Waxy - American Chemical Society

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Solids Deposition from Two-Phase Wax−Solvent−Water “Waxy” Mixtures under Turbulent Flow Adebola S. Kasumu and Anil K. Mehrotra* Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4 ABSTRACT: The deposition of solids from two-phase waxy mixtures (comprising a multicomponent paraffinic wax dissolved in a multicomponent solvent and water) was studied under turbulent flow conditions in a flow-loop apparatus, incorporating a cocurrent double-pipe heat exchanger. The deposition experiments were performed with 6 mass % wax solutions, containing 0, 5, 10, 15, 20, 25, and 30 vol % water, at different flow rates over 5600 < Re < 25 300, and at different hot and cold stream temperatures. In the bench-scale apparatus, the deposit was formed rapidly such that a thermal steady state was attained within 10−20 min in all experiments. The water content of the deposit was found to be not related to the water content of the waxy mixture. The deposit mass was found to decrease with an increase in Re, the waxy mixture temperature, and/or the coolant temperature. The deposit mass also increased as the water content of the waxy mixture was increased to about 10 vol % and decreased thereafter. The deposition data, analyzed with a steady-state heat-transfer model, indicated that the liquid−deposit interface temperature was close to the wax appearance temperature of the waxy mixture. The average thermal conductivity of the deposit was estimated to be 0.38 W m−1 K−1. Overall, the results of this study confirm that the deposition process from waxy mixtures is primarily thermally driven.

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success.5 Another method proposed to control wax deposition is “cold flow”. In this method, crude oil is subjected to systematic cooling to precipitate wax crystals, giving rise to a slurry that is transported through pipelines. The deposition of solids during “cold flow” is decreased because of a reduced thermal driving force and a lowering of the WAT of the remainder liquid phase together with the preferential crystallization of wax onto the solid crystals flowing in the slurry that act as nucleation sites.6,7 The process of deposit formation from waxy mixtures or crude oils is complex, and it may involve several processes and considerations, such as crystallization kinetics, mass transfer, heat transfer, fluid dynamics, rheology, solid−liquid multiphase equilibria, and thermophysical and transport properties. A number of mechanisms have been suggested for explaining the process of wax deposition and for estimating the amount of deposition that will occur in a system under a particular set of operating conditions. Of these, molecular diffusion and heat transfer are currently regarded as the most relevant mechanisms. The molecular diffusion mechanism8−12 is based on the assumption that a radial temperature gradient is created when oil flows in a pipeline with the pipeline wall temperature lower than the WAT of the oil, which gives rise to a concentration gradient that causes the diffusion of wax from the region of higher concentration within the bulk, toward the wall where the concentration of dissolved wax is lower. In the underlying pseudo-steady-state mathematical model, the amount of deposit is obtained from the rate of mass transfer

INTRODUCTION The precipitation and deposition of wax is of significant importance in the production, transportation, and processing of crude oil because wax deposition can damage oil reservoir formations and wells, and cause blockage of pipelines and process equipment. The deposition of wax in pipelines and process equipment leads to increased pressure drop, increased pumping power requirements, and/or reduction in efficiency. Wax deposition problems are more severe in cold environments, most notably in subsea conditions, where temperatures at the bottom of the ocean can reach 4 °C.1 With deepwater oil recovery becoming increasingly more prevalent, the fraction of offshore wells at depths greater than 500 m has been noted to increase from 55% in 2007 to 67% in 2012. 2 Such developments imply that the crude oil is transported over greater distances and that the exposure to low temperatures is increased. Problems associated with wax precipitation and deposition are expected to become worse and so is the cost of its control and remediation. In an extreme case, repeated wax deposition problems forced an oil platform to be abandoned at a cost of $100 million.3 Crude oils are complex mixtures of different hydrocarbons, including high molecular weight alkanes (waxes). “Waxy” crude oils, in particular, contain significant proportions of heavy paraffins (alkanes). High molecular weight n-alkanes or waxes tend to crystallize and deposit on cooler surfaces because they are less soluble in the crude oil at lower temperatures. The temperature at which the first wax crystals start to appear in the crude oil during cooling is commonly referred to as the wax appearance temperature (WAT) or the cloud point temperature (CPT). Wax-related problems are typically dealt with by using mechanical, thermal, chemical, and/or any combination of these methods.4 Other methods, such as bacterial and electromagnetic treatments, have also been tried with limited © 2013 American Chemical Society

Special Issue: 13th International Conference on Petroleum Phase Behavior and Fouling Received: November 21, 2012 Revised: March 14, 2013 Published: March 15, 2013 1914

dx.doi.org/10.1021/ef301897d | Energy Fuels 2013, 27, 1914−1925

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degree of gelation, resulting from decreased shear stress. Sarica and Volk36 used the Tulsa loop to study two-phase wax deposition in both horizontal and vertical pipes. They concluded that wax deposition is a flow-pattern-dependent phenomenon, with annular flows producing the thickest deposits in horizontal flow tests. In vertical flow tests, they reported that an increase in the oil superficial velocity results in thinner deposits. This study extends the single-phase laminar13,14 and turbulent flow17,18 deposition studies from our laboratory into the two-phase regime. A bench-scale flow-loop apparatus was developed for two-phase flow. A design of experiments was implemented to study the deposition of solids from prepared multicomponent waxy mixtures of defined composition. The experimental program investigated the effects of water content, waxy mixture temperature (above the WAT), coolant temperature (below the WAT), and Reynolds number (or shear rate). Because all experiments were performed with the wax mixture temperature held above the corresponding WAT, the liquid phase did not contain any solid phase; that is, all of the experiments were performed under the “hot flow” conditions. The results of this study provide further confirmation that the deposition process is predominantly a thermally driven process.

at the liquid−deposit interface, and an energy balance is used to back-calculate the liquid−deposit interface temperature (denoted here by Td). An inherent assumption in the molecular diffusion modeling approach is that the deposit−liquid interface temperature is variable, which is predicted to increase with deposit growth from an initial value close to the pipe-wall temperature and ultimately to the WAT at steady state. In the heat-transfer mechanism,13−18 the deposit formation and growth is taken to be a (partial) solidification or freezing process involving crystallization. The rate of heat transfer through the deposit layer is dependent on the thermal driving force between the bulk “waxy” oil or mixture temperature and the cooler pipe-wall temperature. The overall rate of heat transfer is influenced by the convective (from the flowing crude oil and surroundings) and the conductive (from the pipe wall and deposit layer) thermal resistances in series. Mathematical models have been developed based on the moving boundary problem formulation for heat transfer associated with phase transformation.19−24 In the models based on this heat-transfer approach, involving (partial) freezing or solidification, the release of the latent heat of phase change accompanies the growth of a wax deposit layer close to the pipe wall, which is held at a temperature lower than the WAT of the flowing “waxy” crude oil. An assumption made in the heat-transfer mechanism is that the liquid−deposit interface temperature is equal to the WAT of the crude oil, or waxy mixture, throughout the deposition process. This assumption has been confirmed through measurements involving batch cooling experiments under static and sheared conditions.25,26 It is pointed out that the heat-transfer-based deposition mechanism is able to explain solids deposition under both “hot flow” (Th > WAT) and “cold flow” (Th < WAT) conditions.7,27 Most wax deposition studies reported in the literature have focused on single-phase oil and two-phase oil−gas flow. However, water is inevitably found in the produced oil and its fraction in the oil stream, called the water-cut, generally increases with the lifetime of a production well. Relatively few studies have been conducted to study the effects of water on the deposition process.28−32 A literature review showed that the wax deposition process is not well-established for two-phase oil−water flow conditions, perhaps due to the increased complexity caused by the addition of the water phase and the difficulty in obtaining consistent results with oil−water mixtures.29 The presence of water has been reported to decrease the amount of wax deposited, especially on a water-wet surface.33 Using a cold-finger experimental apparatus, a few studies have reported a decrease in the amount of solids deposition with increasing water cut for a two-phase oil−water deposition process.28,29,31,32 The same trend was also reported by Bruno et al.,30 who used a flow-loop experimental setup. They stated that the increase in water cut diminishes the flow path of dissolved wax due to a higher concentration of water droplets. Couto et al.29 observed no difference in the amount of wax deposited when salt water was used instead of fresh water. Gao34 conducted oil/water two-phase wax deposition experiments with different water cuts in a 1.5 in. flow loop and found that the wax deposition rate in the oil/water two-phase flow was higher than that in single-phase flow. More recently, Hoffmann et al.35 performed two-phase, stratified oil/water flow-loop experiments and reported a higher deposit mass per unit area at a lower total flow rate. They also reported higher deposit thicknesses at higher water cuts and attributed this to a higher

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HEAT-TRANSFER CONSIDERATIONS In the steady-state heat-transfer model used in this study, the “hot” waxy mixture (comprising wax, solvent, and water), held at a temperature higher than its WAT (Th > WAT) and flowing through a tube, is cooled by a coolant, held at a temperature below its WAT (Tc < WAT) and flowing through an annular region. Heat transfer from the waxy mixture to the coolant results in a radial temperature gradient, which leads to the formation of a deposit layer, provided the inside tube-wall temperature, Twi, is less than the WAT. The rate of heat transfer is decreased because of the additional thermal resistance offered by the deposit layer. The deposit layer continues to grow in thickness until a thermal steady state is attained, when all thermal resistances become constant. At thermal steady state, the rate of heat transfer across the waxy mixture, the deposit layer, the tube wall, and the coolant will be equal. Figure 1 shows the temperature profile during wax deposition. For the double-pipe heat exchanger configuration, used cocurrently in the flow-loop apparatus, the rate of heat transfer at steady state is equal to the rate of thermal energy

Figure 1. Temperature profile during wax deposition. 1915


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released by the waxy mixture and the rate of thermal energy accepted by the coolant, as follows: q = ṁ h C h(Thi − Tho) = ṁcCc(Tco − Tci) − qgain ⎡ ⎤ ⎢ (Thi − Tci) − (Tho − Tco) ⎥ = UA ⎥ i i⎢ ⎡ (T − T ) ⎤ ⎢ ⎥ ln⎣⎢ (Thi − Tci ) ⎦⎥ ⎣ ⎦ ho co

(1)

The term qgain accounts for the rate of thermal energy gained by the coolant from the ambient. The combined thermal resistance can be expressed as a sum of four individual thermal resistances in series,7,13,14,17,18 that is, ln(ro/ri) ln(ri /(ri − xd)) 1 1 = + + UA 2π (ri − xd)Lhh 2πk mL 2πkdL i i 1 + 2πroLhc (2)

where Rh = [2π(ri − xd)Lhh]−1, Rd = [(2πLkd)/ln{ri/(ri − xd)}]−1, Rm = [(2πLkm)/ln{ro/ri}]−1, and Rc = [2πroLhc]−1. Next, the following equalities are obtained by equating the heat flux through each of the four thermal resistances included in Ui

Figure 2. Predicted effect of deposit-layer thickness (xd) on the rate of heat transfer (q) and the inside tube-wall temperature (Twi). A similar combination of wax and solvent, used in previous singlephase wax deposition studies, included the Conros Parowax and Norpar 13.17,18,26 Both waxes were similar in physical and chemical properties, and so were the solvents. Conros Parowax was supplied by Conros Corporation (Scarborough, ON, Canada), and it comprises hydrocarbons in the range of C19−C60, with a melting point range of 57−62 °C and a density (at 23 °C) of 915 kg m−3. Norpar 13 (Imperial Oil, Canada) comprises n-alkanes ranging from C9 to C16 and has a density of 754 kg m−3 at 23 °C. GC Analyses. All compositional analyses were performed using an HP6890 gas chromatograph (GC) 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 was calibrated using the ASTM D2887 Extended method, with a C5−C66 n-alkanes standard obtained from Separation Systems Inc. (Gulf Breeze, FL). The calibration standard used consisted of only n-alkanes; hence, any branched or cyclic paraffins would show as “equivalent” linear paraffins. The GC analyses indicated trace amounts ( 0.97, R2 > 0.99, and R2 = 1.0, respectively. The viscosity of the two-phase waxy mixture was estimated using the Brinkman38 correlation for the viscosity of dispersions, given in eq 7

μm = μc (1 − φd)−2.5

(7)

where μm is the viscosity of the mixture, μc is the viscosity of the continuous phase, and φd is the volume fraction of the dispersed phase. The density and specific heat capacity of the two-phase waxy mixture were estimated as weighted averages of those for the wax− solvent mixture and water. Flow-Loop Apparatus for Heat-Transfer Deposition Experiments. A bench-scale flow-loop apparatus was designed and fabricated to conduct the two-phase deposition experiments under a turbulent flow regime. Figure 5 shows a schematic diagram of the apparatus. The flow-loop apparatus consisted of a temperatureregulated cooling bath with a submersible pump for circulating the coolant water; a temperature-regulated heating bath holding a 10 L

Table 1. Values of WAT, WDT, and PPT for Waxy Mixtures at Different Wax Concentrations Conros Parowax

Bernardin Parowax

wax concentration (mass %)

WAT (°C)

WDT (°C)

PPT (°C)

WAT (°C)

2 4 6 8 10 15 20

28.0 32.0 35.0 36.0 38.0 41.0 43.0

22.0 27.0 30.0 32.0 38.0 43.0 48.0

2.0 8.0 12.0 17.0 22.0 27.0 33.0

20.0 25.0 28.0 30.0 32.0 36.0 38.0

1917


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Table 2. Constants in eqs 4, 5, and 6, Correlations for Viscosity, Density, and Specific Heat Capacity of the Solutions of Bernardin Parowax in Linpar 1416V (Applicable at Temperatures Higher than the Respective WAT) constants in viscosity correlation, eq 4

a

constants in density correlation, eq 5

constants in specific heat capacity correlation, eq 6a

wax concentration

a1

a2

b1

b2

c1

c2

0 mass % 6 mass %

−4.25 ± 0.05 −4.53 ± 0.08

1441 ± 16 1540 ± 25

774.6 ± 0.8 779.3 ± 0.3

−0.522 ± 0.017 −0.535 ± 0.007

2326 2330

1.313 1.305

Estimated.

Figure 5. Schematic of bench-scale flow-loop apparatus for turbulent flow wax deposition experiments. provide fully developed hydrodynamic flow conditions, leading into the removable deposition section. As mentioned earlier, the deposition section was a cocurrent double-pipe heat exchanger such that the coolant flowed in the annulus of the deposition section. All parts of this flow loop were insulated to minimize heat loss to the surrounding. The thermocouple data acquisition system included four thermocouples to monitor the temperatures of the waxy mixture inlet (Thi), coolant inlet (Tci), coolant outlet (Tco), and the room (Troom). The outlet temperature of the waxy mixture (Tho,) exiting the deposition section, could not be measured reliably due to the existence of a radial temperature gradient;7,17,18 hence, it was estimated from the energy balance given by eq 1. From the heat-transfer calculations, qgain was estimated to be less than 2% of the rate of heat transfer, q. The deposition took place on the inner surface of the machined aluminum tube. The air vent close to the outlet of the deposition section was used to facilitate the rapid draining of the waxy mixture at the end of each run. The coolant (water) was circulated cocurrently through the annulus of the heat exchanger at a constant rate of 0.0082 L/s. Procedure for Deposition Experiments. After assembling the flow-loop apparatus, the 10 L mixture reservoir was filled with the waxy mixture heated to about 65 °C and allowed to remain at this temperature for 1 h, while stirring continuously to ensure homogeneity and to erase any thermal history. The temperatures of the heating, cooling, and recirculating baths were set to the desired temperatures for each experiment. The deposition tube was weighed to a precision of ±0.1 mg before inserting into the wax deposition section. After attaining the desired heating bath and cooling bath temperatures, the wax−solvent pump and the temperature data acquisition system were

waxy mixture reservoir with three submersible pumps, each having a flow rate of 0.037 L/s, used to aid circulation in the bath; another temperature-regulated recirculating bath; a centrifugal pump for circulating the waxy mixture in the flow loop; a variable speed stirrer driven by air pressure; a flowmeter; calibrated T-type thermocouples; a data acquisition system; a 1 in. ID copper flow line; an air vent valve; a sample valve, a flow-regulating valve, and a deposition section. The deposition section consisted of a machined aluminum tube, 2.54 cm (i.d.) × 3.30 cm (o.d.) × 10.16 cm (long), which formed the inner tube of the double-pipe heat exchanger. The outer-tube of the heat exchanger was made of plexiglass, 3.80 cm (i.d.) × 4.60 cm (o.d.) × 10.16 cm (long). The outside surface of the plexiglass tube was insulated with 2 cm thick styrofoam insulation to minimize heat exchange (qgain) with the surroundings. To ensure that the wax−solvent−water mixture was well-mixed, the wax reservoir (28.6 cm i.d.) had four baffles, each with a width of 2.4 cm. Stirring was done with a four-blade disc turbine. The diameter of the turbine was 9.5 cm while each blade had dimensions of 2.4 cm (L) × 1.9 cm (W). The height of disc turbine was adjusted to be 0.33 times the height of the liquid in the reservoir. The wax−solvent−water mixture in the wax reservoir was stirred for about 15 min at a rate of 500 rpm at the beginning of each experiment to ensure complete dispersion of the water phase in the oil phase. The stirring was continued throughout the duration of the experiments. The temperature of the waxy mixture was maintained above the WAT of the wax mixture by placing the vessel in the temperatureregulated heating bath. The flow-regulating valve downstream of the deposition section was used to vary the waxy mixture flow rate, which was measured by the flowmeter downstream of the flow-regulating valve. The flow line downstream of the pump was sufficiently long to 1918


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turned on. The flow-regulating valve was adjusted to achieve the desired flow rate. The deposition process was commenced by circulating the coolant (water) from the refrigerated bath, through the annular side of the heat exchanger. During each deposition experiment, the readings of Troom, Thi, Tci, and Tco were recorded using a data logger connected to a computer. The waxy mixture flow rate was measured and recorded using a flow sensor in conjunction with a Florite 700 series ratemeter. After a predetermined duration, the deposition experiment was terminated by stopping the waxy mixture pump, followed by quickly draining the waxy mixture from the deposition section (by opening the air-vent valve). Note that the previous deposition studies from our laboratory have reported the likelihood of continued deposition unless the deposition tube is drained quickly.17,18 The draining process was accelerated by quickly opening the air vent after each run, as well as an upward inclination of the heat exchanger assembly. The coolant circulation was discontinued, and after draining the coolant, the deposition section was dismantled to carefully recover the aluminum tube. The tube was then weighed to a precision of ±0.1 mg. The mass of the deposition tube was subtracted from the mass of the deposition tube with deposit to obtain the deposit mass. The water content of the deposit was determined by dissolving the complete deposit in the tetrahydrofuran and titrating the solution in a C20 Coulometric KF Titrator. To avoid any significant compositional changes between experiments, each prepared batch of waxy mixtures was used for up to six deposition experiments. It was estimated that the wax depletion from the wax mixture reservoir was not more than 3.5% of the original. When dealing with two-phase liquid−liquid mixtures, it was considered important to provide sufficient agitation to ensure the homogeneity of the mixture throughout the apparatus. For the experiments with two-phase waxy mixtures, samples of the waxy mixture were taken using the sample valve located at the end of the flow loop just before the mixture exited into the reservoir. The samples of waxy mixture flowing through the deposition tube and held in the reservoir were centrifuged to measure their water contents. The water contents of the two samples were compared to confirm that the water fraction in the waxy mixture flowing through the flow loop was the same as that in the reservoir. Figure 6 presents a comparison of the water content in the waxy mixture flowing in the flow loop versus the water content of the waxy mixture held in the reservoir. For all

experiments performed, the absolute average deviation between the water contents of the two sets of samples is 3.8%. Another set of batch experiments was conducted to study the stability of the oil−water waxy mixtures by observing phase separation in the suspension, under gravity, with time. These experiments indicated that the time required for a significant extent of phase separation was in the order of minutes and much more than about 1− 2 s residence time in the flow loop. Design of Experiments. A total of 43 deposition experiments, including 6 repeat experiments, were performed in this investigation according to a factorial design of experiments summarized in Table 3. The values of Thi were (WAT + 7 °C) and (WAT + 15 °C), while the values of Tci were (WAT − 10 °C) and (WAT − 20 °C). The flow rate of waxy mixtures was varied over 0.50−1.05 L/s (corresponding to 5600 < Re < 25300), while a constant coolant flow rate of 0.0082 L/ s was used in all experiments. From the six repeated experiments, the average variability in the deposit mass was estimated to be ±4.1% for the total deposit mass (including water) and ±8.1% for the deposit mass on a water-free basis. Each deposition experiment was run for 1 h. To ensure that steady state was achieved within the 1 h duration, four extended experiments were conducted over durations of 2 and 4 h of deposition time. These “extended” experiments were performed at Re ≈ 10 000, with Th = (WAT + 7 °C) and Tc = (WAT − 10 °C). Results, shown in Figure 7, indicate that a deposition time of 1 h was sufficient to achieve a constant deposit mass. Estimation of hh and hc. To solve the four equalities in eq 3, the two heat-transfer coefficients, hh and hc, must be known. These were obtained through a series of calibration heat-transfer experiments performed with the waxy mixture and coolant held at temperatures higher than WAT, that is, Th, Tc > WAT, such that there was no deposition. These calibration experiments were performed at the same coolant rate of 0.0082 L/s (used in the deposition experiments); hence, hc was assumed to be constant. Any variations in the properties of waxy mixtures were ignored over the relatively small temperature range; thus, the assumption that hh ∝ Reα could be made. With these assumptions, eq 2 for the nondepositing calibration experiments was simplified as follows: Ui = (βRe−α + γ )−1

(8)

The calibration experiments were carried out with two waxy mixtures containing 0 and 10 vol % water, and the results were extrapolated for other compositions. The experimental Ui was obtained from eq 1. From a regression analysis with eq 8, using all of the data, α and γ were estimated to be 0.8 and 0.0003, respectively. The values of β for 0 and 10 vol % water waxy mixtures were 0.001 and 0.0007, respectively. The average relative deviations between the experimental and calculated Ui were 8.0% and 2.9% for 0 and 10 vol % water content in waxy mixtures, respectively. With γ = 0.0003 and km = 238 W m−1 K−1, hc was estimated to be 2140 W m−2 K−1. Depending on the flow rate (or Re) of waxy mixtures, hh was found to vary from 460 to 1900 W m−2 K−1. Deposit Density. The deposit density values were required for estimating the average deposit-layer thickness, xd. Using similar mixture compositions, and under similar operating conditions of temperature, flow rate, and deposition time, Fong and Mehrotra17 measured the average density of deposit samples at several temperatures below the respective WAT. The measured deposit densities for each wax−solvent mixture were fitted to a correlation relating the deposit density to Re and temperature.

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RESULTS AND DISCUSSION The results for the mass of the deposit layer from 1 h experiments performed with waxy mixtures of different water contents, flow rates (or Re), and the temperatures of the waxy mixture (hot) and coolant water (cold) streams are presented in Tables 4 and 5. The results were analyzed with eqs 1 and 3 to predict the liquid−deposit interface temperature, Td, and the average deposit thermal conductivity, kd.

Figure 6. Comparison of the water content of the waxy mixture in the reservoir with the water content of the waxy mixture flowing in the flow loop. 1919


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Table 3. Design of Experiments for Investigating Deposition from Parowax−Linpar1416 V−Water Waxy Mixtures variable wax concentration (mass %) water content (total volume basis) (vol %) inlet temperature of waxy mixture (Thi) (°C) inlet temperature of coolant (Tci) (°C) Reynolds number of waxy mixture (Re) time for deposition (h) all experiments extended experiments

number of levels

values of each variable tested

1 7 2 2 3 (plus 1 repeat)

6 0, 5, 10, 15, 20, 25, 30 WAT + 7 and WAT + 15 WAT − 10 and WAT − 20 5600 < Re < 25300

1 2

1h 2 and 4 h at Th = WAT + 7 Tc = WAT − 10, Re = 10 000

to a decrease in the convective thermal resistance, Rh, and a corresponding smaller deposit-layer thickness at higher Re. As shown in eq 1, (Tco − Tci) is directly proportional to the rate of heat transfer. Thus, an increase in the Re would yield a higher rate of heat transfer at steady state. Effect of Water Content on Deposit Mass. Figure 9 presents the results for the variation in the deposit mass with the water content in the waxy mixture. The three plots in Figure 9 show the individual effects of the waxy mixture temperature, Th, the coolant temperature, Tc, and the Reynolds number, Re. The specific effects of these parameters on the deposition process and the deposit mass are discussed in the following subsections. Effect of Th on Deposit Mass. For the two-phase wax deposition study, the effect of Th was evaluated relative to the WAT of each waxy mixture in terms of (Th − WAT). Figure 9a shows that the deposit mass increased with decreasing Th. That is, the deposit mass was observed to be higher for a lower (Th − WAT). These results are consistent with those reported previously from single-phase experiments in both laminar13,14 and turbulent17,18 flow regimes as well as the model predictions.19−22 Previous experimental investigations have established that the deposit mass is not directly related to the overall thermal driving force for heat transfer, (Th − Tc); instead, the extent of solid deposition has been shown to depend on two thermal driving forces, namely, (T h − WAT) and (WAT − Tc).7,13,14,17,18 As mentioned previously, in the thermally controlled wax deposition approach, it is assumed that Td ≈ WAT throughout the deposition process, which has been verified through batch deposition experiments under static and sheared cooling.25,26 Effect of Tc on Deposit Mass. Previous studies on singlephase wax deposition have shown that the deposit mass increases with a decrease in Tc or an increase in (WAT − Tc).7,13,14,17,18 Again, this observation has been supported by the predictions from a mathematical model based on the moving boundary problem formulation.19−22 The effect of Tc in this two-phase wax deposition study was also evaluated relative to the WAT of each waxy mixture in terms of (WAT − Tc). Figure 9b shows that the deposit mass increased with decreasing Tc. That is, the deposit mass was observed to be higher for a higher (WAT − Tc) or a lower Tc. These results are consistent with those reported previously from single-phase experiments in both laminar13,14 and turbulent17,18 flow regimes as well as the model predictions.19−22 Effect of Re on Deposit Mass. Figure 9c shows the variation of Ω with water content at three average Reynolds numbers. As shown by the three sets of results in Figure 9c, the deposit mass

Figure 7. Variation of deposit mass per unit area, Ω, with time for extended experiments.

The deposit mass per unit deposition area is denoted by Ω (in kg m−2). For the deposition experiments performed in this study, xd varied from about 0.1 mm (Ω ≈ 0.075 kg m−2) to about 0.9 mm (Ω ≈ 0.639 kg m−2). Thus, for the 2.5 cm diameter deposition tube, the relative deposit thickness, xd/ri, varied from about 0.008 to 0.068. It is noted that the depositlayer thickness values in this study are much smaller than those obtained under single-phase laminar flow,13,14 but are comparable to those from single-phase turbulent flow17,18 of similar waxy mixtures. Thermal Steady State. Deposition experiments indicated that the thermal steady state was attained within 10−20 min. The data for the gain in coolant temperature, (Tco − Tci), versus deposition time are shown in Figure 8 for the experiments at Th = (WAT + 7 °C) and Tc = (WAT − 10 °C) with 0, 10, 20, and 30 vol % water at three levels of Re. In all experiments, (Tco − Tci) was high initially but it decreased rapidly to about 1−3 °C within 10 min and the thermal steadystate was reached in less than 10−20 min. The temperature profiles in Figure 8 are similar to those reported previously for single-phase deposition studies under laminar13,14 and turbulent flow,17,18 which also showed the deposition process to be relatively fast, requiring less than 10−20 min to reach the thermal steady state in the bench-scale apparatus. The temperature profiles in Figure 8 also show that (Tco − Tci) is larger at higher Re of the waxy mixture. This is attributed 1920


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Table 4. Experimental Data for 1 h Deposition Experiments Performed at Thi = WAT + 7 °C (WAT = 28 °C) coolant temperature Tci (°C)

water content (vol %)

Re

total deposit mass/area (kg/m2)

deposit water content (mass %)

water-free deposit mass/area (kg/m2)

estimated Td (°C)

WAT − 10

0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 10 20 30

12 500 11 300 9970 8850 7610 6550 5590 18 900 16 800 15 300 13 000 11 600 9840 8620 25 300 22 400 20 100 17 600 15 400 12 800 11 500 13 000 10 300 7980 5810

0.310 0.327 0.413 0.307 0.317 0.335 0.331 0.263 0.253 0.371 0.262 0.293 0.262 0.350 0.208 0.171 0.281 0.211 0.228 0.212 0.314 0.557 0.646 0.558 0.537

0.0 0.6 6.6 2.8 0.0 13.5 0.4 0.0 1.1 8.2 3.9 0.1 9.9 15.3 0.0 0.1 13.6 6.5 13.3 12.2 15.8 0.0 1.1 0.4 6.7

0.310 0.325 0.386 0.298 0.317 0.290 0.330 0.263 0.250 0.340 0.251 0.292 0.236 0.296 0.208 0.171 0.243 0.197 0.198 0.186 0.265 0.557 0.639 0.555 0.501

26.5 27.2 26.4 27.4 27.6 29.1 30.1 26.8 27.4 28.1 28.7 28.1 28.7 30.0 26.9 26.7 28.0 28.8 28.1 29.7 30.4 27.1 26.9 26.0 29.6

WAT − 10

WAT − 10

WAT − 20

Table 5. Experimental Data for 1 h Deposition Experiments Performed at Thi = WAT + 15 °C (WAT = 28 °C) coolant temperature Tci (°C)

water content (vol %)

Re

total deposit mass/area (kg/m2)

deposit water content (mass %)

water-free deposit mass/area (kg/m2)

estimated Td (°C)

WAT − 10

0 10 20 30 0 10 20 30

22 600 18 000 13 900 10 300 23 400 18 300 14 100 10 500

0.131 0.100 0.146 0.232 0.351 0.322 0.249 0.363

0.0 24.9 4.3 14.5 0.0 8.2 5.1 10.6

0.131 0.075 0.139 0.199 0.351 0.296 0.237 0.324

27.9 30.2 30.8 34.9 26.2 29.4 26.3 32.9

WAT − 20

waxy mixture increases Ω/Ωo at 10 and 30 vol % water content. It also shows the variation of the average values of Ω/Ωo (at all three Re values) with water content. Figure 11 shows a scatter plot of the variation of the measured water content in the deposit with the water concentration in the waxy mixture. The water content in the deposit is observed to be consistently lower than that in the waxy mixture; however, a trend or correlation between the two quantities is not observed. That is, there does not appear to be a relationship between the water content in the deposit and the water concentration in the waxy mixture. As shown in Figure 11, the water content of several deposit samples was measured to be close to 0 vol %. It is, therefore, likely that the measured water content of the deposit may not be related to the deposition process but it might represent “wetness” of the deposit surface. The scatter plot in Figure 12 shows the variation of the measured deposit water content with Re, where no trend is observed between these two quantities. Since the deposit mass is known to decrease with an increase in Re, the results in Figure 12 offer further confirmation that the measured water

per unit area, Ω, decreases with an increase in Re. This is because an increase in Re causes an increase in hh (and a corresponding decrease in the convective thermal resistance, Rh). For the same Th and Tc, a lower Rh implies that the deposit thermal resistance, Rd, would also decrease, which implies a decrease in the deposit-layer thickness, xd, and, consequently, a lower deposit mass or Ω. The overall effect of these changes is that the rate of heat transfer is higher at higher Re due to a lower convective thermal resistance, Rh, as well as a lower conductive thermal resistance, Rd, offered by the deposit layer.13,14,17,18 For the hot and cold stream temperatures of (WAT + 7) and (WAT − 10), respectively, Ω increased as the water content increased from 0 vol %, reaching a peak at 10 vol % water content. As the water content in the waxy mixture increased further, Ω decreased and remained almost constant until the water content reached 30 vol %, when another increase was observed. This same trend was noted for all three average Re. Figure 10 is a plot of the ratio (Ω/Ωo), which relates the deposit masses obtained from waxy mixtures with water and without water. It shows that increasing the water content in the 1921


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Figure 9. Variation in the deposit mass at different water contents: (a) effect of waxy mixture temperature, Th, (b) effect of coolant temperature, Tc, and (c) effect of Reynolds number, Re. Figure 8. Approach to thermal steady state during deposition for 1 h experiments, at Th = (WAT + 7 °C) and Tc = (WAT − 10 °C), for waxy mixtures with 0, 10, 20, and 30 vol % water content.

content of the deposit may not be related to the deposition process. Figure 13 shows a scatter plot for the variation of Ω with Re for all deposition experiments at Th = (WAT + 7 °C) and Tc = (WAT − 10 °C). The results indicate that the deposit mass decreases with an increase in Re; a similar trend has been reported previously from single-phase deposition experiments under both laminar3,7,13,14 and turbulent flow conditions.17,18 Estimation of Td and kd. The four heat-flux equalities in eq 3 were solved to obtain Twi, Two, Td, and kd. From the steadystate data of each experimental run, the measured Tc was used to estimate Two, which was then used to estimate Twi. The measured Th was then used to estimate Td, which was, in turn, used to estimate the average thermal conductivity of the deposit, kd. The ratio ri/(ri − xd) in the first two equalities of eq 3 can be written as (1 − xd/ri)−1. When xd/ri ≪ 1, Td estimated from the first equality of eq 3 is less sensitive to xd. The heat flux through the deposit layer, described by the second equality in eq 3, contains Td, kd, and xd, which makes the calculated kd

Figure 10. Effect of the water content in waxy mixtures on the deposit mass per unit area, Ω. 1922


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Figure 13. Variation of water-free deposit mass per unit area, Ω, with Reynolds number, Re, for all deposition experiments at Th = (WAT + 7 °C) and Tc = (WAT − 10 °C).

Figure 11. Comparison of the water content of the deposit to the water content of the waxy mixture.

deviation, indicated by ±0.13 W m−1 K−1, in the calculated average kd, can be attributed partly to the variations in Re, which resulted from changes in the viscosity of waxy mixtures because of the addition of water. The results did not show any trend between the deposit water content and the estimated deposit thermal conductivity.

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CONCLUSIONS Bench-scale, flow-loop experiments were carried out to investigate solids deposition from two-phase wax−solvent− water mixtures under turbulent flow conditions. The deposition experiments were performed with a wax concentration of 6 mass %, with seven water fractions of 0, 5, 10, 15, 20, 25, and 30 vol % (total volume basis), at three levels of Reynolds number, two levels of waxy mixture temperature, and two levels of coolant temperature. Extended experiments, lasting up to 4 h, were performed to ascertain that steady state was achieved within the 1 h duration of the deposition experiments. The deposition data were analyzed with a steady-state heat-transfer model, which indicated the deposition process to be predominantly thermally driven. Similar to the previous single-phase deposition experimental studies under laminar and turbulent flow, the deposition process in the two-phase experiments under turbulent flow was found to be relatively fast, attaining a thermal steady state in less than 10−20 min. It was observed that, as the water content of the waxy mixture was increased from 0 vol %, the mass of the deposited solid increased, with a maximum at 10 vol % water content. As the water content in the mixture increased further, Ω decreased and remained fairly constant thereafter. A decrease in the temperature of both the waxy mixture and the coolant, relative to the WAT, resulted in an increase in the mass of deposited solid, while increasing the flow rate of the waxy mixture resulted in a decrease in the mass of deposited solid. The liquid−deposit interface temperature, Td, for all experiments was found to be approximately equal to the experimentally measured WAT. The average deposit thermal conductivity was estimated to be 0.38 W m−1 K−1. Overall, the results of this study confirm the solids

Figure 12. Variation of the water content of deposit with Reynolds number, Re.

more sensitive to xd. This is because, even though the term (1 − xd/ri) remained close to 1 for most experiments, the term −ln(1 − xd/ri) in the second equality in eq 3 varied with xd/ri. Thus, a small experimental uncertainty in xd caused a relatively larger variation in the estimated kd than in Td. Using the heat-transfer calculations for all 1 h deposition experiments, the calculated Td was found to be 28.5 ± 2.0 °C, which compares very well with the experimentally measured WAT of 28.0 °C. Note that Bidmus and Mehrotra25,26 also reported an experimentally measured liquid−deposit interface temperature to be approximately equal to the WAT of waxy mixtures. The average deposit thermal conductivity, kd, was calculated to be 0.38 ± 0.13 W m−1 K−1, which compares well with those reported for single-phase deposition experiments under turbulent flow.17,18 The relatively high standard 1923


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Two = temperature at the outside tube surface (°C) Ui = overall heat-transfer coefficient based on inside tube surface area (W m−2 K−1) xd = deposit layer thickness (m)

deposition from waxy mixtures to be primarily a thermal process that can be explained by heat-transfer considerations.

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AUTHOR INFORMATION

Greek Letters

Corresponding Author

α, β, γ = empirical constants in eq 8 εf = volume fraction of water in waxy mixture flowing through the flow loop εr = volume fraction of water in waxy mixture in the reservoir μ = viscosity of waxy mixture (Pa s) μc = viscosity of continuous phase (waxy mixture) (Pa s) μm = blend viscosity of waxy mixture (Pa s) ρ = density of waxy mixture (kg m−3) φd = volume fraction of dispersed (water) phase Ω = mass of deposit per unit deposition surface area (kg m−2) Ωο = mass of deposit per unit deposition surface area at 0 % water content (kg m−2)

*Phone: (403) 220−7406. Fax: (403) 284−4852. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Department of Chemical and Petroleum Engineering, the University of Calgary, is gratefully acknowledged. We thank Dr. Hamid Bidmus, Mr. Nelson Fong, and Mr. Sridhar Arumugam for their valuable input and discussions. We also thank Mr. Jean-Mark Labonté for the technical support.

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Acronyms

NOMENCLATURE a1, a2, b1, b2, c1, c2 = regression constants in eqs 4, 5, and 6 Ai = inside surface area of tube or deposition surface area (m2) Cc = average specific heat capacity of coolant (J kg−1 K−1) Ch = average specific heat capacity of waxy mixture (J kg−1 K−1) hc = heat-transfer coefficient for coolant (W m−2 K−1) hh = heat-transfer coefficient for waxy mixture (W m−2 K−1) kd = average thermal conductivity of deposit (W m−1 K−1) km = average thermal conductivity of aluminum tube wall (W m−1 K−1) L = length of aluminum tube, m ṁ c = mass rate of coolant (kg s−1) ṁ h = mass rate of waxy mixture (kg s−1) q = rate of heat transfer at steady state (W) qo = initial rate of heat transfer without deposition (i.e., at xd = 0) (W) qgain = rate of heat gain by the coolant from the surroundings, < 0.02 q (W) R2 = coefficient of determination Rc = thermal resistance of coolant (K W−1) Rd = thermal resistance of deposit layer (K W−1) Rh = thermal resistance of waxy mixture (K W−1) Rm = thermal resistance of aluminum tube wall (K W−1) ri = inside tube radius (m) ro = outside tube radius (m) Re = Reynolds number rpm = rotations per minute T = temperature (°C) Tc = average temperature of coolant ≡ 0.5(Tci + Tco) (°C) Tci = inlet temperature of coolant (°C) Tco = outlet temperature of coolant (°C) Td = average temperature at the interface of deposit and waxy mixture (°C) Th = average temperature of waxy mixture ≡ 0.5(Thi + Tho) (°C) Thi = inlet temperature of waxy mixture (°C) Tho = outlet temperature of waxy mixture (°C) Troom = ambient or room temperature (°C) Twi = temperature at the inside tube surface (°C) (Twi)o = temperature at the inside tube surface without deposition (i.e., at xd = 0) (°C)

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GC = gas chromatograph WAT = wax appearance temperature (°C) WDT = wax disappearance temperature (°C) PPT = pour point temperature (°C)

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