Modeling Two-Phase Flow in Porous Media With Consideration of Jump Interfaces

Abstract

Abstract Discontinuities of rock and fluid properties are very common in the reservoir due to variations of formation lithology and oil-water gravity differentiation. Fluid discontinuity also exists at the water front in the water-flooding reservoir. Interfaces with discontinuous fluid properties are called jump interfaces. It is known that fluid flow at these jump interfaces is neither continuous flow, which is dealt with conventional multiphase flow model in porous media, nor purely piston-like drive, which is the problem of dynamic interface tracking. In practice, however, by neglecting jump interfaces, fluid flow is widely treated as continuous flow by adding relative permeability into each phase equation in black oil simulation. Also, single-point upstream weighting and high order schemes have no improvement on flux rate and moving speed of phase interfaces. This paper starts from analyzing two-phase flow with consideration of jump interfaces. In porous media, flow channels of oil and water are relatively stable at low rates: one fluid always takes first priority of displacing the same type of fluid and then displaces the other fluid when the channels of the same type of fluid are not sufficient. Therefore, the flow of a specified fluid through jump interfaces includes two parts: displacing the same type of fluid and displacing the other type of fluid. Based on this analysis, we develop a new two-phase flow model, considering discontinuities of flow properties. Unlike currently available flow models, our model takes account the effect of one fluid displacing the other fluid across jump interfaces. We apply to a 1-D case and compare with Buckley-Leverett equation. The example demonstrates that our new model has more capabilities to describe the physical flow at the jump interface. We also discuss applications of our model on connection condition construction for jump interfaces in the numerical model and relative permeability measurements.