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.

毛细压力是储层数值模拟中的关键参数。通常认为，毛细作用力是当前传统储层数值模拟方法中水饱和度的唯一函数。但是，大量的室内实验表明，毛细作用力不仅取决于水的饱和度，还取决于流体的流速。在这项工作中，我们将动态毛细管压力引入油水两相流方程。然后，用差分方法将修正的油水相基本控制方程式离散化。选择完全隐式方法求解压力方程。最后，建立了基于全隐式方法的动态毛细力耦合数值模拟方法。我们讨论了动态毛细管压力对二维均质和非均质多孔介质中油水两相流的影响。与静态毛管压力模型相比，动态毛管压力模型预测注入井和生产井附近较高的水饱和度。另外，在水饱和度曲线中会出现“漏斗”状的压力曲线。在低含水率阶段，含水率的增加率相对较高，而在高含水率阶段则相反。我们还通过与分析方法和实际油田生产数据进行比较，对我们新提出的模型进行了校准。我们的工作应为动态毛细作用力对油水两相流的影响提供重要见解，并更好地估算油气藏中的流动行为。