Generalized analytical solutions of imbibition characteristic behavior in shale matrix blocks under different boundary conditions

Abstract

Continental shale reservoirs are rich in reserves, imbibition is an essential mechanism for enhancing the oil recovery of the shale matrix system. The pores of shale matrix are divided into organic pores, brittle mineral pores and clay pores. The clay pores have the osmosis of the semi-permeable membrane, which increases the driving force of imbibition, while the non-semi-permeable membrane components are mixed-wet. Based on this, the 1-D mathematical models under different boundary conditions (including Two Ends Open, TEO; One End Open, OEO; and TEO-Oil-Water, TEO-OW) are established using the analytical solution method, and the water saturation distribution and oil recovery characteristics of matrix blocks are studied, revealing distinct imbibition phenomena: (1) Under OEO boundary conditions, counter-current imbibition dominates, with oil recovery proportional to the square root of time before the imbibition front reaches the block end. (2) For TEO boundary conditions, spontaneous imbibition exhibits symmetric counter-current flows from both ends, resulting in approximately twice the oil recovery of OEO. (3) Under TEO-OW conditions, a hybrid process of counter-current and co-current imbibition occurs, with delayed saturation evolution near the outlet. Additionally, forced imbibition under TEO demonstrates co-current flow dominated by oil-water interaction, showing earlier breakthrough with increased oil viscosity. The imbibition models of shale matrix blocks under different boundary conditions effectively reveal the control mechanism of SI and FI, and provide practical guidance for determining shut-in time and optimizing fracturing parameters.