Diffusion coefficients of supercritical CO2 in oil-saturated cores under low permeability reservoir conditions

Journal of CO2 Utilization 14 (2016) 47–60

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Diffusion coefficients of supercritical CO2 in oil-saturated cores under low permeability reservoir conditions Songyan Li* , Zhaomin Li* , Quanwei Dong College of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China

A R T I C L E I N F O

A B S T R A C T

Article history: Received 2 November 2015 Received in revised form 18 January 2016 Accepted 4 February 2016 Available online xxx

CO2 diffusion in oil-saturated porous media with low permeability is of great importance for the project design, risk assessment, and performance forecast of carbon capture and storage (CCS) or enhanced oil recovery (EOR). This paper developed a method to determine CO2 diffusion in oil-saturated cores under low permeability reservoir conditions. Core, crude oil and experimental parameters were taken from the representative low permeability reservoir. In the solution of the mathematical model, oil saturation was introduced in to diffusion equation, an oil-phase swelling caused by gas dissolution was considered, but a water-phase swelling was not, which is in agreement with the actual diffusion situation. The error caused by the state equation of carbon dioxide was eliminated, improving the calculation accuracy of the diffusion coefficient. The effects of pressure (6.490–29.940 MPa), temperature (70–150
C), oil saturation (0–63.58%) and permeability (8.62–985.06 mD) on the diffusion coefficient of supercritical CO2 in lowpermeability reservoirs were studied. The order of the diffusion coefficient is from 1010 to 109 m2/s. The results show that with an increase in pressure and temperature, the CO2 diffusion coefficient in the porous media saturated with oil firstly increases significantly and then the rate of increase gradually slowed down. The CO2 diffusion coefficient increases greatly with the oil saturation in porous media. The CO2 diffusion coefficient first increases greatly with permeability, and when the permeability of the core is greater than approximately 100 mD, it remains almost stable. The experimental results can provide theoretical support for CO2 transport in porous media. ã 2016 Elsevier Ltd. All rights reserved.

Keywords: Supercritical CO2 Porous media Diffusion coefficient

1. Introduction 1.1. Carbon capture, utilization and storage Global warming caused by the excessive emission of greenhouse gases has become one of the most significant environmental problems. Flue gas from fossil fuel power plants is the largest longterm carbon dioxide emission source, which accounts for 30% of the total emissions. Carbon dioxide capture from power plant flue gas and geological storage is one of the potential ways of reducing greenhouse gas emissions to address global climate change [1–5]. Carbon capture and storage (CCS) has been widely regarded as a potential, alternative solution for the reduction of carbon dioxide in the atmosphere to mitigate climate warming [6–9]. However, the problem for CCS is that the profit is very small and that it cannot make up for the high cost. CO2 enhanced oil recovery can not only achieve the reduction in carbon dioxide emissions but also

* Corresponding authors. E-mail addresses: [email protected] (S. Li), [email protected] (Z. Li). http://dx.doi.org/10.1016/j.jcou.2016.02.002 2212-9820/ ã 2016 Elsevier Ltd. All rights reserved.

improve the crude oil recovery of reservoirs; this process has been widely used in oil field development. CO2 enhanced oil recovery possesses the most potential for carbon capture, utilization and storage (CCUS) [10–15]. 1.2. Carbon dioxide diffusion in porous media In the process of oil displacement by carbon dioxide, the diffusion of the injected carbon dioxide in porous media saturated with crude oil is particularly important. Therefore, determining the carbon dioxide diffusion coefficient in the porous media saturated with crude oil is important for the development of carbon dioxide flooding technology [16–20]. Many researchers have conducted the experiments on gas diffusion coefficients in bulk liquids since the 1930s using a PVT cell. The PVT method has been successfully used to measure the diffusion coefficient of gases in liquids under different pressures [21–25]. The dissolution of these gases into the liquids decreases the liquid density, which will not cause natural convection. However, the PVT method cannot be applied to measure CO2 diffusion in most liquids with natural convection [26–29].

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S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Grogan et al. used a glass capillary instead of a PVT cell to measure the diffusion coefficient of CO2 in light oil under high pressures [22]. To reduce the natural convection induced by the density decrease, the glass capillary was positioned horizontally. A CO2 gas slug was injected into the middle of a capillary that was filled with oil. Although this method can be used to determine the diffusion coefficient of CO2 in the liquid phase, it is difficult to be applied to the measurement of the diffusion coefficient in liquidsaturated porous media. Renner proposed an experimental method using liquid saturated Berea cores to test the effective diffusion coefficient of CO2 in porous media [17]. Glass fiber and epoxy resins were used for sealing one end face and the side surface of the Berea core in his measurement, so gas could only diffuse from one end face of the core. He found that the measured diffusion coefficient was much greater when the core was vertically placed than when the core was located horizontally due to the natural convection caused by the changes in density of the oil phase in the porous media. Krooss developed an experimental method for measuring the effective diffusion coefficient of hydrocarbon gases in sedimentary rocks saturated with water at atmospheric pressure and at different temperatures [30,31]. A rock layer with a thickness of 3.10 mm that was cut from a rock plug was used as the porous media in their experiments. The authors noted that great care should be taken during the preparation and installation of the core samples, particularly for weakly consolidated rocks. They also suggested that the experimental apparatus was not appropriate for obtaining measurements under high pressures. Li and Dong suggested an experimental method and mathematical model for measuring the diffusion coefficient of a gas in porous media saturated with oil. They used Berea cores saturated with water or crude oil as porous media in their experiments. Two end faces of the core were sealed for the physical model, and the gas could only diffuse from the radial direction through the core, which provided a greater diffusion area. The authors confirmed that the pressure decay was less sensitive to the environment [19,20,32]. 1.3. Carbon dioxide capture and utilization in the Shengli Oilfield The Shengli Oilfield of Sinopec in China has a coal-fired power plant (Shengli Power Plant), with the capacity of 1040 MW, and annual carbon dioxide emissions of 570  104 t. The Shengli Power

Plant has built a carbon dioxide capture system with a capacity of 100t/d. At the same time, the Shengli Oilfield has low permeability reservoirs with crude oil reserves of approximately 3  108 t, which is suitable for carbon dioxide flooding. San 121 Block in Shengli Oilfield is located in the Fanjia nose structure zone of the Jiyang sag with a reservoir depth from 2695.1 m to 2711.2 m. The initial reservoir formation pressure is 31.1 MPa, and formation temperature is 130.2
C. The reservoir porosity is 11.6–16.4%, and permeability is from 1.7 mD to 29.2 mD. The reservoir is with low porosity and low permeability. 1.4. Purpose of this paper The CO2 diffusion coefficient is an important input parameter for the large-scale modeling and stimulating of CCS or CO2-EOR. However, few studies of the CO2 diffusion coefficient in low permeability reservoirs are available, and we do not have sufficient information about the effects of temperature, pressure, oil saturation and permeability on the CO2 diffusion. In this study, a method to determine CO2 diffusion in oilsaturated cores under low permeability reservoir conditions was developed. Through physical simulation experiments for the diffusion of carbon dioxide, the effects of temperature, pressure, oil saturation and permeability on the diffusion of CO2 were investigated. Compared with the literatures related to the CO2 diffusion coefficients in porous media [17,19,22,30,32], this paper presents three improvements. First, the core, crude oil and experimental parameters were taken from the representative low permeability reservoir from China, which has an important guiding significance for carbon dioxide storage and flooding. The experimental parameters are great enough to stimulate the actual low permeability reservoir. Second, the practical core of low permeability has a high irreducible water saturation, which is as high as 30–50%. In the mathematical model solution, oil saturation was introduced in to diffusion equation, and the effect of oil saturation on diffusion coefficient was considered. The oil-phase swelling caused by gas dissolution was considered and waterphase swelling was not, which is in agreement with the actual diffusion situation. Third, the corresponding physical parameters for carbon dioxide are from the database of the National Institute of Standards and Technology (NIST), eliminating the error caused by the state equation of carbon dioxide. The objective of this study

Fig. 1. Experimental apparatus.

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

was to investigate the diffusion of supercritical CO2 under lowpermeability reservoir conditions.

49

with a pressure open error of less than 0.01 MPa. The temperature of the experiments was controlled by an oil bath shown by the dotted area in Fig. 1, with an accuracy within 1
C.

2. Experimental 2.3. Materials 2.1. Physical model

2.2. Apparatus The diffusion apparatus schematically shown in Fig. 1 was utilized in the experiments. A diffusion cell with an inner diameter of 6.0 cm and depth of 12.0 cm was used as a holder for the cores and CO2 during the experiment. Cores with almost the same permeabilities and porosities from a low permeability reservoir were used in the experiments, except for experiments No. 15–17. For all of the experiments, the cores were placed vertically in the diffusion cell. CO2 was supplied from a cylinder into an intermediate container, whose pressure can be controlled by a high-pressure pump (Model 100DX, Teledyne Technologies). Pressures in the diffusion cell were measured using pressure transducers (Model 3210PD, Haian Group). Another high-pressure pump was used to control the back pressure with the assistance of a back-pressure regulator (BPR) during the gas diffusion period

2.3.1. Oil and gas The crude oil used in the experiment was obtained from the San 121 Block in the Shengli Oilfield. The CO2 was from the Tianyuan Gas Company with a purity of 99.9%. The saturate, aromatic, resin and asphaltene concentrations of the crude oil used in the experiments were tested, which were 66.28%, 13.86%, 16.61 wt% and 3.25 wt%, respectively. The resin and asphaltene concentrations were slightly high compared with other light oils [33,34]. The viscosity–temperature and density–temperature curves for the crude oil are shown in Fig. 2. The viscosity was measured by viscometer (Brookfield DV II), and the density was measured by a density bottle (25 mL). The test results revealed that the viscosity for the crude oil at the reservoir temperature was 7.5 mPa s. With an increase in temperature from 50
C to 80
C, the viscosity

Surface tension of CO2 and oil (mN/m)

The physical model for the CO2 diffusion used in this paper is shown in Fig. 1. During the experiment, the two end faces of the cylindrical core were sealed, and the core was positioned vertically in the center of the cylinder. CO2 could only diffuse through the side surface of the core along the radial direction. During the experiment, the gas pressure of the diffusion cell decreased with time and could thus be recorded using a pressure transducer. The CO2 diffusion coefficient in porous media was obtained through the corresponding mathematical model. As discussed in previous studies, the physical model has three advantages. (1) The physical model is simple and easy to use, and the core is easy to prepare and install. (2) The two end faces of the core were sealed, and the gas can only diffuse through the side surface into the core. This model provided a large area for gas diffusion. (3) It was easy to stimulate high temperature and high pressure conditions in the low permeability reservoir [17,19,22,30,32].

15 14 13 12 11 10 9 8 7 6

0

500

1000

1500

2000

Time (s) Fig. 3. Surface tension of CO2 with time under 9.3 MPa and 70
C.

Fig. 2. Viscosity–temperature and density–temperature curves for the crude oil.

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S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

2.3.2. Core The cores used in the experiment were obtained from the San 121 Block in the Shengli Oilfield, except for those used in experiments No. 15–17. The permeabilities were between 8.39 mD and 9.37 mD, and the porosities were between 13.59% and 14.79%. The permeabilities of the cores from No. 15–17 were much higher than the others to study the effects of permeability on the diffusion coefficient, which were obtained from other reservoirs. The key properties of the cores are listed in Table 1. 2.3.3. Brine Analytically pure CaCl2 and NaCl solutions at concentrations of 690 mg/L and 48,000 mg/L were employed in the experiments to simulate the formation water. Distilled water served as the liquid. The density and viscosity of the brine at 25
C are 1037 kg/m3 and 1.13 mPa s, respectively. 2.4. Procedure Fig. 4. Surface tension of CO2 with pressure.

decreased rapidly. The density of the crude oil was nearly linear with regards to temperature from 15.5
C to 150
C. The surface tensions of CO2 and the crude oil under different pressures and temperatures were measured using an Interface Tensiometer (Model TRACKER-H, TECLIS), which is shown in Fig. 3 and Fig. 4. In Fig. 3, the equilibrium surface tension of CO2 and oil with time was measured. The equilibrium surface tension test was lasting for about 2000s for every value. The surface tension descended slowly in the first 1000s, and once it reached its lowest point it almost kept stable and almost changed no more. The pendant drop method is difficult to execute with precision, and therefore we conducted three observations for one value with different pressure, and error bars are shown in Fig. 4. The multiple were more appropriate. The minimum miscible pressures (MMPs) for 70
C and 130
C were determined by interface tension method, which were 25.1 MPa and 36.2 MPa. The results illustrates that the oil phase and CO2 are immiscible under the experimental conditions. The MMP was much higher than that of other light oils because the oil in the reservoir was formed by continental sedimentary and there was an increase in the heavy components [35–38].

CO2 diffusion experiments at different temperatures, pressures, oil saturations and permeabilities were performed in the laboratory using the experimental apparatus shown in Fig. 1. The experimental procedures were as follows: (1) Each core was drilled from core plugs from the San 121 Block to ensure that they possessed similar permeabilities and porosities, except for experiments No. 15–17. The cores were evacuated for more than 4 h using a vacuum pump before they were saturated with brine, and the pore volumes and permeabilities were measured. (2) The cores were then displaced with the crude oil from the San 121 Block at a rate of 0.1 mL/min until the water production ceased. The initial oil saturations and irreducible water saturations were calculated. (3) The two end faces of the cores saturated with crude oil were sealed with epoxy resin, and the cores were placed in an indoor environment for 24 h for phase equilibrium. (4) The sealing of the diffusion cell was tested by CO2 under 30 MPa. The sealed core was placed in the center of the cylinder vertically, and the crude oil was injected into to the annular volume formed by the core and the diffusion cell. All of the valves of the experimental device were closed. (5) The temperature of oil bath was set to the desired temperature, and the diffusion cell and intermediate container were heated until the temperature reached steady-state. The pressure of the

Table 1 Summary of the experiments of the CO2 diffusion coefficients in low-permeability cores. Core No.

Core diameter (mm)

Core length (mm)

Permeability (mD)

Porosity (%)

Oil saturation (%)

Average pressure (MPa)

Temperature (
C)

CO2 volume (mL)

Diffusion coefficient (1010 m2/ s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

38.02 38.04 38.06 38.00 38.02 38.04 38.02 38.04 38.00 38.10 38.04 38.04 37.96 38.00 38.05 38.02 38.01

99.90 98.90 100.34 102.08 98.92 95.06 100.18 96.24 95.94 97.10 102.30 101.16 100.10 98.76 100.05 100.11 99.78

8.92 9.34 9.26 8.62 8.85 8.52 9.05 9.17 9.33 9.21 8.39 9.37 9.05 8.99 78.62 275.37 985.06

14.32 14.12 14.56 13.87 13.98 14.27 13.69 14.79 14.71 13.82 14.39 14.27 13.59 14.11 17.87 19.21 20.23

63.58 61.06 57.84 59.23 61.43 58.89 59.66 58.27 60.11 61.28 58.91 0 22.30 40.88 59.72 63.27 62.78

6.490 9.615 15.050 20.145 24.447 29.940 19.889 20.073 19.985 20.620 20.535 20.350 20.220 20.260 19.582 21.840 20.884

130 130 130 130 130 130 70 80 100 140 150 130 130 130 130 130 130

74.5 73.0 72.0 62.5 75.5 79.0 75.0 78.5 75.0 79.0 86.0 75.5 89.0 84.0 84.6 81.9 79.5

2.407 7.628 9.535 11.627 12.246 12.756 2.005 4.346 8.924 11.742 12.063 0.246 1.650 7.601 22.642 26.928 28.274

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

intermediate container was observed and adjusted. If the pressure was lower than the required pressure, valve 6 was opened, and the CO2 was compressed with the high-pressure pump until the pressure reached the required value. If the pressure was higher than the required value, valve 5 was slowly opened, and CO2 was released from the intermediate container until the required pressure was obtained. (6) Valve 7 was opened, and the pressure regulator was adjusted until the pressure was approximately 0.5 MPa. Then, valves 3 and 1 were opened, and the free oil in the annular was displaced from the diffusion cell by the CO2. The volume of free oil removed from the diffusion cell was determined, which was also the initial CO2 volume for diffusion. (7) Valves 2 and 4 were opened, and then CO2 was injected into the diffusion cell until the pressure reached the required pressure. The pressure of diffusion cell was measured with pressure transducers that were connected to a computer, and pressure values with different times were recorded by the data acquisition system. (8) The diffusion process was stopped when it reached steadystate. Valve 1 was then opened slowly, and the remaining CO2 in the diffusion cell was discharged. The core was then removed from the diffusion cell and the experimental apparatus were cleaned and prepared for the next measurement.

3. Mathematical model development 3.1. Assumptions The assumptions made for the mathematical model were as follows: (1) The cores used in the experiment were homogeneous and isotropic. Oil and water were uniformly distributed in the cores. (2) The CO2 diffusion coefficients in the cores were constant during the measurement process. (3) CO2 concentrations in the liquid phase on the core surface were constant during the measurement process. (4) Natural convection caused by liquid density difference was ignored. (5) Evaporation of liquid phase into the CO2 was ignored.

51

(6) The oil phase and CO2 phase were immiscible.

3.2. Mathematical model According to the aforementioned assumptions, the mathematical description of the CO2 diffusion in the physical model under nonswelling conditions can be obtained from Fick’s first law and the continuity equation, as shown in Eq. (1). 8 ! > @C @2 C 1@C > 0 > > < @t ¼ D eff @r2 þ r @r ; 0 < r < r0 ; t  0 ð1Þ > > Cj t¼0 ¼ 0; 0 < r < r0 > > : Cj ¼ C ;t  0 r¼r0

0

where C is the concentration of CO2 in the core pore, mol/m3; D0 eff is the diffusion coefficient of CO2 in the core pore, m2/s; r0 is core radius, m; r is the CO2 diffusion radius, 0 < r < r0, m; and t is the CO2 diffusion time, t  0, s. The mathematical expression of the CO2 diffusion coefficient under nonswelling conditions is determined by Eq. (2), which has been proved by other literatures [19,20]. D0eff ¼

p



r0 kV 16 N1 ZRT

2 ð2Þ

where N1 is the mass of CO2 diffused into the core when the diffusion time tends to infinity, mol; Z is the compressibility factor of CO2; V is the annular volume formed by the rock and the diffusion cell which is filled with CO2, m3; R is the gas constant, 8.314 J/(mol.K); T is the temperature, K; and k is the slope of the straight line formed by the CO2 pressure drop in the diffusion cell and 1/2 times the square of the corresponding time. The mathematical description of CO2 diffusion under oil swelling conditions can be obtained by Fick’s first law and the convection equation, as shown in Eq. (3). The oil saturation was introduced into the mathematical model. The solubility of CO2 in oil is one order greater than that in water under the reservoir conditions, because CO2 and oil are all non-polar, and water is polar. The oil-phase swelling caused by gas dissolution is much greater than water-phase swelling under the same pressure and temperature [39–41]. The oil-phase swelling in the mathematical model was considered and water-phase swelling was not, which is

Fig. 5. Experimental results of the CO2 diffusion coefficient for core No.1.

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S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

ð3Þ

where t is the dimensionless time, which is defined as t ¼ r2 =Dt 0 ; r 0

eff

is the dimensionless radius, which is defined as r ¼ rr0 ; u is the dimensionless velocity caused by oil swelling, which is defined as u ¼ D0 u=r ; c is the dimensionless concentration of CO2, which is eff

0

defined as c ¼ cc0 ; l is defined as l ¼ u  1; and So is the oil r saturation in the core. Numerical solution of the mathematical model for the CO2 diffusion in the core is shown in Appendix A. The low permeability cores used in the experiment possessed high irreducible water saturations, which were as high as 36.42–42.16%, as shown in Table 1. In the mathematical model solution process, oil saturation was introduced in to diffusion equation, the oil-phase swelling caused by the gas dissolution was considered and water-phase swelling was not, which is in agreement with the actual situation. The corresponding physical parameters for carbon dioxide were obtained from the database of the NIST, which eliminated the error caused by the state equation of the carbon dioxide and improved the calculation accuracy of the diffusion coefficient. The solubility of CO2 in brine was calculated by the thermodynamic model established by Duan and Sun [42]. The solubility of CO2 in crude oil was calculated by the genetic algorithm method proposed by Emera and Sarma [43]. 4. Results and discussions The effects of pressure (6.490–29.940 MPa), temperature (70– 150
C), oil saturation (0–63.58%) and permeability (8.62– 985.06 mD) on the diffusion coefficient of supercritical CO2 under a low-permeability reservoir condition were studied in this paper. A single-factor design was used in the experiments, where only one value of a factor was changed in each experiment and the other parameters were kept constant. Experiments were conducted in accordance with the procedure presented above, and the relationship between the pressure decay of supercritical CO2 in the diffusion cell as a function of time was obtained. The experiment results for core No. 1 are displayed in Fig. 5, and results for other cores are shown in Appendix B. The first group of experimental data that was analyzed here possessed a temperature of 130
C, an initial pressure of 6.62 MPa, and an oil saturation of 63.58%. The relationship of pressure with respect to time is shown in Fig. 5(1)a. In the initial stage, the pressure decayed very quickly, then it decayed slowly, and the diffusion of CO2 achieved steady-state. The explanation for the initial rapid pressure decrease is as follows: (1) When supercritical CO2 was injected into the diffusion cell, the temperature and pressure had a small fluctuation before achieving steady-state. (2) During the initial stage of diffusion, the CO2 contacted with the oil film on the core surface for the first time after CO2 was injected into the diffusion cell. A small amount of CO2 dissolved into the oil film on the core surface, forming a stable CO2 concentration in the liquid phase on the core surface during the measurement process.

The curve formed by the pressure drop and t1/2 is shown in Fig. 5(1)b. We can see from the figure that there was an initial stage of diffusion before reaching the steady-state diffusion stage indicated by the straight line. According to the above assumptions, the mathematical model under nonswelling conditions was based on the steady-state. The CO2 diffusion coefficient under nonswelling conditions was calculated using Eq. (2), where k is the slope of the line in the steady-state diffusion stage. The CO2 diffusion coefficient was introduced into equation (5) as the initial value, and the diffusion coefficient under the oil swelling condition was calculated using the numerical method. All of the experimental data are summarized in Table 1. The diffusion coefficient of supercritical CO2 in porous media is related not only to the physical and chemical properties of CO2 itself but also to the environmental diffusion parameters, such as temperature, pressure, oil saturation, permeability of the porous media, and the physical and chemical properties of the saturated fluid. This paper primarily discusses the influences of pressure, temperature, oil saturation and permeability on supercritical CO2 diffusion in oil-saturated porous media. The experimental results for the four factors are shown in Table 1 and Figs. 6–9 . Every value of diffusion coefficient under different condition was measured for three times using the same core, and the mean coefficients were shown in the last column in Table 1. The error bars were marked in Figs. 6–9. It can be observed from Fig. 6 that with an increase in pressure, the CO2 diffusion coefficient in porous media saturated with oil first increased significantly, and the rate of increase then gradually slowed down. This changing rate can be explained by the fact that the molecular density increases with pressure at the same temperature, which can result in an increase in the mass of the diffusing gas. The diffusion capability of CO2 in a supercritical state is much greater than that in the liquid and gas states. When the pressure was 6.490 MPa at 130
C, the CO2 was under gas phase. When the pressure increased to 9.615 MPa, the CO2 state changed from gas state to supercritical state. The value of the first data point in Fig. 5 under a gas state is much lower than the others under supercritical state. The results reveal that the diffusion of CO2 is faster in the deeper reservoirs with higher pressure. Fig. 7 shows that with an increase in temperature, the CO2 diffusion coefficient in the low-permeability cores saturated with oil increased significantly, and the rate of increase gradually slowed down. Gas diffusion is related to irregular molecular motion. As the temperature increases, thermal molecular motion increases, thereby enhancing the diffusion capability of CO2 in the 14

CO2 diffusion coefficient O10-10m2/sP

in agreement with the actual diffusion situation. 8 > c u cu c @2 c > > @ þ So  c@ þ So  þ l@ ¼ 2 > > > @t @ r r @ r @r > > < c ¼ 1 ðr ¼ 1; t > 0Þ c > ¼ 0 ðr ¼ 0; t > 0Þ u ¼ 0; @ > > > @r > > > u ¼ 0; c ¼ 0 ðt ¼ 0; r < 1Þ > : u ¼ 0; c ¼ 1 ðt ¼ 0; r ¼ 1Þ

12 10 8 6 4 2 0

5

10

15

20

25

30

Pressure (MPa) Fig. 6. Effect of pressure on the CO2 diffusion coefficient.

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S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

CO2 diffusion coefficient O10-10m2/sP

14 12 10 8 6 4 2 60

80

100

120

140

160

Temperature OćP Fig. 7. Effect of temperature on the CO2 diffusion coefficient.

CO2 diffusion coefficient O10-10m2/sP

14 12 10 8 6

Fig. 8 displays that the CO2 diffusion coefficient in porous media increased greatly with a corresponding increase in the oil saturation. The diffusion coefficient in the core with an oil saturation of 59.23% is an order higher than that in the core without oil because the solubility of supercritical CO2 in crude oil is much greater than that in brine. The concentration of supercritical CO2 in crude oil is much greater than that in brine, and the mass transfer capability of supercritical CO2 in low-permeability cores with higher oil saturation is also greater, which significantly enhances the gas diffusion coefficient. The results reveal that in the reservoirs with higher oil saturation the diffusion of CO2 is faster. It can be observed from Fig. 9 that with an increase in the permeability of the cores, the CO2 diffusion coefficient in the porous media initially possessed a large increase and then remained stable. The reason is that the tortuosity factors of the cores obviously decreased with the increase in permeability, which allows for supercritical CO2 to transfer more easily in the porous media. When the permeability of the core was greater than approximately 100 mD, an increase in the diffusion coefficient was not obvious. The results reveal that CO2 diffuses much slower in the low-permeability reservoirs. The proposed method can be used to determine the tortuosity factor of the porous media according to Eq. (8), if the diffusion coefficient of CO2 in a bulk liquid phase can be measured. The conditions for the four experiments in Fig. 8 are almost the same, such as pressure, temperature, and oil saturation. The diffusion coefficients of CO2 in a bulk liquid phase are almost the same. The diffusion coefficients of CO2 measured reflect the relative tortuosity factors under different permeabilities. As the permeability decreases from 985.06 mD to 8.62 mD, the tortuosity factor increases by 2.43 times. D0 eff ¼

4 2 0 0

10

20

30

40

50

60

70

Oil saturation O%P Fig. 8. Effect of oil saturation on the CO2 diffusion coefficient.

Fig. 9. Effect of permeability on the CO2 diffusion coefficient.

porous media. The results illustrate that in the reservoirs with higher temperature the diffusion of CO2 is faster.

53

wD e

ð8Þ

where D is diffusion coefficient of CO2 in a bulk liquid phase, m2/s; e is the tortuosity factor of the porous media. The diffusion coefficient data for CO2 in oil-saturated cores at the same pressure and temperature conditions those in this work are not available in the literatures. However, comparisons were made in Table 2 with the limited experimental results among the diffusion coefficient in bulk brine and oil, and that in brine and oilsaturated cores. As shown in Table 2, the diffusion coefficient in bulk brine or oil is about 10 times greater than those in the brine or oil saturated cores [41,42]. The difference illustrates that the presence of rack matrix in porous media has great effect on the diffusion process. The mathematical model and numerical simulation presented in the paper is validated through comparison with other results. The results from this work have the same trend with others. As the permeability increases, the diffusion coefficient for oil-saturated cores will increase close to that for bulk oil. Based on the same experimental method without considering the effect of oil saturation, Li and Dong tested the CO2 diffusion coefficient in the porous media saturated with oil [32]. Their experimental temperature was 40
C, and the experimental pressures were between 2.3 MPa and 6.3 MPa. The measured CO2 diffusion coefficient was between 5.98  1010 m2/s and 8.01 1010 m2/s, which is much lower than the values in this paper. The reason is that the pressure and temperature in this paper are much higher, which can increase the diffusion coefficient. CO2 is in the supercritical state in this paper, and in the experiments conducted by Li and Dong, CO2 was in the liquid state. However, the core permeabilities in this paper were much lower, between 8.62 mD and 9.37 mD, except for the cores of No. 15–17, which can increase the tortuosity factors and decrease the diffusion capability of the supercritical CO2.

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S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60 Table 2 Comparison of diffusion coefficient under different conditions. System

Experimental conditions

Diffusion coefficient (1010 m2/s)

CO2 + Bulk brine [17] CO2 + Athabasca Bitumen [44] CO2 + Athabasca bitumen [45]

38
C, 1.45–5.86 MPa 20–200
C, 5 MPa 25–90
C, 4 MPa 25–90
C, 8 MPa 38
C, 0.37–2.51 MPa 59
C, 2.4–7.3 MPa, 80–1527 mD 40
C, 2.28–6.26 MPa, 163–263 mD 130
C, 6.49–29.94 MPa, 9 mD, 60% oil saturation 70–150
C, 20 MPa, 9 mD, 60% oil saturation 130
C, 20 MPa, 9 mD, 0–59.23% oil saturation 130
C, 20 MPa, 8.62–985.06 mD, 60% oil saturation

30–73 28–175 13.35–42.80

CO2 + Bulk octane [46] CO2 + Brine-saturated rocks [19] CO2 + Oil-saturated rocks [32] CO2 + Oil-saturated cores (this work)

5. Conclusions (1) This paper improved the experimental procedure and mathematical model for determining the CO2 diffusion coefficient in low permeability cores by utilizing a diffusion cell. The effect of oil saturation was introduced. The core, crude oil and experimental parameters were taken from a representative low permeability reservoir. In solving the mathematical model, the oil-phase swelling caused by gas dissolution was considered, but water-phase swelling was not, which is in agreement with the actual diffusion situation for the low permeability cores. The method is validated to determine CO2 diffusion in oil-saturated cores under low permeability reservoir conditions. (2) The effects of pressure (6.490–29.940 MPa), temperature (70– 150
C), oil saturation (0–63.58%) and permeability (8.62– 985.06 mD) on the diffusion coefficient of supercritical CO2 under the low-permeability reservoir condition were studied. The order of the diffusion coefficient is between 1010 and 109 m2/s. The results demonstrated that an the increase in pressure and temperature, the CO2 diffusion coefficient in the low-permeability cores saturated with oil increased significantly, and the rate of increase gradually slowed down. The CO2 diffusion coefficient increased greatly with a corresponding increase in the oil saturation in porous media, and the diffusion coefficient in the core with an oil saturation of 59.23% is an order higher than that in the core without oil. The CO2 diffusion coefficient initially increased greatly with the permeability, but when the permeability of the core was greater than approximately 100 mD, the diffusion coefficient remained mostly stable.

39.81–81.05 3.14–6.51 5.98–8.01 2.407–12.756 2.005–12.063 0.246–11.627 11.627–28.274

velocity are shown in equations (A.1)–(A.4).

@c 1 nþ1 ¼ ðc  cni Þ þ OðDt Þ @t Dt i

ðA:1Þ

@c 1 nþ1 ðcnþ1  ci1 ¼ Þ þ OðDr2 Þ @r 2Dr iþ1

ðA:4Þ

@2 c 1 nþ1 2 ¼ ðcnþ1 þ cnþ1 iþ1  2ci i1 Þ þ OðDr Þ 2 @r Dr 2

ðA:3Þ

@u 1 2 ¼ ðunþ1  unþ1 i1 Þ þ OðDr Þ @r 2Dr iþ1

ðA:4Þ

Partial differential equations in Eq. (3) can be rewritten as Eq. (A.5) using the finite difference schemes mentioned above. nþ1 þ ei cnþ1 ai cnþ1 i1 þ bi ci iþ1 ¼ f i ; i ¼ 0; 1; 2    ; I

ðA:5Þ

Dt nþ1 þ 2Dt, ai ¼  Dt2  lDt ,bi ¼ 1 þ Dt ðunþ1  unþ1 2 i1 Þ þ r ui 2Dr 2Dr iþ1 i Dr Dr lDt Dt n  2 , and f i ¼ ci . ei ¼ 2Dr Dr nþ1 The discrete boundary conditions can be obtained as cnþ1 1 ¼ c1

where

and cnþ1 ¼ 1. I Discrete Eq. (A.5) can be written as Eq. (A.6) by applying the boundary conditions.

(A.6) Acknowledgments This project was financially supported by the National Key Basic Research Program of China (No. 2015CB250904). The authors sincerely thank colleagues in the Foam Research Center in China University of Petroleum (East China) for assistance with the experimental research. Appendix A. Numerical solution for the mathematical model The dimensionless equations of diffusion and convection that considered oil swelling, as shown in Eq. (3), were solved using the implicit finite difference method. In the discrete process, the central difference format was used in one order of the differential velocity and one and two orders of the differential concentration, and the forward difference format was used in one order of the differential time. Discrete equations of time, concentration and

The CO2 diffusion coefficient solved by Eq. (2) under the nonswelling condition was inserted into Eq. (A.6) as the initial value. The implicit finite difference method was used to solve the dimensionless Eq. (A.6) under the oil swelling condition. The velocity and concentration distributions for each time step were calculated using the Gauss-Seidel iterative method. For each time step, the CO2 concentration in the previous time step was used as the initial value to calculate the velocity distribution of this time step. The velocity distribution of this time step was used to calculate the velocity distribution in the next time step. The end condition of the iteration is the maximum relative error of each node that was less than the error limit, which was 0.001 in this

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

program. Dimensionless distributions of the carbon dioxide concentration and the oil velocities caused by the oil swelling can be obtained. The CO2 pressure drop under oil swelling condition can be calculated by Eq. (A.7) using the CO2 concentration and oil velocity distributions determined through the numerical solutions (Li and Dong, 2009).

DPTh ¼

qZRT  P0 DV V  DV

ðA:7Þ

55

where DV is the cylinder volume reduction in the diffusion cell caused by oil swelling, [32] which is calculated by Eq. (A.8), m3; and q is the mass of CO2 for the different times that diffused into the oil saturated core combined by the CO2 dissolved in the oil swelling diffusing out of the core, mol. t X ur¼1;t Dt

DV ¼ 2pr20 hf

t ¼0

ðA:8Þ

where h is the length of the core, m; and f is the core porosity, %.

Fig. B1. Experiment results of the CO2 diffusion coefficient for core No. 2–17.

56

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Fig. B1. (Continued)

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Fig. B1. (Continued)

57

58

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Fig. B1. (Continued)

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Fig. B1. (Continued)

59

60

S. Li et al. / Journal of CO2 Utilization 14 (2016) 47–60

Fig. B1. (Continued)

Equation (A.7) was used to compare the plot of the experimentally measured pressure drop versus t1/2, thereby determining the CO2 diffusion coefficient in the oil-saturated porous media. q and DV were determined through numerical solutions. If the maximum relative error of the experimentally measured pressure drop and the calculated pressure drop was less than the error limit, which was 0.001 in this program, the iteration process was stopped. Then, the real CO2 diffusion coefficient in the core saturated with oil was obtained. Appendix B. Experimental results for core No. 2–17 (Fig. B1). References [1] M. Wilson, M. Monea, The 7th International Conference on Greenhouse Gas Control Technologies, 5–9 September (2004). [2] D. Kay, F. André, T. Wim, Int. J. Greenh. Gas Control 3 (2009) 217–236. [3] H.W. Liu, G.T. Berenice, A. Tarek, B. Murad, Int. J. Greenh. Gas Control 11 (2012) 163–171. [4] v.E. Sander, P.H. Marko, Int. J. Greenh. Gas Control 11 (2012) S148–S159. [5] Z. Paul, H. Mike, Int. J. Greenh. Gas Control 1 (2007) 94–100. [6] K.K. Osman, N.T. Nazan, L. h. Robert, SPE/DOE Symposium on Improved Oil Recovery, 17–21 April, Tulsa, Oklahoma, 2004. [7] S. Secaeddin, K. Ulker, C. Demet, Latin American & Caribbean Petroleum Engineering Conference, 15–18 April, Buenos Aires, Argentina, 2008. [8] K.W. Stanley, J. Pet. Technol. 42 (1990) 630–636. [9] H. Agustssen, G.H. Grinestafr, SPE/DOE Symposium on Improved Oil Recovery, 17–21 April, Tulsa, Oklahoma, 2004. [10] S. Siregar, P. Mardisewojo, D. Kristanto, R. Tjahyadi, SPE Asia Pacific Improved Oil Recovery Conference, 25–26 October, Kuala Lumpur, Malaysia, 1999. [11] S. Bachll, J.C. Shaw, SPE/DOE Symposium on Improved Oil Recovery, 17– 21 April, Tulsa, Oklahoma, 2004. [12] F. Yang, J. Deng, Y. Xue, SPE International Conference on CO2 Capture, Storage, and Utilization, 10-12 November, New Orleans, Louisiana, USA, 2010.

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