Characterization of Injection into Deep Saline Aquifers Using Two-Phase Darcy-Forchheimer Flow
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 7
Abstract
In this study the generalized Darcy-Forchheimer model is used to characterize two-phase fluid flow where spatial flow characteristics may transition between Darcy and Forchheimer flow behavior. The local transition between the two flow regimes is characterized using the Forchheimer number as the criterion. A three-dimensional numerical model is developed that utilizes a control-volume method to simulate two-phase inertial, immiscible, and incompressible flow in a nondeformable homogeneous porous medium. The numerical model is validated by comparing its results with those obtained using a semianalytical solution of the Buckley-Leverett problem. The critical Forchheimer number is characterized using experimental data and is used to transition the local flow domain between Darcy and Forchheimer flow regions for both single-phase and multiphase analysis. The saturation-dependent distribution of the critical Forchheimer number is then used to analyze the Darcy and Forchheimer flow regions to provide a coupled solution to the problem. The proposed approach simulates injection of into saline aquifers. The simulation results show that local Forchheimer flow transition reveals critical conditions that need to be addressed in field applications. The findings are discussed in reference to deep saline injection of .
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References
Abou-Kassem, J. H., Farouq Ali, S. M., and Islam, M. R. (2006). Petroleum reservoir simulation: A basic approach, Gulf Publishing, Houston, TX.
Ahmadi, A., Arani, A. A. A., and Lasseux, D. (2010). “Numerical simulation of two-phase inertial flow in heterogeneous porous media.” Transp. Porous Media, 84(1), 177–200.
Ahmed, N., and Sunada, D. K. (1969). “Nonlinear flow in porous media.” J. Hydraul. Div., 95(6), 1847–1857.
Andrade, J. A., Jr., Costa, U. M. S., Almeida, M. P., Makse, H. A., and Stanley, H. E. (1999). “Inertial effects on fluid flow through disordered porous media.” Phys. Rev. Lett., 82(26), 5249–5252.
Brooks, R. H., and Corey, A. T. (1964). “Hydraulic properties of porous media.” Hydrology Papers, No. 3, Colorado State Univ., Ft. Collins, CO.
Buckley, S. E., and Leverett, M. C. (1942). “Mechanism of fluid displacement in sands.” Trans. AIME, 146(01), 107–116.
Chilton, T. H., and Colburn, A. P. (1931). “Pressure drop in packed tubes.” Ind. Eng. Chem., 23(8), 913–919.
Cornell, D., and Katz, D. L. (1953). “Flow of gases through consolidated porous media.” Ind. Eng. Chem., 45(10), 2145–2152.
Ergun, S. (1952). “Fluid flow through packed columns.” Chem. Eng. Prog., 48(2), 89–94.
Evans, E. V., and Evans, R. D. (1988). “Influence of an immobile or mobile saturation on non-Darcy compressible flow of real gases in propped fractures.” J. Petrol. Technol., 40(10), 1343–1351.
Evans, R. D., Hudson, C. S., and Greenlee, J. E. (1987). “The effect of an immobile liquid saturation on the non-Darcy flow coefficient in porous media.” J. SPE Prod. Eng. Trans. AIME, 283, 331–338.
Firoozabadi, A., and Katz, D. L. (1979). “An analysis of high-velocity gas flow through porous media.” J. Petrol. Technol., 31(2), 211–216.
Forchheimer, P. (1901). “Wasserbewegung durch boden.” Zeit. Ver. Deutsch. Ing., 45, 1781–1788.
Geertsma, J. (1974). “Estimating the coefficient of inertial resistant in fluid flow through porous media.” SPE J., 14(05), 445–450.
Green, L., Jr., and Duwez, P. (1951). “Fluid flow through porous metals.” J. Appl. Mech., 18, 39–45.
Hitchon, B. (1996). Aquifer disposal of carbon dioxide, Geoscience Publishing, Sherwood Park, AL, Canada.
Karimi-Fard, M., and Firoozabadi, A. (2003). “Numerical simulation of water injection in 2D fractured media using discrete-fracture model.” SPE Reservoir Eval. Eng., 6(02), 117–126.
Katz, D. L., and Lee, R. L. (1990). Natural gas engineering, production and storage, chemical engineering series, McGraw-Hill, New York.
Lee, R. L., Logan, R. W., and Tek, M. R. (1987). “Effects of turbulence on transient flow of real gas through porous media.” SPE Form. Eval., 2(1), 108–120.
Li, D., and Engler, T. W. (2001). “Literature review on correlations of the non-Darcy coefficient.” SPE paper 70015.
Liu, X., Civan, F., and Evans, R. D. (1995). “Correlations of the non-Darcy flow coefficient.” J. Can. Petrol. Technol., 34(10), 50–54.
Lopez-Hernandez, H. D., Valko, P. P., and Pham, T. T. (2004). “Optimum fracture treatment design minimizes the impact of non-Darcy flow effects.” Paper SPE 90195 presented at the SPE Annual Technical Conf. and Exhibition, Houston, TX.
Ma, H., and Ruth, D. W. (1993). “The microscopic analysis of high Forchheimer number flow in porous media.” Transp. Porous Media, 13(2), 139–160.
Mijic, A., and LaForce, T. C. (2010). “Effects of non-Darcy flow in CO2 injection into saline aquifers.” 12th European Conf. on the Mathematics of Oil Recovery.
Scheidegger, A. E. (1972). The physics of flow through porous media, Univ. of Toronto Press, Canada.
Sobieski, W., and Trykozko, A. (2012). “Darcy and Forchheimer laws in experimental and simulation studies of flow through porous media.” Transp. Porous Media, in press.
Swift, G. W., and Kiel, O. G. (1962). “The prediction of gas-well performance including the effects of non-Darcy flow.” J. Petrol. Technol. Trans. AIME, 14(07), 791–798.
Tek, M. R., Coats, K. H., and Katz, D. L. (1962). “The effects of turbulence on flow of natural gas through porous reservoirs.” J. Petrol. Technol. Trans. AIME, 14(07), 799–806.
Wahyudi, I., Montillet, A., and Khalifa, A. O. A. (2000). “Darcy and post-Darcy flows within different sands.” J. Hydraul. Res., 40(4), 519–525.
Welge, H. J. (1952). “A simplified method for computing oil recovery by gas or water drive.” Trans. Am. Inst. Min. Metall. Petrol. Eng., 195, 91–98.
Whitney, D. D. (1988). “Characterization of the non-Darcy flow coefficient in propped hydraulic fractures.” Master’s thesis, Univ. of Oklahoma, Oklahoma.
Wu, Y. S. (2001). “Non-Darcy displacement of immiscible fluids in porous media.” Water Resour. Res., 37(12), 2943–2950.
Wu, Y. S. (2002). “Numerical simulation of single-phase and multiphase non-Darcy flow in porous and fractured reservoirs.” Transp. Porous Media, 49(2), 209–240.
Zeng, Z. W., and Grigg, R. (2006). “A criterion for non-Darcy flow in porous media.” Transp. Porous Media, 63(1), 57–69.
Zhang, J., and Xing, H. (2012). “Numerical modeling of non-Darcy flow in near-well region of a geothermal reservoir.” Geothermics, 42, 78–86.
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© 2014 American Society of Civil Engineers.
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Received: Feb 19, 2014
Accepted: Sep 4, 2014
Published online: Oct 10, 2014
Discussion open until: Mar 10, 2015
Published in print: Jul 1, 2015
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