Ind. Eng. Chem. Res. 2009, 48, 9023–9027
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GENERAL RESEARCH Molecular Diffusion Coefficients of the Multicomponent Gas-Crude Oil Systems under High Temperature and Pressure Ping Guo,*,† Zhouhua Wang,†,‡ Pingping Shen,§ and Jianfen Du† State Key Laboratory of Oil and Gas ReserVoir Geology and Exploitation, Southwest Petroleum UniVersity, Chengdu, Sichuan, 610500, China, PetroChina Southwest Oil and Gas Field Branch, Exploration and DeVelopment Research Institute, Chengdu, Sichuan, 610051, China, and PetroChina Exploration and DeVelopment Research Institute, Beijing, 100083, China
The molecular diffusion of an oil-gas system is a key factor to determine the mass transfer rate. The actual mass transfer between oil and gas is an unsteady-state process. In this paper, the diffusion coefficients of the N2-rich gas-crude oil, CO2-rich gas-crude oil, and CH4-rich gas-crude oil systems were determined at 60 °C and 20 MPa by the mutual diffusion model developed. Results of the coefficient measurements show obvious transit characteristics of the gas-oil diffusion processes. Both the required equilibrium time and the diffusion rate depend on not only the diffusion gas but also the diffusion system. The diffusion gas concentration affects the diffusion coefficients slightly. 1. Introduction Molecular diffusion plays a vital role in miscible gas flooding. An effective molecular diffusion process between the injected gas and oil promotes oil-gas mixing, and prevents viscous fingering, therefore improving the sweep efficiency for enhancing oil recovery. At present molecular diffusion coefficients are usually obtained by experimental measurements as it is hard to accurately predict them for complex systems. A number of testing methods for determining gas-liquid diffusion coefficients have been reported.1-5 These methods can be divided into two main categories. The first method determines diffusivity by analyzing the composition of fluids at different times. The second one obtains the mutual diffusion coefficient using an empirical formula by experimental measurements of the self-diffusion coefficient. The PVT tube method developed by Riazi7 is a typical approach for experimental determination of molecular diffusion coefficients of the gas-oil systems. Zhang et al.8 further improved Riazi’s method for black oil. Oballa and Butler,9 Das and Butler,10 and Wen et al.11 used laser and X-ray scanning technologies respectively to obtain the diffusion coefficients in the black oil-liquid hydrocarbon systems by measuring the saturation curves. Yang and Gu12 established a new method to test CO2 diffusivity in black oil by dynamic pendant prop shape analysis (DPDSA). In 2004 Islas-Juarez et al.13 determined the effective diffusion coefficient of a nitrogen-hexane system in porous media, and discussed the relationship between the effective diffusion coefficient and the molecular diffusion coefficient. Among the experimental methods mentioned above, the pressure draw-down analysis developed by Riazi, Zhang, and * To whom correspondence should be addressed. Tel.: +86 02883033014. E-mail:
[email protected]. † Southwest Petroleum University. ‡ Exploration and Development Research Institute. § PetroChina Exploration and Development Research Institute.
Tharanivasan17 for gas-oil systems at static conditions was widely used. However, this method was based on the following assumptions: no volume expansion and volatility of oil, constant gas Z-factor, and no effect of the molecular concentration on molecular diffusion processes. Furthermore, for simplicity, most laboratory tests used pure gases and single-component oils instead of multicomponent gases and crude oils, and avoided measuring the diffusion coefficients of gas-oil systems at high pressure and temperature. These assumptions and simplified experimental conditions resulted in great deviation from the actual cases, in particular, for such oil fields that have strong heterogeneity, low permeability, high viscosity and paraffin content, and high miscibility pressure of oil and CO2. In this work the transit characteristics of molecular diffusion were investigated for the multicomponent gas-crude oil systems
Figure 1. Schematic diagram of the physical model.
10.1021/ie801671u CCC: $40.75 2009 American Chemical Society Published on Web 09/10/2009
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Table 1. Composition of the Gases Used component, mol % gas
N2
CO2
C1
C2
C3
iC4
nC4
iC5
nC5
C6
N2 CO2 dry gas
98.23 0.0796 3.1951
98.181 2.5062
1.67 1.6939 92.7098
1.3957
0.1182
0.0141
0.0278
0.0129
0.0032
0.0169
under high pressure and temperature, including CO2-rich gas-crude oil, CH4-rich gas-crude oil, and N2-rich gas-crude oil systems. The diffusion coefficients were determined at 60 °C and 20 MPa. The effect of diffusion gas concentrations on the diffusion coefficients was also discussed. A mathematical model has been developed for describing the mutual diffusion process. 2. Mutual Molecular Diffusion Model In Figure 1 a PVT cell has a constant volume and contains oil and gas at nonequilibrium state. The component concentrations are known. During the whole experimental process, the temperature remains constant. Consider that at a minor time quantum of ∆t, the system is at equilibrium state. When diffusion occurs, the system pressure, volume, and composition of each phase will change with time until the system reaches equilibrium. xi and yi are i-component molar concentrations of the liquid phase and the gas phase, respectively. Coi and Cgi are i-component mass concentrations of the liquid phase and the gas phase, respectively. ni is the total mole fraction of the i-component; mi is the total mass of the i-component. Lo and Lg are the column heights of the liquid phase and the gas phase, respectively. ub is the movement rate of the gas-liquid interface, defined as ∂Lo/∂t. z, zo, and zg denote the coordinate axes shown in Figure 1. If there is component concentration gradation, diffusion between the gas phase and the liquid phase will occur. Under the specific physical conditions in the PVT cell, the density of the oil phase will decrease when the gas molecules diffuse into the oil phase. According to the physical characteristics of diffusion, the concentration of light components in the oil phase at the gas-liquid interface is higher than that at the bottom of the PVT cell; i.e., the vector direction of the concentration gradient of light components in the oil phase is consistent with the coordinate direction of the oil phase zo. As a result, oil density gradually decreases along the coordinate of the oil phase; therefore, there is no natural convection.
gas phase:
[
∂Cgi ∂Cgi ∂ ) D ∂t ∂zg gi ∂zg Cgi(zg, 0) ) Cgi(0, t) ) Cgbi ∂Cgi(Lg, t) )0 ∂zg
C1gi(zg)
] (2)
1 1 and Cgi are the initial molar concentrations of the iCoi component of the oil phase and the gas phase, respectively, in kmol/m3. Cobi and Cgbi are the molar concentrations of the i-component of the oil phase and the gas phase at the oil-gas interface, respectively, in kmol/m3. Equations 1 and 2 describe the mutual diffusion between different components. Effective diffusion coefficients of individual components directly affect the required time to reach equilibrium for the entire system. There are no general equations that can accurately determine the diffusion coefficient of the i-component in the oil phase and the gas phase; therefore, some empirical equations must be used. The diffusion factor of the i-component in the oil phase usually was calculated using the empirical equation developed by Wilke and Chang14 and that in the gas phase using the empirical formula developed by Chapman-Enskog.15 The initial K value of each component was calculated by the Wilson function, and was further corrected using the fugacity coefficient of each time step, while the fugacity coefficient was calculated using the Peng-Robinson equation of state. Compared with the conventional computation model for a single-component system, this model has considered the mutual influence between the different components, which could provide a better description of the molecular diffusion process in a real gas-oil system.
3. Experimental Measurements of Molecular Diffusion Coefficients Three groups of gas diffusion tests were conducted for the CO2-rich gas-crude oil system (CO2-oil), CH4-rich gas-crude oil system (CH4-oil), and N2-rich gas-crude oil system
The established models with the specific boundary conditions are below: oil phase:
[
∂Coi ∂Coi ∂ ) Doi ∂t ∂zo ∂zo Coi(zo, 0) ) ∂Coi(0, t) )0 ∂zo Coi(Lo, t) ) Cobi
C1oi(zo)
] (1) Figure 2. Schematic diagram of the experimental setup: 1, 2, Ruska pump; 3, gas vessel; 4, oil vessel; 5, bake oven; 6, PVT cell; 7, flash vessel; 8, gas meter; 9, chromatograph analyzer; 10, densimeter.
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Table 2. Compositional Analysis Results of the Oils at the End of Each Test upper oil phase, mol %
lower oil phase, mol %
component
N2-oil
CH4-oil
CO2-oil
N2-oil
CH4-oil
CO2-oil
CO2 N2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C11+ GOR (m3/m3) Fo (kg/m3)
16.7464 0.0256 0.0052 0.0394 0.1532 0.1981 0.4111 0.3091 1.2669 1.9029 4.3693 3.4355 3.9898 67.1475 13.62 822.6
1.1115 0.8037 34.3391 0.7732 0.1065 0.2481 0.3724 0.9540 0.7560 5.6477 5.6401 7.1465 5.2515 4.6165 32.2331 71.78 821.9
66.6284 0.1354 2.8402 0.0231 0.0397 0.1208 0.1715 0.4520 0.3594 2.6848 2.2140 3.5759 2.1883 1.5017 17.0647 255 825
10.8768 0.0711 0.0045 0.0279 0.1084 0.1594 0.4545 0.3594 1.6267 2.9228 5.7419 4.9054 4.5018 68.2393 11.53 823.8
0.7231 1.9091 37.6201 0.3081 0.0240 0.1225 0.2431 0.4554 0.5611 2.4097 3.3796 3.8080 2.7312 2.6389 43.0661 61 822.9
66.3558 0.0549 1.9226 0.0000 0.0245 0.1035 0.1499 0.2850 0.2056 0.8201 1.0394 2.1943 1.6908 1.9596 23.1940 232.8
(N2-oil), respectively. All molecular diffusion coefficients were measured using a DBR phase behavior analyzer under identical temperature and pressure (20 MPa, 60 °C). The compositions of the test gases are shown in Table 1. The test oil was from a separator at surface conditions. Its average molecular weight was 231.5 and its density was 0.8305 g/cm3. Figure 2 shows a schematic diagram of the experimental setup. First, the oil vessel and gas vessel were placed in a thermostatic oven at 60 °C for more than 24 h. Then the preheated oil and gas vessels were pressurized to 20 MPa; the temperature and pressure of the PVT cell were increased to 60 °C and 20 MPa, where the plunger position was recorded. Next, the test oil was transferred into the PVT cell and the plunger position was recorded again when the oil system became steady. The volume of the injected oil was determined by the difference of the two plunger positions previously recorded. Third, the test gas was slowly transferred into the PVT cell from the port at the top of the PVT cell. The gas transferring rate was maintained very low to avoid any convection during the entire gas transfer process. The plunger position and the oil level were recorded once the gas transfer process was completed. Fourth, the diffusion test started immediately after the gas transfer process. The system pressure, oil level, and time were recorded until the gas-oil system reached the diffusive equilibrium where the pressure
830.2
variation was less than 1 psi (1/145 MPa) in 30 min. At the end of each test the composition of the gas phase was analyzed by a gas chromatograph. The oil samples were taken by a constant-pressure flash method, and their composition and density were analyzed by an oil chromatograph. The test results are shown in Figure 3 and Table 2. In Figure 3 the system pressure declined gradually with time due to the gas molecules diffusing into the oil phase. The CO2 diffusion into the oil phase is the fastest, while the rate of N2 diffusion is the slowest. Furthermore, the pressure draw down for the three gas-oil systems is also different. The pressure drop is 1.14 MPa for the N2-oil system, 4.55 MPa for the CH4-oil system, and 3.9 MPa for the CO2-oil system. Table 2 shows that the property of the upper oil is different from that of the lower oil to a certain extent. Both the component concentration of C11+ and the flash density of the oil in the upper level (upper oil) are lower than in the lower level (lower oil). On the contrary, the gas-oil ratio (GOR) of the upper oil is obviously higher than that of the lower oil. By comparing the oil properties of the three groups of experiments, it is found that the CO2 concentration in the oil phase and the GOR in the CO2-oil diffusion experiment are significantly higher than those of the other two gases after the system reaches equilibrium. This is attributed to the fact that CO2 has a high diffusion rate, strong dissolving power, and extraction to heavy components. The diffusion coefficients were obtained by use of the established model, i.e., eqs 1 and 2, to match the measured pressure profiles. Figure 3 demonstrates that the modeling pressure variation well matches the measured pressure. The diffusion coefficients determined in the three diffusion tests are shown in Figure 4. It can be clearly seen that, for all three typical gases, the diffusion coefficients increase with time, while the system pressure decreases correspondingly. The increase of the diffusion coefficients does not stop until the end of the entire diffusion process, where the system pressure becomes stable. The model predicted final gas Table 3. Equilibrium Time for the Three Gas-Oil Systems Tested
Figure 3. Model predicted pressure profiles well matching the experimental test.
dissuasive gas
experimental conditions
equilibrium time, h
N2-oil CH4-oil CO2-oil
20 MPa, 60 °C 20 MPa, 60 °C 20 MPa, 60 °C
42 91.5 27.33
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Figure 4. Determined diffusion coefficients in oil phase increasing with time.
concentrations in oil phase are also in agreement with the experimental measurements. At the end of the N2-oil diffusion test, the predicted final mole percentage of N2 in oil phase is 12.86 mol %, while the measured values are 16.75 mol % (upper oil) and 10.89 mol % (lower oil). For the CH4-oil test, the model predicted final concentration of CH4 in the oil phase is 35.34 mol %, while the measured values are 34.34 mol % (upper oil) and 37.62 mol % (lower oil). For the CO2-oil test, the model predicted result of
Figure 5. Dependence of the diffusion coefficients on the diffusion gas concentration in the oil phase.
CO2 in the oil phase is 67.26 mol %, while the measured values are 66.63 mol % (upper oil) and 66.36 mol % (lower oil). 4. Discussion 4.1. Equilibrium Time. Table 3 shows the equilibrium times for the N2-oil, CO2-oil, and CH4-oil systems at 20 MPa and 60 °C. The equilibrium time for the CO2-oil system is obviously less than those for the N2-oil and CH4-oil
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Table 4. Diffusion Coefficients of Individual Gas Components in Gas Phase and Oil Phase diffusion coefficient in gas phase (final value) component N2 CH4 CO2
N2-oil
CH4-oil -11
1.932 × 10 1.944 × 10-11 -
-11
8.281 × 10 6.081 × 10-11 6.743 × 10-11
diffusion coefficient in oil phase (final value)
CO2-oil
N2-oil
-10
2.403 × 10 2.690 × 10-10 2.723 × 10-10
CH4-oil -12
5.555 × 10 3.559 × 10-12 -
-12
3.978 × 10 2.287 × 10-12 3.985 × 10-12
CO2-oil 1.082 × 10-11 1.263 × 10-11 1.869 × 10-11
systems, and the diffusion rate of CO2 in the oil phase is also higher than those for the other two gases, which is indicated by the total increase of CO2 concentration in the oil phase in Table 2. However, by comparison to the equilibrium time for the CH4-oil system, the short equilibrium time for the N2-oil system does not necessarily mean the N2 diffusion rate is higher that of CH4. This is mainly
to the diffusion gas, but also strongly depend on the diffusion system. The diffusion gas concentration slightly alters the
due to the relatively low solubility of N2 in the oil, which is also indicated by the total changes of the gas concentrations in the oil in Table 2. Another possible reason may be the use of the dry gas, rather than pure methane, that contains some heavier hydrocarbon components from C2H6 through C6H14. The presence of the heavy components will increase the molecular intereaction and decrease the solubility of the injecting gas. Similar results were previously reported by Lohhong Siang18 that the final equilibrium times for the CO2-light crude oil system were 35 min at 1.36 MPa and 20 °C, and 27 min at 0.8 MPa and 20 °C. The measured equilibrium times could be referred to for estimating the required shut-in time for a maximum oil recovery.
This work was financially supported by the National Basic ResearchProgrammeofChina(973ProgrammeNo.2006CB705804), which is acknowledged.
4.2. Influence of Diffusion Systems on Diffusion Coefficients. The predicted final diffusion coefficients of the N2-oil, CH4-oil, and CO2-oil systems are shown in Table 4. At the identical temperature and pressure, the diffusion coefficients depend on not only the gases but also the diffusion systems. Among N2, CO2, and CH4, CO2 always has the highest diffusion coefficient in both the gas phase and the oil phase; in the CO2-oil system all three injected gases show their highest diffusion coefficients in both the gas phase and the oil phase. 4.3. Influence of Molar Concentrations on Diffusion Coefficients. It has been argued whether or not the component concentration has an influence on diffusion coefficients.5,6,12-14,16 Figure 5 shows that the diffusion coefficients rise as the diffusion gas content in the oil phase increases. From the start to the end of the diffusion process the three diffusion coefficients of N2, CH4, and CO2 increased by 0.21%, 1.88% and 0.93%, respectively. However, in terms of engineering significance, such an extent of the gas concentration influence on the diffusion coefficients may be negligible. 5. Conclusions A mutual diffusion model has been developed for multiplecomponent systems. The diffusion coefficients of the N2-rich gas-crude oil, CO2-rich gas-crude oil, and CH4-rich gas-crude oil systems were determined at 60 °C and 20 MPa by use of the developed model. The model predictions are in good agreement with the experimental pressure history. The determined diffusion coefficients demonstrate obvious transit characteristics of the gas-oil diffusion processes. The diffusion coefficients rapidly increased at the beginning of the diffusion processes. Furthermore, both the required equilibrium time and the diffusion rate are not only related
diffusion coefficients, however, which may be negligible for practical engineering applications. Acknowledgment
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ReceiVed for reView November 3, 2008 ReVised manuscript receiVed August 1, 2009 Accepted August 26, 2009 IE801671U
