Analysis and Correlations of Viscous Fingering in Low-Tension

Nov 8, 2010 - Petroleum Systems Engineering Department, The University of Regina, Regina, Saskatchewan S4S 0A2, Canada. Energy Fuels , 2010, 24 (12) ...
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Energy Fuels 2010, 24, 6384–6392 Published on Web 11/08/2010

: DOI:10.1021/ef101061b

Analysis and Correlations of Viscous Fingering in Low-Tension Polymer Flooding in Heavy Oil Reservoirs Benyamin Yadali Jamaloei,*,†,‡ Riyaz Kharrat,‡ and Farshid Torabi§ † Department of Chemical and Petroleum Engineering, The Schulich School of Engineering, The University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada, ‡Petroleum Research Center, The Petroleum University of Technology, Tehran, Iran, and §Petroleum Systems Engineering Department, The University of Regina, Regina, Saskatchewan S4S 0A2, Canada

Received August 11, 2010. Revised Manuscript Received October 7, 2010

Low-tension polymer flooding (LTPF) can be an alternative for improving the recovery from some problematic heavy oil reservoirs, especially thin formations, where thermal methods face some challenges. A major technical challenge in LTPF is that a fingered displacement front may occur. Therefore, it is important to predict the nature of instability, to avoid viscous fingering, or, where it is inevitable, to be capable of including it as an additional factor in modeling displacement. Previous experiments of viscous fingering in immiscible displacements have been conducted in the presence of high permeabilities and linear displacement schemes. The question is whether previous findings are valid in displacement schemes similar to oil-field patterns (e.g., five-spot) in which one should deal with varying velocity profiles from injector(s) to producer(s). Hence, the effect of dispersion caused by varying velocity profiles has not been tested completely on viscous fingering. To help understand viscous fingering in LTPF in heavy oil reservoirs and to overcome the aforementioned limitations, we conducted experiments in relatively low-permeability, one-quarter, five-spot patterns. Foremost parameters, including oil recoveries at different times to breakthrough, pressure drops, cumulative saturation profiles, mean local saturations, finger lengths and widths, the dynamic level of bypassing, the dynamic population of fingers, the rate of growth of the population of fingers, and the number frequency of the fingers, were measured. We have correlated some of these parameters with the displacement time and front position. In summary, three distinct regions were identified for the viscous fingering patterns: onset of fingering, spreading phase, and end of sideways growth. The results also show that the finger width is comparable with the pore size and the fingerlike instabilities exist both in front of and behind the unstable front. Furthermore, the dynamic population of the macrofingers is well correlated with the square root of the time, and the profile of mean local oil saturation versus traveled distance is almost linear. Finally, the sharpest increase in the rate of growth of the finger population versus dimensionless pressure drop is accompanied with the sharpest pressure drop occurring at the onset of fingering and axial finger propagation during the early stages. A subsequent relatively uniform trend of the pressure drop versus time occurs during the spreading phase. Analysis of the experimentally observed fingering patterns of LTPF in this study is the most detailed interpretation performed to date, which provides new insight into the onset of fingering and finger development.

processes. Thus, other alternatives should be employed to improve the heavy oil recovery when steam-based thermal methods do not function properly. The suggested alternatives include vapor extraction (VAPEX),4,5 toe-to-heel in situ combustion,6 toe-to-heel waterflooding,7 surfactant-based chemical flooding in the presence and absence of polymer

1. Introduction A substantial fraction of the worldwide heavy oil and bitumen reserves is located in Western Canada.1 Often located in high-porosity, high-permeability, unconsolidated sand deposits with low net pay,2 the primary recovery from these reserves is usually 5-15%.3 The most widely used method for heavy oil and bitumen recovery is the steam-based thermal method. However, these techniques are facing environmental challenges and technical difficulties. The high cost of steam production and the excessive heat loss to the underburden and overburden in thin formations are the major economical and technical concerns associated with steam-based thermal

(4) Butler, R. M.; Mokrys, I. J. J. Can. Pet. Technol. 1991, 30, 56–62. (5) Upreti, S. R.; Lohi, A.; Kapadia, R. A.; El-Haj, R. Energy Fuels 2007, 21 (3), 1562–1574. (6) Xia, T. X.; Greaves, M.; Turta, A. T.; Ayasse, C. Chem. Eng. Res. Des. 2003, 81 (3), 295–304. (7) Turta, A. T.; Singhal, A. K. J. Can. Pet. Technol. 2004, 43 (2), 29–38. (8) Liu, Q.; Dong, M.; Ma, S. SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 2006. (9) Mai, A.; Bryan, J.; Goodarzi, N.; Kantzas, A. J. Can. Pet. Technol. 2009, 48 (3), 27–35. (10) Thomas, S.; Farouq Ali, S. M.; Scoular, J. R.; Verkoczy, B. J. Can. Pet. Technol. 2001, 40 (3), 56–61. (11) Yadali Jamaloei, B. Recent Pat. Chem. Eng. 2009, 2 (1), 1–10. (12) Yadali Jamaloei, B.; Kharrat, R.; Ahmadloo, F. SPE Kuwait International Petroleum Conference and Exhibition, Kuwait City, Kuwait, 2009.

*To whom correspondence should be addressed. E-mail: byadalij@ ucalgary.ca or [email protected]. (1) Burrowes, A.; Marsh, R.; Ramdin, N.; Evans, C.; Kirsch, M.-A.; Brugger, M.; Philip, L.; et al. EUB ST98-2007: Annual Report; Alberta Energy and Utilities Board: Calgary, Alberta, Canada, 2007. (2) Albartamani, N. S.; Farouq Ali, S. M.; Lepski, B. International Operations and Heavy Oil Symposium, Bakersfield, CA, 1999. (3) Firoozabadi, A. J. Can. Pet. Technol. 2001, 40 (3), 15–20. r 2010 American Chemical Society

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and alkali, low-rate waterflooding, variable-rate waterflooding,16 immiscible CO2 flooding,17 miscible CO2 flooding,18 and water-alternating-CO2 injection.10,19,20 Among the suggested methods, a miscible gas injection process and, in particular, VAPEX suffers from low initial production rates, premature breakthrough, and possible formation damage due to in situ deasphalting. Also, in waterflooding, the large difference between the heavy oil and water viscosities leads to an unfavorable mobility ratio and low sweep efficiency. Although waterflooding has been carried out in heavy oil reservoirs in Western Canada for the last 50 years,21,22 the results are generally disappointing. Lowtension polymer flooding (LTPF) can be an alternative in some problematic heavy oil reservoirs, especially in thin formations, where thermal methods face some challenges. However, a major technical challenge in LTPF is that an uneven displacement front may occur. This may invalidate the normal method of simulating the LTPF based on relative permeability and capillary pressure concepts. This instability also introduces an additional scaling requirement for field scales. Therefore, mathematical and experimental studies are required to understand the inherently unstable nature of viscous fingering in LTPF in heavy oil reservoirs.

The research on viscous fingering continued in the 1960s. An approximate theory for the growth of fingers was developed by Sheldon28 involving the approximations similar to those used in the first-order shallow-water theory for water waves. Using the developed theory, he determined the transient qualitative behavior of large-amplitude fingers. Outmans29 improved the first-order theory for frontal stability and viscous fingering of immiscible liquids by including the nonlinear terms in the equations describing conditions at the interface. The results of his modeling show that the gravity and IFT invalidate that the shape of a finger after a given displacement is independent of the displacement velocity. Also, he showed that the similarity of fingering requires a geometrical similarity of the initial disturbance. In 1968, Croissant showed that the number of fingers decreases and that finger widths and lengths grow with time. The breakup of the fingers into a graded saturation zone in the presence of connate water was noted by Perkins and Johnston.30 They also studied the transverse-flow phenomenon under controlled conditions by simultaneous injection of oil and water in linear models. They indicated that transition zones form that grow broader as the distance from the inlet increases, and the saturation distribution in the transition zones can be described mathematically by an immiscible dispersion coefficient. In the early 1970s, Gupta et al.31 noted that fingering is a macroscopic process and neither the initial wavelength nor the wavelength late in the displacement depends on microscopic irregularities. They also reported that fingering is not independent of the local macroscopic irregularity in the porous medium. Two years later, Gupta and Greenkorn32 indicated that the developed fingers at the beginning of displacement can be transformed into a single finger at a later stage. In the 1980s, for the first time, Peters and Flock33 interpreted the viscous fingering patterns in cylindrical 3D sandpacks. They noted that fingers are almost one order of magnitude wider in a water-wet system than in an oil-wet system. Bentsen and Saeedi34 presented the evidence of a stable 0.5 saturation zone at the inlet end. Paterson et al.35 presented the viscous fingering patterns that occur when water or a surfactant solution displaces the oil in an oil-wet porous medium composed of fused plastic particles. Their results indicated that the flow structure changes significantly within the range of capillary numbers between 10-4 and 10-3. They also found that narrower fingers in a more dispersive fashion are created under the low-IFT flow condition. In 1984, Vossoughi et al.36 discussed a method for modeling the viscous fingering in miscible displacement using the convection-dispersion equation and representing the convection term by a fractional flow function. They also illustrated the extension of this method to polymer flooding by including Langmuir-type retention and inaccessible pore volume.

2. Literature Survey The study of viscous fingering dates back to the 1950s. To the best of the authors’ knowledge, the term “viscous fingering” was first used by Engelberts and Klinenberg.23 They showed that, at viscosity ratios above unity, a linear relationship exists between breakthrough recovery and the logarithm of the viscosity ratio. van Meurs24 showed that the oil production rate decreases slowly after breakthrough at high viscosity ratios. van Meurs and van der Poel25 visualized the linear displacement of oil by water from a porous medium in transparent models. They developed formulas of both oil production and pressure drop across the formation as a function of cumulative water injection with the oil-water viscosity ratio as a parameter. In 1959, Chuoke et al.26 discussed the contribution of the capillary pressure to the enlargement of fingers. They showed that fingers are small for high oil viscosity or low interfacial tension (IFT). Finally, de Haan27 showed that water fingers in drainage can be on the order of the magnitude of the pores. (13) Yadali Jamaloei, B.; Ahmadloo, F.; Kharrat, R. Fluid Dyn. Res. 2010, 42 (5), 055505. (14) Yadali Jamaloei, B.; Asghari, K.; Kharrat, R.; Ahmadloo, F. J. Pet. Sci. Eng. 2010, 72 (3-4), 251–269. (15) Mai, A.; Kantzas, A. J. Can. Pet. Technol. 2010, 49 (3), 44–50. (16) Torabi, F.; Yadali Jamaloei, B.; Zarivnyy, O.; Paquin, B.; Rumpel, N. Pet. Sci. Technol. 2010, in press. (17) Spivak, A.; Chima, C. M. SPE Enhanced Oil Recovery Symposium, Tulsa, OK, 1984. (18) Yadali Jamaloei, B.; Kharrat, R. Pet. Sci. Technol. 2010, in press. (19) Farouq Ali, S. M. SPE Rocky Mountain Regional Meeting, Casper, WY, 1976. (20) Rojas, G. A.; Zhu, T.; Dyer, S. B.; Thomas, S.; Farouq Ali, S. M. SPE Reservoir Eng. 1991, 6 (2), 169–178. (21) Miller, K. A. J. Can. Pet. Technol. 2006, 45 (4), 7–11. (22) Alikhan, A. A.; Farouq Ali, S. M. SPE Rocky Mountain Regional Meeting, Salt Lake City, UT, 1983. (23) Engelberts, W. F.; Klinkenberg, L. J. Third World Petroleum Congress, The Hague, The Netherlands, 1951. (24) van Meurs, P. Pet. Trans., AIME 1957, 210, 295–301. (25) van Meurs, P.; van der Poel, C. Pet. Trans., AIME 1958, 213, 103–112. (26) Chuoke, R. L.; van Meurs, P.; van der Pod, C. Pet. Trans., AIME 1959, 216, 188–194. (27) de Haan, H. J. World Petroleum Congress, New York, 1959.

(28) Sheldon, J. W. Fall Meeting of the Society of Petroleum Engineers of AIME, Denver, CO, 1960. (29) Outmans, H. D. Soc. Pet. Eng. J. 1962, 2 (2), 165–176. (30) Perkins, T. K.; Johnston, O. C. Soc. Pet. Eng. J. 1969, 9 (1), 39–46. (31) Gupta, H. P.; Varnon, J. E.; Greenkorn, R. A. SPE Paper Number 3675-MS, 1971. (32) Gupta, S. P.; Greenkorn, R. A. Water Resour. Res. 1974, 10 (2), 371–374. (33) Peters, E. J.; Flock, D. L. Soc. Pet. Eng. J. 1981, 21 (2), 249–258. (34) Bentsen, R. G.; Saeedi, J. J. Can. Pet. Technol. 1981, 93–103. (35) Paterson, L.; Hornof, V.; Neale, G. Soc. Pet. Eng. J. 1984, 24 (3), 325–327. (36) Vossoughi, S.; Smith, J. E.; Green, D. W.; Willhite, G. P. Soc. Pet. Eng. J. 1984, 24 (1), 56–64.

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Vossoughi and Seyer developed an analytical model for the prediction of oil recovery and saturation distribution of an unstable immiscible displacement in the absence of capillary and gravity forces by introducing relative flow areas for each phase. They predicted the saturation profile, breakthrough recovery, and pressure drop of the mixed zone and validated their results with the experiments. A theoretical analysis for growth of a single, large elliptical finger in a porous medium was provided by Mui and Miller.38 They found that linear analysis can appropriately be used to specify the conditions of large finger growth. Their findings also suggest that the elliptical finger model is capable of predicting the width and speed of growth of the fastest-growing finger. Lenormand39 presented a theoretical description of drainage-type immiscible displacements in 3D porous media taking into account viscous and capillary forces. He also included the stochastic theories of percolation and diffusion-limited aggregation in a general description of displacement patterns. For the first time, Ni et al.40 conducted the immiscible displacement experiments in consolidated porous media using a radial plate of sintered glass beads. They confirmed the previous findings of the trend of breakthrough recovery versus flow rate for linear displacements. Also, Stokes et al.41 found that the finger width is comparable with the pore size in drainage. Sarma42 conducted experiments of viscous fingering as a function of the viscosity ratio between displaced and displacing fluids, the displacement rate, IFT, and the directions of saturation changes (i.e., in drainage and imbibition). His results indicated that fingering is more pronounced in the drainage than in the imbibition and the tip length of the fastest-growing finger tends to grow linearly in most cases. Peters et al.43 utilized computer image processing to study the patterns of viscous fingering in laboratory corefloods. They used the frequency contents of the fingering patterns in conjunction with stability theory to estimate the effective IFT required for calculating the stability numbers of the floods. A decrease in the oil relative permeability and an increase in the water relative permeability with an increase in instability were reported by Peters and Khataniar.44 In 1987, Nasr-El-Din et al.45 reported that breakthrough recovery in radial displacements in consolidated porous media is an almost linear, decreasing function of the logarithm of the flow rate. Finally, Odeh46 showed that, for 1D oil-water displacement in sandpacks, the macroscopic effect of viscous fingering can be modeled with a reservoir simulator and one set of relative permeability values, calculated directly from the experimental data. A great deal of research on viscous fingering also exists in the 1990s. In the early 1990s, Brock and Orr47 investigated the combined effects of viscous fingering and permeability heterogeneity in four different 2D glass bead packs. They visualized

the floods and also simulated them using a particle tracking simulator. Their results show that fingering patterns in a homogeneous model are sensitive to the mobility ratio and not to the flow rate, and in the heterogeneous models, the flow is mainly determined by the patterns of heterogeneity. In a homogeneous model, analysis of the pressure distributions showed that viscous crossflow causes finger growth. Pavone48 reported observations showing the instabilities that looked like fingers and stable displacements behind the unstable front in waterfloods in 3D natural consolidated porous media. He also pointed out that in some experiments a stable zone exists, which progresses along the sample at constant velocity. In 1994, Tehelepi and Orr49 compared 2D and 3D computations of unstable displacements with a hybrid finite-difference/particletracking technique. They found that gravity segregation is much more effective in 3D than in 2D in both homogeneous and heterogeneous media. They also stated that the heterogeneity narrows the range of the ratio of viscous-to-gravity over which the transition from gravity- to fingering-dominated flow takes place in 2D or 3D flow. Zolotukhin and Frick50 developed a mobility-driven fingering model for a field-scale simulation of oil recovery. Their results were used for the screening of different instability phenomena caused by reservoir heterogeneity and differences in fluid mobilities. In 1999, Vives et al.51 reported that macroscopic fingering exists in water-alternatinggas (WAG) floods where no saturation shock is expected from 1D fractional flow theory. They also reported that bypassing due to both fingering and gravity override is higher in drainage than in imbibition. Their findings suggested that the macroscopic flow theory should include capillarity and viscous fingering to match the WAG experiments. The fingering patterns and flow instability have also been studied under the low-IFT flow conditions in media containing high-viscosity oil. Yadali Jamaloei and Kharrat52 concluded that, in LTPF in a medium saturated with heavy oil and connate water, the number of fingers is strongly dependent upon the size and shape of the pores. They also showed that, with an increase in the pore body diameter, the displacement front becomes less unstable. In the presence of the connate water within a mixed-wet medium, an increase in the number of fingers and/or much thinner fingers with many tiny branches was observed in dilute surfactant flooding of a medium saturated with heavy oil and connate water. This was reported by Yadali Jamaloei and Kharrat53 and confirms the result reported by Thibodeau and Neale.54 The effect of the pore throat size on the flow instability in dilute surfactant flooding of media containing heavy oil and connate water was investigated by Yadali Jamaloei and Kharrat.55 They reported that the macroscopic flow pattern in the model with the largest pore throat size was dispersed throughout the entire model and the flow after breakthrough developed in the form of bewildered clusters. However, in the model with the intermediate

(37) Vossoughi, S.; Seyer, F. A. Ind. Eng. Chem. Fundam. 1984, 23 (1), 64–74. (38) Mui, K. C.; Miller, C. A. Soc. Pet. Eng. J. 1985, 25 (2), 255–267. (39) Lenormand, R. SPE Annual Technical Conference and Exhibition, New Orleans, LA, 1986. (40) Ni, L. W.; Hornof, V.; Neale, G. Rev. IFP 1986, 41 (2), 217–228. (41) Stokes, J. P.; Weitz, D. A.; Gollub, J.P.; Dougherty, A.; Robbins, M.O.; Chaikin, P.M.; Lindsay, H. M. Phys. Rev. Lett. 1986, 57 (14), 1718–1721. (42) Sarma, H. K. Powder Technol. 1986, 48 (1), 39–49. (43) Peters, E. J.; Broman, J. A.; Broman, W. H., Jr. SPE Reservoir Eng. 1987, 2 (4), 720–728. (44) Peters, E. J.; Khataniar, S. SPE Form. Eval. 1987, 2 (4), 469–474. (45) Nasr-El-Din, H.; Hornof, V.; Neale, G. Rev. IFP 1987, 42 (6), 783–796. (46) Odeh, A. S. SPE Reservoir Eng. 1989, 4 (3), 304–308. (47) Brock, D. C.; Orr, F. M., Jr. SPE Annual Technical Conference and Exhibition, Dallas, TX, 1991.

(48) Pavone, D. SPE Reservoir Eng. 1992, 7 (2), 187–194. (49) Tehelepi, H. A.; Orr, F. M., Jr. SPE Reservoir Eng. 1994, 9 (4), 266–271. (50) Zolotukhin, A. B.; Frick, T. P. Latin America/Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 1994. (51) Vives, M. T.; Chang, Y. C.; Mohanty, K. K. SPE J. 1999, 4 (2), 260–267. (52) Yadali Jamaloei, B.; Kharrat, R. Transp. Porous Media 2009, 76 (2), 199–218. (53) Yadali Jamaloei, B.; Kharrat, R. J. Porous Media 2010, 13 (8), 671–690. (54) Thibodeau, L.; Neale, G. H. J. Pet. Sci. Eng. 1998, 19 (3-4), 159– 169. (55) Yadali Jamaloei, B.; Kharrat, R. J. Porous Media 2011, 14, in press.

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pore throat size, they observed the development of some fingers within the macroscopic flow structures after breakthrough, and in the model with the smallest pore throat size, a less unstable macroscopic front occurred. Yadali Jamaloei et al.14 reported that, in forced imbibition under low-IFT conditions, the frontal drive of the displacing phase occurred with minor cluster growth and entailing microfingers that normally fill the entire pore. Also, the secondary, subsidiary front advances ahead of the primary front along the pore edges and pore wall surfaces, which causes severe disconnection of the oil by pinch-off. They also showed that, in imbibition under high-IFT conditions, the emptying proceeds in the absence of both the frontal drive and infinite percolation cluster (at the percolation threshold). Most of the previous experiments of viscous fingering in immiscible displacements from the 1950s to the 1990s have been conducted in high-permeability media with linear displacement schemes. In fact, except those studies reviewed in the previous paragraph, the authors could not find any study conducted using intermediate- and low-permeability media with displacement schemes similar to the oil-field injectionproduction patterns. Thus, the question that arises is, are previous findings valid in displacement schemes similar to oil-field patterns (e.g., five-spot) using intermediate- and low-permeability media? In oil-field patterns, one has to deal with varying velocity profiles from injector(s) to producer(s). Therefore, the effect of dispersion caused by varying velocity profiles has not been tested on viscous fingering. We have conducted experiments in a relatively low-permeability [i.e., (1.79 ( 0.12)  10-12 m2], one-quarter, five-spot pattern so as to evaluate the viscous fingering in LTPF in heavy oil reservoirs. The medium used in this study is the lowest-permeability medium, which has been used in a nonlinear injection-production scheme (i.e., one-quarter, five-spot pattern) for studying the viscous fingering to date. Analysis of the fingering patterns of LTPF in this study provides new insight into the onset of fingering and finger development. It is expected that the results from this study would help simulation and theory in order to satisfactorily reproduce some features of the fingering patterns and finger growth.

Table 1. Composition of the Injected Displacing Wetting Phase Concentration of Components in 100 cm3 of Distilled Water surfactant, cm3 ethanol, cm3 xanthan, mg

16 10 12.5

Table 2. Physical Properties of the Injected Surfactant Solution and Crude Oil at Experiment Conditions surfactant solution viscosity, mPa 3 s surfactant solution-crude oil IFT, mN 3 m-1 crude oil viscosity, mPa 3 s crude oil density, kg 3 m-3

5.70 0.0065 80.61 927.4

designing, etching, and fusing procedures can be found elsewhere.56 The physical properties of the micromodel are given in ref 14. Details on the determination of these properties can be found in previous publications.14,52,56,57 It is worth noting that the purpose of the present study is to solely focus on the viscous fingering effect not the combined effect of the capillary and viscous fingering. Therefore, a medium with uniform pore body and pore throat sizes has been utilized in this study. The physical properties of the crude oil and the properties of the surfactant are given in ref 14. Table 1 shows the composition of the injected displacing phase. Ethanol (purity of 99.8%) was used in the displacing wetting phase to minimize surfactant adsorption and precipitation.58 Further details can be found elsewhere.14,57 Hydrofluoric acid and nitric acid were used in the etching process to etch the desired porous network onto the glass plate. Table 2 summarizes the physical properties of the injected surfactant solution and crude oil. The density and viscosity of the crude oil were measured using a digital densitometer (512P, Anton Paar) and a rolling-ball viscometer (P/N, Chandler Engineering), respectively. All of the measurements and the experiment were conducted at a constant temperature of 25 ( 0.2 °C. For conducting the experiment, first the micromodel is saturated with the heavy oil using a syringe pump. Then it is flooded with the polymer-contained surfactant solution. The injection flow rate of the chemical solution was 0.0008 cm3 3 min-1. A digital Nikon camera captured high-quality images during the displacement process. These images were then loaded into SigmaScan Pro 5 software for processing. The captured images were processed, and different qualitative and quantitative features of LTPF were extracted at different times of the displacement. These features include the dimensionless distance traveled by the displacement front, oil recoveries at any time before breakthrough, dimensionless mean local saturations, the level of bypassing, cumulative saturation profiles versus diagonal distance traveled by the front, the number of macrofingers formed, the cumulative rate of growth of the finger population, the instantaneous rate of growth of the finger population, and minimum and maximum finger lengths and widths at different times of the displacement. A complete description of the image analysis can be found in ref 59.

3. Experimental Section The experimental setup is the same setup that was used in previous publications. For a detailed description of the setup components, see ref 13. An etched glass micromodel has been used as the porous medium. Previous experiments of viscous fingering in immiscible displacements have been conducted in the presence of linear displacement schemes. It is therefore of particular interest to examine as to whether previous findings are valid in displacement schemes similar to oil-field patterns (e.g., fivespot pattern). Thus, in order to simulate the oil-field patterns, the porous micromodel used in this study was etched onto the glass in the form of a one-quarter, five-spot pattern. The main reason why the authors have considered a one-quarter, five-spot injection pattern rather than a conventional five-spot pattern (in which the injector is placed at the center and four producers are placed at each corner of the micromodel) is to prevent a possible overlapping of the fingering patterns between the injector (at the center of the micromodel) and each producer (at each corner of the micromodel). Such overlapping of the fingering patterns makes it very difficult to identify and analyze the individual fingering patterns associated with each producer and injector. A schematic of the synthetic porous medium is given in ref 14. To make the porous medium, first the pattern of the synthetic porous medium is designed, then etched, and fused. Details on the

4. Results and Discussion Figure 1 shows the displacement fronts and fingering patterns at different times during the displacement until breakthrough of the injected chemical solution to the production point. The macrofingers develop at the very early stage of the process (displacement time = 120 s). Afterward, macrofinger growth along the diagonal distance traveled by the front is (56) Yadali Jamaloei, B.; Rafiee, M. Canadian International Petroleum Conference, Calgary, Alberta, Canada, 2008. (57) Yadali Jamaloei, B.; Kharrat, R. Transp. Porous Media 2010, 81 (1), 1–19. (58) Novosad, J. SPE J. 1982, 22 (6), 962–970. (59) Yadali Jamaloei, B.; Asghari, K.; Kharrat, R. Exp. Therm. Fluid Sci. 2011, 35 (1), 253-264.

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Figure 1. Displacement fronts and fingering patterns at different displacement times in LTPF.

Also, he reported that in some high-IFT waterflood experiments a stable zone exists and progresses along the sample at constant velocity. In the LTPF experiment conducted in this study, the captured images (Figure 1) do not show any stable zone before breakthrough of the injected chemical solution. This can be attributed to the presence of a low-IFT flow condition in the LTPF. The condition of low-IFT flow in LTPF causes the creation of extremely irregular fingers in the absence of connate water saturation (Figure 1). According to Paterson et al.,60 at high-IFT flow condition and in the absence of connate water saturation, injection of water creates less irregular fingers. The captured images in Figure 1 were loaded into SigmaScan Pro 5, and the foremost features of the LTPF were extracted from the image processing. Table 3 lists the experimental results for the LTPF, which were obtained from the image processing. Here a brief explanation of the parameters in Table 3 is provided. The dimensionless displacement time is the time of the displacement divided by the breakthrough time (i.e., 720 s). The distance traveled by the front is the diagonal distance from the injection point at a desired time, and the dimensionless distance traveled by the front is the diagonal distance from the injection point divided by the diagonal distance between the injection and production points in the utilized one-quarter, five-spot scheme. The oil recovery values reported in Table 3 are the produced oil saturation at any time of the displacement, expressed as a percentage of the initial oil saturation. The pressure drops in Table 3 were recorded by the Quizix pump. Also, the reported dimensionless pressure drop is the pressure drop at any time divided by the pressure drop at the breakthrough time. The level of bypassing (reported in terms of a percentage of the initial oil saturation) is the average oil saturation, which is bypassed by the fingered displacement pattern at any time. The dimensionless mean local saturation is the level of bypassing at any time divided by the level of bypassing at the breakthrough time. Table 3 also lists the

observed (displacement time = 240 s). During this time, the injection pressure declines rapidly and a very sharp pressure drop is recorded by the Quizix pump (see Figure 6a). During the intermediate displacement time, the onset of sideway growth of the fingers is observed (displacement time=300 s). The sideway growth of the fingers (or spreading phase of the viscous fingering pattern), orthogonal to the diagonal distance traveled by the front, continues until near-breakthrough of the injected chemical solution (displacement time = 300-420 s). During the sideway growth of the fingers, the injection pressure declines slowly until near-breakthrough. During this time, the pressure drop decreases slowly (see Figure 6a). When the fingered front approaches the production point, the sideway growth of the fingers ends. At this time, the front fingers reach the production point and breakthrough occurs (displacement time=720 s). Stokes et al.41 reported that the finger width is comparable with the pore size in immiscible drainage-type displacement. The qualitative observations in this study confirm the results of Stokes et al.41 It is worth noting that in this study it is assumed that the wettability of the porous medium is determined to a large extent by the first fluid contacting the porous medium, which is crude oil. Also, the viscous fingering patterns observed in this study are different from the results reported by Gupta and Greenkorn32 for unfavorable mobility ratio displacement at high-IFT flow. They showed that numerous incipient fingers occur at the very beginning of the displacement and that they degenerated into a single finger at a later stage. The patterns shown in Figure 1 suggest that the fingers that occurred at the very beginning do not degenerate into a single finger at a later stage. Another implication from the fingering patterns (Figure 1) of the LTPF in this study is that the fingerlike instabilities are present both in front of and behind the unstable front. However, the viscous fingering patterns of drainage-type waterfloods in 3D consolidated media at high-IFT flow, which were reported by Pavone,48 showed the instabilities that looked like fingers and the presence of stable displacements behind the unstable front.

(60) Paterson, L.; Hornof, V.; Neale, G. Rev. IFP 1984, 39, 517–521.

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Table 3. Summary of the Experimental Results for the LTPF displacement time, s dimensionless displacement time dimensionless distance traveled by the front oil recovery, % of initial oil saturation pressure drop, kPa dimensionless pressure drop dimensionless mean local saturation level of bypassing, % of initial oil saturation number of macrofingers formed cumulative rate of growth of the finger population, s-1 instantaneous rate of growth of the finger population, s-1 minimum finger length, mm dimensionless minimum finger length maximum finger length, mm dimensionless maximum finger length minimum finger width, mm dimensionless minimum finger width maximum finger width, mm dimensionless maximum finger width

120 0.1667 0.1969 5.1 188.8 1.0233 1.5208 94.9 2 0.0167 0.0167 7.8 2.2941 11.7 0.5021 3.9 3.5454 5.7 0.6333

240 0.3333 0.3929 9.5 186.1 1.0087 1.4503 90.5 3 0.0125 0.0083 4.7 1.3824 20.8 0.8927 3.0 2.7272 7.3 0.8111

300 0.4167 0.4286 13.1 185.7 1.0065 1.3926 86.9 5 0.0167 0.0333 4.2 1.2353 20.8 0.8927 1.1 1.0000 7.3 0.8111

360 0.5000 0.4745 17.0 185.2 1.0038 1.3301 83.0 6 0.0167 0.0167 4.2 1.2353 23.3 1.0000 1.1 1.0000 8.8 0.9778

420 0.5833 0.5255 21.4 185.0 1.0027 1.2596 78.6 9 0.0214 0.0500 3.4 1.0000 25.1 1.0773 1.1 1.0000 9.0 1.0000

720 1.0000 1.0000 37.6 184.5 1.0000 1.0000 62.4 11 0.0153 0.0067 3.4 1.0000 23.3 1.0000 1.1 1.0000 9.0 1.0000

Figure 2. Correlation of the number of macrofingers formed with (a) the square root of the dimensionless time and (b) the ratio of the dimensionless distance traveled by the front to the dimensionless displacement time.

Figure 3. Trend of change in the (a) dimensionless finger length (minimum and maximum) versus dimensionless displacement time and (b) dimensionless finger width (minimum and maximum) versus dimensionless displacement time.

number of distinct macrofingers that exist at any time of the displacement. Once the number of distinct macrofingers is known, one can readily determine the cumulative and instantaneous rate of growth of the finger population. The cumulative rate of growth of the finger population is the difference between the number of macrofingers formed at any time and the start of the displacement, divided by the elapsed displacement time. On the other hand, the instantaneous rate of growth of the finger population is the difference between the number of macrofingers formed at any two consecutive times

of the displacement, divided by the difference between the two consecutive displacement times. In order to better analyze the results, the parameters in Table 3 have been plotted in Figures 2-6. Figure 2 shows the correlation of the number of the macrofingers formed with (a) the square root of the dimensionless time and (b) the ratio of the dimensionless distance traveled by the front to the dimensionless displacement time. Figure 2a shows that the dynamic population of the macrofingers is well correlated with the square root of the displacement time. The number of 6389

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Figure 4. Correlation of the dimensionless mean local oil saturation with (a) the ratio of the dimensionless distance traveled by the front to the dimensionless displacement time and (b) the dimensionless distance traveled by the front.

Figure 5. Trend of change in (a) the cumulative rate of growth of the finger population versus dimensionless pressure drop and (b) the instantaneous rate of growth of the finger population versus dimensionless pressure drop.

macrofingers grows almost linearly with the square root of the time. Also, Figure 2b illustrates that the number of macrofingers increases linearly by a decrease in the ratio of the dimensionless distance to the dimensionless time. This ratio is analogous to the definition of the superficial velocity in linear displacement schemes. Therefore, one would expect that an increase in the injection flow rate would probably cause a decrease in the dynamic population of fingers. These results are contrary to the results reported by Amiell61 in the absence of surfactant and polymer in the injected solution. He showed that the number of fingers is almost independent of the flow rate but that the shape of the finger was flow-ratedependent. Our results suggest that the results obtained by Amiell61 are not valid for the LTPF where the flow is viscousmodified in the presence of the low-IFT condition. Figure 3 illustrates the trend of change in the dimensionless finger length (minimum and maximum) versus dimensionless displacement time and also the dimensionless finger width (minimum and maximum) versus dimensionless displacement time. According to parts a and b of Figure 3, the dimensionless minimum finger length and width both decrease as the dimensionless time decreases. On the contrary, the dimensionless maximum finger length and width both increase as the dimensionless time decreases except at breakthrough, where the dimensionless maximum finger length decreases. It is worth noting that the dimensionless quantities in Figure 3

are the quantity at each time divided by that quantity at the breakthrough time. Figure 4 demonstrates the correlation of the dimensionless mean local oil saturation with (a) the ratio of the dimensionless distance traveled by the front to the dimensionless displacement time and (b) the dimensionless distance traveled by the front. Figure 4a indicates that the dimensionless mean local oil saturation increases almost linearly with an increase in the ratio of the dimensionless distance traveled by the front to the dimensionless displacement time. Sigmund et al.62 inferred that the cumulative saturation profiles of waterfloods are almost linear versus the length of the porous sample. Also, Pavone48 concluded that the saturation profiles along the sample are linear for 16 drainage-type waterfloods in 3D consolidated media at high-IFT flow. The results of our study show that the trend of change in the mean local oil saturation is almost linear with the dimensionless distance traveled by the front (see Figure 4b). In fact, Figure 4b illustrates that the mean local oil saturation is well correlated with the dimensionless distance traveled by the front. A close look at the saturation data points depicted in Figure 4b reveals that the shape of the dimensionless mean local oil saturation versus dimensionless distance resembles an inverted s-shape profile (dotted line in Figure 4b). Figure 5 illustrates the trend of change in both the cumulative rate of growth of the finger population and the instantaneous

(61) Amiell, P. Ph.D. Dissertation, Ecole Natl. Sup. des Mines de Paris, Paris, France, 1988.

(62) Sigmund, P. M.; Sharma, H.; Sheldon, D.; Aziz, K. SPE Reservoir Eng. 1988, 3 (2), 401–409.

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Figure 6. Trend of change in (a) dimensionless pressure drop versus dimensionless displacement time and (b) oil recovery versus dimensionless displacement time.

rate of growth of the finger population versus dimensionless pressure drop. The general trend of change in both the cumulative and instantaneous rates of growth of the finger population versus dimensionless pressure drop is the same. Both curves encompass three minima: one minimum occurs at the beginning of the displacement, one at the middle, and another right before breakthrough. The foremost feature of the two curves is the occurrence of the first maximum at the onset of finger development and propagation (see Figure 1; displacement time = 120-240 s). The sharpest increase in the cumulative and instantaneous rates of growth of the finger population versus dimensionless pressure drop is accompanied with a sharp pressure drop across the porous medium (see Figure 6a). This sharpest increase in the rate of growth of the finger population occurs at the onset of fingering and finger propagation along the diagonal distance (Figure 1a,b). It was previously explained that the macrofingers develop during the very early stages of the process and then they grow along the diagonal distance. At this time, a very sharp pressure drop is observed. Figure 6 shows the trend of change in the dimensionless pressure drop versus dimensionless displacement time and the oil recovery versus dimensionless displacement time. Figure 6a depicts the sharpest pressure drop during the early stages of displacement (displacement time =120-240 s). As was explained before, this sharp pressure drop is synonymous with the onset of fingering and further axial growth and propagation of the fingers along the diagonal distance traveled by the displacement front. Later, the pressure drop versus time becomes relatively uniform (displacement time = 300-420 s). This relatively uniform trend of the pressure drop versus time is synonymous with the spreading phase of the viscous fingering pattern, which is the second stage of the fingering pattern identified in this study. Figure 6b shows the quasi-linear trend of the oil recovery versus dimensionless time. This figure suggests that a substantial amount of the heavy oil is recovered before breakthrough of the chemical solution. The main reason why the trend of the oil recovery versus dimensionless time is quasi-linear is the presence of some trapped air saturation (approximately 2.8%) in the porous medium. The air saturation is trapped in the micromodel during saturation with the heavy oil (because the heavy oil is displacing air during saturation of the micromodel). As the displacing phase is injected into the micromodel, it starts to replace and displace the trapped air saturation at some locations. Thus, some of the trapped air saturation is produced along with the heavy oil during the early stages of the displacement.

5. Summary and Conclusions 1. Three distinct regions were identified for the viscous fingering patterns in LTPF of the heavy oil. In the first region, the macrofingers start to propagate (onset of fingering) and finger growth along the diagonal distance is observed. During this time, the pressure drops sharply. In the second region, which is called the spreading phase of the viscous fingering pattern, the sideway growth of the fingers is observed. During this time, the pressure drops slowly. In the third region, the spreading phase ends, and shortly after, the front channels to the producer when breakthrough occurs. 2. The results show that the finger width is comparable with the pore size in LTPF. Also, numerous incipient fingers at the beginning of displacement do not degenerate into a single finger at a later stage. The fingerlike instabilities are present both in front of and behind the unstable front. Furthermore, in the LTPF, there exists no stable zone before breakthrough, mainly because of the low-IFT flow. The low-IFT flow causes creation of the extremely irregular fingers in the absence of connate water saturation. 3. The dynamic population of the macrofingers is well correlated with the square root of the displacement time, where the number of macrofingers grows almost linearly with the square root of the time. Also, the number of macrofingers increases linearly by a decrease in the ratio of the dimensionless distance to the dimensionless time. Although it is known that the number of fingers is almost independent of the flow rate in high-IFT waterfloods, our results suggest that this may not be valid for LTPF (i.e., viscous-modified low-IFT waterflood). 4. The dimensionless minimum finger length and width both decrease as the dimensionless time decreases. On the contrary, the dimensionless maximum finger length and width both increase as the dimensionless time decreases except at breakthrough, where the dimensionless maximum finger length decreases. 5. The dimensionless mean local oil saturation increases almost linearly with an increase in the ratio of the dimensionless distance to the dimensionless time. Also, the profile of the mean local oil saturation versus distance is almost linear, showing a correlation of the mean local oil saturation with the dimensionless distance. 6. The curve of both the cumulative and instantaneous rates of growth of the finger population versus dimensionless pressure drop encompasses the first maximum at the onset of finger development and propagation. In other words, the sharpest increase in the rate of growth of the finger population 6391

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versus dimensionless pressure drop is accompanied with the sharpest pressure drop occurring at the onset of fingering and axial finger propagation along the diagonal distance during the early stages of displacement. The subsequent relatively uniform trend of the pressure drop versus time is synonymous with the second stage of the fingering pattern in LTPF (i.e., the spreading phase of the viscous fingering pattern).

Acknowledgment. The first author thanks the Petroleum Research Center at The Petroleum University of Technology, Tehran, Iran, for providing the laboratory facilities and the Research and Development Directorate of the National Iranian Oil Company for financial support in conducting the experiments. This paper was originally presented as SPE 137445 at the 2010 Canadian Unconventional Resources & International Petroleum Conference held in Calgary, Alberta, Canada.

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