A multi-dimensional, analytical model for counter-current water imbibition into gas-saturated matrix blocks

This paper presents multi-dimensional analytical models for counter-current water imbibition into a gas-saturated rectilinear matrix blocks and into finite-sized cylindrical matrix blocks. The models are developed by matching the water imbibition rate determined from Darcy's law, where the driving force is capillary pressure, to the instantaneous change in water saturation in the matrix block, determined from a material balance. The basic assumption in the models is that water imbibes in a piston-like manner. 1-D and 2-D experiments were performed to validate the models. The experiments showed that the piston-like assumption of water into a gas saturated matrix block is reasonable and the predictions by the models compare favorably with the experimental data.