Effects of Viscous and Capillary Forces on CO2 Enhanced Oil

Canada) was executed to acquire its sequential digital images as CO2 was gradually dissolved into it. ..... Stalkup , Jr. , F. I. Miscible Displac...
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Energy & Fuels 2007, 21, 3469–3476

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Effects of Viscous and Capillary Forces on CO2 Enhanced Oil Recovery under Reservoir Conditions Morteza Nobakht, Samane Moghadam, and Yongan Gu* Petroleum Technology Research Centre (PTRC), Petroleum Systems Engineering, Faculty of Engineering, UniVersity of Regina, Regina, Saskatchewan S4S 0A2, Canada ReceiVed July 9, 2007. ReVised Manuscript ReceiVed September 21, 2007

Carbon dioxide flooding has been proven to be one of the most effective and viable enhanced oil recovery (EOR) processes for light and medium oil reservoirs. In the past, an extremely large number of laboratory experiments and numerical simulations have been conducted to study the CO2 EOR process. However, the specific effects of viscous and capillary forces on this tertiary oil recovery process are neither thoroughly studied nor well understood yet. In this paper, an experimental study is carried out to examine the detailed effects of viscous and capillary forces on the CO2 EOR under the actual reservoir conditions. First, the equilibrium interfacial tensions between a light crude oil and CO2 are measured at different equilibrium pressures. Second, a series of CO2 coreflood tests are performed to measure the CO2 EOR at different CO2 injection pore volumes, pressures, and rates. Each CO2 coreflood test is terminated after a total of 1.5 pore volume of CO2 is injected. The detailed experimental results show that, in general, the measured equilibrium interfacial tension is reduced with the equilibrium pressure but the measured CO2 EOR at 1.5 pore volume of CO2 is increased with the CO2 injection pressure and rate. Finally, the measured CO2 EOR at 1.5 pore volume versus injection pressure data at different CO2 injection rates are related to the measured equilibrium interfacial tension versus equilibrium pressure data in terms of the complete capillary number, which is defined as the ratio of the viscous force to the capillary force for each CO2 coreflood test. This study shows that if the complete capillary number is in an intermediate range, the CO2 EOR increases quickly with the complete capillary number. Otherwise, the CO2 EOR is lower and remains almost constant for a smaller complete capillary number, or it is higher and remains unchanged for a larger complete capillary number.

Introduction Enhanced oil recovery (EOR) becomes increasingly important to the petroleum industry. After the primary recovery and secondary recovery, a typical residual oil saturation in a light or medium oil reservoir is in the range of 50–60% of the original oil in place (OOIP). For example, the total volume of unrecovered oil in the existing reservoirs in Canada is about 5 billion cubic meters.1 The extensive survey published every two years by Oil & Gas Journal shows that, at present, the EOR processes contribute significantly to overall oil production.2,3 Among the EOR methods for light and medium oil reservoirs, carbon dioxide flooding has been successful to a large extent under some favorable reservoir conditions.1,3,4 It is worthwhile to emphasize that the CO2 EOR method not only effectively enhances oil recovery but also considerably reduces greenhouse gas emissions.1 In the past five decades, there have been extensive laboratory studies, numerical simulations, and field applications of CO2 EOR processes. In general, it has been found that these tertiary processes can enhance oil recovery by 8–16% of the OOIP.5 * Corresponding author: Tel 1-306-585-4630; Fax 1-306-585-4855; e-mail [email protected]. (1) Farouq Ali, S. M.; Thomas, S. J. Can. Pet. Technol. 2000, 39 (2), 7–11. (2) Moritis, G. Oil Gas J. 2004, 102 (4), 45–65. (3) Moritis, G. Oil Gas J. 2006, 104 (15), 37–57. (4) Stalkup Jr., F. I. Miscible Displacement; SPE: Richardson, TX, 1983; Monogr. Ser., Vol. 8. (5) Rogers, J. D.; Grigg, R. B. SPE ReserVoir EVal. Eng. 2001, 4 (3), 375–386.

It has long been attempted to understand the effects of the interfacial interactions, such as the interfacial tension and wettability, on the reservoir productivity and ultimate oil recovery.6,7 In particular, the interfacial tension is considered to be an important factor that may cause one-third of the OOIP unrecoverable by solution gas drive or water flooding alone.8 In the CO2 flooding process, the oil and CO2 relative permeabilities and the residual oil saturation can be related to the crude oil–CO2 interfacial tension through a dimensionless number, which compares either the capillary force with the viscous force in the horizontal displacement processes or the capillary force with the gravity force in the gravity drainage processes.9,10 Although there have been some studies on the effects of interfacial tension of a crude oil–CO2 system on the oil and CO2 relative permeabilities in the CO2 flooding process,11,12 there are not enough experimental data available in the literature for analyzing the effect of interfacial tension between a crude oil and CO2 on the CO2 EOR in this process. It has been found that the interfacial tension of a crude oil–CO2 system is (6) Morrow, N. R. J. Pet. Technol. 1990, 42 (12), 1476–1484. (7) Rao, D. N. Pet. Sci. Technol. 2001, 19 (1), 157–188. (8) Grattoni, C. A.; Dawe, R. A. J. Pet. Sci. Eng. 2003, 39 (3), 297– 308. (9) Blom, S. M. P.; Hagoort, J. How to Include the Capillary Number in Gas Condensate Relative Permeability Functions. Presented at SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept 27– 30, 1998; Paper SPE 49268. (10) Grattoni, C. A.; Jing, X. D.; Dawe, R. A. J. Pet. Sci. Eng. 2001, 29 (1), 53–65. (11) Bardon, C.; Longeron, D. G. SPE J. 1980, 20 (10), 391–401. (12) Asar, J.; Handy, L. L. SPE ReserVoir Eng. 1988, 3 (1), 257–264.

10.1021/ef700388a CCC: $37.00  2007 American Chemical Society Published on Web 11/03/2007

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significantly reduced when CO2 is injected into an oil reservoir at a high reservoir pressure.13,14 The reduced interfacial tension alters the viscous force–capillary force balance and thus lowers the residual oil saturation. Therefore, it is of fundamental and practical importance to study the detailed effects of the viscous and capillary forces on various CO2 flooding processes. Among many existing methods for determining the interfacial tension, the pendant drop method is probably the most suitable for measuring the interfacial tension between a crude oil and a test solvent at high pressures and elevated temperatures.13,14 In essence, this method determines the interfacial tension from the drop shape analysis. In the past, the pendant drop method has been used to measure the interfacial tension by photographing a pendant drop and then measuring the drop dimensions from the negative film.15 Recently, the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case has been developed by Neumann and co-workers16,17 and employed to measure the dynamic and equilibrium interfacial tensions of different crude oil–solvent systems at high pressures and temperatures.13,14,18 In comparison with the other methods, the ADSA technique for the pendant drop case is accurate for the interfacial tension measurement ((0.05 mJ/m2), fully automatic, and completely free of the operator’s subjectivity.14,16,17 The purpose of this paper is to study the effects of the viscous and capillary forces on the CO2 flooding performance under the actual reservoir conditions. More specifically, first, the ADSA technique for the pendant drop case is applied to measure the dynamic and equilibrium interfacial tensions between a crude light oil sample and CO2 at 12 different equilibrium pressures and T ) 27 °C. Second, a total of 13 CO2 coreflood tests are conducted at different CO2 injection pore volumes, pressures, and rates as well as a constant temperature of T ) 27 °C to recover the crude oil sample from a horizontal sand pack with the porosity of 36.8–37.2% and the permeability of 16.9–18.0 darcy. Both the porosity and permeability of the sand pack are measured prior to each coreflood test. The accumulative oil production from the sand pack at each different injected pore volume of CO2 is measured. Each CO2 coreflood test is terminated after 1.5 pore volume of CO2 is injected. The accumulative oil production at the end of each test is then used to determine the CO2 EOR under the coreflood test conditions. Finally, the complete capillary number, which is defined as the ratio of the viscous force to the capillary force, is calculated for each CO2 coreflood test. The oil recovery versus complete capillary number data are used to examine the detailed effects of the viscous and capillary forces on the CO2 EOR. Experimental Section Materials. The light crude oil sample was collected from the Weyburn oilfield in Saskatchewan, Canada. The density and viscosity of the cleaned crude oil sample were measured to be Foil ) 901.0 kg/m3 and µoil ) 16.6 mPa · s at the atmospheric pressure and T ) 27 °C, respectively. The asphaltene content of the crude oil was measured to be wasp ) 5.7 wt % (n-pentane insoluble) by using the standard ASTM D2007 method and 0.2 µm polytetrafluoroethylene (PTFE) syringe filters (Target, National Scientific). The (13) Yang, D.; Tontiwachwuthikul, P.; Gu, Y. J. Chem. Eng. Data 2005, 50 (4), 1242–1249. (14) Yang, D.; Gu, Y. Pet. Sci. Technol. 2005, 23 (9), 1099–1112. (15) McCaffery, F. G. J. Can. Pet. Technol. 1972, 11 (3), 26–32. (16) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93 (1), 169–183. (17) Cheng, P.; Li, D.; Boruvka, L.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43 (2), 151–167. (18) Rao, D. N.; Lee, J. I. J. Colloid Interface Sci. 2003, 262 (2), 474– 482.

Nobakht et al. Table 1. Compositional Analysis Result of the Weyburn Light Crude Oil carbon number

wt %

carbon number

wt %

C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7 C8 C9 C10 C11 C12 C13 C14

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.20 4.68 7.79 6.53 4.63 4.17 4.20 4.05

C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30+

4.08 3.92 3.75 4.33 3.42 2.45 2.55 1.55 1.87 1.69 1.57 1.60 1.49 1.48 1.43 23.57

compositional analysis result of this crude oil was obtained by using the simulated distillation method and is given in Table 1. It can be seen from this table that there are no hydrocarbon components under C7 and that heavy hydrocarbon components of C30+ are found to be 23.57 wt %. The purity of carbon dioxide (Praxair, Canada) is 99.99%. The densities of CO2 at different pressures and T ) 27 °C were calculated by using the CMG Winprop module (Version 2006.11, Computer Modelling Group Limited, Canada) with the Peng–Robinson equation of state.19 Interfacial Tension Measurement. ADSA Setup. In this study, the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case was used to measure the dynamic and equilibrium interfacial tensions of the crude oil–CO2 system at different equilibrium pressures and a constant temperature of T ) 27 °C. A schematic diagram of the ADSA system for the pendant drop case used in this study is shown in Figure 1. The major component of this experimental setup was a see-through windowed high-pressure cell (IFT-10, Temco). The maximum operating pressure and temperature of this pressure cell are equal to 69 MPa and 177 °C, respectively. A stainless steel syringe needle was installed at the top of the pressure cell and used to form a pendant oil drop, whose outer diameter and wall thickness were equal to 1.18 and 0.39 mm, respectively. The crude oil was introduced from a crude oil sample cylinder (DBR, Canada) to the syringe needle by using a programmable syringe pump (100DX, ISCO Inc.). The constant temperature during the interfacial tension measurement was maintained by wrapping the pressure cell with a heating tape (HT95504x1, Electrothermal), which was connected to a temperature controller (Standard-89000-00, Cole-Parmer, Canada). The equilibrium pressure inside the pressure cell was measured by using a digital pressure gauge (DTG-6000, 3D Instruments). A light source and a glass diffuser were used to provide uniform illumination for the pendant oil drop. A microscope camera (MZ6, Leica, Germany) was used to capture the sequential digital images of the dynamic pendant oil drop inside the pressure cell at different times. The high-pressure cell was positioned between the light source and the microscope camera. The entire ADSA setup and the high-pressure cell were placed on a vibration-free table (RS4000, Newport). The digital images of the dynamic pendant oil drop at different times were acquired in tagged image file format (TIFF) by using a digital frame grabber (Ultra II, Coreco Imaging, Canada). A Dell desktop computer was used to store the digital oil drop images and perform subsequent image analysis, digitization, and computation. The PC-based digital image system can grab the sequential digital oil drop images at the speed of three digital images per second. Experimental Procedure. Prior to each experiment, the highpressure cell was cleaned with kerosene and acetone, then flushed (19) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15 (1), 58–64.

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Figure 1. Schematic diagram of the experimental setup used for measuring the dynamic and equilibrium interfacial tensions between the crude oil and CO2 by applying the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case.

with nitrogen, and finally purged with CO2 for at least five times. The pressure cell was then pressurized with CO2 to a prespecified pressure by using a manual positive displacement pump (PMP500-1-10-HB, DBR, Canada). After the CO2 was injected, it usually took 30–60 min for the pressure and temperature inside the pressure cell to reach their stable values. Then the crude oil was introduced from the crude oil sample cylinder, whose pressure was maintained 0.1–0.5 MPa higher than that of CO2 phase inside the pressure cell. The pendant oil drop was formed at the tip of the syringe needle, which was installed at the top of the high-pressure cell. Once a well-shaped pendant oil drop was formed, a digital image acquisition program (TciPro, Coreco Imaging, Canada) was executed to acquire its sequential digital images as CO2 was gradually dissolved into it. The time interval for the sequential digital drop image acquisition was properly set so that it was smaller at the beginning but larger when the pendant oil drop was almost saturated with CO2. The acquired digital drop images were automatically stored in the computer as TIFF files. For each acquired digital oil drop image, a high-precision calibration grid was used to calibrate and correct possible optical distortions. After the sequential digital images of the dynamic pendant oil drop at different times were acquired and stored in the computer, the ADSA program for the pendant drop case was executed to determine the dynamic and equilibrium interfacial tensions of the pendant oil drop and the drop profile from each digital drop image. The output data also included the radius of curvature at the apex point, the surface area, and volume of the pendant oil drop. Only the local gravitational acceleration and the density difference between the crude oil and CO2 were required as input data for this program. The interfacial tension measurement was repeated for at least three different pendant oil drops to ensure satisfactory repeatability at each prespecified pressure and constant temperature. In this study, the crude oil–CO2 interfacial tensions were measured at a constant temperature of T ) 27 °C and 12 different equilibrium pressures of P ) 2.4–11.0 MPa. Coreflood Test. Coreflood Apparatus. In this study, highpressure coreflood tests were performed to study the effects of CO2 injection pressure and rate as well as injected pore volume of CO2 on the CO2 enhanced oil recovery. A schematic diagram of the coreflood apparatus used in the coreflood test is shown in Figure 2. The experimental setup consisted of the following major parts: a personal computer, an automatic positive displacement pump, three hydraulic cylinders, a sand-packed high-pressure coreholder, a back-pressure regulator (BPR), and a gas flow meter. The

automatic positive displacement pump (PMP-1000-1-10-MB, DBR, Canada) was used to pump the crude oil or CO2 through the sand pack or the distilled water to apply the so-called overburden pressure. Three hydraulic cylinders (DBR, Canada) were used to contain and deliver the crude oil, CO2, and the distilled water. These three hydraulic cylinders and the sand-packed coreholder were placed inside an air bath. An electric heater (Super Electric Co., Canada) and a temperature controller (Standard-89000-00, ColeParmer, Canada) were used to heat the air bath and keep its constant temperature. The BPR was used to maintain the prespecified injection pressure inside the coreholder during each CO2 coreflood test. The gas flow meter (GFM 17, Aalborg) was used to measure CO2 production rate during the CO2 coreflood test. Experimental Preparations. The sand pack used in this study was 12 in. long and 2 in. in inner diameter and was packed with 60–80 mesh Ottawa sands (U.S. Silica Co.). The porosity of each sand pack was measured by using the imbibition method and found to be in the range of φ ) 36.8–37.2%. After the porosity measurement, the permeability of each sand pack was measured. A homemade manometer was used to measure the small pressure drop along the sand pack. Two liquids were used in the manometer, distilled water with the density of 1000 kg/m3 and 1,3-dichlorobenzene (Fisher Scientific) with the density of 1288 kg/m3. These two liquids were immiscible so that an interface was formed between them. During the permeability measurement, the distilled water was used as a working medium. The permeability of each sand pack was in the range of k ) 16.9–18.0 darcy. After the permeability measurement, the wet sands were dried by using the pressurized air for at least 48 h. Then the dry sand pack was saturated with the crude oil, and the initial oil saturation was found to be in the range of Soi ) 97.2–99.3%. The detailed physical properties of the 13 sand packs used for the CO2 coreflood tests at T ) 27 °C are summarized in Table 2. Experimental Procedure. The CO2 coreflood test was conducted with each sand pack at different CO2 injection pressures and rates and T ) 27 °C. After the sand pack was initially saturated with the crude oil, the temperature inside the air bath was set at T ) 27 °C. After at least 48 h, the crude oil was injected into the sand pack to pressurize the sand pack. Meanwhile, the BPR was set at a slightly higher pressure than the pressure inside the sand pack. In this way, the pressure drop along the sand pack during the pressurization period was small. Once the pressure inside the coreholder reached the prespecified injection pressure, the crude oil injection was

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Figure 2. Schematic diagram of the coreflood apparatus used for measuring the CO2 EOR. Table 2. Physical Properties of Sand Packs and the Experimental Conditions, Complete Capillary Numbers and EOR Data for 13 CO2 Coreflood Tests at T ) 27 °Ca test no.

φ (%)

k (µm2)

Soi (%)

P (MPa)

qCO2 (cm3/min)

µCO2 (µPa · s)

σeq (mJ/m2)

NCA

R (%)

1 2 3 4 5 6 7

37.2 37.1 37.1 37.0 36.9 36.9 36.9

18.0 17.4 18.0 17.6 17.7 17.1 17.1

97.8 99.0 98.1 99.3 98.6 98.8 97.5

2.77 5.51 5.93 6.48 7.17 9.58 11.03

0.5 0.5 0.5 0.5 0.5 0.5 0.5

16.3 18.7 19.6 21.7 62.6 87.8 101.2

16.61 7.89 6.34 4.22 2.11 1.47 1.13

6.72 × 10-4 1.65 × 10-3 2.12 × 10-3 3.57 × 10-3 2.06 × 10-2 4.21 × 10-2 6.32 × 10-2

13.2 14.4 15.7 33.7 53.7 57.7 57.8

8 9 10 11 12 13

37.2 37.1 37.2 37.2 37.0 36.8

18.0 18.0 17.1 17.3 17.4 16.9

98.7 99.1 99.0 97.9 97.2 98.9

2.43 4.51 5.17 6.45 9.31 10.69

1.0 1.0 1.0 1.0 1.0 1.0

16.2 17.4 18.2 21.6 85.3 98.0

17.53 11.68 9.28 4.33 1.53 1.21

1.27 × 10-3 2.04 × 10-3 2.76 × 10-3 6.97 × 10-3 7.79 × 10-2 1.15 × 10-1

13.7 14.5 21.8 47.1 58.0 58.2

a Notes: φ ) porosity, k ) permeability, S ) initial oil saturation, P ) CO injection pressure, q oi 2 CO2 ) CO2 volume injection rate, µCO2 ) viscosity of the injected CO2, σeq ) equilibrium interfacial tension between the crude oil and the injected CO2, NCA ) complete capillary number, and R ) CO2 EOR at 1.5 injected pore volume of CO2.

terminated and the CO2 injection was commenced with a constant volume injection rate to recover the crude oil from the sand pack. After the produced oil from the sand pack passed through the BPR and flowed to an oil sample collector, it was weighed at a certain time interval to determine the accumulative oil production. The CO2 dissolved into the produced oil was flashed from the oil sample collector and passed through the gas flow meter, where the CO2 production rate was measured every second and automatically stored in a personal computer. The CO2 production rate versus time data were then integrated to determine the accumulative CO2 production. In this study, each CO2 coreflood test was terminated when a total of 1.5 pore volume of CO2 was injected. After the CO2

injection was stopped, a blow-down process was commenced. This process was continued until the pressure inside the coreholder reached the atmospheric pressure and no more oil and CO2 were produced.

Results and Discussion Dynamic Interfacial Tension. As described in the interfacial tension measurement, the high-pressure cell was first filled with CO2 at a prespecified pressure and a constant temperature of T ) 27 °C. Then a crude oil sample was introduced into the pressure cell. Once the pendant oil drop was formed, CO2 was

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Figure 3. Measured dynamic interfacial tensions between the Weyburn crude oil and CO2 at 12 different equilibrium pressures and T ) 27 °C.

Figure 4. Measured equilibrium interfacial tension of the Weyburn crude oil–CO2 system versus equilibrium pressure data at T ) 27 °C.

gradually dissolved into the oil drop. The dissolution of CO2 into the pendant oil drop was continued until the latter was completely saturated with the former.20 In order to examine the effect of dissolution of CO2 into the pendant oil drop on the crude oil–CO2 interfacial tension, the dynamic interfacial tension was measured during the CO2 dissolution process. In the past, the dynamic interfacial tension phenomenon was studied for different EOR processes.13,14,21–23 The measured dynamic interfacial tension of the crude oil–CO2 system versus time data under 12 different equilibrium pressures at T ) 27 °C are shown in Figure 3. All the dynamic interfacial tension measurements lasted about 140 min, except at P ) 6.6 MPa. It was found that the pendant oil drop could only stay at the tip of the syringe needle for about 30 min at P ) 6.6 MPa. This is probably due to wettability alteration of the oil phase on the stainless steel syringe needle surface,14 which is caused by phase change of the injected CO2. It should be mentioned that the density of the oil with dissolved CO2 is assumed to be constant for the dynamic interfacial tension measurement, as variations of the oil density with the CO2 dissolution at these pressures are negligible.13,14,24 Figure 3 shows that the measured dynamic interfacial tensions reach their equilibrium values after at most 30 min under different equilibrium pressures. This fact indicates that the pendant oil drop surface is quickly saturated with CO2, whereas the CO2 dissolution into the entire pendant oil drop proceeds for a relatively long time.20 It can also be seen from this figure that the dynamic interfacial tension is lower at a higher equilibrium pressure. This is because the solubility of CO2 in the crude oil is higher when the equilibrium pressure is higher.13,14 In addition, the dynamic interfacial tension reaches its equilibrium value more quickly at a higher equilibrium pressure. In the dynamic interfacial tension measurement, one important physical phenomenon was observed. At the equilibrium pressures equal to or higher than 6.6 MPa, the light hydrocarbon components were observably extracted from the pendant oil drop into CO2 phase at the beginning, which is referred to as the

initial strong light-components extraction process.14 During this strong extraction process, the crude oil was continuously introduced from the crude oil sample cylinder such that a wellshaped pendant oil drop could be formed eventually for the interfacial tension measurement. Hence, some light components of the original crude oil were quickly extracted, and the final pendant oil drop formed at the tip of the syringe needle was mainly composed of the heavy components of the original crude oil. These remaining heavy components made the measured dynamic interfacial tension between the crude oil and CO2 slightly reduced with the equilibrium pressure at P g 7.2 MPa. Equilibrium Interfacial Tension. In the dynamic interfacial tension measurement, it was found that at any equilibrium pressure the dynamic interfacial tension for the crude oil–CO2 system ultimately reaches a constant value, which is referred to as the equilibrium interfacial tension. The average value of the equilibrium interfacial tensions of three repeated dynamic interfacial tension measurements at the same equilibrium pressure and temperature is reported in this paper. The measured equilibrium interfacial tensions between the crude oil and CO2 at different equilibrium pressures and T ) 27 °C are plotted in Figure 4. It is found from this figure that the measured equilibrium interfacial tension is reduced almost linearly with the equilibrium pressure as long as the equilibrium pressure is equal to or lower than 7.2 MPa. The interfacial tension reduction with the equilibrium pressure is attributed to the increased solubility of CO2 in the crude oil at an increased equilibrium pressure.13,14 Figure 4 also shows that once the equilibrium pressure is higher than a threshold pressure (i.e., 7.2 MPa), an equilibrium interfacial tension of as low as 1–2 mJ/m2 is achieved. In this case, the equilibrium interfacial tension reduction is small if the equilibrium pressure is further increased. Similar results were also reported for other crude oil–CO2 systems in the literature.13,14 On the basis of these experimental results, it becomes obvious that there is no need to overemphasize the pressure effect on the equilibrium interfacial tension for the crude oil–CO2 system as long as the reservoir pressure exceeds the threshold pressure, e.g., P ) 7.2 MPa at T ) 27 °C in the present case. Effects of CO2 Injection Pressure and Rate on Oil Recovery. In this study, a total of 13 CO2 coreflood tests were carried out along the horizontal sand packs at a constant temperature of T ) 27 °C to examine the effects of CO2 injection pressure and rate on the enhanced oil recovery by CO2 flooding. Parts a and b of Figure 5 show the measured oil recovery versus

(20) Yang, C.; Gu, Y. Ind. Eng. Chem. Res. 2005, 44 (12), 4474–4483. (21) Borwankar, R. P.; Wasan, D. T. AIChE J. 1986a, 32 (3), 455– 466 (22) Borwankar, R. P.; Wasan, D. T. AIChE J. 1986b, 32 (3), 467– 476 (23) Taylor, K. C.; Hawkins, B. F.; Islam, M. R. J. Can. Pet. Technol. 1990, 29 (1), 50–55. (24) Sayegh, S. G.; Rao, D. N.; Kokal, S.; Najman, J. J. Can. Pet. Technol. 1990, 29 (6), 31–39.

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Figure 6. Measured CO2 EOR at 1.5 pore volume of CO2 versus the injection pressure at two different constant CO2 volume injection rates and T ) 27 °C.

Figure 5. (a) Measured CO2 EOR versus the injected pore volume of CO2 at a constant volume injection rate of qCO2 ) 0.5 cm3/min and T ) 27 °C. (b) Measured CO2 EOR versus the injected pore volume of CO2 at a constant volume injection rate of qCO2 ) 1.0 cm3/min and T ) 27 °C.

the injected pore volume of CO2 at different injection pressures and two different constant volume injection rates of 0.5 and 1.0 cm3/min, respectively. The ordinate of these two figures represents the CO2 EOR and is defined as the ratio of the mass of the produced oil to that of the initial oil in the sand pack. It is seen from Figure 5a,b that, expectedly, the CO2 EOR is increased with the injected pore volume of CO2. However, the oil recovery at each injection pressure and rate reaches its maximum after ∼1.5 pore volume of CO2 is injected. Therefore, each CO2 coreflood test was terminated when the injected pore volume of CO2 reached 1.5. The measured oil recovery at 1.5 pore volume of CO2 versus injection pressure data at two different volume injection rates and a constant temperature of T ) 27 °C are further summarized in Figure 6. It is noted from this figure that, roughly speaking, there are three different regions in the injection pressure range tested. First, at the injection pressures equal to or lower than 4.51 MPa, the CO2 EOR is low and almost independant of CO2 injection pressure and rate. In this injection pressure range, the injected CO2 is in gas phase with an extremely low viscosity, which causes the early CO2 breakthrough in the coreflood tests. Low oil recovery in this region is attributed to the early CO2 breakthrough and relatively high equilibrium interfacial tensions of the crude oil–CO2 system. Second, as the injection pressure increases, the CO2 EOR increases significantly. In this region, the oil recovery also increases with the volume injection rate.

The increased oil recovery with CO2 injection pressure is due to the increased viscosity of injected CO2 and the reduced equilibrium interfacial tension of the crude oil–CO2 system. The latter is caused by the increased CO2 solubility in the crude oil at an increased injection pressure. Third, when the CO2 injection pressure exceeds 7.17 MPa, the CO2 EOR remains high but becomes insensitive to the injection pressure and rate. In this case, the maximum oil recovery at 1.5 pore volume of CO2 is achieved, and the residual oil saturation in the sand pack is reached. It is worthwhile to note that the equilibrium interfacial tensions between the crude oil and CO2 remain low and almost constant at the equilibrium pressures higher than 7.2 MPa, which makes the CO2 EOR almost unchanged with the CO2 injection pressure and rate in the third region. Complete Capillary Number. In general, viscous, capillary, hydrodynamic, and gravity forces control fluid flow through a porous medium. A ratio between any two of these four forces can be expressed as a dimensionless number.10 Thus, a total of three independant dimensionless numbers can be defined and used to quantify the effects of these four controlling forces on the CO2 EOR process. One important dimensionless number is the capillary number, which is defined as the ratio of the viscous force to the capillary force and is traditionally calculated by using the following equation:4,25,26 Nca )

vCO2µCO2

(1) φσ where vCO2 is the linear velocity of the injected CO2 through the porous medium, which is equal to the CO2 volume injection rate divided by the cross-sectional area of the porous medium; µCO2 is the viscosity of the injected CO2 at a given injection pressure; φ is the porosity of the porous medium; and σ is the interfacial tension between the crude oil and CO2. In general, the capillary number can be used to study the effects of the viscous and capillary forces on the oil recovery during an immiscible displacement, whether it is an imbibition or drainage process. In this study, the equilibrium interfacial tensions, σeq, between the crude oil and CO2 under different coreflood experimental conditions are used to calculate the capillary number. This is because the dynamic interfacial tension of the crude oil–CO2 system reaches the equilibrium interfacial tension within a relatively short period (at most 30 min) in the (25) Chatzis, I.; Morrow, N. R. SPE J. 1984, 24 (5), 555–562. (26) Islam, M. R.; Bentsen, R. G. AOSTRA J. Res. 1987, 3 (2), 69–90.

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equilibrium pressure range tested. However, the retention time in each CO2 coreflood test, which is equal to the pore volume of the sand pack divided by the CO2 volume injection rate, was approximately 8 and 4 h at qCO2 ) 0.5 and qCO2 ) 1.0 cm3/min, respectively. It should be noted that the above-defined capillary number, Nca, does not take account of the length and pore size of a porous medium,27 which affect the viscous force through the porous medium. In the literature, the complete capillary number, NCA, for a circular capillary, is defined as27 NCA )

4vCO2µCO2l φσeqr

(2)

where l and r are the length and radius of the circular capillary, respectively. In comparison of eq 1 and eq 2, it becomes clear that Nca defined in eq 1 represents the ratio of the viscous force to the capillary force when r ) 4l. In consideration of the actual pore size and shape distributions in a real oil reservoir, it is useful to relate the above-defined complete capillary number, NCA, to some measurable reservoir characteristics, such as permeability and porosity of the oil reservoir. For conduit flow through a bundle of identical circular capillaries, Dullien27 derived the following relation: k)

φr2 8

Figure 7. Calculated complete capillary number versus injection pressure data for the CO2 coreflood tests at two different constant CO2 volume injection rates and T ) 27 °C.

(3)

Here, k is the permeability, φ is the porosity, and r is the radius of the identical circular capillaries. Alternatively, the complete capillary number can be defined in terms of the permeability and porosity of the porous medium: NCA )

√2vCO µCO l 2 2 σeq√kφ

(4)

It is worthwhile to mention that a capillary number, which is similar to the above-defined complete capillary number, NCA, has been recently used for fluid flow through different porous media.28,29 Based on eq 4, with known permeability, porosity, length, and cross-sectional area of the porous medium and CO2 volume injection rate, the complete capillary number, NCA, can be calculated from the CO2 viscosity and the equilibrium interfacial tension of the crude oil–CO2 system. In this study, the CO2 viscosity is calculated by applying the Jossi–Stiel–Thodos correlation.30 The equilibrium interfacial tension between the crude oil and CO2 at a prespecified injection pressure is obtained by applying the linear interpolation of the measured equilibrium interfacial tension versus equilibrium pressure data at T ) 27 °C given in Figure 4. The length and cross-sectional area of the sand packs used in the CO2 coreflood tests are equal to 30.48 and 20.27 cm2, respectively. The complete capillary numbers, NCA, for the 13 CO2 coreflood tests are calculated and listed in Table 2. Furthermore, the variations of the calculated complete capillary number, NCA, with the CO2 injection pressure for these CO2 coreflood tests at two different constant CO2 volume injection rates and T ) 27 °C are shown in Figure 7. It is seen from this figure that at a constant CO2 volume injection rate (27) Dullien, F. A. L. Porous Media: Fluid Transport and Pore Structure, 2nd ed.; Academic Press: San Diego, CA, 1992. (28) Melean, Y.; Bureau, N.; Broseta, D. SPE ReserVoir EVal. Eng. 2003, 6 (4), 244–254. (29) Cinar, Y.; Orr Jr., F. M. SPE ReserVoir EVal. Eng. 2005, 8 (1), 33–43. (30) Jossi, J. A.; Stiel, L. I.; Thodos, G. AIChE J. 1962, 8 (1), 59–63.

Figure 8. Measured CO2 EOR versus the calculated complete capillary number for the CO2 coreflood tests at two different constant CO2 volume injection rates and T ) 27 °C.

the complete capillary number, NCA, increases with the CO2 injection pressure. This is because the viscosity of the injected CO2, µCO2, is increased (i.e., larger viscous force), but the equilibrium interfacial tension, σeq, of the crude oil–CO2 system is reduced (i.e., smaller capillary force) at an increased injection pressure. Figure 7 also shows that at a given injection pressure the complete capillary number slightly increases with the injection rate due to a larger viscous force at an increased CO2 volume injection rate (i.e., an increased νCO2). Combining Figures 6 and 7 together, Figure 8 shows the relation between the measured CO2 EOR and the calculated complete capillary number. This figure shows that, in general, the CO2 EOR increases with the complete capillary number. The remaining oil in the porous medium can be displaced by an increased viscous force, which pushes the oil out, and/or by a reduced capillary force, which holds the oil in the porous medium.31 This can explain a higher CO2 EOR at a larger complete capillary number. There are also three regions in the complete capillary number range tested. First, at small complete capillary numbers (NCA e 2.12 × 10-3), the CO2 EOR increases marginally with the complete capillary number. This is the region where the large capillary force dominates the CO2 (31) Lake, L. W. Enhanced Oil RecoVery; Prentice Hall: Englewood Cliffs, NJ, 1989.

3476 Energy & Fuels, Vol. 21, No. 6, 2007

displacement process, which leads to low CO2 EOR. In this case, because of small viscous force relative to large capillary force, CO2 displaces the oil from the largest pores, which have the lowest capillary entry pressures.5 Second, as the complete capillary number becomes larger, the CO2 EOR increases more drastically with the complete capillary number. For example, the CO2 EOR at NCA ) 2.06 × 10–2 is 53.7%, which is about 3.4 times the 15.7% CO2 EOR at NCA ) 2.12 × 10–3. In this region, the CO2 displacement changes from the capillary force dominated displacement to a rather different process, in which there is an obvious competition between the viscous force and the capillary force. This change occurs in the range of NCA ) 2.12 × 10–3–4.21 × 10–2. Finally, if the complete capillary number is equal to or larger than 4.21 × 10–2, the CO2 EOR reaches its maximum and becomes the least sensitive to the complete capillary number. The maximum oil recovery at 1.5 pore volume of CO2 is achieved, and the unrecovered crude oil (i.e., the residual oil saturation) remains in the smallest pores, which have the highest capillary entry pressures. Because of extremely high capillary entry pressures in the small pores, the viscous force is still not strong enough to completely overcome the capillary force and mobilize the remaining oil in the smallest pores. Also, the “oil-phase network” loses its continuity due to low residual oil saturation in this case.5 As a result, the displacement efficiency of the residual oil by CO2 flooding is maximized, and an almost constant high oil recovery is reached at a large complete capillary number. Conclusions In this paper, the dynamic and equilibrium interfacial tensions between a crude oil and CO2 are measured at 12 different equilibrium pressures and T ) 27 °C by using the ADSA technique for the pendant drop case. It is found that the dynamic interfacial tension is reduced to a constant value in a short time. It is also found that the measured equilibrium interfacial tension is reduced almost linearly with the equilibrium pressure as long

Nobakht et al.

as the equilibrium pressure is lower than a threshold pressure. Once the equilibrium pressure is higher than the threshold pressure, the measured equilibrium interfacial tension is slightly reduced. In addition, a total of 13 CO2 coreflood tests are conducted to study the effects of injection volume of CO2, injection pressure, and rate on the CO2 enhanced oil recovery (EOR). The CO2 EOR data versus the injected pore volume of CO2 at different injection pressures and rates show that, in general, the CO2 EOR is increased with the injected volume of CO2. However, the CO2 EOR at a given injection pressure and rate achieves its maximum after 1.5 pore volume of CO2 is injected. The detailed experimental data of the CO2 coreflood tests also show that there are three different regions in the CO2 EOR versus injection pressure plot at two different injection rates. The measured CO2 EOR is increased almost linearly with the injection pressure when the injection pressure is in an intermediate range. In this case, the measured oil recovery is found to increase with the CO2 injection rate under the same injection pressure. Otherwise, the measured oil recovery at a lower or higher injection pressure remains almost unchanged, regardless of the injection rate. Finally, the complete capillary number is calculated and related to the CO2 EOR for each CO2 coreflood test. This experimental study shows that the CO2 EOR versus complete capillary number plot can be roughly divided into three regions. In an intermediate range of the complete capillary number, the oil recovery is increased quickly with the complete capillary number. Otherwise, the CO2 EOR has an almost constant lower or higher value if the complete capillary number is smaller or larger. Acknowledgment. The authors acknowledge the discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and the innovation fund from the Petroleum Technology Research Centre (PTRC) at the University of Regina to Y. Gu. EF700388A