 l k W Time Fouling Res. (min) (m 2 K/kW) 86 0.2727 88 0.2553 90 0.0913 92 0.1912 94 0.2414 96 0.2527 98 0.2231 100 0.2085 102 0.2251 104 0.2214 106 0.2417 108 0.2349 110 0.2385 112 0.2517 114 0.2861 116 0.2464 118 0.2602 120 0.2292 122 0.2452 124 0.2624 126 0.2245 128 0.2219 130 0.2554 132 0.2183 134 0.2369 136 0.2383 138 0.1824 140 0.2508 142 0.2348 144 0.2333 146 0.2150 148 0.2844 150 0.2817 Unc(BDC)% 14.06 172 Run 55 Bulk concentration (%) 20.0 Mixture Re 9513. Water Re 7472. Water average Temp.( °C) 7.19 M . average Temp. ( °C) 35.92 Q w at9=0 = 0.519 kW Time Fouling Res. Time Fouling (min) (m 2K/kW) (min) (m 2 0 0.0000 86 0.2738 2 0.1038 88 0.2382 4 0.2043 90 0.2481 6 0.2049 92 0.2210 8 0.2242 94 0.1734 10 0.2012 96 0.2415 12 0.1586 98 0.2416 14 0.2165 100 0.2798 16 0.2415 102 0.2542 18 0.2204 104 0.2342 20 0.2102 106 0.2527 22 0.2366 108 0.2595 24 0.2064 110 0.2502 26 0.0930 112 0.2789 28 0.2337 114 0.2604 30 0.2061 116 0.2936 32 0.2055 118 0.3010 34 0.1909 120 0.2939 36 0.1867 122 0.2747 38 0.2428 124 0.2411 40 0.2591 126 0.2321 42 0.2455 128 0.2140 44 0.2068 130 0.2352 46 0.2572 132 0.2342 48 0.0798 134 0.2410 50 0.2606 136 0.2483 52 0.3210 138 0.2967 54 0.2651 140 0.2921 56 0.3297 142 0.2343 58 0.2354 144 0.2192 60 0.2304 146 0.2193 62 0.1820 148 0.2323 64 0.2442 150 0.2796 66 0.2690 68 0.2444 70 0.2234 72 0.2474 74 0.2317 76 0.2388 78 0.2501 80 0.2375 82 0.3393 84 0.3006 R*(rnKlkW) 6C (min) Unc(BDC)% 0.2409 3.38 23.03 173 Run 56 Bulk concentration (%) 20.0 Mixture Re 9616. Water Re 8542. Water average Temp.( C) 11.82 M . average Temp. (C ) 37.32 Q at 9=0 = 0.647 kW Time Fouling Res. Time Foulin (min) (m 2K/kW) (min) (m 2 0 0.0000 86 0.1355 2 0.1566 88 0.1516 4 0.2040 90 0.1673 6 0.2204 92 0.1386 8 0.2402 94 0.2503 10 0.2010 96 0.2893 12 0.2340 98 0.2413 14 0.2666 100 0.2109 16 0.2424 102 0.1935 18 0.2197 104 0.1860 20 0.2198 106 0.1994 22 0.0651 108 0.1884 24 0.1588 110 0.1734 26 0.1837 112 0.1573 28 0.2605 114 0.1774 30 0.2603 116 0.1467 32 0.2592 118 0.1493 34 0.2390 120 0.1261 36 0.2389 122 0.0579 38 0.2165 124 0.2739 40 0.2192 126 0.2665 42 0.2028 128 0.2478 44 0.1917 130 0.2176 46 0.1695 132 0.2384 48 0.2800 134 0.2366 50 0.3123 136 0.2361 52 0.2644 138 0.2460 54 0.2579 140 0.2531 56" 0.2312 142 0.0007 58 0.2550 144 0.2171 60 0.2260 146 0.2245 62 0.2051 64 0.1993 66 0.2277 68 0.2530 70 0.2556 72 0.2167 74 0.2173 76 0.1110 78 0.1610 80 0.1982 82 0.1716 84 0.1609 R*(m 2K/kW) 6c(min) Unc(BDC)% 0.2056 1.27 42.46 174 Run 57 Bulk concentration (%) 20.0 Mixture Re 10163. Water Re 8577. Water average Temp.( C) 11.97 M . average Temp. (C ) 40.90 Q w at 9=0 =0.816 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m 2 K/kW) 0 0.0000 86 0.1184 2 0.0540 88 0.1262 4 0.0876 90 0.0980 6 0.1477 92 0.1078 8 0.1345 94 0.0949 10 0.0853 96 0.0821 12 0.1385 98 0.1057 14 0.1273 100 0.0779 16 0.1292 102 0.1412 18 0.1444 104 0.1452 20 0.1684 106 0.1536 22 0.1324 108 0.1145 24 0.1365 110 0.1468 26 0.1351 112 0.1401 28 0.1829 114 0.1465 30 0.1993 116 0.1244 32 0.1725 118 0.1252 34 0.2113 120 0.1132 36 0.1792 122 0.1150 38 0.0418 124 0.1321 40 0.1807 126 0.1040 42 0.1826 128 0.1208 44 0.1443 130 0.1217 46 0.1324 132 0.1385 48 0.1286 134 0.1067 50 0.1165 136 0.1414 52 0.1395 138 0.1378 54 0.1426 140 0.1441 56 0.1291 142 0.1207 58 0.1352 144 0.1213 60 0.1220 146 0.1314 62 0.1117 148 0.1580 64 0.1741 150 0.1336 66 0.1758 68 0.0341 70 0.1481 72 0.1117 74 0.1434 76 0.1210 78 0.1188 80 0.1266 82 0.1153 84 0.1071 R*(m2K/kW) 9C (min) Unc(BDC)% 0.1187 2.31 21.10 175 Run 59 Bulk concentration (%) 20.0 Mixture Re 9060. Water Re 8478. Water average Temp.( C) 11.55 M . average Temp. ( C) 33.56 0.816=0 = 0.489 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.5576 2 0.4047 88 0.4584 4 0.3847 90 0.4641 6 0.4104 92 0.5339 8 0.3811 94 0.5685 10 0.3716 96 0.5212 12 0.4111 98 0.4959 14 0.3182 100 0.4869 16 0.3439 102 0.6139 18 0.3217 104 0.5114 20 0.4286 106 0.5482 22 0.3976 108 0.3622 24 0.4018 110 0.4526 26 0.4505 112 0.4141 28 0.3660 114 0.5955 30 0.3904 116 0.4292 32 0.3702 118 0.5666 34 0.4147 120 0.5492 36 0.4123 122 0.6008 38 0.4420 124 0.5824 40 0.4781 126 0.5439 42 0.2152 ' 128 0.5422 44 0.4189 130 0.0700 46 0.4130 132 0.5372 48 0.3768 134 0.5751 50 0.5064 136 0.6082 52 0.4973 138 0.5514 54 0.4145 140 0.4998 56 0.4899 58 0.4629 60 0.5046 62 0.2791 64 0.2596 66 0.4848 68 0.5618 70 0.2910 72 0.5372 74 0.5512 76 0.5198 78 0.5203 80 0.4621 82 0.5260 84 0.4760 RArnKlkW) 9C (min) Unc(BDC)% 0.4572 1.14 20.21 176 Run 60 Bulk concentration (%) 20.0 Mixture Re 9583. Water Re 8635. Water average Temp.( C) 12.21 M . average Temp. (C ) 37.11 CL at 6=0 = 0.585 kW Time Fouling Res. Time Foulinj (min) (m 2K/kW) (min) (m 2 0 0.0000 86 0.3654 2 0.1075 88 0.3688 4 0.1442 90 0.3149 6 0.2120 92 0.3675 8 0.1883 94 0.3638 10 0.2382 96 0.3107 12 0.2254 98 0.3726 14 0.2749 100 0.4059 16 0.2632 102 0.3802 18 0.2999 104 0.3454 20 0.2941 106 0.3513 22 0.2215 108 0.3618 24 0.2748 110 0.3735 26 0.3207 112 0.3890 28 0.2928 114 0.4318 30 0.2760 116 0.3663 32 0.2521 118 0.3292 34 0.3373 120 0.3589 36 0.3867 122 0.3649 38 0.3269 124 0.3629 40 0.3314 126 0.3888 42 0.3048 128 0.3710 44 0.3398 130 0.4104 46 0.3031 132 0.4046 48 0.3514 134 0.3467 50 0.3421 136 0.3892 '52 0.3083 138 0.3758 54 0.3368 140 0.3798 56 0.3717 142 0.4057 58 0.3385 144 0.4176 60 0.3640 146 0.3910 62 0.3776 148 0.3713 64 0.3373 150 0.4013 66 0.3721 68 0.3586 70 0.3366 72 0.3608 74 0.4209 76 0.3265 78 0.3280 80 0.3672 82 0.3909 84 0.3744 RAtnKlkW) 0C (min) Unc(BDC)% 0.3645 12.82 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2 K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.2818 2 0.1327 88 0.2887 4 0.1373 90 0.2893 6 0.1883 92 0.2729 8 0.1994 94 0.2999 10 0.1223 96 0.2773 12 0.1883 98 0.2810 14 0.2154 100 0.2761 16 0.2258 102 0.2958 18 0.2217 104 0.2896 20 0.2216 106 0.3104 22 0.2245 108 0.2815 24 0.3464 110 0.2770 26 0.2424 112 0.2911 28 0.2534 114 0.2645 30 0.2497 116 0.3020 32 0.2118 118 0.2985 34 0.2204 120 0.2805 36 0.2175 122 0.2680 38 0.2381 124 0.0580 40 0.2585 126 0.2780 42 0.2189 128 0.2883 44 0.2379 130 0.2732 46 0.2583 132 0.2810 48 0.2605 134 0.2700 50 0.2613 136 0.3267 52 0.2494 138 0.2812 54 0.2726 140 0.2679 56 0.2692 142 0.2961 58 0.2638 144 0.2914 60 0.2723 146 0.2763 62 0.2649 148 0.2458 64 0.2388 150 0.2652 66 0.2613 68 0.2525 70 0.2813 72 0.2804 74 0.2570 76 0.2931 78 0.2953 80 0.2918 82 0.2647 84 0.2769 RArnKlkW) 0C (min) Unc(BDC)% 0.2664 7.79 11.14 178 Run 63 B u l k concentration (%) M ix ture Re Water Re Water average Temp.( C) M . average Temp. ( C ) CL at 9=0 = 0.422 k W T ime Fou l ing Res. (min) ( m 2 K / k W ) 0 0.0000 2 0.2092 4 0.2234 6 0.2361 8 0.2262 10 0.2481 12 0.2609 14 0.2851 16 0.2897 18 0.2478 20 0.2730 22 0.2669 24 0.3683 26 0.2973 28 0.2724 30 0.2921 32 0.2668 34 0.3164 36 0.2658 38 0.2387 40 0.3241 42 0.2897 44 0.2900 46 0.2495 48 0.3001 50 0.2721 52 0.2793 54 0.2954 56 0.2742 58 0.2619 60 0.3084 62 0.2652 64 0.2771 66 0.2770 68 0.2547 70 0.3078 72 0.2321 74 0.2792 76 0.3032 78 0.3762 80 0.4356 82 0.3983 84 0.4211 R*(tnKlkW) 0c(min 0.3180 4. 20.0 9054. 9288. 12.91 33.52 T ime Fou l ing Res. (min) (m 2 K/kW) 86 0.2669 88 0.2799 90 0.3267 92 0.3548 94 0.3641 96 0.3249 98 0.4037 100 0.3947 102 0.3092 104 0.2802 106 0.4029 108 0.4361 110 0.4602 112 0.3846 114 0.3927 116 0.2882 118 0.2752 120 0.3046 122 0.3045 124 0.2238 126 0.2983 128 0.3159 130 0.3943 132 0.4272 134 0.4541 136 0.4759 138 0.3094 140 0.3746 142 0.3591 144 0.2949 146 0.1824 148 0.3654 150 0.2595 U n c ( B D C ) % 16.61 179 Run 64 Bulk concentration (%) 20.0 Mixture Re 9555. Water Re 9460. Water average Temp.( C) 12.61 M . average Temp. (C) 36.92 Q at 6=0 = 0.506 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.2612 2 0.0723 88 0.2179 4 0.1383 90 0.2259 6 0.0159 92 0.1910 8 0.2059 94 0.1964 10 0.1919 96 0.2271 12 0.2024 98 0.1814 14 0.2034 100 0.1797 16 0.1875 102 0.1885 18 0.2036 104 0.2452 20 0.1981 106 0.2047 22 0.2276 108 0.1856 24 0.2109 110 0.2459 26 0.2340 112 0.1421 28 0.2144 114 0.2312 30 0.2658 116 0.2537 32 0.2072 118 0.0906 34 0.0918 120 0.1388 36 0.1612 122 0.2275 38 0.1322 124 0.2267 40 0.2221 126 0.1384 42 0.2115 128 0.2301 44 0.2220 130 0.2450 46 0.2359 132 0.2008 48 0.1922 50 0.1960 52 0.2141 54 0.2152 56 0.2292 58 0.2170 60 0.2633 62 0.2208 64 0.2436 66 0.2576 68 0.2700 70 0.2617 72 0.2159 74 0.2294 76 0.2031 78 0.1651 80 0.1677 82 0.2273 84 0.2235 RJrnKlkW) 6C (min) Unc(BDC)% 0.2098 5.73 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m 2 K/kW) 0 0.0000 86 0.0679 2 0.0115 88 0.0468 4 0.0092 90 0.0255 6 0.0138 92 0.0924 8 0.0073 94 0.0857 10 0.0320 96 0.0752 12 0.0134 98 0.0263 14 0.0469 100 0.0454 16 0.0477 102 0.0515 18 0.0444 104 0.0406 20 0.0515 106 0.0349 22 0.0746 108 0.0342 24 0.0648 110 0.0911 26 0.0531 112 0.0526 28 0.0649 114 0.0615 30 0.0453 116 0.0617 32 0.0690 118 0.0451 34 0.0628 120 0.0157 36 0.0657 122 0.1036 38 0.0803 124 0.0921 40 0.0208 126 0.1298 42 0.1161 128 0.0944 44 0.1172 130 0.1045 46 0.0981 132 0.0897 48 0.1247 50 0.1339 52 0.0596 54 0.0523 56 0.0859 58 0.0807 60 0.0655 62 0.0558 64 0.0565 66 0.0405 68 0.0265' 70 0.0198 72 0.0467 74 0.0121 76 0.0386 78 0.0597 80 0.0690 82 0.0026 84 0.0875 RArnKlkW) 6C (min) Unc(BDC)% 0.0640 12.51 60.64 181 Run 66 Bulk concentration (%) Mixture Re Water Re Water average Temp.( C) M . average Temp. ( C) Q . at 9=0 = 0.415 Time Fouling Res. (min) (m 2K/kW) 0 0.0000 1 0.0537 2 0.0646 3 0.0855 4 0.2220 5 0.1957 6 0.2030 7 0.2125 8 0.1552 9 0.2139 10 0.3424 11 0.0459 11 0.1351 13 0.2437 14 0.2432 15 0.3089 16 0.2034 17 0.3244 18 0.3275 19 0.2177 20 0.4804 21 0.3417 22 0.2734 23 0.3227 24 0.2076 25 0.2063 26 0.2638 27 0.2645 28 0.2689 29 0.2703 30 0.2190 31 0.2766 32 0.2781 33 0.2795 34 0.2824 35 0.3447 36 0.2840 37 0.0686 38 0.0252 39 0.3126 40 0.2535 41 0.3156 42 0.3143 43 0.3211 44 0.3286 45 0.4024 46 0.3355 5.0 11942. 17980. 8.71 32.57 Time Fouling Res. (min) (m 2 K/kW) 90 0.3855 91 0.3217 92 0.2680 93 0.3268 94 0.3355 95 0.4738 96 0.5219 97 0.5072 98 0.5158 99 0.5193 100 0.5215 101 0.4458 102 0.4458 103 0.4456 104 0.4532 105 0.4644 106 0.3927 107 0.2156 108 0.4005 109 0.4785 110 0.4042 111 0.3994 112 0.4815 113 0.4823 114 0.4839 115 0.4502 116 0.5044 117 0.4230 118 0.5956 119 0.3569 120 0.5162 121 0.5241 122 0.5294 123 0.3113 124 0.4611 125 0.2729 126 0.3950 127 0.3399 128 0.5659 129 0.6075 130 0.5034 131 0.5900 132 0.5039 133 0.5109 134 0.4424 135 0.4490 136 0.4521 182 4 7 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 0.3638 145 0.6557 56 0.3523 146 0.4123 57 0.2819 147 0.5756 58 0.3415 148 0.4436 59 0.3431 149 0.5846 60 0.3492 150 0.4923 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 0.3064 155 0.5171 66 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 0.9511 79 0.4129 169 0.6955 80 0.425 170 0.6016 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 88 0.3630 0.3754 177 0.6480 89 0.3123 RAtnKlkW) 0C (min) Unc(BDC)% 0 . 5 3 6 8 7 9 . 6 0 3 5 . 9 9 183 Run 67 Bulk concentration (%) 10.0 Mixture Re 11428. Water Re 17827. Water average Temp.( C) 8.42 M . average Temp. (C) 32.46 Q at 6=0 = 0.448 kW Time Fouling Res. Time Fouling Res. (min) (m2K/kW) (min] (m2 K/kW) 0 0.0000 90 0.9493 1 0.1148 91 0.9325 2 0.4597 92 1.3345 3 0.5181 93 1.1199 4 0.9055 94 1.0653 5 1.0652 95 1.2695 6 1.0965 96 0.8923 7 1.1144 97 1.2945 8 1.1506 98 0.9310 9 0.975 99 0.9512 10 1.2037 100 0.9736 11 1.1289 101 0.9926 12 1.5169 102 1.1003 13 2.1637 103 1.7710 14 2.6787 104 2.7675 15 3.7632 105 2.2302 16 3.8769 106 1.5204 17 4.036 107 1.5477 18 3.0749 108 1.3175 19 1.9706 109 0.9359 20 1.1497 110 1.1499 21 1.2134 111 0.9887 22 0.8910 112 0.8433 23 0.9127 113 1.5833 24 1.1085 114 1.3138 25 0.8744 115 1.5732 26 1.1738 116 1.5996 27 1.4238 117 1.1257 28 1.7968 118 1.3718 29 1.2801 119 0.9876 30 0.9366 120 1.6006 31 1.0432 121 1.3158 32 0.8840 122 1.3377 33 1.5301 - 123;. 1.1247 34 1.2988 i 124- 1.1394 35 1.3160 125 1.1638 36 0.9340 126 1.6722 37 1.7418 127 1.4041 38 2.7991 128 1.0008 39 1.2304 129 0.8537 40 1.2864 130 1.0224 41 1.1137 131 1.1314 42 0.9298 132 1.8427 43 1.3290 133 1.4973 44 1.0913 134 1.5099 45 1.0900 135 1.8860 46 0.7917 136 1.9106 184 47 0.6788 137 1.3261 48 0.6244 138 1.3336 49 1.5084 139 1.1465 50 0.9112 140 1.6491 51 1.0963 141 1.1574 52 0.6706 142 1.3997 53 1.0795 143 1.6508 54 0.8946 144 1.1473 55 1.5328 145 0.9624 56 1.0793 146 1.1638 57 1.3082 147 1.3835 58 1.0354 148 0.8234 59 1.8297 149 0.8311 60 1.2590 150 0.9996 61 0.8896 151 1.1399 62 0.9131 152 1.1278 63 0.9225 153 1.1372 64 0.9151 154 1.3615 65 1.2963 155 0.8207 66 1.2825 156 0.9912 67 1.2834 157 1.0033 68 1.2602 158 1.2050 69 1.2668 159 1.0238 70 1.0587 160 1.1691 71 .1:2682 161 0.6712 72 1.2762 162 1.3792 73 1.0652 163 1.1617 74 1.0757 164 0.9863 75 1.5264 165 1.1871 76 1.2682 166 0.8324 77 1.0704 167 1.0021 78 1.2820 168 0.9425 79 1.0743 169 1.1007 80 1.0848 170 1.1047 81 1.2935 171 0.9364 82 0.9159 172 1.1355 83 0.9171 173 0.9680 84 1.0911 174 0.9814 85 1.1017 175 1.1865 86 1.1124 176 0.8508 87 1.0955 177 1.3435 88 0.9298 89 1.1147 R*(m 2K/kW) 0c(min) Unc(BDC)% 1.2719 2.89 15.07 185 Run 68 B u l k concentration (%) M ix ture Re Water Re Water average Temp.( C ) M . average Temp. ( C ) Q at 9=0 = 0.300 k W T ime Fou l ing Res. (min) ( m 2 K / k W ) 0 0.0000 1 0.3328 2 0.5510 3 0.5977 4 0.8991 5 0.9206 6 0.9383 7 0.9608 8 1.3666 9 1.3960 10 1.4395 11 1.8498 12 1.8742 13 1.8996 14 0.9907 15 1.9733 16 2.0319 17 2.8777 18 2.1085 19 2.1443 20 2.1749 21 1.6285 22 2.2606 23 2.8008 24 2.743 25 4.0884 26 2.7943 27 2.8360 28 2.8841 29 2.9322 30 2.9834 31 2.1512 32 2.1822 33 1.6115 34 2.9037 35 2.8326 36 4.2239 37 2.8810 38 2.9230 39 2.9682 40 2.1392 41 3.0927 42 2.2290 43 1.6449 44 2.2174 45 2.1846 46 2.9977 15.0 10195. 18695. 10.06 32.49 T ime Fou l ing Res. (min) ( m 2 K/kW) 90 3.2422 91 2.3186 92 1.7064 93 1.7356 94 2.4129 95 2.4102 96 2.3374 97 1.6759 98 3.2732 99 3.2557 100 3.2828 101 1.2649 102 1.6647 103 4.6109 104 7.7140 105 3.1573 106 2.2269 107 3.1750 108 3.2625 109 3.3064 110 1.7199 111 1.7277 112 1.7737 113 2.3294 114 2.3240 115 1.6974 116 2.3591 117 2.3672 118 3.3208 119 2.3401 120 • 3.3630 121 2.3645 122 3.1914 123 3.2257 124 3.2566 125 4.9554 126 2.3591 127 2.3646 128 1.7358 129 2.3837 130 2.2006 131 3.1192 132 3.1433 133 2.2070 134 2.2799 135 2.3073 136 2.3129 186 47 2.9943 48 3.0175 49 3.0571 50 3.0967 51 3.1264 52 3.1522 53 3.1388 54 3.2018 55 3.2186 56 3.2253 57 2.3001 58 2.3295 59 2.3298 60 2.3565 61 2.2948 62 1.6295 63 3.1180 64 7.5226 65 7.4824 66 7.5361 67 4.5918 68 4.6634 69 4.7260 70 3.2490 71 2.2970 72 2.3051 73 4.9046 74 3.2760 75 3.2625 76 3.2794 77 3.3165 78 3.3651 79 2.3509 80 2.3374 81 3.3379 82 2.3428 83 1.6398 84 0.8562 85 2.2916 86 3.2220 87 3.1848 88 2.2613 89 3.1949 R*(m2K/klV) 0c(i 2.7913 I 137 1.71548 138 1.7426 139 1.7896 140 1.8170 141 0.9938 142 1.0091 143 1.3800 144 1.0312 145 1.0481 146 0.7727 147 1.0854 148 2.2163 149 4.5536 150 3.0528 151 4.6321 152 4.7788 153 3.2156 154 2.2878 155 1.6756 156 2.3730 157 2.4143 158 1.7736 159 1.7248 160 2.3620 161 2.4149 162 2.4225 163 1.7782 164 1.3193 165 1.8394 166 3.3067 167 3.2928 168 2.3235 169 3.3264 170 2.3730 171 2.4088 172 2.3785 173 3.2840 174 4.9599 175 5.0108 176 3.3447 177 2.3998 178 2.3974 179 2.4083 nin) Unc(BDC)% .51 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 kW Time Fouling Res. (min) (m 2 K/kW) 0 0.0000 1 0.6930 2 2.3525 3 4.9826 4 2.7740 5 3.0367 6 5.8166 7 6.3371 8 6.3307 9 6.3307 10 6.6772 11 3.4662 12 14.6704 13 15.3872 14 15.5039 15 6.5651 16 16.0695 17 6.7084 18 6.7754 19 16.1230 20 16.9078 21 6.9179 22 16.5213 23 16.5626 24 15.9089 25 16.5626 26 16.4934 27 17.2331 28 16.6318 29 16.5902 30 17.2331 31 15.9892 32 16.7837 33 16.7837 34 7.09290 35 17.5472 36 17.7326 37 7.3763 42 16.7147 43 17.2902 44 17.2902 45 17.2617 46 17.8336 47 17.9665 48 18.1587 49 17.5045 50 17.5045 Time Fouling Res. (min) (m 2 K/kW) 55 7.4835 56 7.4978 57 7.4835 58 7.5478 59 7.4531 60 19.3502 61 7.5257 62 7.6350 63 18.8928 64 18.8161 65 7.6276 66 19.6836 67 19.5248 68 19.5565 69 19.4930 70 19.6518 71 19.6518 73 18.9234 74 7.5258 77 19.6836 85 7.6663 94 22.4439 99 21.0500 100 20.9510 101 21.1159 102 21.3302 103 20.4560 106 20.5880 109 19.8267 110 18.9386 111 18.2178 117 18.4394 118 18.2771 119 7.3094 120 19.0152 122 19.0152 127 18.9231 128 18.9537 129 19.0304 130 19.2292 131 7.5907 132 18.6784 138 20.3026 170 21.6542 171 21.5685 172 22.5811 173 21.6372 188 51 17.0903 176 21.8778 52 7.2761 178 22.5633 53 7.3476 179 21.7916 54 7.4191 R*(tnKlkW) dc (min) Unc(BDC)% 1 7 . 1 1 9 3 15 .25 3 2 . 9 9 189 Run 70 Bulk concentration (%) 5.0 Mixture Re 11185. WateRe 9344. , Water average Temp.( C) 15.14 M. average Temp. ( C) 29.02 Q w at 9=0 = 0.439 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.0959 2 0.0594 88 0.0967 4 0.0619 90 0.0857 6 0.0587 92 0.0973 8 0.0681 94 0.0783 10 0.0817 96 0.0771 12 0.0845 98 0.0636 14 0.0834 100 0.0660 16 0.0878 102 0.0842 18 0.0889 104 0.0686 20 0.0750 106 0.0650 22 0.0726 108 0.0652 24 0.0821 110 0.0669 26 0.0705 112 0.0637 28 0.0728 114 0.0586 30 0.0873 116 0.0908 32 0.0813 118 0.0794 34 0.0772 120 0.0747 36 0.0727 122 0.0901 38 0.0396 124 0.0800 40 0.0760 128 0.0779 42 0.0816 130 0.0852 44 0.0818 132 0.0684 46 0.0786 134 0.0743 48 0.0742 136 0.0592 50 0.0742 138 0.0906. 52 0.0701 140 0.0794 54 0.0898 142 0.0751 56 0.0840 144 0.0692 58 0.0876 146 0.0862 60 0.0804 148 0.0667 62 0.0911 150 0.0729 64 0.0616 66 0.1030 68 0.0802 70 0.0860 72 0.0581 74 0.0587 76 0.0971 78 0.0711 82 0.0797 84 0.0835 Rf{mKlkW) 0c(min) Unc(BDC)% 0.0774 1.99 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min] (m 2 K/kW) 0 0.0000 86 0.0644 2 0.0508 88 0.0855 4 0.0543 90 0.0741 6 0.0517 92 0.0712 8 0.0678 94 0.0674 10 0.0573 96 0.0885 12 0.0396 98 0.0763 14 0.0548 100 0.0845 16 0.0639 102 0.0834 18 0.0578 104 0.0841 20 0.0551 106 0.0794 22 0.0610 108 0.0875 24 0.0703 110 0.1000 26 0.0084 112 0.0763 28 0.0577 114 0.0969 30 0.0692 116 0.0963 32 0.0683 118 0.0893 34 0.0915 120 0.0850 36 0.0204 122 0.0968 38 0.0923 124 0.0843 40 0.0508 126 0.1029 42 0.0729 128 0.0828 44 0.0946 130 0.0867 46 0.0574 132 0.0862 48 0.0486 152 0.0934 50 0.0474 154 0.1037 52 0.0683 156 0.0561 54 0.0695 158 0.0941 56 0.0601 160 0.0847 58 0.0724 162 0.1172 60 0.0816 164 0.0617 62 0.0706 166 0.0743 64 0.0651 168 0.0938 66 0.0914 68 0.0826 70 0.0635 72 0.1114 74 0.0776 76 0.0864 78 0.0663 80 0.0755 82 0.0629 84 0.0449 RArnKlkW) 0C (min) Unc(BDC)% 0.0799 13.62 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 kW Time Fouling Res. Time Fouling Res. (min) (m 2K/kW) (min) (m2 K/kW) 0 0.0000 86 0.4989 2 0.2776 88 0.4640 4 0.2370 90 0.4692 6 0.2157 92 0.5005 8 0.2997 94 0.5442 10 0.3144 96 0.5721 12 0.3085 98 0.4882 14 0.3084 100 0.4303 16 0.3423 102 0.5028 18 0.3490 104 0.4480 20 0.3665 106 0.5602 22 0.3837 108 0.5066 24 0.4079 110 0.4563 26 0.3780 112 0.4820 28 0.3971 114 0.5424 30 0.4162 116 0.4079 32 0.3990 118 0.5746 34 0.4105 120 0.5187 36 0.4194 122 0.5274 38 0.4217 124 0.6135 40 0.4354 126 0.5233 42 0.4396 128 0.6838 44 0.2138 130 0.4487 46 0.3940 132 0.5107 48 0.4720 134 0.5271 50 0.4293 136 0.5289 52 0.4663 138 0.4795 54 0.4725 140 0.5058 56 0.4650 142 0.5133 58 0.4629 144 0.4803 60 0.4601 146 0.4873 62 0.4359 148 0.3886 64 0.4252 150 0.5446 66 0.4777 68 0.4507 70 0.4857 72 0.4876 74 0.5164 76 0.4869 78 0.5135 80 0.4835 82 0.5706 84 0.5398 RjtrnKlkW) 0C (min) Unc(BDC)% 0.4899 13.62 13.06 192 R u n 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) (m2K/kW) 0 0.0000 2 0.3669 4 0.4297 6 0.5662 8 0.5522 10 0.5533 12 0.6390 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 52 0.9929 54 0.9518 56 0.9822 58 0.9247 60 0.9574 62 0.9986 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 R*(m2K/kW) 6c(min, 1.1080 26.! 20.0 8545. 8765. 12.76 29.28 Time Fouling Res. (min) (m2 K/kW) 86 1.0446 88 1.0454 90 1.0078 92 1.0852 94 1.0644 96 1.0288 98 1.0782 100 1.2041 102 1.0552 104 1.0891 106 1.1399 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 132 1.1053 134 1.0912 136 1.1378 138 1.1053 140 0.9872 142 1.1022 144 1.0480 146 1.1268 148 1.1855 Unc(BDC)% 15.48 193 

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