Solids Deposition from Multicomponent Wax−Solvent Mixtures in a

Prashanth Parthasarathi and Anil K. Mehrotra*. Department of Chemical and Petroleum Engineering, University of Calgary,. Calgary T2N 1N4, Alberta, Can...
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Energy & Fuels 2005, 19, 1387-1398

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Solids Deposition from Multicomponent Wax-Solvent Mixtures in a Benchscale Flow-Loop Apparatus with Heat Transfer† Prashanth Parthasarathi and Anil K. Mehrotra* Department of Chemical and Petroleum Engineering, University of Calgary, Calgary T2N 1N4, Alberta, Canada Received November 13, 2004. Revised Manuscript Received February 10, 2005

The deposition of solids from mixtures of a paraffinic wax (C20-C40) dissolved in a multicomponent solvent (C9-C16) was studied under laminar flow conditions. A novel benchscale flow loop was developed, which consisted of a jacketed heat-exchange section for solids deposition on the inner surface of an aluminum tube. Experiments were performed to investigate the effects of the wax-solvent mixture composition, hot and cold stream temperatures, flow or shear rate, deposition residence time, and hydrodynamic entry length on the deposition process. The data were analyzed with a pseudo-steady-state heat-transfer model, which validated the solids deposition process to be controlled primarily by heat transfer. The mass of deposited solids was related to the ratio of temperature difference across the deposit layer and the overall temperature difference. Gas chromatography (GC) analyses of the deposited layer showed significant shifts in the carbon number distribution. The C20+ content of the deposit layer was observed to be higher, by ∼70%-200%, than that of the corresponding wax-solvent mixture.

Introduction The precipitation and deposition of paraffins from waxy crude oils is observed commonly in the production, transportation, and processing operations of the oil and gas industry. The precipitation of paraffinic solids from the liquid phase has been studied in regard to topics such as crystal structure, crystallization kinetics, phase behavior, rheology, and their deposition tendency.1-7 Wax deposition is undesirable, because it leads to the plugging of pipelines and process equipment, resulting in a reduction of flow rate and/or an increase in pressure drop. Wax deposition also causes substantial expenditures for its control and remediation. The liquid-solid phase transformation of paraffins in waxy crude oils, under nonisothermal flowing condi† Presented at the 5th International Conference on Petroleum Phase Behavior and Fouling. * Author to whom correspondence should be addressed. Telephone: (403) 220-7406. Fax: (403) 284-4852. E-mail address: mehrotra@ ucalgary.ca. (1) Turner, W. R. Normal Alkanes, Technical Review. Ind. Eng. Chem. Prod. Res. Dev. 1971, 10, 238. (2) Burger, E. D.; Perkins, T. K.; Striegler, J. H. Studies of Wax Deposition in the Trans Alaska Pipeline. J. Pet. Technol. 1981, 33, 1075. (3) Coutinho, J. A. P.; Andersen, S. I.; Stenby, E. H. Evaluation of Activity Coefficient Models in Prediction of Alkane Solid-Liquid Equilibria. Fluid Phase Equilib. 1995, 103, 23. (4) Creek, J. L.; Lund, H. J.; Brill, J. P.; Volk, M. Wax Deposition in Single Phase Flow. Fluid Phase Equilib. 1999, 158-160, 801. (5) Singh, P.; Venkatesan, R.; Folger, H. S.; Nagarajan, N. Formation and Aging of Incipient Thin Film Wax-Oil Gels. AIChE J. 2000, 46, 1059. (6) Tiwary, D.; Mehrotra, A. K. Phase Transformation and Rheological Behaviour of Highly Paraffinic “Waxy” Mixtures. Can. J. Chem. Eng. 2004, 82, 162. (7) Bidmus, H. O.; Mehrotra, A. K. Heat-Transfer Analogy for Wax Deposition from Paraffinic Mixtures. Ind. Eng. Chem. Res. 2004, 43, 791.

tions, is a complex process, which is influenced by cooling or crystallization rates, thermal and/or shear history, and composition. Upon cooling, paraffins or waxes in the solution phase crystallize and deposit on cooler surfaces, because of their low solubility in crude oils (or solvents) at lower temperatures. The effects of wax precipitation are also manifested in a peculiar timedependent rheological behavior displayed by waxy crude oils below their pour point temperature, because of individual wax crystals giving rise to an interlocking structural network, which leads to a gelled, solidlike state.8 At temperatures below the pour point temperature, waxy mixtures and crude oils exhibit non-Newtonian rheology, along with a rapid increase in the viscosity.6,8 The highest temperature, at which the first crystals of paraffin wax appear upon cooling of waxy crude oils, is known commonly as the wax appearance temperature (WAT). Wax particles start to precipitate at crude oil temperatures below the WAT, which may lead to solids deposition on the pipe wall. A recent study reported quantitative differences between the WAT and the wax disappearance temperature (WDT), which was recorded during heating.9 It was shown that the WDT, rather than the WAT, is closer to the liquidus or saturation temperature of wax-solvent mixtures. That is, although WAT is the temperature of significance for wax deposition, which occurs during cooling, WDT would represent the highest temperature for the coexistence of liquid and solid phases under thermodynamic equilibrium.9 (8) Wardhaugh, L. T.; Boger, D. V. Flow Characteristics of Waxy Crude Oils: Application to Pipeline Design. AIChE J. 1991, 37, 871. (9) Bhat, N. V.; Mehrotra, A. K. Measurement and Prediction of the Phase Behavior of Wax-Solvent Mixtures: Significance of the Wax Disappearance Temperature. Ind. Eng. Chem. Res. 2004, 43, 3451.

10.1021/ef0497107 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/16/2005

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Studies on wax deposition during the flow of crude oil in pipelines have identified the heat-transfer process as an important factor.4,10-15 It has been shown that insulation and increased shear rate can decrease wax deposition. The difference between the bulk oil temperature and the temperature of the pipe wall or outside environment is generally regarded as the driving force for solids deposition. Although earlier studies reported an increase in wax deposition with an increase in the overall temperature difference, recent research has shown that the temperature difference across the deposit layer is more significant.7,13,15 The deposited solids undergo an “aging” process, which results in compositional changes in the liquid and solid phases present in the deposit.5,7 Other factors that affect wax deposition are the composition, thermal history, flow rate, and pressure.16 The paraffin wax content in crude oils affects the likelihood of solids deposition; i.e., an increase in wax content results in a higher WAT. The normal paraffins and iso-paraffins are flexible hydrocarbon molecules that have a tendency to cluster together and precipitate from crude oil in the form of wax solids, although isoparaffins have a tendency to delay the formation of wax nuclei and usually form unstable waxy solids.17 The temperatures of the liquid phase and pipe wall have an important role in the deposition of solids. As the hot crude oil flows in a pipeline, heat is transferred from the liquid phase across the deposit layer, creating a radial temperature gradient, which causes the deposition of solids on the cooler pipe wall.4,10,13-15 Several other possible wax deposition mechanisms have also been suggested, including molecular diffusion, shear dispersion, Brownian movement, and gravity settling.16 The molecular diffusion approach has received considerable interest. It is based on the premise that the flow of hot crude oil in a pipeline with a wall temperature below the cloud point or wax appearance temperature provides a radial temperature gradient, which, in turn, creates a radial concentration gradient. With the reduced solubility of paraffins at lower temperatures, a deposit layer is formed on the pipeline surface. Burger et al.2 proposed a relationship for estimating the wax flux, in terms of the wax solubility coefficient of the oil and the radial temperature gradient at the wall. A similar approach was used in several subsequent studies.4,5,16,18,19 Singh et al.5 combined the diffusion equation with expressions for mass and heat (10) Cole, R. J.; Jennsen, F. W. Paraffin Deposition. Oil Gas J. 1960, 58, 87. (11) Patton, C. C.; Casad, B. M. Paraffin Deposition from Refined Wax-Solvent Systems. Soc. Pet. Eng. J. 1970, 10 (1), 17. (12) Bott, T. R.; Gudmunsson, J. S. Deposition of Paraffin Wax from Kerosene in Cooled Heat Exchanger Tubes. Can J. Chem. Eng. 1977, 55, 381. (13) 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.; Begell House: New York, 1997; pp 473-489. (14) 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. (15) Mehrotra, A. K. Comments on: Wax Deposition of Bombay High Crude Oil under Flowing Conditions. Fuel 1990, 69, 1575. (16) Azevedo, L. F. A.; Teixeira, A. M. A Critical Review of the Modeling of Wax Deposition Mechanisms. Pet. Sci. Technol. 2003, 21, 393. (17) Hammami, A.; Raines, M. A. Paraffin Deposition from Crude Oils, Comparison of Laboratory Results with Field Data. Soc. Pet. Eng. J. 1999, 4, 9.

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balance, and reported agreement of the predicted results with experimental data from a laboratory flow loop. The Brownian diffusion approach assumes that the wax crystals precipitate out and remain suspended, and the existence of a concentration gradient of crystals results in their transport in the direction of decreasing concentration.16 However, there is a lack of agreement on the importance of Brownian diffusion in wax deposition.2,18-20 Shear dispersion has also been proposed as a contributing mechanism to wax deposition; this mechanism involves shear transport of precipitated wax particles to the wall, because of the velocity gradient.2,18 The possibility of wax particles settling because of gravity has been explored in the presence of minimal or no shear rate, because these are denser than the liquid phase.2 The role of surface properties on the deposition process and sloughing has also been explored, and the effects have been explained in terms of the surface wettability or free surface energy21-24 and the surface roughness.11 The flow rate or the rate of shear is considered to have an important effect on the wax deposition process.4,12 Singh et al.5,25 and Wu et al.14 showed that the amount of wax deposited decreases as the flow rate increases, regardless of the flow being laminar or turbulent. Pressure is not considered as an important factor for wax deposition, which influences the process indirectly by increasing the WAT or by a loss of light ends when the pressure of live oils is decreased.26-29 Wax deposition studies have shown that the deposit composition varies with time and the deposits become harder with time; this hardening process is called “aging”.4,5,30 A critical carbon number (CCN) has been (18) Weingarten, J. S.; Euchner, J. A. Methods for Predicting Wax Precipitation and Deposition, Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, October 5-8, 1986, SPE Paper No. 15654. (19) Majeed, A.; Bringedai, B.; Overa, S. Model Calculates Wax Deposition for N. Sea Oils. Oil Gas J. 1990, 18, 63. (20) Singh, P.; Folger, H. S.; Nagarajan, N. Prediction of the Wax Content of the Incipient Wax-Oil Gel in a Pipeline: An Application of the Controlled-Stress Rheometer. J. Rheol. 1999, 43, 1437. (21) Parks, C. F. Chemical Inhibitors Combat Paraffin Deposition. Oil Gas J. 1960, 58, 97. (22) Zisman, W. A. Influence of Constitution on Adhesion. Ind. Eng. Chem. 1963, 55, 19. (23) Charles, J. G.; Marcinew, R. P. Unique Paraffin Inhibition Technique Reduces Well Maintenance. J. Can. Pet. Technol. 1986, 25 (4), 40. (24) Li, M.; Su, J.; Wu, Z.; Yang, Y.; Ji, S. Study of the Mechanisms of Wax Prevention in a Pipeline with a Glass Inner Layer. Colloids Surf., A 1997, 123-124, 635. (25) Singh, P.; Venkatesan, R.; Folger, H. S.; Nagarajan, N. Morphological Evolution of Thick Wax Deposits during Aging. AIChE J. 2001, 47, 6. (26) Meray, V. R.; Volle, J. L.; Schranz, C. J. P.; Le Marechal, P.; Behar, E. Influence of Light Ends on the Onset Crystallization Temperature of Waxy Crudes within the Frame of Multiphase Transport, Presented at the SPE Annual Technology Conference and Exhibition, Houston, TX, October 3-6, 1993, SPE Paper No. 26540. (27) Brown, T. S.; Niesen, V. G.; Erickson, D. D. The Effects of Light Ends and High Pressure on Paraffin Formation, Presented at the SPE Annual Technology Conference and Exhibition, New Orleans, LA, September 25-28, 1994, SPE Paper No. 28505. (28) Karan, K.; Ratulowski, J.; German, P. Measurement of Waxy Crude Properties Using Novel Laboratory Techniques, Presented at the SPE Annual Technology Conference and Exhibition, Dallas, TX, October 1-4, 2000, SPE Paper No. 62945. (29) Pauly, J.; Daridon, J. L.; Coutinho, J. A. P.; Lindeloff, N.; Anderson, S. I. Prediction of Solid-Liquid Phase Diagrams of Light Gases-Heavy Paraffin Systems up to 200 MPa Using an Equation of State GE Model. Fluid Phase Equilib. 2000, 167, 145. (30) Coutinho, J. A. P.; Lopes da Silva, J. A.; Ferreira, A.; Soares, M. R.; Daridon, J. L. Evidence for the Aging of Wax Deposits in Crude Oils by Ostwald Ripening. Pet. Sci. Technol. 2003, 21, 381.

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defined to describe this aging process. With time, paraffins heavier than the CCN diffuse into the deposit from the liquid while those lighter than the CCN diffuse out of the deposit layer.5 Paso and Fogler31 showed that the CCN value increased with the addition of low molar mass n-alkanes. The thermal conductivity of the deposited solids is also an important property, because the deposition of waxes in flowing crude oil is a thermally driven process. The thermal conductivity values for paraffins reported in the literature are in the range of 0.10-0.35 W m-1 K-1.32-35 Recently, Bidmus and Mehrotra7 examined wax deposition under pseudo-steady-state conditions and suggested a dimensionless parameter (θd), which is the ratio of the temperature difference across the deposit layer and the overall temperature difference. Parameter θd was derived by equating, at steady state, the rate of heat transfer across one thermal resistance (for the deposit) with that across all thermal resistances in series.7 The amount of solids deposited was related to θd for several concentrations of wax dissolved in dodecane (n-C12). As shown by eq 1, parameter θd at steady state is also equal to the ratio of the thermal resistance offered by the deposit layer and the total thermal resistances:

θd ≡

∆Td ∆Toverall

)

Rd

∑ Ri

(1)

In this study, a novel benchscale flow loop is described, which was developed to study the deposition of solids from prepared wax-solvent mixtures of known composition. An experimental program was undertaken to investigate the effects of the mixture composition, mixture and coolant temperatures, shear rate, and residence time on the extent of solids deposition, as well as the roles of these factors on the composition and properties of the deposited solids. The experimental and modeling results presented here support the findings of Bidmus and Mehrotra7 that the wax deposition process can be explained with a heat-transfer approach. The sequence of events in all of the experiments can be interpreted in terms of heat transfer as follows. Because of heat transfer from the “hot” wax-solvent mixture to the “cold” tube surface, a deposit layer was formed that offered a thermal resistance. The deposit thermal resistance increased with time, because of the growth of the deposit layer. The increasing thermal resistance of the deposit layer slowed the rate of deposit growth until the attainment of thermal steady state. Note that the decrease in the rate of solids deposition with time was because of increased thermal insulation offered by the deposit layer, and not due to a depletion of C20+ “waxy” constituents in the wax-solvent mixture.7,36 (31) Paso, K. G.; Fogler, H. S. Influence of n-Paraffin Composition on the Aging of Wax-Oil Gel Deposits. AIChE J. 2003, 49, 3241. (32) Dick, M. F.; McCready, D. W. The Thermal Conductivities of Some Organic Liquids. Trans. ASME 1954, 76, 831. (33) Missenard, F. A. Foreword: Measurement of the Thermal Conductivity of Several Liquids. Rev. Gen. Therm. 1968, 7 (76), 365. (34) Filippov, L. P. Liquid Thermal Conductivity Research at Moscow University. Int. J. Heat Mass Transfer 1968, 11, 331. (35) Jamieson, D. T.; Irving, J. B.; Tudhope, J. S. The Thermal Conductivity of Petroleum Products; Institute of Petroleum: London, 1974. (Paper No. IP 74-015.)

Figure 1. Gas chromatography (GC) analyses for carbon number distribution of wax and solvent (Norpar13).

Experimental Section Materials. A sample of paraffin wax (melting point (mp) of 59-62 °C) was obtained from Sigma-Aldrich (Oakville, ON, Canada). This wax sample was also used in recent studies by Mehrotra and co-workers.6,7,9 The solvent used was a commercially available mixture of n-paraffins (Norpar13), which was obtained from Imperial Oil Ltd. (Canada). With a flash point of 93 °C, Norpar13 is essentially nonvolatile over the temperature range considered in this study. Batches of waxsolvent mixtures were prepared by mixing ∼3 L of Norpar13 with the required mass of wax for 2 h at 70 °C. There were many reasons to perform this laboratory investigation with prepared mixtures of wax dissolved in Norpar13, instead of crude oil samples. It was more convenient (i) to prepare and work with these mixtures in the laboratory, (ii) to vary the mixture composition, (iii) to perform modeling calculations, and (iv) to conduct GC analyses to characterize the mixture and deposit samples. As shown below, both the wax and the solvent (Norpar13) used in this study were multicomponent mixtures of n-alkanes. The results from this study could be validated with waxy crude oil samples in future investigations. GC Analyses. All gas chromatographic analyses were performed using a Hewlett-Packard model HP6890 gas chromatograph that was equipped with a nonpolar fused-silica column (10 m × 0.53 mm × 0.88 µm) and a hydrogen flame ionization detector (FID). The GC equipment was calibrated using the ASTM D2887 extended method, using a C5-C66 hydrocarbon standard (SD-SS3E-05, Separation Systems, Inc., Gulf Breeze, FL). The results from GC analyses were used to calculate the average molar mass of the wax sample to be 390.8 kg/kmol, which corresponds to a mean carbon number of 28. The carbon number distributions for Norpar13 and the wax sample are shown in Figure 1. These results show that Norpar13 is a mixture of n-alkanes, ranging from C9 to C16, with C13 and C14 being the two predominant constituents, with concentrations of 51.3 and 32.8 mass %, respectively. The average molar mass of Norpar13 was calculated to be 185.7 kg/kmol, which corresponds to an equivalent carbon number of ∼13. Note that there is no overlap in the carbon number distribution for the wax and Norpar13 samples, which was an important requirement for calculating the composition of C20+ n-alkanes in the deposit samples, on a solvent-free basis. (36) Parthasarathi, P. Deposition and Aging of Waxy Solids from Paraffinic Mixtures, M.Sc. Thesis, University of Calgary, Calgary, Canada, 2004.

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Figure 2. Data for the wax appearance temperature (WAT) of wax-solvent mixtures, compared with those reported by Bhat and Mehrotra.9 WAT Measurements. The procedure used to measure the WAT has been described in detail elsewhere.6,7,9,36 In this study, seven wax-Norpar13 mixtures were prepared with wax concentrations in the range of 7-20 mass %. All WAT measurements were performed at atmospheric pressure in a temperature-regulated bath that was equipped with a programmable temperature controller. Briefly, each wax-solvent mixture held in a pour point tube was maintained at 70 °C for 1 h. Samples were cooled at a rate of 10 °C/h from 70 °C to 50 °C, after which the temperature was decreased in steps of 1 °C and held at that temperature for 15 min. At each constant temperature, the samples were checked visually for any sign of turbidity. The highest temperature at which the sample showed turbidity was recorded as the WAT. The WAT values ranged from a high of 35 °C (for a 20 mass % wax mixture) to a low of 22 °C (for a 5 mass % wax mixture). The results, which are plotted in Figure 2, are in agreement with those reported by Bhat and Mehrotra.9 Note that the error bars for data points in Figure 2 indicate that the actual WAT values would be between the recorded WAT and WAT + 1 °C. Benchscale Flow-Loop Apparatus for Heat-Transfer Experiments. A novel benchscale flow-loop design was developed to conduct the wax deposition experiments under laminar flow conditions. As shown schematically in Figure 3, the flow loop consisted of two sections. The first section was submerged in a temperature-regulated water bath, and it included a deposition section and a 3.6-L reservoir for holding the wax-solvent mixture. The deposition section consisted of a double-pipe heatexchange section, in which the solids deposition occurred on the inner surface of the inside tube. The circulation of waxsolvent mixtures was accomplished with a submersible pump located inside the wax-solvent reservoir located in the water bath. Downstream of the deposition section, flexible tubing was used to connect the submerged line to the flow measurement line outside the bath. Note that, with the first section of the flow loop submerged in the water bath, no solids precipitation or deposition could occur in any part other than the deposition section. The second section of the flow loop, following the deposition section, was for performing flow measurements using an electronic turbine-flow sensor, which could not be submerged in water; therefore, the second section was placed outside the water bath. All flow lines in the second section were insulated to minimize any solids deposition due to cooling. Two identical flow-loops were placed in the water bath, allowing two experi-

Parthasarathi and Mehrotra ments to be conducted simultaneously for different deposition residence times. As mentioned previously, the wax deposition occurred in the deposition section, which was a small double-pipe heat exchanger. In the heat exchanger, the wax-solvent mixture flowed through the inner tube made of machined aluminum while the coolant (water) flowed countercurrently through the annular region. No surface treatment of the machined aluminum tube was performed. The coolant flow was achieved by another submersible pump that was placed in a second refrigerated, temperature-controlled bath. The dimensions of the aluminum deposition tube were as follows: inside diameter, 2.5 cm; outside diameter, 3.0 cm; and length, 10.8 cm. The outer tube was made of plexiglass, with a 2.0-cm thick layer of Styrofoam wrapped around it, to minimize heat gain by the coolant from the water bath. The inside and outside diameters of the plexiglass tube were 3.8 and 4.6 cm, respectively. A 23-cm long copper tube with an inside diameter of 2.5 cm was placed before the deposition section for flow development. Calibrated T-type thermocouples were used to measure the temperatures of the inlet and outlet water streams and the inlet wax-solvent stream, which was at the water bath temperature, and the signals were transmitted to a data acquisition system. A fourth thermocouple, which was placed at the outlet of the aluminum tube, showed significant variations, depending on its radial placement; that is, it did not provide a reliable measurement of the bulk or “mixing cup” temperature of the outlet wax-solvent mixture stream. The outlet wax-solvent mixture temperature (Tho) was estimated from the following energy balance equation:

q≡m ˘ cCc(Tco - Tci) - qgain ) m ˘ hCh(Thi - Tho)

(2)

where m ˘ c and m ˘ h are mass rates of coolant and wax-solvent streams, Cc and Ch are specific heat capacity of coolant and wax-solvent mixture, Tci and Tco are inlet and outlet coolant temperatures, Thi and Tho are inlet and outlet wax-solvent mixture temperatures, and qgain is the rate of heat transfer across the Styrofoam insulation. From heat-transfer calculations, qgain was estimated to vary between ∼5% and 10% of the overall rate of heat transfer (q). Further details of the apparatus and procedure were reported by Parthasarathi.36 Design of Experiments. In total, ∼100 deposition experiments were performed by following the factorial design criteria. As summarized in Table 1, solids deposition experiments were conducted at four wax concentrations, two waxsolvent mixture temperatures, two coolant temperatures, two wax-solvent mixture flow rates, and three deposition residence times. At the wax-solvent flow rates (Fh) of 30 and 50 cm3/s, the flow of wax-solvent mixtures was in the laminar range, with the initial values of the average Reynolds numbers (Re) of ∼600 and 1000.36 Even though most crude oil pipelines operate under turbulent conditions, the laminar flow of waxsolvent mixtures was selected as a starting point to investigate the transport processes involved in solids deposition. For the coolant, a constant flow rate (Fc) of 5 cm3/s was used in all experiments. Deposit Mass and Analysis. At the conclusion of each experiment, the aluminum tube with deposited solids was removed from the apparatus and weighed on an electronic balance to (10 mg, and the deposit mass was determined by difference. A small sample of the deposited solids was saved for the GC analysis and the rest was recycled into the waxsolvent mixture so that its composition did not change much from one experiment to the next.36 Each batch of the waxsolvent mixture was used for only four sets of experiments.

Heat-Transfer Calculations The pseudo-steady-state heat-transfer model proposed by Bidmus and Mehrotra7 was used to analyze the

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Figure 3. Schematic of the benchscale heat-transfer flow-loop apparatus. Table 1. Design of Experiments for Solids Deposition from Wax-Norpar13 Mixtures variable

value(s) of each variable tested

wax concentration (mass %) temperature of wax-solvent mixture, T h h (°C) flow rate of wax-solvent mixture, Fh (cm3/s) temperature of coolant, Tc (°C) deposition residence time (h)

7, 10, 12.5, and 15 WAT + 5 and WAT + 10 30 (Re ) 600) and 50 (Re ) 1000) WAT - 5 and WAT - 10 1, 2, and 4 (4, 6, and 12 h for 12.5 mass %)

deposition results in this study. Briefly, the transfer of thermal energy from the (hot) wax-solvent mixture to the coolant stream involved four thermal resistances in series, i.e., two convective resistances (for the waxsolvent mixture and the coolant) and two conductive resistances (for the metal tube and the deposit layer). For one-dimensional radial heat transfer, the heattransfer rate was expressed in terms of the inside overall heat-transfer coefficient (Ui):

q ) UiAi(T hh - T h c)

(3)

where Ai is the inside tube surface area, and T h h and T hc are the average hot and cold fluid temperatures, respectively. The following expression was obtained by equating the heat flux through each thermal resistance at the pseudo-steady state:

h h - Td) kd(Td - Twi) hh(T q ) ) ) Ai ri/(ri - xd) ri ln[ri/(ri - xd)] km(Twi - Two) ri ln(ro/ri)

)

h c) hc(Two - T (4) ri/ro

In eq 4, the known quantities from experimental measurements are the average wax-solvent mixture (hot) and coolant temperatures (T h h and T h c, respectively), the deposit thickness (xd), the tube inner and outer radii (ri and ro, respectively), and the thermal conductivity of the aluminum tube (km). The deposit layer thickness xd was assumed to be uniform over the entire deposition surface. Bidmus and Mehrotra7 showed that the interface temperature Td at the thermal steady state was equal to the WAT of the wax-solvent mixture. As described in the following section, the two heat-transfer coefficients (hh and hc) were obtained by a nonlinear regression of several calibration experiments. Equation 4 was solved for the inside and outside wall tempera-

tures (Twi and Two, respectively) and the deposit thermal conductivity (kd). Calibration Experiments for the Heat-Transfer Coefficients hh and hc. Correlations for the two heattransfer coefficients were developed experimentally through a series of calibration experiments. For both cases, the heat-transfer coefficient was assumed to be a function of the Reynolds number Re, the Prandtl number (Pr), and the entry length. Over the narrow range of temperatures involved in the experiments, average fluid properties were used for both fluids, and each heat-transfer coefficient was expressed in terms of the “cold” fluid flow rate (Fc) or the “hot” fluid velocity (vh). For the hot stream, the average velocity of the wax-solvent mixture vh, instead of Fh, was used to account for the varying cross-sectional area for flow due to the deposit layer thickness. Accordingly, the functional forms for the two heat-transfer coefficients were assumed as: hh ≡ vbh/a and hc ≡ Fdc /c. The following equation was used to obtain the four regression constants a, b, c, and d, from experimental data for each wax-solvent mixture:7,36

Ai c 1 a ) b+ + Rm Ui v Ao F d h

(5)

c

where Rm is the thermal resistance of the aluminum tube. The heat-transfer coefficient experiments were performed for all four concentrations of wax-solvent mixtures listed in Table 1. Note that these experiments were performed over temperatures at which solids deposition did not occur. Detailed results of regression calculations and the optimum values of a, b, c, and d for each wax-solvent mixture have been reported elsewhere.36 A comparison of the experimental and calculated values of the overall heat-transfer coefficient (Ui) for all wax-solvent mixtures is shown in Figure 4. Overall, the average relative deviation between the experimental and calculated values of Ui was 4.4%.

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Figure 4. Comparison of experimental and calculated values of the overall heat-transfer coefficient (Ui) for wax-solvent mixtures.

Fractional Thermal Resistance of Deposited Solids (θd). The total thermal resistance, Rtotal, for the heat-transfer experiments involving solids deposition from wax-solvent mixtures is the sum of four individual resistances:

Rtotal ) Rh + Rd + Rm + Rc

(6)

where Rh ≡ 1/[2π(ri - xd)Lhh] is the convective resistance due to the flowing wax-solvent mixture, Rd ≡ ln [ri/(ri - xd)]/(2πkdL) is the conductive resistance due to the deposit layer, Rm ≡ ln(ro/ri)/(2πkmL) is the conductive resistance due to the tube wall, and Rc ≡ 1/(2πroLhc) is the convective resistance due to the coolant. The fractional contribution of each resistance is the ratio of the individual thermal resistance and the total thermal resistance, which, at steady state, is also equal to the ratio of the corresponding temperature difference and the total temperature difference, i.e., θh ≡ Rh/Rtotal ) (T h h - Td)/(T hh - T h c), θd ≡ Rd/Rtotal ) (Td - Twi)/(T hh - T h c), hh - T h c), and θc ≡ Rc/Rtotal θm ≡ Rm/Rtotal ) (Twi - Two)/(T ) (Two - T h c)/(T hh - T h c). Calculations were performed for θh, θd, θm, and θc under typical conditions of solid deposition experiments over a range of deposit thicknesses, expressed as a fraction of the tube radius, xd/ri. A comparison of the magnitudes of all four thermal resistances is shown in Figure 5 for the two wax-solvent mixture flow rates used in this study. The contribution of two of the thermal resistances (Rm and Rc) is small for all values of xd/ri. The convective thermal resistance for the waxsolvent mixture is the predominant resistance when there is no deposition, i.e., at xd/ri ) 0. The contribution of thermal resistance due to the deposit layer (θd) is small initially but it exceeds the value of θh after the deposit thickness becomes larger than ∼10% of the tube radius. In the following section, predictions from this heat-transfer model will be used to explain the trends observed in the experimental results. Results and Discussion: Mass of the Deposit Layer Detailed results of ∼100 solids deposition experiments, performed according to the factorial design of

Figure 5. Predictions for the variation of fractional thermal resistances θc, θd, θh, and θc, with changes in the deposit layer thickness.

experiments summarized in Table 1, were reported by Parthasarathi.36 To determine the repeatability of the experimental procedure, two experiments with 7 and 15 mass % wax-solvent mixtures were performed twice under similar conditions, and the difference in the mass of deposited solids was 3.1% and 1.4%, respectively.36 In the following sections, experimental results are discussed and compared with predictions from the heattransfer model. Results are presented first for the mass of deposited solids with changes in the deposition residence time, mixture composition, and the average wax-solvent mixture (hot) and coolant stream temperatures, and the wax-solvent mixture flow rate. In the next section, the results from GC analyses of the deposit layer are used to study the compositional changes. The amount of deposited solids was expressed in terms of the mass of deposit per unit inside tube surface area (Ω), which is related to the deposit layer thickness (xd), as follows:

Ω)

[

]

ri2 - (ri - xd)2 deposit mass ) Fd Ai 2ri

(7)

where Fd is the average density of the deposited solids. The average deposit thickness xd was calculated using eq 7 over the range of experimental values of Ω; xd was found to vary from ∼0.1 mm (for Ω ) 0.5 kg/m2) to ∼2.5 mm (for Ω ) 1.8 kg/m2). That is, for the 2.5-cm diameter deposition tube, the relative deposit thickness (xd/ri) varied from ∼1% to 20%. Effect of Deposition Residence Time. Figure 6 shows the variation of Ω for three wax-solvent mixture compositions of 7, 10, and 15 mass % at three deposition residence times of 1, 2, and 4 h. In all cases, much of the deposition was accomplished in 1 h, and there was only a slight increase in Ω with time, up to 4 h. As mentioned previously, the experiments with 12.5 mass % wax-solvent mixture were performed over longer deposition residence times (in the range of 4-12 h), which did not show any appreciable increase in Ω beyond 4 h.36

Solid Deposition from Wax-Solvent Mixtures

Energy & Fuels, Vol. 19, No. 4, 2005 1393

Figure 7. Effect of overall temperature difference, T hh - T h c, on the mass of deposit per unit area for wax-solvent mixtures at a Reynolds number of Re ) 1000: ‘a’, T h h - WAT ≈ WAT T h c ≈ 5 °C; ‘b’, T h h - WAT ≈ 5 °C and WAT - T h c ≈ 10 °C; ‘c’, T hh - WAT ≈ 10 °C and WAT - T h c ≈ 5°C; and ‘d’, T h h - WAT ≈ WAT - T h c ≈ 10 °C. Figure 6. Effect of deposition residence time on the mass of deposit per unit area for wax-solvent mixtures: (a) 7 mass %, (b) 10 mass %, and (c) 15 mass %.

The results in Figure 6 confirm the observation of Bidmus and Mehrotra,7 in regard to the relatively short time needed for the solids deposition from wax-solvent mixtures. The fact that thermal steady-state was attained in relatively short times of