Green Element solution of one-dimensional counter-current spontaneous imbibition in water wet porous media

A Green Element numerical formulation is used to solve the time-dependent nonlinear one-dimensional counter-current spontaneous imbibition diffusion equation in which water enters a water wet rock spontaneously while oil escapes by flowing in the opposite direction. The Green Element Method (GEM) is an element by element approach of the boundary element method. In this new method, by generating large sparse global matrices and yet taking advantage of properties of Green's function, solution of more complicated physical problem is achievable while at the same time much less computational effort is needed rather than boundary element method (BEM). By discretizing both the boundary and problem domain, GEM is capable of solving the whole system for the saturation and its derivative. For these calculations no approximation for simplification of nonlinearities is performed except interpolating the variables with linear shape function. The GEM results are compared with experimental imbibition measurements available in approachable literatures and also, analytical solution of the problem. The comparison reveals good agreement between them.