Abstract

We developed one-dimensional, fully implicit numerical scheme to investigate the dynamic effect in the capillary pressure–saturation relationship used in the modeling of two-phase flow in porous media. Its validity was investigated by means of semianalytical solutions developed by McWhorter and Sunada (1990) and the authors. The numerical scheme was used to simulate a drainage experiment where the sand and fluid properties were known. Then the numerical scheme was used to simulate a laboratory experiment in a homogeneous column, including three major models of the dynamic effect coefficient τ. This numerical scheme can handle porous medium heterogeneity and was used to simulate a fictitious experimental setup with two different sands. As a result, the penetration time of the air phase through a layered porous medium for models including dynamic effects varied between 50 and 150% compared with static models of the capillary pressure–saturation relationship. Additionally, the accumulation time of air at a material interface (i.e., the delay of the air at the interface due to the capillary barrier effect) was investigated as a function of the ratio between the air-entry pressure values of the adjacent sands, emphasizing the differences between the dynamic and static capillary pressure models.

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