Measurement of the Liquid− Deposit Interface Temperature during

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Measurement of the Liquid-Deposit Interface Temperature during Solids Deposition from Wax-Solvent Mixtures under Static Cooling Conditions Hamid Bidmus and Anil K. Mehrotra* Department of Chemical and Petroleum Engineering, UniVersity of Calgary, Calgary, Alberta, Canada T2N 1N4 ReceiVed October 5, 2007. ReVised Manuscript ReceiVed December 9, 2007

The liquid-deposit interface temperature for solids deposition was measured under static cooling (i.e., without any induced shear stress) from prepared mixtures of a petroleum wax (C20-C40) and a multicomponent paraffinic solvent (C9-C16) at different coolant temperatures. Two designs for the cooling of wax-solvent mixtures were developed for monitoring the temperature at fixed radial locations in a cylindrical vessel. The wax-solvent mixture was cooled from a temperature higher than its wax appearance temperature (WAT), and the movement of the liquid-deposit interface was obtained from the rate of change of temperature at different radial locations. The deposit-layer thickness increased more rapidly with a larger heat-transfer area and a lower coolant temperature. The interface temperature was observed to be equal to the WAT of the wax-solvent mixture, and it decreased slightly when the liquid-region temperature became less than the WAT of the original mixture (causing the precipitation of wax crystals). The results of this study support the constant-interface-temperature assumption made in the heat-transfer approach for modeling solids deposition from waxy mixtures, but not the increasing-interface-temperature assumption in the molecular-diffusion approach.

Introduction Petroleum crude oils are complex mixtures containing multitudes of hydrocarbons ranging from alkanes, aromatics, naphthenes, and resins to high-molecular-weight waxes and asphaltenes. Most of the high-molecular-weight wax components are soluble in crude oil under reservoir conditions; however, precipitation and deposition of waxy solids is initiated when the crude oil is exposed to lower temperatures causing the wax to crystallize out of the solution. The deposition of waxy solids results in high pressure drops and increased energy consumption during crude oil transportation. The highest temperature at which the first wax crystals start to appear, upon cooling of a waxy crude oil, is called the wax appearance temperature (WAT). This temperature has been shown to be somewhat lower than the thermodynamic liquidus temperature, which is closer to the wax disappearance temperature (WDT) that is measured during heating.1 In the flow of waxy crude oils in pipelines exposed to cooling environments, wax particles start to crystallize out when the crude-oil temperature falls below the WAT. This occurs due to the lower solubility of the heavier waxes (i.e., n-alkanes with carbon number greater than about 18) in the liquid phase. As the crude oil is cooled further toward the pour-point temperature (PPT), an interlocking network structure is formed when sufficient quantities of paraffin crystals are formed, which leads to the formation of a gel-like structure with entrapped liquid oil. Visual observations of wax deposits have shown them to consist of both solid and liquid phases with platelet-shaped wax crystallites * Corresponding author. Phone: (403) 220-7406. Fax: (403) 284-4852. E-mail: [email protected]. (1) Bhat, N. V.; Mehrotra, A. K. Measurement and Prediction of Phase Behavior of Wax-Solvent Mixtures: Significance of the Wax Disappearance Temperature. Ind. Eng. Chem. Res. 2004, 43, 3451.

that overlap and interlock around liquid crude oil.2 As little as 2% of precipitated wax solids is sufficient to give rise to gel or deposit formation from a waxy crude oil.2,3 The deposit-layer formed due to the cooling of crude oils or waxy mixtures is exposed to variations in temperature, concentration, and shear stress (due to the flowing crude oil) across its thickness. All of these factors have been shown to play important roles in the amount and properties of deposits formed in tubes or pipelines.3–12 Thus, a complete description of depositlayer formation and growth could involve a combination of (2) Holder, G. A.; Winkler, J. Wax Crystallization from Distillate Fuels. I. Cloud and Pour Phenomena Exhibited by Solutions of Binary n-Paraffin Mixtures. J. Inst. Pet. 1965, 51, 228. (3) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. Formation and Aging of Incipient Thin Film Wax-Oil Gels. AIChE J. 2000, 46, 1059. (4) Cole, R. J.; Jessen, F. W. Paraffin Deposition. Oil Gas J. 1960, 58 (38), 87. (5) Bott, T. R.; Gudmunsson, J. S. Deposition of Paraffin Wax from Kerosene in Cooled Heat Exchanger Tubes. Can. J. Chem. Eng. 1977, 55, 381. (6) Ghedamu, M.; Watkinson, A. P.; Epstein, N. Mitigation of Wax Buildup on Cooled Surfaces. In Fouling Mitigation of Industrial HeatExchange Equipment; Panchal, C. B., Bott, T. R., Somerscales, E. F. C., Toyama, S., Eds.; Begel House: New York, 1997; pp 473-489. (7) Creek, J. L.; Lund, H. J.; Brill, J. P.; Volk, M. Wax Deposition in Single Phase Flow. Fluid Phase Equilib. 1999, 801, 158. (8) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. Morphological Evolution of Thick Wax Deposits during Aging. AIChE J. 2001, 47, 6. (9) Wu, C.; Wang, K. S.; Shuler, P. J.; Tand, Y.; Creek, J. L.; Carlson, R. M.; Cheung, S. Measurement of Wax Deposition in Paraffin Solutions. AIChE J. 2002, 48, 2107. (10) Bidmus, H. O.; Mehrotra, A. K. Heat-Transfer Analogy for Wax Deposition from Paraffinic Mixtures. Ind. Eng. Chem. Res. 2004, 43, 791. (11) Parthasarathi, P.; Mehrotra, A. K. Solids Deposition from Multicomponent Wax-Solvent Mixtures in a Benchscale Flow-Loop Apparatus with Heat Transfer. Energy Fuels 2005, 19, 1387. (12) Chevallier, V.; Bouroukba, M.; Petitjean, D.; Dirand, M.; Pauly, J.; Daridon, J. L.; Ruffier-Meray, V. Crystallization of a Multiparaffinic Wax in Normal Tetradecane. Fuel 2000, 79, 1743.

10.1021/ef700588y CCC: $40.75  2008 American Chemical Society Published on Web 01/19/2008

Wax-SolVent under Static Cooling

several considerations, such as thermodynamics and solid–liquid multiphase equilibiria, heat transfer, fluid dynamics, rheology, and molecular diffusion. Several of the recent models for describing wax deposition assumethatmoleculardiffusionisthecontrollingmechanism.3,7,8,13–16 This modeling approach is based on estimating the amount of wax deposited from the radial transport of wax molecules that is caused by a radial concentration gradient. The concentration gradient is assumed to be induced by the temperature gradient resulting from the difference between the flowing bulk-crudeoil temperature (higher than the WAT) and the cold-pipe-wall temperature (lower than the WAT). In the molecular-diffusion modeling approach, the liquid-deposit interface temperature is back-calculated from an energy balance, which predicts a gradual increase in its initial value from being close to the pipewall temperature to the WAT at steady-state. A plot of predicted changes in the liquid-deposit interface temperature with time was presented by Singh et al.,3 but the predictions were not validated with any experimental measurements. The assumption relating to a gradually increasing liquid-deposit interface temperature is crucial for the molecular-diffusion approach because the concentration driving force will exist only if the interface temperature during deposit-layer formation is below the WAT. Merino-Garcia et al.17 suggested that molecular diffusion may not be the controlling mechanism for the deposition process because it is a relatively slow process. Recent experimental evidence10,11,17,18 indicates that the deposit-layer formation in bench-scale apparatuses occurs over a relatively short period of time. Recent studies have identified the role of heat transfer as an important factor in the deposition of waxy solids from waxy mixtures.10,11,17–19 Laboratory investigations10,11,18 have reported a relatively rapid attainment of a thermal pseudo-steady-state during wax deposition from paraffinic mixtures flowing under laminar as well as turbulent conditions. Results from these studies correlated well with predictions from a steady-state heattransfer model, which also identified the temperature difference across the deposit layer to be an important parameter in the deposition process. A dimensionless parameter, defined as the ratio of the temperature difference across the deposit layer to the overall temperature difference, was shown to correlate well with the mass of deposited solids.10,11,18 This parameter was also shown to be equal to the ratio of the thermal resistance of the deposit to the sum of all thermal resistances involved in the deposition process at steady-state. Note that the temperature drop across the deposit layer is the difference between the liquiddeposit interface temperature (hereafter referred to as the interface temperature, Td) and the pipe-wall temperature. It was obtained by assuming the interface temperature to be equal to the WAT of the wax-solvent mixture. This was confirmed (13) Burger, E. D.; Perkins, T. K.; Striegler, J. H. Studies of Wax Deposition in the Trans Alaska Pipeline. J. Pet. Tech. 1981, 33, 1075. (14) Svendsen, J. A. Mathematical Modeling of Wax Deposition in Oil Pipeline Systems. AIChE J. 1993, 39, 1377. (15) Kok, M. V.; Saracoglu, R. O. Mathematical Modeling of Wax Deposition in Crude Oil Pipelines (Comparative Study). Pet. Sci. Tech. 2000, 18, 1121. (16) Ramirez-Jaramillo, E.; Lira-Galeana, C.; Manero, O. Modeling Wax Deposition in Pipelines. Pet. Sci. Tech. 2004, 22, 821. (17) Merino-Garcia, D.; Margarone, M.; Correra, S. Kinetics of Waxy Gel Formation from Batch Experiments. Energy Fuels 2007, 21, 1287. (18) Fong, N.; Mehrotra, A. K. Deposition under Turbulent Flow of Wax-Solvent Mixtures in a Bench-Scale Flow-Loop Apparatus with Heat Transfer. Energy Fuels 2007, 21, 1263. (19) Mehrotra, A. K.; Bhat, N. V. Modeling the Effect of Shear Stress on Deposition from “Waxy” Mixtures under Laminar Flow with Heat Transfer. Energy Fuels 2007, 21, 1277.

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experimentally to be valid for the deposition from wax-solvent mixtures, under thermal pseudo-steady-state, for both laminar and turbulent flows.10,11,18 Recently proposed mathematical models based on the heattransfer approach incorporate the moving boundary formulation, which assumes that the interface temperature, Td, remains at the WAT throughout the deposit growth.17,19–21 In contrast, as mentioned previously, the molecular-diffusion approach is based on the assumption that Td varies during the growth of deposit, starting from an initial value close to the pipe-wall temperature and increasing gradually to reach the WAT at steady-state.3,8,14–16 However, there is no experimental evidence available to support either of these assumptions for the interface temperature, Td, during deposit growth. Suitable techniques are required for estimating the physical, transport, rheological, and thermophysical properties of the deposit. The measurement of Td with a thermocouple probe during the transient stage of the deposition process under flowing conditions is a challenging task, especially because the interface location would move radially with time even at the same axial location. It may not be easy to insert an instrument for temperature measurement into the crude-oil pipeline without affecting the properties of the deposit being formed. Likewise, it is difficult to carry out an in-situ analysis of the deposit-layer because, as mentioned above, it consists of liquid and solid phases, whose ratio and properties are sensitive to temperature and hydrodynamic changes. These difficulties offer limitations to measuring the important deposition parameters, such as the transient interface temperature, Td, that could assist in fully understanding the deposition mechanism. This investigation was undertaken to develop an experimental method for measuring the interface temperature, Td, with time during the formation and growth of the deposit-layer under static conditions. It involved the development of an experimental protocol for wax deposition using prepared wax-solvent mixtures that allowed the measurement of Td without affecting the deposition process. All of the deposition experiments were performed under static conditions, i.e. without any externally induced shear stress. With suitable modifications to the experimental apparatus, the approach presented here could be extended to “waxy” crude-oil samples to study the effects of isoparaffin and aromatic hydrocarbons on the deposition process under both transient and steady-state conditions. Experimental Section Materials. The deposition experiments were carried out with two prepared mixtures of a paraffinic wax in a petroleum solvent. The wax sample, Aldrich wax, was obtained from Sigma-Aldrich (Oakville, Ontario, Canada). It has a melting point of 58–62 °C and consists of n-alkanes ranging from C20 to C40.1,10,11,22 Norpar13, obtained from Imperial Oil (Toronto, Ontario, Canada), was used as the solvent for preparing the wax-solvent mixtures. This solvent comprises n-alkanes ranging from C9 to C16 and has a density of 754 kg m-3 at 23 °C.1,11,18 The average molar mass of Norpar13 is 185.7 kg kmol-1, which corresponds to an average carbon number (20) Bhat, N. V.; Mehrotra, A. K. Modeling of Deposit Formation from “Waxy” Mixtures via Moving Boundary Formulation: Radial Heat Transfer under Static and Laminar Flow Conditions. Ind. Eng. Chem. Res. 2005, 44, 6948. (21) Bhat, N. V.; Mehrotra, A. K. Modeling of Deposition from “Waxy” Mixtures in a Pipeline under Laminar Flow Conditions via Moving Boundary Formulation. Ind. Eng. Chem. Res. 2006, 45, 8728. (22) Tiwary, D.; Mehrotra, A. K. Phase Transformation and Rheological Behaviour of Highly Paraffinic Waxy Mixtures. Can. J. Chem. Eng. 2004, 82, 162.

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Figure 1. Carbon number distribution of Norpar13 and Aldrich wax.1,11,17

of about 13. The results from simulated distillation analyses on both Aldrich wax and Norpar13 are presented in Figure 1. WAT and PPT Measurements. The deposition experiments were carried out at two wax concentrations, 14 and 20 mass % wax in Norpar13. The WAT and PPT were measured using a visual method with cooling in steps of 1 °C.1,18,22 The error associated with the WAT and PPT measurements is up to +1 °C.1,11,18 The measured WATs of the 14 and 20 mass % wax-Norpar13 mixtures were 31+1 and 34+1 °C, respectively, while the PPTs were measured as 29+1 and 31+1 °C, respectively. These results are consistent with the data reported previously for similar mixtures of Aldrich wax and Norpar13.1,10,11 Static Cooling Apparatus. The deposition experiments were carried out in a cylindrical vessel made of copper, with 10.2 cm (or 4 in.) inside diameter and 15.2 cm (or 6 in.) height, under static conditions, i.e. without any forced circulation or shear stress. The apparatus consisted of two temperature-regulated baths for maintaining the temperature of the wax-solvent mixture and a pump for circulating the coolant. Two sets of deposition experiments were designed and performed. In the first design, mimicking the typical pipeline geometry, the cold surface was the vessel wall such that the flow of thermal energy was radially outward, i.e. from the wax-solvent mixture into the lower-temperature, temperature-regulated bath held at the coolant temperature. The deposit-layer in the first design started at the vessel wall, and its growth was radially inward, which caused the liquid-deposit interfacial area to decrease with time. In the second design, mimicking the coldfinger deposition experiment, the cold surface was a cylindrical copper tube located concentrically at the center of the vessel such that the flow of thermal energy from the wax-solvent mixture was radially inward. The copper coldfinger was designed as a small heat exchanger. It consisted of two concentric copper tubes, of 0.635 cm (0.25 in.) and 0.953 cm (0.375 in.) outside diameters, with the coolant entering through the inner tube and exiting through the annulus. The coolant flow rate was maintained sufficiently high for achieving a low convective thermal resistance as well as for accomplishing a constant surface temperature throughout the deposition process (i.e., the difference between the inlet and outlet coolant temperatures was small). The deposit-layer in the second design started at the center (i.e., on the outer surface of the coldfinger tube) and its growth was radially outward such that the liquid-deposit interfacial area increased with time. The two static cooling designs are shown schematically in Figures 2 and 3, respectively. It is pointed out that the two designs provided significantly different heat-transfer areas at the deposit-wall interface, which

Figure 2. Experimental apparatus for static cooling from the vessel wall.

Figure 3. Experimental apparatus for static cooling from the center (coldfinger).

resulted in different rates of heat transfer for the same temperatures of the wax-solvent mixture and the coolant. The ratio of the heattransfer areas was (10.2/0.953 )) 10.7.

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Table 1. Radial Locations of Thermocouples in the Cylindrical Vessel used for Static Deposition Experiments cooling from the vessel wall

cooling from the center (coldfinger)

thermocouple no.

radial distance from the cooling surface (in.)

thermocouple no.

radial distance from the cooling surface (in.)

TC1 TC2 TC3 TC4 TC5 TC6 TC7

0.250 0.375 0.500 0.625 0.750 1.500 2.000

TC1 TC2 TC3 TC4 TC5 TC6 TC7

0.313 0.438 0.563 0.688 0.813 1.313 1.563

Placement of Thermocouples. The temperatures inside the cylindrical vessel at different radial locations were measured with seven precalibrated J-type thermocouples. All of the thermocouples were inserted into the vessel from the top at specific radial locations. The 1/8-in. diameter stainless-steel thermocouples were used for their rigidity to ensure that they did not bend while setting up or dismantling the experimental setup, thereby maintaining their radial locations. The thermocouples were separated by an angular distance of 30° to minimize any interference in the movement of liquid-deposit interface (hereafter referred to as the interface). The thermocouples were attached to the plexiglass lid of the vessel (i.e., these were inserted from the top). As shown in Figures 2 and 3, the tips of all thermocouples were dipped about halfway into the wax-solvent mixture. To minimize any heat loss by conduction, the exposed surfaces of all thermocouples were covered with a tightfitting tygon tube, except for their tips for temperature measurement. The radial locations of thermocouples in both designs of static cooling apparatus are listed in Table 1. For both cases, the thermocouples are labeled TC1-TC7 based on their distances from the cooling surface. All thermocouples were connected to a datalogger and a PC for continuous recording of all temperatures with time. Minimizing Heat Losses. To ensure that the heat transfer took place only between the wax-solvent mixture and the coolant in the radial direction, appropriate steps were taken to insulate all other surfaces. As shown in Figures 2 and 3, a circular disk of styrofoam insulation, 3.8 cm (1.5 in.) in thickness, was placed on the bottom of the vessel. A ring of styrofoam insulation, 5.1 cm (2 in.) in thickness and outer radius of 17.8 cm (7 in.), was attached to the outside of the vessel for static cooling from the wall. As shown in Figure 3 for static cooling from the center, the entire outer surface of the vessel was covered uniformly with styrofoam insulation, which had an outer radius of 30.5 cm (12 in.) to prevent outward heat losses. The top of the plexiglass lid with the thermocouples attached was covered with liquid foam. Static Deposition Experiments. Each batch of wax-Norpar13 mixtures was heated to 70 °C in a water bath and held isothermally for 30 min to erase any thermal history. The wax-Norpar13 mixture was allowed to cool down slowly to the initial temperature of about WAT + 21 °C, after which it was poured into the cylindrical vessel. For the experiments with static cooling from the wall, the vessel was placed immediately in the cooling water bath maintained at the preset coolant temperature. The plexiglass lid with thermocouples was placed instantly on top of the vessel. The TC1-TC7 temperatures were recorded using the data-logger. For the experiments with cooling from the center, the lid, with the coldfinger and thermocouples attached, was placed on top of the cooling vessel after the wax-Norpar13 mixture reached the initial temperature of WAT + 21 °C. The submersible pump was turned on to commence the coolant circulation from the temperatureregulated bath through the coldfinger. The TC1-TC7 temperatures were recorded using the data-logger. In some of the preliminary experiments, the growth of the deposit-layer was also monitored visually by viewing through the plexiglass lid. Design of Experiments. As mentioned above, 14 and 20 mass % wax-Norpar13 mixtures were used for these experiments. Also,

Figure 4. Radial temperature profile during static cooling of the 20 mass % wax-Norpar13 mixture with coolant temperature at WAT 10 ) 24 °C; cooling from (a) the wall and (b) the center.

two cooling surface areas were used (i.e., cooling from the vessel wall and cooling from the center of the vessel with a coldfinger of much smaller surface area). The initial temperature for all experiments was WAT + 21 °C. The deposition experiments with cooling from the vessel wall were carried out with three coolant temperatures of WAT - 5, WAT - 7, and WAT - 10 °C. Because of the much lower rate of heat transfer in the experiments with cooling from the center, the deposition experiments were carried out with two coolant temperatures of WAT - 10 and WAT - 20 °C. An additional experiment with cooling from the center was carried out with the 20 mass % wax-Norpar13 mixture at a coolant temperature of WAT - 5 °C. All experiments were continued until the lowest temperature of the wax-Norpar13 mixture in the vessel reached a value well below the WAT. A few experiments were continued for a much longer duration, lasting up to 12 h, when the lowest temperature in the vessel approached the coolant temperature. Most experiments with cooling from the vessel wall lasted 60–200 min whereas those with cooling from the center lasted 200–350 min.

Results and Discussion Temperature Profiles during Cooling. Figure 4 shows the temperature profiles obtained from the experiment with the 20 mass % wax-Norpar13 mixture with the two cooling surfaces held at WAT - 10 °C. Note that, in both cases, the thermocouple TC1 is the closest to the cooling surface and TC7 is the farthest. It is observed that, in both cases, the temperatures at different radial locations are not much different initially in the cooling process. That is, there is no temperature variation in the radial direction until the temperatures approach about 36 °C, after which TC1 (closest to the cooling surface) starts to decrease faster than TC2-TC7. The visual observations indicated that the interface had grown close to the location of TC1,

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Figure 7. Change in temperature with radial location for cooling from the wall for the 20 mass % wax-Norpar13 mixture with coolant temperature at WAT - 10 ) 24 °C. Figure 5. Determining the interface location from rate of change of the temperature profile for the 20 mass % wax-Norpar13 mixture with coolant temperature at WAT - 10 ) 24 °C; cooling from (a) the wall and (b) the center.

Figure 8. Effect of cooling surface area on the rate of deposit growth.

Figure 6. Comparison of the two methods for locating the liquid-deposit interface.

which caused the temperature at this location to change at a different rate than those at other thermocouple locations. The results in Figure 4 do not show any temperature variation in the liquid region initially under static conditions. The predictions from a modeling study20 for deposition from wax-solvent mixtures under static conditions, with heat transfer in the liquid region assumed to be by conduction, showed a radial temperature gradient within the liquid region at all times.

Carslaw and Jaeger23 provided an analytical solution for conduction heat transfer in cylindrical coordinates, which for the relatively low thermal conductivity of wax-Norpar13 mixtures (i.e., 0.1–0.2 W/m K), shows a radial temperature profile with time. Thus, it is likely that the flow of thermal energy in the liquid region initially might be via convection heat transfer, which could be attributed to natural convection and/or liquid circulation induced by shrinkage during the cooling and solidification of liquid. The regions labeled as “WAT” in Figure 4a and b indicates the upper and lower values of the WAT. After about 67 min (23) Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids, 2nd ed; Oxford University Press: London, UK, 1959; Chapter 7, pp 198–201.

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Table 2. Liquid-Deposit Interface Temperature Results for all Static Deposition Experiments TC1 cooling surface vessel wall

wax concentration 20 mass % (WAT ) 34 °C) 14 mass % (WAT ) 31 °C)

center, coldfinger 20 mass % (WAT ) 34 °C) 14 mass % (WAT ) 31 °C)

TC2

TC3

TC4

coolant temperature (°C) Td (°C) time (min) Td (°C) time (min) Td (°C) time (min) Td (°C) time (min) WAT - 10 ) 24 WAT - 7 ) 27 WAT - 5 ) 29 WAT - 10 ) 21 WAT - 7 ) 24 WAT - 5 ) 26 WAT - 20 ) 14 WAT - 10 ) 24 WAT - 5 ) 29 WAT - 20 ) 11 WAT - 10 ) 21

34.7 34.6 34.5 31.2 31.1 31.2 34.9 34.9 34.9 31.5 31.5

for cooling from the wall and 160 min for cooling from the center, a radial temperature variation is observed for all TC1-TC7 temperatures with time. Liquid-Deposit Interface Location. As mentioned previously, the lid of the vessel was made of plexiglass to enable the visual monitoring of the deposit-layer growth with time. However, as explained below, the visual monitoring of the growth of the interface proved to be difficult. The temperature of the liquid region was observed to reach the WAT well before the interface reached halfway radially across the vessel. Upon reaching the WAT, the liquid region was observed to become cloudy, which made it difficult to monitor the interface visually. As shown in Figure 4, a radial temperature variation was noticed only after the interface reached TC1. This observation was used to locate the interface with time. The time at which the rate of change of temperature at a particular thermocouple location started to deviate from those of other thermocouples (which were still within the liquid region) was taken to indicate the interface position at the surface of the thermocouple at that radial location. For each set of temperature versus time data in Figure 4, the rate of change of temperature, dT/dt, at each thermocouple location, was calculated, and the results are shown in Figure 5. In both plots of Figure 5, dT/dt is the same initially for all thermocouple locations until the value for TC1 starts to deviate, indicating that the interface had advanced to this location. The regions highlighted by circles for both cases in Figure 5 indicate the time it took for the thermocouple at TC1 to be completely immersed in the deposit layer. Beyond this period, dT/dt for TC1 follows the same trend as TC2 to TC7 after the immersion of those locations in the deposit layer. The average time and temperature of the highlighted regions were taken to correspond to the location of the interface at the radial location of TC1. With time, the dT/dt values for TC2-TC7 also started to deviate and the regions of deviation indicated the location of the interface at other thermocouples. For longer deposition times, however, the magnitude of dT/dt became very small, which made it difficult to locate the interface precisely. Hence, the location of the interface was estimated using this method for up to the fourth thermocouple location, TC4. The estimated interface temperatures and the corresponding times for the data in Figures 4b and 5b, along with those recorded from visual observations, are plotted in Figure 6. Note that the horizontal bars on data points for the dT/dt method represent the time interval for the interface to advance a distance equal to the diameter of the thermocouples while the vertical bars indicate the temperature change over this time. The results in Figure 6 are for the experiments with cooling from the center, which afforded a longer time period for the visual observation (before the liquid region started to become cloudy) due to slower

11.2 12.8 15.0 10.9 12.3 13.3 54.6 78.8 97.7 55.8 88.5

34.5 34.4 34.4 31.1 31.0 31.1 34.6 34.4 34.9 31.3 31.3

13.7 15.3 17.5 13.1 14.9 16.3 64.5 89.8 105.3 65.1 100.3

34.2 33.6 33.6 30.1 30.1 30.5 34.6 34.4 34.5 31.2 31.2

22.7 23.3 28.0 20.9 24.2 24.9 71.3 97.0 116.6 72.4 109.0

33.9 33.8 33.9 30.2 30.6 30.6 34.6 34.1 30.9 31.1

25.4 31.0 33.3 25.3 25.7 29.5 74.5 107.6 78.0 113.6

cooling. Furthermore, visual observations could only be carried out up to TC3 before the liquid region became cloudy. The results in Figure 6 indicate that the interface temperatures and the times obtained from the dT/dt method are within (0.2 °C and (2 min of those from visual observations, respectively. All of the results presented in the following sections were obtained using the dT/dt method. Temperature Profile during the Static Cooling Process. As mentioned previously, these deposition experiments were carried out by cooling wax-Norpar13 mixtures statically from an initial temperature of WAT + 21 °C. The temperature at each of the seven thermocouple locations was monitored with time until all of the temperatures, TC1-TC7, became close to the coolant temperature. These temperature-radial-location-time data were analyzed to determine the location of the interface (or the deposit-layer thickness) with time. Figure 7 shows the variation of temperature profile radially with time for an experiment with the 20 mass % wax-Norpar13 mixture, which was cooled from an initial temperature of WAT + 21 °C () 55 °C) with a coolant temperature of WAT - 10 °C () 24 °C) at the vessel wall. At t ) 5 min (i.e., before the interface reached TC1), the temperature of the liquid region was the same throughout. At t ) 11 min, the interface reached TC1, and the temperature at this location was close to the WAT. At t ) 14 min, the temperature at TC2 reached the WAT while TC1 fell below the WAT as it became immersed in the deposit layer. At t ) 14 min, the temperature in the liquid region was still above the WAT. At t ) 23 min, the interface reached TC3, and the temperature in the liquid region was at the WAT throughout. The movement of the interface was slowed between TC2 and TC3 because of the transfer of the additional latent heat released from the wax crystals formed in the liquid region (which made it cloudy). The temperature in the liquid region decreased only slightly at t ) 25 min as the interface reached TC4, while the temperatures TC1-TC3 decreased to below the WAT. The deposit occupied the entire vessel at about t ) 67 min as TC7 reached the lower limit of WAT. Beyond this point, further cooling of the deposit layer took place with the transfer of the sensible heat as well as the latent heat corresponding to the gradual solidification of the liquid phase within the deposit. The center temperature, TC7, reached the PPT at t ) 108 min. At t ) 667 min, the deposit temperature throughout the vessel became uniform and close to the coolant temperature. Similar temperature profiles were also observed with cooling from the center; however, the times were much longer due to the slower rate of cooling. Also, the liquid region was noted to reach the WAT when the interface had reached TC4. Effect of Cooling Heat-Transfer Area. Figure 8 shows the variation of the deposit-layer thickness to be approximately linear with time for experiments with both cooling surfaces.

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Figure 9. Variation in interface temperature, Td, with time for cooling from the wall; (a) 20 and (b) 14 mass % wax-Norpar13 mixture.

Note that the results in Figure 8 are for the same experiments as those for Figures 4, 5, and 6. The deposit-layer thickness grew faster with cooling from the wall, which is attributed to a higher cooling rate due to the larger area for heat transfer. For the case of cooling from the center (with a smaller area for heat transfer), it took about 80 min longer for the deposit to reach TC1 than for the cooling from the vessel wall. In addition, as mentioned previously, the outward deposit growth for cooling from the center case caused a gradual increase in the interface area with time whereas the inward deposit growth for the wall cooling caused a gradual decrease in the interface area with time. Variation of Liquid-Deposit Interface Temperature, Td. Following the procedure described in Figure 5, the time taken for the interface to reach each of TC1-TC4 locations was determined. The corresponding average temperature at that radial location was taken to be the interface temperature, Td. These calculations were repeated for all deposition experiments and the results are summarized in Table 2. Figures 9 and 10 show the changes in Td with time for both the 20 and 14 mass % wax-Norpar13 mixtures with cooling from the wall and the center, respectively. The region labeled as WAT in both figures indicates the upper and lower values of the WAT. The results for cooling from the wall, in Figure 9, are with all three coolant temperatures of WAT - 5 °C, WAT - 7 °C, and WAT - 10 °C for both wax-solvent mixtures. In both plots of Figure 9, all Td results corresponding to TC1 and TC2 fall within the WAT region; i.e., Td at early deposition times is equal to the WAT, which supports the constant-interfacetemperature assumption made in the heat-transfer approach. For both sets of results, Td is seen to decrease slightly with time after about t ) 20 min; i.e., Td results for TC3 and TC4 are less than the WAT by up to 1 °C. The visual observations indicated the liquid region at these times to be considerably cloudy (due to the suspended wax crystals). The temperature measurements showed the liquid temperature to be close to its WAT during this period. When the liquid temperature reached the WAT, the liquid became a two-phase mixture, with (solid)

Bidmus and Mehrotra

Figure 10. Variation in interface temperature, Td, with time for cooling from the center; (a) 20 and (b) 14 mass % wax-Norpar13 mixture.

crystals suspended in the liquid phase. Due to the formation of (wax) solid particles, the wax concentration in the associated liquid phase would be less than the original concentration. The precipitation of a fraction of wax from the wax-Norpar13 mixture would cause a lowering of the WAT of the liquid phase. This new “effective” WAT of the liquid phase has been suggested to be the same as the fluid temperature itself, since the fluid is saturated with wax.24 However, by definition, the WAT of the liquid phase should be the next lower temperature at which the first wax crystals would start to appear. Hence, it is plausible that the slightly lower values of Td for TC3 and TC4 actually correspond to the WAT of the liquid phase (with depleted wax content). The two plots in Figure 10 present similar results with cooling from the center, for both wax-Norpar13 mixtures, at coolant temperatures of WAT - 10 °C and WAT - 20 °C. The results with a coolant temperature of WAT - 5 °C are also presented for the 20 mass % wax-solvent mixture in Figure 10a. The trends in Figure 10 are similar to those in Figure 9, except that the interface temperatures for TC3 and TC4 are also within the WAT region. Due to the smaller heat transfer area, the cooling times in Figure 10 are 3 to 4 times larger than those in Figure 9. Hence, the liquid-region temperature did not reach the WAT until the interface had reached TC4. Effect of Coolant Temperature. As shown in both Figures 9 and 10, the lower the coolant temperature, the faster the movement of the interface (or growth of the deposit layer). For the results in Figure 9 (with a larger heat transfer area but a gradually decreasing interface area due to the inward deposit growth), the interface temperatures are close together. The results in Table 2 indicate that the time taken for the interface to reach TC1 with the coolant temperature of WAT - 10 °C is about 2 min less than that with the coolant temperature of WAT - 7 °C, which in turn is about 2 min less than that with the (24) Venkatesan, R.; Creek, J. L. Wax Deposition during Production Operations. Offshore Technology Conference, Houston, TX, April 30-May 2, 2007; paper OTC18798.

Wax-SolVent under Static Cooling

Figure 11. Change in interface temperature, Td, with radial location for cooling from the wall; (a) 20 and (b) 14 mass % wax-Norpar13 mixture.

coolant temperature of WAT - 5 °C. Similar time differences are observed for TC2, while the time differences for TC3 and TC4 increase only slightly to about 5 min. It is also interesting to note that the wax concentration does not seem to influence the interface movement provided both the interface and coolant temperatures are represented as differences from the WAT. A comparison of the results in Figure 10 (with a smaller heat transfer area at the coolant surface but a gradually increasing interface area due to the deposit outward growth) shows that the time taken for the interface to reach TC1 with the coolant temperature of WAT - 20 °C is about 30 min faster than that with the coolant temperature of WAT - 10 °C. And, this time difference remains about the same for TC2, TC3, and TC4. For the 20 mass % results, the interface reached the locations TC1, TC2, and TC3 about 20 min faster with the coolant temperature of WAT - 10 °C than with the coolant temperature of WAT - 5 °C. Again, the wax concentration does not seem to influence the interface movement provided the interface and coolant temperatures are represented as differences from the WAT. Deposit-Layer Thickness (or Interface Radial Location). Figures 11 and 12 present the interface temperatures for both wax-Norpar13 mixtures, obtained from the two designs of cooling experiments, with respect to the thickness of the deposit layer, δ/R (which also represents the radial location of the interface), respectively. In all cases, the coolant temperature does not seem to influence Td at each radial location. As explained before, the decrease in Td at later cooling times is attributed to the lowering of the liquid-phase WAT due to the precipitation of wax particles. Finally, Figure 13 is an attempt to relate the variation of Td, represented as (Td - WAT), with δ/R for all of the data obtained with both wax-Norpar13 mixtures using both designs of the deposition apparatus with different coolant temperatures. These results do not show any noticeable effect of the wax-Norpar13 mixture composition and the coolant temperature because these have been incorporated via the difference from the respective

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Figure 12. Change in interface temperature, Td, with radial location for cooling from the center; (a) 20 and (b) 14 mass % wax-Norpar13 mixture.

Figure 13. Relationship between (Td - WAT) and (δ/R) for all deposition experiments with wax-Norpar13 mixtures; (a) cooling from the wall and (b) cooling from the center.

WAT values. The light dashed lines represent the region between the WAT and WAT+1 °C, whereas the dark dashed line corresponds to WAT+0.5 °C. These lines, extending to TC2 for cooling from the wall in Figure 13a and to TC3 for cooling from the center in Figure 13b, represent the interface

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temperature, Td, before the liquid-region temperature decreases to the WAT. The solid lines, beyond TC2 for cooling from the wall and beyond TC3 for cooling from the center, show the trend in data between (Td - WAT) and δ/R. It is noted that most of the data points are enclosed within the dotted lines for the WAT and WAT+1 °C. Thus, the results in Figure 13 show that the interface temperature, Td, remains between WAT and WAT+1 °C when the liquid-region temperature is higher than the WAT. When the liquid-region temperature becomes less than the WAT, Td decreases slightly to the “effective” WAT of the liquid phase. That is, the liquid-deposit interface temperature, Td, at all times is between the WAT and WAT+1 °C of the liquid phase. This observation is supportive of the constant-interface-temperature assumption in the heat-transfer approach for modeling solids deposition from waxy mixtures, but not the increasing-interfacetemperature assumption in the molecular-diffusion approach. Conclusions An experimental technique was developed to study the formation and growth of a deposit layer from the cooling of prepared wax-solvent mixtures under static conditions. Thermocouples were placed at different radial and angular locations in the cylindrical vessel to measure temperatures with time. The location of the liquid-deposit interface was determined from the rate of change in temperature at each thermocouple location, and the results were validated with visual observations. The results of these experiments allowed the determination of liquid-deposit interface temperature at different radial locations with time under static conditions. Two designs of the static cooling apparatus, with significantly different heat transfer areas for cooling, were used. In the first design with a larger heat transfer area, the cooling occurred from the wall of the cylindrical vessel, which resulted in a decrease in the liquid-deposit interfacial area with time. The second design utilized a coldfinger configuration with a smaller heat transfer area for cooling, which resulted in an increase in the liquid-deposit interfacial area with time. Experiments were performed by statically cooling the prepared mixtures of a multicomponent paraffinic wax dissolved in a mixed solvent at

Bidmus and Mehrotra

different coolant temperatures. In all experiments, the temperature of the wax-solvent mixture decreased rapidly to the WAT much before the deposit layer filled the entire vessel. The liquid-deposit interface temperature during the growth of the deposit layer remained constant and equal to the WAT of the wax-Norpar13 solution. The interface temperature declined slightly as the temperature of the liquid region decreased gradually to at or below the WAT, at which point the liquid region became a two-phase mixture, with (solid) crystals suspended in the liquid phase. The small decrease in the interface temperature was attributed to a lowering of the WAT of the liquid phase with lower wax content. The results of this study indicated that the liquid-deposit interface temperature, Td, during the deposit-layer growth under static conditions remains constant at the WAT of the liquid phase. These results were shown to validate the constantinterface-temperature assumption made in the heat-transfer approach for modeling the deposition of solids from waxy mixtures. The results of this study did not show the interface temperature to increase from an initial value close to the wall (or coolant) temperature to reach the WAT ultimately. That is, the results of this study do not support the increasing-interfacetemperature assumption made in the molecular-diffusion approach. Acknowledgment. Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. We thank Mr. Bernie Then for technical support.

Nomenclature r ) radial distance (m) R ) radius of cylindrical vessel (m) t ) time (min) T ) temperature (°C) Td ) liquid-deposit interface temperature (°C) Greek Letter δ ) deposit-layer thickness (m) Acronyms PPT ) pour point temperature (°C) WAT ) wax appearance temperature (°C) WDT ) wax disappearance temperature (°C) EF700588Y