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• W4230331671 abstract "Analytical Solutions for 1-D Countercurrent Imbibition in Water-Wet Media Dimo Kashchiev; Dimo Kashchiev RERI Search for other works by this author on: This Site Google Scholar Abbas Firoozabadi Abbas Firoozabadi RERI Search for other works by this author on: This Site Google Scholar Paper presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, April 2002. Paper Number: SPE-75166-MS https://doi.org/10.2118/75166-MS Published: April 13 2002 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Kashchiev, Dimo, and Abbas Firoozabadi. Analytical Solutions for 1-D Countercurrent Imbibition in Water-Wet Media. Paper presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, April 2002. doi: https://doi.org/10.2118/75166-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Improved Oil Recovery Conference Search Advanced Search AbstractAnalytical solutions for the initial stage of one-dimensional countercurrent flow of water and oil in porous media are presented. Expressions are obtained for the time dependence of the water saturation profile and the oil recovered during spontaneous countercurrent imbibition in rod-like, cylindrical and spherical cores for which water is the wetting liquid. Some of the analytical solutions are found to be in good agreement with existing numerical solutions and available experimental data for oil recovery from cores with strong water wettability.IntroductionCapillary-driven fluid flow is often important in two-phase flow in fractured porous media and in layered media where individual layers are thin. In such cases, the parameters in the flow equations are complicated functions of saturation due to high nonlinearity arising from a realistic shape of the capillary-pressure curve. The common approach to the problem solution is the use of numerical techniques.Analytical solutions to fluid flow problems are desirable, because they allow a better understanding of the underlying physics and verification of numerical models. For capillary-driven flow, only a handful of authors have proposed analytical solutions of various degrees of complexity and with certain restrictive assumptions.Yortsos and Fokas [1983] obtained an analytical solution for a one-dimensional flow with account of capillary pressure; the relative permeabilities and capillary pressure were, however, severely restricted in functional form. Chen [1988] proposed combined analytical-numerical techniques for analysis of radial one-dimensional flow. His work is based on the use of certain asymptotic conditions; it has a strong numerical component.McWhorter and Sunada [1990] reported quasi-analytical solutions for one-dimensional linear and radial flow. Their work includes both countercurrent and cocurrent flow. These authors limited their solution to an infinite acting medium and assumed that the volume flux at the inlet is of the form At-1/2 where A is constant and t is time.Pavone et al. [1989] also solved the one-dimensional and two-dimensional (gravity drainage) problem analytically; several assumptions were made by these authors to provide a closed-form solution. The assumptions included (i) infinite gas mobility, (ii) linear liquid-phase relative permeability, and (iii) capillary-pressure dependence on saturation in the form of logarithmic function. As a result of these assumptions, the flow equations became linear.In this paper, we provide approximate analytical solutions for the initial stage of linear, cylindrical and spherical countercurrent flow of water and oil in a porous medium. We solve the flow equations without restricting the functional form of the relative permeabilities and the capillary pressure. We only assume that the imbibing and the displaced liquids are incompressible and that the porous medium is water-wet. These two assumptions have been made in the work of all authors referred to above.The Diffusion CoefficientThe flow of water and oil in a porous medium is described by a diffusion-type equation in which the quantityEquation 1plays the role of diffusion coefficient [McWhorter and Sunada, 1990; Pooladi-Darvish and Firoozabadi, 2000]. In this expression Sw is the water saturation, k (m2) is the absolute permeability of the medium, krw and kro are the relative permeabilities to water and oil, respectively, µw (Pa. s) and µo (Pa. s) are the viscosities of water and oil, respectively, f is the fractional porosity of the medium, Pc=po-pw is the capillary pressure (positive when water is the wetting liquid), and pw (Pa) and po (Pa) are the water and the oil pressures, respectively. Keywords: water saturation profile, linear imbibition, capillary pressure, saturation profile, countercurrent imbibition, initial stage, dependence, imbibition, relative permeability, flow in porous media Subjects: Reservoir Fluid Dynamics, Improved and Enhanced Recovery, Formation Evaluation & Management, Flow in porous media This content is only available via PDF. 2002. Society of Petroleum Engineers You can access this article if you purchase or spend a download." @default.
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• W4230331671 title "Analytical Solutions for 1-D Countercurrent Imbibition in Water-Wet Media" @default.
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