Exact Analytical Solutions of Countercurrent Imbibition with Both Capillary and Gravity Effects

Spontaneous imbibition (SI) is a key mechanism for hydrocarbon recovery within the matrix system in fractured reservoirs. The production of SI is primarily achieved through the countercurrent imbibition of water, which displaces the hydrocarbon. Various analytical and semianalytical methods have been suggested for the prediction of this process. However, as claimed by further studies, most of these analytical solutions are valid only for rather restrictive and/or unrealistic functions of capillary pressure and relative permeabilities. Some other semianalytical solutions assumed a specific form of inlet boundary condition. Thus, in this paper, a new analytical solution is proposed that does not possess these limitations, fully based on the physics and mathematics of two-phase flow in porous media. In the proposed model, imbibition front movement through the porous medium is termed the pore connectivity concept, which was not considered in any previous studies to date. Pore connectivity, tortuosity, shape factor, and permeability as interconnected parameters have been used in this study, where the relationship between these parameters assisted in the development of the mathematical model. Accordingly, this model has relaxed some of the limitations of previously proposed analytical solutions. Capillary and gravity forces and their relative contributions have been considered, and exact solutions were derived. These analytical solutions were then verified with experimental results, where they showed an acceptable match. A sensitivity analysis of contributing parameters was also performed to identify the most significant parameters and their contributing effect on final recovery. Previous studies showed that displacement efficiency has been shown to be independent of density difference, initial water saturation, and residual oil saturation. These findings were confirmed by previous experimental results. Applying this novel methodology improves the prediction of fluid saturations, reservoir recovery, and hydrocarbon production strategies.