Abstract
Water Alternated Gas (WAG) flooding is largely used as an Enhanced Oil Recovery (EOR) method in oil fields. It is based on the high sweep efficiency of the water phase and the high displacement efficiency of the gas phase. Additionally, other components may be dissolved in both displacing phases, increasing the oil recovery factor and leading to modern WAG schemes such as PWAG (Polymer WAG), MWAG (Miscible WAG), and others. In this paper, we present approximate analytical solutions for the linear immiscible Water Alternated Gas problem. The mathematical model is composed by a 2×2 system of nonlinear hyperbolic Partial Differential Equations (PDE), solved by the Method of Characteristics (MOC) for a set of reservoir properties. The analytical solution is compared with numerical simulation showing the accuracy and robustness of the method under different WAG configurations. The presented solutions can be used to select the best recovery technique for a particular field in a fast and efficient way.
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References
Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Applied Science Publishers, Basel (1979).
Bedrikovetsky, P., Shapiro, A., Pires, A., 2004. New analytical solutions for 1-D multicomponent gas injection problems. In: Abu Dhabi International Petroleum Exhibition and Conference. Society of Petroleum Engineers. https://doi.org/10.2118/88760-ms
Bell, J.B., Trangenstein, J.A., Shubin, G.R.: Conservation laws of mixed type describing three-phase flow in porous media. SIAM J. Appl. Math. 46(6), 1000–1017 (1986). https://doi.org/10.1137/0146059
Buckley, S., Leverett, M.: Mechanism of fluid displacement in sands. Trans. AIME 146(01), 107–116 (1942). https://doi.org/10.2118/942107-g
Christensen, J., Stenby, E., Skauge, A., 1998. Compositional and relative permeability hysteresis effects on near-miscible WAG. In: SPE/DOE Improved Oil Recovery Symposium. Society of Petroleum Engineers. https://doi.org/10.2118/39627-ms
Christensen, J., Stenby, E., Skauge, A.: Review of WAG field experience. SPE Reserv. Eval. Eng. 4(02), 97–106 (2001). https://doi.org/10.2118/71203-pa
Corey, A., Rathjens, C., Henderson, J., Wyllie, M.: Three-phase relative permeability. J. Pet. Technol. 8(11), 63–65 (1956). https://doi.org/10.2118/737-g
Fayers, F., Sheldon, J.: The effect of capillary pressure and gravity on two-phase fluid flow in a porous medium. Trans. AIME 216(01), 147–155 (1959). https://doi.org/10.2118/1089-g
Holden, L.: On the strict hyperbolicity of the buckley-leverett equations for three-phase flow in a porous medium. SIAM J. Appl. Math. 50(3), 667–682 (1990). https://doi.org/10.1137/0150039
Holtz, M. H., 2016. Immiscible water alternating gas (IWAG) EOR: Current state of the art. In: SPE Improved Oil Recovery Conference. Society of Petroleum Engineers. https://doi.org/10.2118/179604-ms
Johns, R., Orr, F.: Miscible gas displacement of multicomponent oils. SPE J. 1(01), 39–50 (1996). https://doi.org/10.2118/30798-pa
LeVeque, R., J, L., Crighton, D., 2002. Finite Volume Methods for Hyperbolic Problems In Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge.
Li, D., Kumar, K., Mohanty, K. K., 2003. Compositional simulation of WAG processes for a viscous oil. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. https://doi.org/10.2118/84074-ms
Lin, E., Poole, E.: Numerical evaluation of single-slug, WAG, and hybrid CO2 injection processes, Dollarhide Devonian unit, Andrews County, Texas. SPE Reserv. Eng. 6(04), 415–420 (1991). https://doi.org/10.2118/20098-pa
Marchesin, D., Plohr, B.J.: Wave structure in WAG recovery. SPE J. 6(02), 209–219 (2001). https://doi.org/10.2118/71314-pa
Rhee, H-K., Aris, R., Amundson, N. R.: On the theory of multicomponent chromatography. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 267 (1182), 419–455 (1970). https://doi.org/10.1098/rsta.1970.0050
Sanchez, N. L., 1999. Management of water alternating gas (WAG) injection projects. In: Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers. https://doi.org/10.2118/53714-ms
Sheldon, J., Cardwell, W.: One-dimensional, incompressible, noncapillary, two-phase fluid flow in a porous medium. Trans. AIME 216(01), 290–296 (1959). https://doi.org/10.2118/978-g
Sohrabi, M., Tehrani, D., Danesh, A., Henderson, G.: Visualization of oil recovery by water-alternating-gas injection using high-pressure micromodels. SPE J. 9(03), 290–301 (2004). https://doi.org/10.2118/89000-pa
Stone, H.: Probability model for estimating three-phase relative permeability. J. Petrol. Technol. 22(02), 214–218 (1970). https://doi.org/10.2118/2116-pa
Acknowledgements
This research was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001. Alvaro Peres acknowledges the Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF) for financial support.
Funding
This research was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Alvaro Peres acknowledges the Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF) for financial support.
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All authors contributed to the mathematical model. W.B. developed the codes and first draft of the manuscript.
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Pires, A.P., Barros, W.Q. & Peres, A.M.M. Approximate Analytical Solutions for 1-D Immiscible Water Alternated Gas. Transp Porous Med 151, 171–191 (2024). https://doi.org/10.1007/s11242-023-02037-w
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DOI: https://doi.org/10.1007/s11242-023-02037-w