“Revisiting” the enduring Buckley–Leverett ideas

Abstract

For more than 60 years, the ideas imbedded in the watershed paper of Buckley and Leverett [Buckley, S.E., Leverett, M.C., 1942. Mechanism of fluid displacement in sands. Trans. AIME, 146, 107–116.] have been employed by geo-scientists of various persuasions to forecast what specifically might happen when fluids are either produced from and/or injected into subsurface porous rock domains through systems of wells drilled for that purpose that connect near surface petrochemical facilities with subsurface transport source and/or sink interface locations. Example cases of related applications are those when and where the accessed local pore space already contains desired quantities of producible valuable fluid-phase species (e.g., such entities as potable water; certain and mineral-rich brines; petroleum liquids and gases; other valuable gases such as helium, LPGs, CO 2; semi-solids like bitumens, tars and methane hydrates; fluid and/or entrained solid Waste Disposal Materials; etc.) which, for example, can hopefully be produced and/or economically injected into repositories and/or subsurface basin-wide storage strata and/or along subsurface transport paths. In Rose [Rose, W., 1988. Attaching new meanings to the Equations of Buckley and Leverett. Journal of Petroleum Science and Engineering 1, 223–228.], however, it was suggested that the Darcian-based algorithm originally and even currently employed by many traditionalist reservoir transport process simulation authorities only poorly models actual reservoir transport process events. The thought behind this presumption has to do with the fact that viscous and/or other related coupling effects for dynamic multiphase-saturated media are not quantitatively accounted for in Darcy's law that more often than not is seen to empirically only describe low-intensity single-phase flow data for Newtonian fluids. Accordingly, an algorithmic form was prospectively adopted that was based on the theorems of non-equilibrium thermodynamics variously referenced in Truesdell and Toupin [Truesdell C., Toupin, R.A, 1960. Classical field theories. Handbuch der Physik III/1, 226–793.], in the DeGroot and Mazur [DeGroot S.R., Mazur P., 1962. Non-Equilibrium Thermodynamics, North-Holland Publishing, Amsterdam.] rendition of Onsager [Onsager, Lars, 1931. Physical Review 37, 405–426. Physical Review 38, 2265–2279.] dogma, by Rose [Rose, W., 1969. Transport through interstitial paths of porous solids, METU (Turkey). Journal of Pure and Applied Science 2, 117–132.] as applied to porous media transport phenomena, similarly by Bear [Bear, J., 1972. Dynamics of Fluids in Porous Media, American Elsevier, New York.], and in many other places. Accordingly, in this paper, our goal in revisiting the ideas of Buckley and Leverett one more time is to search for modified schemes to conduct coherent reservoir process simulation studies that involve less computational and parameter measurement work than is required, for example, by the standard procedures given in the definitive Bear and Bachmat [Bear, J., Bachmat, Y., 1990. Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer Academic Publishers.] monograph that refers to aspects of the famous (Onsager, [Onsager, Lars, 1931. Physical Review 37, 405–426. Physical Review 38, 2265–2279.], et. seq.) related schemes that are only somewhat akin (but not identical) to the several unique methodologies we shall be proposing here that includes the so-called APTPA formulations of Rose and Rose [Rose W., Rose, D., 2004. An upgraded porous medium coupled transport process algorithm. Transport in Porous Media, Reference # TIPM2. (in press). See also Rose, W., Gallegos, R., Rose, D., 1988. Some Guidelines for Core Analysis Studies of Oil Recovery Processes. Journal of the Society of Professional Well Logging Analysts (SPWLA) 29 (May–June Issue), 178–183.].