Cyclic Flow of Two Immiscible Phases

We derive an analytical solution for two-phase cyclic flow assuming incompressible fluid and rock, one dimensional flow and negligible capillary pressure effects. The solution is intended to model subsequent periods of injection and production in a reservoir or core sample. It pertains to applications such as gas storage in water bearing formations or enhanced oil recovery by CO2 cyclic injection. Derivation is based on the method of characteristics and leads to an extension of the Buckeley-Leverett solution to cyclic injection. The saturation profile consists of two functions separated by a discontinuity. It is shown that the moving front advances during injection and recedes during production until returning back to the well. Some injected phase may remain in the reservoir after production and this in turn contributes to a deeper penetration during the next injection period. The solution for saturation profile as a function of time is analyzed and shown to become steady periodic after a number of cycles. We investigate the solution dependence on the controlling parameters: relative permeability (power n in krw, krnw functions), viscosity ratio μw/μnw and nondimensional production time t˜prod.