Energy Fuels 2010, 24, 4396–4401 Published on Web 07/21/2010
: DOI:10.1021/ef100617p
Study of Asphaltene and Metal Upgrading in the Vapor Extraction (VAPEX) Process Kobra Pourabdollah,† Abdolsamad Zarringhalam Moghadam,*,† Riyaz Kharrat,‡ and Bahram Mokhtari§ †
Chemical Engineering Faculty, Tarbiat Modares University, Tehran, Iran, ‡Petroleum University of Technology Research Center, Tehran, Iran, and §Lavan Engineering Department, Iranian Offshore Oil Company, Tehran, Iran Received May 18, 2010. Revised Manuscript Received July 6, 2010
The effect of the vapor dew point and matrix permeability on the movement of deposited streaks in the vapor extraction (VAPEX) process was investigated. Furthermore, the distribution of residual hydrocarbons, asphaltenes, resins, and metal chelate in the VAPEX cell was determined. Finally, the pattern of viscosity distribution in the VAPAX cell was calculated using a Computer Modelling Group (CMG) simulator. The experiments were conducted in sand packed on the Iranian bitumen by propane solvent. Asphaltene, resin, and vanadium chelate were measured in residual hydrocarbon of swept zone via American Society for Testing and Materials (ASTM) D6560 and D1548 test methods. The results demonstrated that in vapor dew point and high permeable matrices, precipitated streaks moved faster than other conditions. Distributions of asphaltene, resin, and vanadium chelate showed a reduction in their facial concentration from the vapor injection port to the oil production port, while the distribution of dissolved vanadium chelate in asphaltene and resin precipitated following a reverse pattern. Moreover, there was a good agreement between the Gillespie equation and experimental data, in which the colloidal volume fraction was divided into volume fractions of asphaltenes, resins, and metal chelates.
heavy oil because this may cause higher solvent consumption, which results in higher oil production cost.4 VAPEX applicability for light crude oils also has been investigated by Kok et al.5 They used different solvents, compared their effects, and proposed a new mechanism, including both gravity drainage and solvent pushing. Abu-Khader and Speight defined the asphaltene constituents as a solubility class that was precipitated from petroleum, heavy oil, and bitumen by the addition of an excess of liquid paraffin hydrocarbon.6 Mousavi-Dehghani et al. reported many factors affecting the asphaltene precipitation inside a reservoir.7 Priyanto et al. discussed that a number of investigators have constructed model structures for asphaltenes, resins, and other heavy fractions based on physical and chemical methods8 but not for the movement of their streaks and distribution in VAPEX. Marques et al. revealed that the aggregation state of asphaltene macromolecules depends upon the experimental conditions, such as concentration, temperature, and solvent.9 The importance of asphaltene determination in crude oil led to the innovation of some new analytical methods.10 Das and Butler11 and Kok et al.12 analyzed the asphaltene deposition by the VAPEX process in a Hele-Shaw cell, while
1. Introduction The resources of heavy oil in the world are more than twice that of conventional light crude oil. Saniere et al. illustrated that, from the available heavy oil, only a fraction is extracted by conventional methods.1 A large amount of heavy oil is still trapped in reservoirs after the traditional oil extraction; thus, a number of enhanced heavy oil recovery processes have been developed for extracting the residual heavy oil.2 Enhanced heavy oil recovery processes are mainly either thermal or nonthermal. In thermal methods [cyclic steam stimulation (CSS), in situ combustion (ISC), steam-assisted gravity drainage (SAGD)], the viscosity is reduced by heating the reservoir and their problems are the heated loss to adjacent formations. Therefore, non-thermal methods, including vapor extraction (VAPEX) and gas-assisted gravity drainage (GAGD), are preferred.3 In the VAPEX process, the viscosity of heavy oil is reduced by dilution. The hydrocarbon is injected into the reservoir via injection wells, and the solvent diluted oil is drained by gravity to production wells. One criterion that should be considered in solvent selecting is that it should be at or near to its dew point to avoid any liquefaction of the solvent before it dissolves into *To whom correspondence should be addressed. E-mail: zarrin@ modares.ac.ir. (1) Saniere, A.; Henaut, I.; Argillier, J. F. Oil Gas Sci. Technol. 2004, 59, 455–466. (2) Karoussi, O. L.; Skovbjerg, L.; Hassenkam, T.; Svane Stipp, S. L.; Hamouda, A. A. Colloids Surf., A 2008, 325, 107–122. (3) Rostami, B.; Etminan, S. R.; Soleymani, A.; Kharrat, R. Effect of capillary and surface tension on the performance of VAPEX process. Proceedings of the 8th Canadian International Petroleum Conference (CIPC); Calgary, Alberta, Canada, 2007; Paper 2007-039. (4) Rahnema, S.; Ghaderi, M.; Farahani, S. Simulation of VAPEX process in problematic reservoirs: A promising tool along with experimental study. Proceedings of the Society of Petroleum Engineers (SPE)/ European Association of Geoscientists and Engineers (EAGE) Reservoir Characterization and Simulation Conference; Abu Dhabi, United Arab Emirates, Oct 2007; SPE 111367. r 2010 American Chemical Society
(5) Kok, M. V.; Yildirim, Y.; Akin, S. Energy Sources, Part A 2008, 30, 20–26. (6) Abu-Khader, M. M.; Speight, J. G. Oil Gas Sci. Technol. 2007, 62, 715–722. (7) Mousavi-Dehghani, S. A.; Vafaie-Sefti, M.; Mirzayi, B.; Fasih, M. Iran. J. Chem. Chem. Eng. 2007, 26 (4), 39–48. (8) Priyanto, S.; Mansoori, G. A.; Suwono, A. J. Chem. Eng. Sci. 2001, 56, 6933–6939. (9) Marques, J.; Merdrignac, I.; Baudot, A.; Barre, L.; Guillaume, D.; Espinat, D.; Brunet, S. Oil Gas Sci. Technol. 2008, 63, 139–149. (10) Rogel, E.; Ovalles, C.; Moir, M. E. Energy Fuels 2009, 23 (9), 4515–4521. (11) Das, S. K.; Butler, R. M. J. Can. Pet. Technol. 1994, 33, 39–45. (12) Kok, M. V.; Yildirim, Y.; Akin, S. Energy Sources, Part A 2009, 31, 377–386.
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: DOI:10.1021/ef100617p
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this work has been studied in a sand-packed cell, with their movement and distribution. Fisher et al. conducted the VAPEX studies using magnetic resonance imaging and revealed that, within the solvent-oil mixing regions, asphaltene precipitated and eventually deposited on the solid surfaces13,14 but the behavior of precipitated asphaltene (streaks), such as their movement and distribution, was not investigated. Vanadium and other metals, such as nickel and iron, are also present in crude oils mainly in the form of porphyrinic and asphaltenic complexes up to 1200 ppm and have a deleterious effect on the refinery operations. Wang et al. discussed the effect of the microwave on removing vanadium from Iranian and Shengli crude oil.15 The importance of vanadium measurement in crude oil led to the creation of some new analytical methods. Lanjwani et al.16 and Olajire and Oderinde17 proposed two methods for vanadium determination in crude oils using high-performance liquid chromatography (HPLC) and dispersive X-ray fluorescence spectroscopy, respectively. Einstein proposed that the viscosity of suspensions only depends upon the volume of the particles and not their size.18 Graham, Gillespie, Potanin, and Escobedo and Mansoori attempted to relate the viscosity of colloidal suspensions to the dispersed particles via numerous theoretical and experimental studies.19-23 Nghiem et al. presented a dynamic model for asphaltene precipitation using an equation of state (EOS) in the VAPEX process, which was run by carbon dioxide. Their model was in agreement with experimental data. However, their model was not based on the viscosity, and they also did not consider the effect of resins in precipitation.24 In another study, Nghiem et al. used a pure solid model for modeling the asphaltene and resin precipitation, including the formation of the second solid through a chemical reaction. However, the ratio of asphaltene, resin, and metal chelate was not determined, separately, and there was no matching to experimental data.25
Figure 1. Flow diagram of the experimental setup, schematically. Table 1. Characteristics of Bitumen in Experiments property or composition
value
N2 CO2 C1 C2 C3 C4-C5 C6-C11 C12þ MW of C12þ specific gravity of C12þ (60/60) asphaltene content resin content viscosity at 60 °C
0.66 mol % 0.23 mol % 10.35 mol % 2.35 mol % 1.95 mol % 11.5 mol % 15.11 mol % 57.86 mol % 485 mol % 1.0473 mol % 24.1 wt % 2.4 wt % 20.229 Pa s
In the first part of this study, the movement of asphalteneprecipitated streaks toward the production well was determined as a function of mixing zone dispersion. This term as a main source of formation damage changes the reservoir wettability. Then, the distribution and upgrading of asphaltene, resin, and metal chelate were measured. Furthermore, using the Computer Modelling Group (CMG) simulator, the pattern of viscosity distribution in the VAPEX cell was calculated. Finally, upgrading of asphaltene, resin, and metal chelate was modeled using a correlation of Gillespie’s equation.
(13) Fisher, D. B.; Singhal, A. K.; Goldman, J.; Jackson, C.; Randall, L. Insight from MRI and micro-model studies of transport of solvent into heavy oil during VAPEX. Society of Petroleum Engineers (SPE) International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference; Calgary, Alberta, Canada, Nov 4-7, 2002; SPE 79024. (14) Fisher, D. B.; Singhal, A. K.; Das, S. K. Use of magnetic resonance imaging and advanced image analysis as a tool to extract information from a 2D physical model of the VAPEX process. Proceedings of the Society of Petroleum Engineers (SPE)/Department of Energy (DOE) Improved Oil Recovery Symposium; Tulsa, OK, April 3-5, 2000; SPE 59300. (15) Wang, S.; Yang, J.; Xu, X.; Gao, J. Pet. Sci. Technol. 2009, 27, 368–378. (16) Lanjwani, S. N.; Mahar, K. P.; Channer, A. H. Chromatographia 1996, 43, 431–432. (17) Olajire, A. A.; Oderinde, R. A. Jap. Bull. Chem. Soc. 1993, 66, 630–632. (18) Einstein, A. Investigation on the Theory of Brownian Movement; Dover: New York, 1956. (19) Graham, A. L. Appl. Sci. Res. 1981, 37, 275–286. (20) Gillespie, T. J. Colloid Interface Sci. 1983, 94 (1), 166–173. (21) Potanin, A. A. J. Colloid Interface Sci. 1991, 145, 140–157. (22) Potanin, A. A. J. Colloid Interface Sci. 1993, 157, 399–410. (23) Escobedo, J.; Mansoori, G. A. Theory of viscosity as a criterion for determination of onset of asphaltene flocculation. SPE Tech. Pap. 28729, 1996. (24) Nghiem, L. X.; Kohse, B. F.; Farouq Ali, S. M.; Doan, Q. Asphaltene precipitation: Phase behaviour modelling and compositional simulation; Proceedings of the 2000 Society of Petroleum Engineers (SPE) Asia Pacific Conference on Integrated Modeling for Asset Management; Yokohama, Japan, April 2000; SPE 59432. (25) Nghiem, L. X.; Sammon, P. H.; Kohse, B. F. Modeling asphaltene precipitation and dispersive mixing in the VAPEX process. Proceedings of the Society of Petroleum Engineers (SPE) Reservoir Simulation Symposium; Houston, TX, Feb 2001; SPE 66361.
2. Experimental Section 2.1. Materials and Tools. The flow diagram of the experimental setup is schematically illustrated in Figure 1. The VAPEX cell was a three-dimentional rectangular visual model as a symbol of the reservoir cross-section, with 673 153 31 mm dimensions and 3300 cm3 volume, containing 5, 3, and 2 ports at the bottom, top, and on both sides, respectively. This model represents a thin slice of the reservoir (two-dimensional rectangle) that is perpendicular to the horizontal well pair. A Plexiglas window allows one to monitor the shape of the swept zone. The tested bitumen was sampled from the Sarvak formation of the Kuh-e-Mond reservoir in the south of Iran, and Table 1 shows its composition. Pure propane was used as the vapor solvent. Dichloromethane, heptane, and toluene were purchased from Merk Company and were analytical-grade. The range of the diameter, permeability, and porosity of the glass beads were 150-212 μm, 15-18 darcy, and 35-35.2%, respectively. 2.2. Experimental Procedure. The mass flow meter was calibrated using nitrogen gas/gas accumulator vessel, and the system was examined for the leakage by nitrogen gas at 150 psi 4397
Energy Fuels 2010, 24, 4396–4401
: DOI:10.1021/ef100617p
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Figure 3. Streaking effect but not mixing zone in the chamber valley.
Figure 2. Chamber valley presents streaking effect and mixing zone.
This trend leads to the increase the mass-transfer resistance and decrease of solvent diffusion gradually. The reduction of viscosity and production rate is prevented sequentially. When the solvent is in the vapor phase, for the sake of a high diffusion coefficient, the mass transfer is promoted and the boundary layer thickness is reduced; hence, the mixing zone was not formed. In this condition, the trend of oil dilution and productivity is improved. As presented in Figure 2, when the reduction of viscosity was prevented, the drained flow of lived oil decreases and precipitated streaks remain on the surface of glass beads irregularly. However, in reference to Figure 3, when the viscosity reduction was promoted, the precipitated streaks flow in the direction of lived oil toward the production well in a parallel pattern. 3.2. Effect of the Matrix Permeability on Asphaltene Streaks and Mixing Zone. Figure 4 shows the photographs of the model during two VAPEX experiments conducted in low and high permeability matrices. The diameter of glass beads in the experiments was 150-212 μm (15-18 darcy) and 212-300 μm (25-30 darcy), respectively. According to Figure 4a, in a low-permeable matrix, precipitated streaks remain in the swept zone, while Figure 4b shows no streaks in higher permeability. In a low-permeable matrix, according to Darcy’s law, the lived oil flow decreases and, therefore, precipitated streaks remain in the pore volume. However, in high-permeable matrices, streaks are drained to a separator without plugging the porous media and formation damage. 3.3. Distribution of Asphaltene, Resin, and Heavy Metal Chelate in the VAPEX Cell. Figure 5 represents the analytical data for residual hydrocarbon in the matrices of the VAPEX cell. According to this figure, fewer hydrocarbons remain in the swept zone than in the bitumen zone. Also, the remaining hydrocarbons in the swept zone do not distribute uniformly. In the central regions of this zone, the recovery is considerably more, while the hydrocarbon precipitation on both sides and around the production well is more than that in the center. The reason for the high precipitation of hydrocarbon on both sides of the swept zone refers to the low slope of the bitumen-solvent interface. Therefore, the gravity drainage of lived oil film reduces. Figure 6 illustrates the asphaltene distribution in the experimental cell. It can be clearly seen that the content of residual asphaltene in the swept zone is more than that in the bitumen chamber. Furthermore, the asphaltene distribution is not uniform in the swept zone. Its concentration around the injection well is maximal, while its concentration around the production well and both sides is minimal. Around the injection well, the concentration gradient between the solvent
pressure to pack the cell. The cell was depressurized, and the cavity of the model was packed uniformly with glass beads by shaking the model. Subsequently, the sand-packed model was saturated with preheated bitumen at 80 °C for 12 h and was allowed to cool (to room temperature). The separator was pressurized by nitrogen gas at 100 psi. Afterward, propane (or propane mixtures) was injected to the injection well at the top of the model. The flow rate of injected gas was measured using a calibrated mass flow meter, while the ambient temperature was set and kept at 22 ((0.5) °C. The amount of lived oil accumulated was monitored through the separator by a calibrated graduated site glass. While the oil samples were being obtained, most of the solution gas was liberated because of pressure reduction and was directed to the solution gas accumulator vessel. After the sample was collected, the rate of free gas production controlled by a needle valve was 11 cm3/min. The experiments were run continuously for about 72 h. After the test run, the systems were depressurized and the glass beads were sampled from both gas and bitumen chambers. Samples were taken from 35 locations on the model by a test tube. Two analyses were carried out on each sample, including asphaltene/resin and vanadium determinations. The samples were weighed by a calibrated Mettler Toledo (AB204-S/FACT) digital balance and were placed into a Lindberg furnace (Sola Basic) for about 4 h at 600 °C to eliminate residual bitumen. After the glass beads were cooled, they were weighed again, and the weight loss was measured for each sample. The weight loss represented the crude distribution in different points of both chambers. The resin/asphaltene and vanadium were determined at the samples from the 35 locations via standard test methods of American Society for Testing and Materials (ASTM) D6560 (or IP-143) and ASTM D1548, respectively. For each test, three measurements were performed and relative standard deviations (RSDs) were calculated to be less than 3%.
3. Results and Discussion The results are based on the mixing zone, which is the area located at the interface of bitumen and the gas chamber, and two parts of the VAPEX interface, which are the chamber valley and chamber wings. The first experiment is located in the center of the cell, and the second experiment is on both sides of the cell. 3.1. Effect of the Gas Dew Point Range on Asphaltene Streaks and Mixing Zone. In the first experiment, the solvent in the gas phase (10 psi less than the dew point pressure) was injected into the VAPEX cell. Figure 2 shows the interface of two phases, but in the second experiment, the same solvent in the vapor phase (at its dew point) was used (Figure 3). As shown in Figures 2 and 3, the solvent diffusion coefficient of gas is less than that of the vapor phase and, therefore, its boundary layer thickness increases like a mixing zone. 4398
Energy Fuels 2010, 24, 4396–4401
: DOI:10.1021/ef100617p
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Figure 4. Streaking effect at matrix permeability of (a) 15-18 darcy and (b) 25-30 darcy.
Figure 7. Presentation of the resin content in the VAPEX cell. Figure 5. Local concentration of residual hydrocarbons in the matrix of the VAPEX cell.
Figure 8. Schematic of asphaltene/resin ratios in the VAPEX cell. Figure 6. Presentation of the asphaltene content in the VAPEX cell.
and bitumen increases and, thereby, the mass transfer is enhanced. Hence, more asphaltene will be precipitated. Far from this zone, the reduction of the solvent concentration leads to a decrease in the concentration gradient and a decline in the asphaltene deposition. Therefore, the precipitated asphaltene decreases around the production well remarkably. Figure 7 presents the residual resin in the VAPEX matrix. The distribution of resin is identical to the distribution pattern of asphaltene precipitations, and all of the asphaltene explanations correspond in this figure. Figure 8 shows the relative distribution of asphaltene to resin in the experimental cell. These proportions of injection and production ports are the most and least, while the other section of the cell is about unit, and this reveals that the distribution of asphaltene and resin is fairly similar throughout the cell. According to the micellization model, in solventrich zones, the percentage of asphaltene surrounding resin reduces and asphaltene precipitates as colloidal particles. This occurs in the production well, and residual hydrocarbon becomes rich with asphaltene. In contrast, around the injection well, the solvent concentration is less and, therefore, the resin content is more than the asphaltene content.
Figure 9. Distribution pattern of the vanadium concentration dissolved in the residual hydrocarbons of the VAPEX cell.
Figure 9 illustrates the distribution of vanadium chelates in the experimental cell. The arrangement of precipitated chelates is similar to the pattern of asphaltenes and resins and follows their explanation. Therefore, this highlights another advantage of the VAPEX process, including vanadium or heavy metal upgrading. In Figure 10, the distribution of dissolved/adsorbed vanadium chelates in/on precipitated asphaltene of the VAPEX cell is demonstrated. In reference to this figure, solubility or adsorption of vanadium chelates in/on asphaltene colloids in 4399
Energy Fuels 2010, 24, 4396–4401
: DOI:10.1021/ef100617p
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Figure 10. Distribution pattern of the vanadium concentration dissolved in the asphaltene precipitates of the VAPEX cell.
Figure 11. Distribution pattern of the vanadium concentration dissolved in the resin precipitates of the VAPEX cell.
the swept zone is less than other points of the cell. According to the micellization model, for the sake of the high solvent concentration, chelates are left around the asphaltene particles. Therefore, the metal chelate content of asphaltene colloids decreases significantly. However, where the solvent concentration is declined, chelate is dissolved or adsorbed on the asphaltenes and forms micelles to neutralize the charge of asphaltenes. Hence, the metal chelate content of precipitated asphaltenes increases. Figure 11 illustrates the distribution of dissolved/adsorbed vanadium chelates in/on precipitated resins. The reason for its pattern follows the explanation of Figure 10. 3.4. Modeling of Asphaltene, Resin, and Heavy Metal Chelate Upgrading in the VAPEX Process. Suspended particles, such as asphaltene, affect the bitumen flow characteristics, resulting in an increase of viscosity. The viscosity pattern in the two-dimensional VAPEX cell was calculated using a CMG simulator (version 2006 from the Computer Modeling Group). On the basis of the fluid characteristics, the viscosity of bitumen was computed using modified Pedersen’s equation (eq 1). μmix ðP, TÞ μ0 ðP0 , T0 Þ !- 1=6 !2=3 !1=2 Tc, mix Pc, mix MWmix Rmix ð1Þ ¼ Tc, 0 Pc, 0 MWc, 0 R0
Figure 12. Distribution pattern of the oil viscosity in the VAPEX cell for the swept zone and bitumen chamber.
By calculating ηr in the swept zone, Φeff was obtained to be unit. Therefore, according to Gillespie’s equation, asphaltene has been considered the only component of precipitated hydrocarbons, while Figures 6-8 have illustrated that precipitates not only consist of asphaltene but also contain resins and heavy metal chelates. On the basis of the resultant figures, eq 6 was proposed for this bitumen. ð6Þ Φeff ¼ Φasp þ Φres þ Φchel
The mixture critical temperature and pressure were calculated using mixing rules of the function of the component critical temperatures, pressures, and mole fractions. The molecular weight of the mixture was determined from eq 2, and the rotational coupling coefficient was calculated from eq 3. MWmix ¼ b1 ðMWw b2 - MWn b2 Þ þ MWn
ð2Þ
R ¼ 1 þ b3 Fr b4 MWb5
ð3Þ
According to the results obtained from Figure 8, Φasp ≈ Φres ≈ 0.33 and, as mentioned before, Φeff = 1. Hence, Φchel ≈ 0.33 was calculated for tested bitumen, and this is in agreement with eq 6 as well. As mentioned above, repetition of these tests for light crude oil can be performed. In this case, it is predicted that, using a solvent at dew point pressure, the maximum recovery occurs. Furthermore, because of low viscosity, the improvement of permeability does not affect the streaks movement. The distribution of predicted asphaltenes, resins, and metal chelates in the cell will be the same as the test of bitumen, but the range between minimum and maximum contents will decrease. We also predict that the proposed correlated model is agreeable with light oils.
The graphical result of this simulation is presented in Figure 12. The viscosity of residual oil in the swept zone was in the range of 0.019-0.033 Pa s, while the viscosity of fluid in the bitumen chamber remained at 18 Pa s. For modeling of asphaltene, resin, and heavy metal chelate, the relative viscosity was defined by eq 4. η ð4Þ ηr ¼ s ηo
Conclusions (1) In the VAPEX experiment, in which the solvent pressure was less than its dew point, precipitated streaks remained on the surface of glass beads irregularly. Moreover, when the solvent pressure was at the dew point, the precipitated streaks flow in the direction of lived oil to the production well as a
Gillespie proposed eq 5 to predict the volume fraction of particles. 1 þ Φeff =2 ð5Þ ηr ¼ ð1 - Φeff Þ2 4400
Energy Fuels 2010, 24, 4396–4401
: DOI:10.1021/ef100617p
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parallel pattern. (2) In the low-permeable matrix, precipitated streaks remained in the swept zone, while in the high-permeable matrix, no streaks were seen because they were drained to a separator without plugging the porous media and formation damage. (3) The remaining hydrocarbons in the swept zone were not distributed uniformly. In the central regions of this zone, the recovery was more, while the hydrocarbon precipitation on both sides and around the production well was more than that in the center. (4) The asphaltene, resin, and vanadium chelate distributions were not uniform in the swept zone, and their concentration around the injection well was maximal, while their concentration around the production well and both sides was minimal. (5) The distribution of the asphaltene/resin ratio in injection and production ports was maximal and minimal, respectively, and it was almost unit in the other section of the cell. (6) Solubility or adsorption of vanadium chelates in/ on asphaltene and resin precipitates in the swept zone was less than other points of the VAPEX cell. (7) Gillespie’s equation was correlated to predict the upgrading of bitumen in the VAPEX process with respect to asphaltenes, resins, and metal chelates. On the basis of this correlation, the volume fraction of colloidal particles was divided into volume fractions of asphaltenes, resins, and metal chelates. (8) Experimental data obtained in the laboratory were in agreement with the correlated model and revealed that upgrading of tested bitumen consisted of onethird of each of the asphaltenes, resins, and metal chelates.
cial support received from the National Iranian Oil Company (NIOC).
Nomenclature b1 and b2 = constants in eq 2 b3, b4, and b5 = constants in eq 3 MW = molecular weight MWw = weight fraction averaged molecular weight MWn = mole fraction averaged molecular weight Pc = critical pressure (Pa s) Tc = critical temperature (K) Greek Symbols R = rotational coupling coefficient Fr = reduced density of the reference substance (kg/m3) ηr = relative viscosity ηs = viscosity of bitumen before the VAPEX process (Pa s) ηo = viscosity of bitumen after the VAPEX process (Pa s) μ = viscosity (Pa s) Φ = volume fraction Subscripts asp = asphaltene chel = chelate eff = effective mix = mixture o = reference res = resin
Acknowledgment. The authors thank Mr. Salimi for his fruitful collaboration. The authors gratefully acknowledge the finan-
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