An oil–water two-phase reservoir numerical simulation coupled with dynamic capillary force based on the full-implicit method

Abstract

Capillary pressure is a key parameter in reservoir numerical simulation. It is generally considered that the capillary force is an only function of water saturation in the current traditional reservoir numerical simulation methods. However, large amount of indoor experiments have shown that capillary force is not only dependent on the water saturation, but also the velocity of fluid flow. In this work, we introduce the dynamic capillary pressure to the oil–water two-phase flow equations. Then, we discrete the modified oil and water phase basic governing equation with difference methods. The full implicit method is selected to solve the pressure equation. Finally, a numerical simulation method coupled with the dynamic capillary force based on the full-implicit method is established. We discussed the effect of dynamic capillary pressure on the oil–water two-phase flow in two-dimensional homogeneous and heterogeneous porous media. Comparing to static capillary pressure model, the dynamic capillary pressure model predicts higher water-saturation near the injection and production wells. In addition, a “funnel” like pressure profile appears in the water saturation profile. At low water cut stage, the rate of water cut increase is relatively high, while opposite is true at high water cut stage. We also calibrated our newly proposed model by comparing to the analytical method and the actual oil field production data. Our work should provide important insights into the effect of dynamic capillary force on the oil–water two-phase flow and better estimation of flow behavior in oil and gas reservoir.