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Ind. Eng. Chem. Res. 2006, 45, 2430-2436
Accelerated Mass Transfer of CO2 in Reservoir Brine Due to Density-Driven Natural Convection at High Pressures and Elevated Temperatures Chaodong Yang and Yongan Gu* Petroleum Technology Research Centre (PTRC), Faculty of Engineering, UniVersity of Regina, Regina, Saskatchewan S4S 0A2, Canada
In this paper, the mass transfer of CO2 into a reservoir brine sample is studied experimentally at high pressures and elevated temperatures. The equilibrium concentration of CO2 in the reservoir brine and the density of CO2-saturated brine are measured by saturating the brine with CO2. The mass-transfer rate of CO2 into the brine is determined by monitoring the pressure decay inside a closed, visual, high-pressure PVT cell. It is found that the density of the brine with dissolved CO2 increases linearly with CO2 concentration. As CO2 gradually dissolves into the brine by molecular diffusion, a concentration-induced density gradient is generated near the CO2-brine interface. Under the influence of gravity, this concentration-induced density gradient causes natural convection, which accelerates the mass-transfer rate of CO2 into the brine. The modified diffusion equation with an effective diffusivity is applied to model the mass-transfer process. It is found that the determined effective diffusivities of CO2 in the reservoir brine are almost two orders of magnitude larger than the molecular diffusivities of CO2 in water or similar reservoir brines. The detailed experimental results show that the density-driven natural convection greatly accelerates the dissolution process of CO2 in brine. This means that loss of CO2 in brine can be significant in an enhanced oil recovery operation using CO2 flooding in an oil reservoir with a bottom water aquifer. More importantly, the accelerated mass transfer due to the density-driven natural convection significantly increases the geological sequestration rate of CO2 in deep saline formations. 1. Introduction Recently, greater attention has been focused on global warming caused by increased emissions of greenhouse gases (mainly CO2) into the atmosphere. To minimize this undesirable climate change, many techniques have been proposed to mitigate the emission of CO2 into the atmosphere.1,2 One of the most viable techniques is to sequester CO2 in geological media. For example, geological sequestration of CO2 can be implemented by injecting CO2 into depleted oil and gas reservoirs, deep unmineable coal seams, and deep saline aquifers.3 In particular, sequestration of CO2 in deep saline aquifers has great potential for storing large amounts of the injected CO2 in saline water by dissolution.4,5 In the literature, a number of theoretical, numerical, and experimental studies on various technical aspects of CO2 sequestration in deep saline aquifers have been reported.6-9 The major technical challenge is to determine the actual performance and long-term safety of CO2 injection into the deep saline formations. This requires knowledge of the CO2 distribution in the geological media during the injection and postinjection periods. Ennis-King and Paterson3 found that the CO2 distribution during the injection phase is controlled by gravity segregation, relative permeability effects, and the permeability anisotropy of the saline formation. In the postinjection period, however, the distribution of the injected CO2 is mainly determined by the dissolution of CO2 in the reservoir brine. Three mechanisms are involved in the dissolution of CO2. First, because of the buoyancy force, CO2 migrates upward and mixes with the upper formation brine. The second mechanism is attributed to the molecular diffusion of CO2 in the formation brine. Third, diffusion of CO2 in the brine phase further induces * To whom correspondence should be addressed. E-mail: peter.gu@ uregina.ca. Tel.: 1 (306) 585-4630. Fax: 1 (306) 585-4855.
so-called density-driven natural convection, which significantly accelerates the dissolution of CO2 in the reservoir brine. This density-driven natural convection results from an increase in the density of brine when it is saturated with CO2. The third mass-transfer mechanism is of great importance in practice because convective dispersion is usually much faster than molecular diffusion and thus plays a dominant role in the dissolution of the injected CO2 in the formation brine. In the past, the effect of density-driven natural convection on the mass transfer of CO2 in the formation brine was not considered in conventional reservoir simulators for predicting CO2 distributions in saline aquifers.10,11 In general, the amount of CO2 dissolved into the reservoir brine by molecular diffusion is extremely small in comparison with the bulk gaseous CO2 phase. Lindeberg and Wessel-Berg12 undertook a theoretical analysis to examine conditions under which natural vertical convection might occur after CO2 is injected into an aquifer. They found that, if there is no high-permeability zone, the injected CO2 accumulates under the cap rock. Then, the CO2 starts to dissolve into the reservoir brine by molecular diffusion. Consequently, the density of CO2-saturated brine increases, and thus, natural vertical convection occurs in the saline formation. It was concluded that natural vertical convection occurs under typical North Sea reservoir conditions. However, Lindeberg and Wessel-Berg did not quantify the effect of the natural vertical convection on the accelerated mass transfer of CO2 in the reservoir brine. A comprehensive literature search shows that insufficient experimental data are available for studying the accelerated mass transfer of CO2 into reservoir brine due to natural convection under practical reservoir conditions.13-18 It has been found that the equilibrium concentration (i.e., solubility) of CO2 in water or brine increases with pressure.19-21 Because a higher CO2 concentration in a brine causes larger density gradient in the brine phase, it is expected that the mass transfer of CO2 in a
10.1021/ie050497r CCC: $33.50 © 2006 American Chemical Society Published on Web 10/06/2005
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2431 Table 1. Physical and Chemical Properties of the Instow Brine Sample
Figure 1. Schematic diagram of the DBR PVT system.
brine at a higher pressure will be much faster than that in a brine at atmospheric pressure. Therefore, it is important to study the mass-transfer process of CO2 in formation brine under practical reservoir conditions, i.e., at high pressures and elevated temperatures. As described in this article, a series of experiments was conducted to study the mass-transfer process of CO2 in a reservoir brine sample in the pressure range of 2.6-7.5 MPa and at two constant temperatures, T ) 27 and 58 °C. First, the equilibrium concentration of CO2 in the brine sample and the density of CO2-saturated brine were measured at different pressures and temperatures by saturating the brine sample with CO2 inside a closed, visual, high-pressure PVT cell. Then, in mass-transfer tests, the mass-transfer rate of gaseous CO2 into the brine sample was determined by monitoring the pressure decay of the gas phase inside the high-pressure cell. With the measured equilibrium properties, the measured mass-transfer rates of CO2 into the reservoir brine were modeled by applying the modified diffusion equation with an effective diffusivity. The determined effective diffusivities were almost two orders of magnitude larger than the molecular diffusivities of CO2 in water or similar reservoir brines. 2. Experimental Section 2.1. Materials. Carbon dioxide with a specified purity of 99.99% (instrument grade) was purchased from Praxair, Canada. The brine sample used in the experiments was collected from the Instow oil field in Saskatchewan, Canada. Prior to use, the brine sample was filtered to remove fine solids. The density of the brine was 999 kg/m3 at 27 °C. Its total dissolved solids (TDS) was 4310 mg/L, and its pH was 8.16. More physical and chemical properties of the Instow brine sample are given in Table 1. 2.2. Apparatus. All mass-transfer experiments were conducted by using a mercury-free DBR pressure-volumetemperature (PVT) system (PVT-0150-100-200-316-155, DBR, Canada). Figure 1 is a schematic diagram of the DBR PVT system. The major component of this system is a visual, highpressure PVT cell, where fluid samples are encapsulated inside a glass tube. The glass tube has an inner diameter of 3.177 cm and a total length of 20.320 cm. Inside the glass tube, fluid samples are isolated from the hydraulic oil by a moveable isolation piston. The cell pressure can be readily varied by changing the pressure in the hydraulic system so as to move the isolation piston downward or upward. The visual PVT cell and a video-based digital cathetometer allow direct and accurate measurements of the phase volumes. The cell is also equipped with a magnetically coupled mixer, which can be used to
density at 27 °C and 1 atm (kg/m3) density at 58 °C and 1 atm (kg/m3) viscosity at 27 °C and 1 atm (mPa s) viscosity at 58 °C and 1 atm (mPa s) pH conductivity at 25 °C (S/m) refractive index at 25 °C chloride (mg/L) sulfate (mg/L) total dissolved solids (mg/L) potassium (mg/L) sodium (mg/L) calcium (mg/L) magnesium (mg/L) iron (mg/L) manganese (mg/L) barium (mg/L)
999 991 0.83 0.49 8.16 6.69 1.3338 1860.00 0) ∂z z)H
(11)
Before the CO2 reaches the bottom of the PVT cell during the mass-transfer test, the brine phase can be considered as a semiinfinite medium. It should be noted that the semi-infinite medium model is applicable in geological sequestration of CO2 because of the large size of aquifers. The analytical solution for the above mass-transfer problem was obtained by Crank25 as
c(z,t) ) cint -
2cint
xπ
∫0z/(2xD
efft)
e-s ds 2
(12)
From the above concentration distribution, the number of moles of CO2 dissolved into the brine phase at any time t is found to be24
nt ) 2cintA
x
Defft π
(13)
The above equation indicates that the number of moles of CO2 dissolved into the brine should be a linear function of the square root of time. The values measured for the number of moles of CO2 dissolved into the brine versus the square root of time for each test are plotted in Figure 5a for T ) 27 °C and in Figure 5b for T ) 58 °C. The experimental data in the period of 180 s < t < 3600 s show good linearity between the number of moles of dissolved CO2 and the square root of time. When t g 3600 s, however, the measured number of moles of dissolved CO2 becomes a nonlinear function of xt. It can be shown from eq 12 that, at t ≈ 3600 s, CO2 has already reached the bottom of the PVT cell, so that the brine phase can no longer be treated as a semi-infinite medium. At 180 s < t < 3600 s, linear correlations of nt versus xt for the experimental data are also given in this figure. It should be noted that these correlations do not pass through the origin point, where nt ) 0 at t ) 0, because eq 13 is applicable only when the density-driven natural convection flow is fully developed in the brine phase. By using these linear correlations together with eq 13, the effective diffusivity was calculated, as tabulated in Table 3. The determined effective diffusivity is in the range of (170.7-183.2) × 10-9 m2/s at T ) 27 °C and in the range of (250.2-269.8)
Figure 5. Measured number of moles of CO2 dissolved into the brine versus square root of time at T ) (a) 27 and (b) 58 °C.
× 10-9 m2/s at T ) 58 °C. At each temperature, the differences among the determined effective diffusivities at different pressures are probably caused by experimental error. The effective diffusivities at T ) 58 °C are larger than those at T ) 27 °C because, at a higher temperature, the viscosity of the brine is lower and, thus, the density-driven natural convection to transport CO2 into the brine is stronger. Comparison of the determined effective diffusivities with the molecular diffusivities of CO2 in water or similar reservoir brines,24,26,27 which are in the range of (1.74-3.72) × 10-9 m2/s, indicates that the former are almost two orders of magnitude larger than the latter. This clearly shows that the density-driven natural convection greatly accelerates the mass transfer of CO2 into the brine phase. 3.4. Mass-Transfer Rates. Based on the modified diffusion equation with an effective diffusivity presented in the preceding section, the mass-transfer rate per unit contact area can be readily derived from eq 13 as
Jt )
1 dnt ) cint A dt
x
Deff πt
(14)
The mass-transfer rates predicted from the above equation with the determined effective diffusivities are shown in Figure 6a,b, in comparison with the experimental data at T ) 27 and 58 °C, respectively. Here, only the experimental data in the period of 180 s < t < 3600 s are plotted in this figure because, as described in the previous section, eqs 13 and 14 are valid only before CO2 reaches the bottom of the PVT cell (t ≈ 3600 s). It can be seen from these two figures that the predicted mass-
Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2435
different constant temperatures of 27 and 58 °C. First, the equilibrium concentration of CO2 in the brine phase and the density of CO2-saturated brine were measured at different equilibrium pressures. Experimental results showed that the equilibrium concentration of CO2 in the brine phase increased linearly with pressure in the pressure range tested and that the density of the brine-CO2 mixture increased linearly with CO2 equilibrium concentration in the brine. Then, the mass-transfer rate of CO2 into the brine phase was measured by monitoring the pressure decay of the CO2 phase inside a closed, visual, high-pressure PVT cell. It was found that the modified diffusion equation with an effective diffusivity could be successfully used to model the mass-transfer process examined in this study. The effective diffusivity was determined to be in the range of (170.7-183.2) × 10-9 m2/s at T ) 27 °C and (250.2-269.8) × 10-9 m2/s at T ) 58 °C, almost independent of pressure. It should be noted that these determined effective diffusivities are almost two orders of magnitude larger than the molecular diffusivities. The experimentally measured mass-transfer rates show that density-driven natural convection substantially accelerates the dissolution of CO2 in the reservoir brine. These experimental results indicate that the amount of CO2 dissolved into an aquifer can be significant in an enhanced oil recovery process using CO2 flooding. On the other hand, the accelerated mass transfer due to density-driven natural convection can greatly increase the geological sequestration rate of CO2 in deep saline formations. Acknowledgment
Figure 6. Comparison of the mass-transfer rates predicted from eq 14 with the experimental data at T ) (a) 27 and (b) 58 °C.
transfer rates are in excellent agreement with the measured data. At the same temperature, the higher the pressure is, the larger the mass-transfer rate is. This is because the interface concentration of CO2 is higher at a higher pressure, as shown in Figure 2, whereas the effective diffusivity is almost independent of pressure. This figure also shows that the mass-transfer rate decreases dramatically with time. This is attributed to the decreased CO2 concentration gradient near the CO2-brine interface as CO2 gradually dissolves into the brine phase. Moreover, it is noted that the measured mass-transfer rates can be readily used to estimate the amount of CO2 dissolved into the brine phase. For instance, at T ) 58 °C and P|t)180s ) 7.536 MPa (test 4), the mass-transfer rate is about 4.3 × 10-6 (kmol/ m2)/s at t ) 3600 s. This means that at least 0.681 kg/m2 of CO2 passes through the CO2-brine interface and dissolves into the brine within 1 h in this test. In consideration of the large contact area between the CO2 and brine and the geological storage time, an extremely large amount of CO2 can be sequestered in a saline aquifer. This conclusion has two practical implications. In an enhanced oil recovery process using CO2 flooding, the loss of CO2 into the reservoir brine can be significant if there exists a large bottom water aquifer in the oil reservoir. On the other hand, the accelerated mass transfer due to density-driven natural convection can greatly increase the sequestration rate of CO2 in a saline aquifer. 4. Conclusions In this paper, mass-transfer tests of CO2 in a formation brine are conducted in the pressure range of 2.6-7.5 MPa and at two
The authors acknowledge a discovery grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada and an innovation fund from the Petroleum Technology Research Centre (PTRC) at the University of Regina to Y.G. The authors also thank Mr. Shuliang Li and Mr. Asok Kumar Tharanivasan for their technical assistance in experiments. Literature Cited (1) Gentzis, T. Subsurface sequestration of carbon dioxide: An overview from an Alberta (Canada) perspective. Int. J. Coal Geol. 2000, 43, 287305. (2) Klara, S. M.; Srivastava, R. D.; McIlvried, H. G. Integrated collaborative technology development program for CO2 sequestration in geologic formationssUnited States Department of Energy R&D. Energy ConVers. Manage. 2003, 44, 2699-2712. (3) Ennis-King, J.; Paterson, L. Engineering aspects of geological sequestration of carbon dioxide. Presented at the Society of Petroleum Engineers (SPE) Asia Pacific Oil and Gas Conference and Exhibition, Melbourne, Australia, Oct 8-10, 2002; Paper SPE 77809. (4) Bachu, S.; Adams, J. J. Sequestration of CO2 in geological media in response to climate change: Capacity of deep saline aquifers to sequester CO2 in solution. Energy ConVers. Manage. 2003, 44, 3151-3175. (5) Shafeen, A.; Croiset, E.; Douglas, P. L.; Chatzis, J. CO2 sequestration in Ontario, Canada. Part I: Storage evaluation of potential reservoirs. Energy ConVers. Manage. 2004, 45, 2645-2659. (6) Klusman, R. W. Evaluation of leakage potential from a carbon dioxide EOR/sequestration project. Energy ConVers. Manage. 2003, 44, 1921-1940. (7) Pruess, K.; Garcia, J. Multiphase flow dynamics during CO2 disposal into saline aquifers. EnViron. Geology 2002, 42, 282-295. (8) Saripalli, P.; McGrail, P. Semianalytical approaches to modeling deep well injection of CO2 for geological sequestration. Energy ConVers. Manage. 2002, 43, 185-198. (9) Spycher, N.; Pruess, K.; Ennis-King, J. CO2-H2O mixtures in the geological sequestration of CO2. I. Assessment and calculation of mutual solubilities from 12 to 100 °C and up to 600 bar. Geochim. Cosmochim. Acta 2003, 67, 3015-3031. (10) Holt, T.; Jensen, J. I.; Lindeberg, E. Underground storage of CO2 in aquifers and oil reservoirs. Energy ConVers. Manage. 1995, 36, 535538.
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ReceiVed for reView April 26, 2005 ReVised manuscript receiVed August 31, 2005 Accepted September 5, 2005 IE050497R
