Numerical Solution of Equation for Dynamic, Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

Abstract

In the oil industry, dynamic spontaneous imbibition plays an important role in several flow processes in porous media. A numerical approach is developed to simulate dynamic spontaneous imbibition with variable inlet saturation and interfacial coupling. The inclusion of interfacial coupling effects invalidates the assumption that the interfaces (fluid/fluid and fluid/solid) act in the same way. The one-dimensional numerical simulation model is developed using a Lagrangian formulation discretized in time and saturation. The solution of the partial differential equations utilizes an iteration process that includes two material balance criteria to ensure the validity of the variable inlet saturation. Furthermore, an error analysis, the validation of the model and a sensitivity study on the optimal number of time steps and saturation grid cells are undertaken. The numerical simulation solution represents an accurate approach to investigate the effect of fluid and rock properties on dynamic spontaneous imbibition.