Simulation of Spontaneous Imbibition Using Rayleigh-Ritz Finite Element Method-ADiscrete Fracture Approach

Abstract

Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different and complex boundary conditions. For the non-linear diffusion saturation equation we cannot apply Rayleigh-Ritz Finite Element Method (FEM). Traditionally, the way around it is to use Galerkin FEM or Mixed FEM formulation, iterative nature of those, makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms, decouple and solve analytically the dependent variables from saturation – the primary variable, this non-linear FEM problem reduces to a simple weighted integral weak form, which can be solved with Rayleigh-Ritz method. The advantage of this method is that it is non-iterative, which reduces computation time. We compared our numerical models with the analytical solution of this diffusion equation. We validated a Finite Difference Method (FDM) numerical model using X-Ray Tomography (CT) experimental data, and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example, using discrete fracture approach, was developed and its results compared with a commercial simulator.