TRAVELING WAVE ANALYSIS OF COCURRENT IMBIBITION IN POROUS MEDIA

摘要

Spontaneous imbibition plays a very significant role in oil recovery during water flooding, steam injection, water-alternating-gas, and production from petroleum reservoirs with natural active aquifer. This phenomenon may involve cocurrent and countercurrent flow of oil and water, jointly or separately, depending on the imposed boundary condition of the matrix block. These modes of imbibition are completely different in the rate and extent of oil recovery and manner of saturation distribution within the porous matrix block. Unfortunately, the majority of numerical, theoretical, and experimental imbibition studies have concentrated on the countercurrent mode of the imbibition process. So, the main focus of this work is on cocurrent imbibitions, which has not received much attention in the previous studies. An analytical solution is presented in this article for linear, one-dimensional, cocurrent imbibition of a wetting phase (water) into a porous medium (reservoir rock) to expel a nonwetting phase (oil) in the same direction. The robust approach of traveling wave solution is employed to solve a generalized unsteady saturation diffusion equation and analytical solution is provided in a closed form. Although the analytical solution is developed for water imbibition into petroleum reservoirs, it is applicable to every liquid-liquid and gas liquid-system with broad application to analysis of flow in geothermal reservoirs, hydrology, soil science, etc. The newly proposed solution has several advantages over the existing ones. The main advantage is that it does not require any simplifying assumptions, discretization, linearization, transformation, self-similarity or perturbation assumption, etc. Fortunately, this solution has the advantage of describing the entire imbibition time including unsteady, late-transient, and pseudo-steady-state periods. Additionally, despite the previous works, the outcome of this paper is not restricted to special forms of saturation functions and capillary diffusion coefficient (e.g., linear). Eventually, the benefit of knowing water saturation profile in the matrix block is utilized to calculate average water saturation and matrix-fracture transfer function.