A new numerical approach for investigation of the effects of dynamic capillary pressure in imbibition process

Capillary pressure is important in simulation of fluid flow in porous media at different scales. In ongoing simulation methods, capillary pressure is considered as a static process. However, recent researches have shown that capillary pressure is dynamic parameter. That is, its value directly depends on the rate of saturation changes. Including the effects of dynamic capillary pressure is especially important in prediction of imbibition process, which is an important mechanism in oil production from naturally fractured reservoirs. In this study, to investigate the effects of dynamic capillary pressure in two-phase flow process, an implicit and iterative method is proposed, and it is implemented in an open-source simulator named Matlab Reservoir Simulation Toolbox (MRST). The convergence results show that the proposed algorithm works well and the obtained results are acceptable. Furthermore, the analysis is made on the effects of dynamic capillary pressure functions in vertical imbibition process cases. The results confirm that considering dynamic capillary effects is critical in the simulation of two-phase flow in porous media. This is more important in imbibition process, where the capillary force is the dominant driving force. It is also found that at high permeability cases, considering dynamic capillary pressure effects is more crucial. Also, it is concluded that in high mobility ratios, due to low imbibition rates, effect of considering dynamic capillary pressure curves is not significant.