oa Mathematical Theory for Two Phase Displacement with Hysteresis (With application to WAG injection)

To describe two-phase displacement with hysteresis we use the Buckley-Leverett model with imbibition, drainage and scanning fractional flows. Mathematical theory for the initial-boundary non-self-similar problems is developed. The structure of solutions is presented together with the physical interpretation of phenomena. Analytical solutions for the injection of water slug with the gas drive and for the sequential injection of water and gas slugs with the water drive are obtained. The solutions show that the hysteresis decreases the gas flux in the case where the drainage relative permeability is lower than the imbibition one, which is a positive effect for the wateraltemate- gas injection.