Speaker
Description
Layering is widely recognized in geologic porous media at multiple length scales ranging from the micrometer scale to the km scale. Incorporating the impact of the multi-phase flow on such heterogeneity on field-scale simulations demands upscaling not only of absolute permeability, but also the saturation functions; relative permeability and capillary pressure. If done correctly, upscaling of saturation functions preserves the flow features (sweep efficiency and micro-displacement) of the small-scale heterogeneity. Relative permeability upscaling, therefore, is one of the most important steps in reservoir simulation studies.
This study presents a mathematical approach for relative permeability upscaling devised specifically for non-communicating strata. Analytical solutions describe saturation and pressure distribution in each layer in the viscous limit. They are presented in a non-dimensional form derived for both linear and radial flow. Unlike the majority of earlier studies that assume piston-type displacement, our new solutions consider the complexities of frontal advance theory, including the rarefaction waves that follow the sharp flood fronts. However, potential gravity tonguing is ignored. The different multiphase flow properties of each layer (e.g. porosity, permeability, relative permeability endpoints, etc.) are taken into account by our new formulation. Three flow stages, each with its unique time-dependent characteristic variable, are considered for each layer. The overlap among the flow stages in the different layers determines the overall shape of the solution.
Our solutions enable a straightforward evaluation of the dynamics enameled in the relative permeability: the unsteady-state ensembled relative permeability is space-dependent with discontinuities associated with the flood-front saturation jumps. A comparison between the unsteady-state performance and the performance based on the commonly used steady-state upscaled relative permeability curves highlights the inadequacy of steady-state upscaling for viscous-limit flows. It also reveals the capability of the new relative permeability functions to predict the behaviour over the whole flow saturation range, not only for when both phases are mobile between the residual saturations. Beyond the interpretation of laboratory experiments, the applicability of this approach to field-scale simulation is discussed under a newly proposed dual-stage simulation technique.
References
Berg, S., Ott, H., 2012. Stability of CO2-brine immiscible displacement. Int. J. Greenh. Gas Control 11, 188–203. https://doi.org/10.1016/j.ijggc.2012.07.001
Bernabé, Y., 1992. On the Measurement of Permeability in Anisotropic Rocks. Int. Geophys. 51, 147–167. https://doi.org/10.1016/S0074-6142(08)62821-1
Buckley, S.E., Leverett, M.C., 1942. Mechanism of Fluid Displacement in Sands. Trans. AIME 146, 107–116. https://doi.org/10.2118/942107-g
Chen, Z., 2007. Reservoir simulation : mathematical techniques in oil recovery, SIAM/Society for Industrial and Applied Mathematics.
Corey, A.T., Rathjens, C.H., 1956. Effect of Stratification on Relative Permeability. J. Pet. Technol. 8, 69–71. https://doi.org/10.2118/744-G
Debbabi, Y., Jackson, M.D., Hampson, G.J., Fitch, P.J.R., Salinas, P., 2017. Viscous Crossflow in Layered Porous Media. Transp. Porous Media 117, 281–309. https://doi.org/10.1007/s11242-017-0834-z
Ekrann, S., Aasen, J.O., 2000. Steady-state upscaling. Transp. Porous Media 41, 245–262. https://doi.org/10.1023/A:1006765424927
Ekrann, S., Dale, M., Langaas, K., Mykkeltveit, J., 1996. Capillary limit effective two-phase properties for 3D media. NPF/SPE Eur. 3-D Reserv. Model. Conf. 119–129. https://doi.org/10.2523/35493-ms
El-Khatib, N.A.F., 2001. The Application of Buckley-Leverett Displacement to Waterflooding in Non-Communicating Stratified Reservoirs, in: SPE Middle East Oil Show. Society of Petroleum Engineers, pp. 1–12. https://doi.org/10.2118/68076-MS
Hearn, C.L., 1971. Simulation of Stratified Waterflooding by Pseudo Relative Permeability Curves. J. Pet. Technol. 23, 805–813. https://doi.org/10.2118/2929-PA
Lohne, A., Virnovsky, G.A., Durlofsky, L.J., 2006. Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale. SPE J. 11, 304–316. https://doi.org/10.2118/89422-PA
Pickup, G., Ringrose, P.S., Sharif, A., 2000. Steady-state upscaling: From lamina-scale to full-field model. SPE J. 5, 208–217. https://doi.org/10.2118/62811-PA
Stein, S.K., 1987. Calculus and analytic geometry, 5th ed. McGraw-Hill Companies.
Volk, M., 2005. Pump Characteristics and Applications 525.
Welge, H.J., 1951. A Simplified Method for Computing Oil Recovery by Gas or Water Drive. Pet. Trans. AIME 195, 91–98. https://doi.org/https://doi.org/10.2118/124-G
Willard E., J., Richard V., H., 1948. Directional Permeability Measurements and Their Significance. Prod. Mon. 13, 17–25.
Woods, F.S., 1934. Advanced Calculus.
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