A model for the flow of gas mixtures in adsorption dominated dual-porosity reservoirs incorporating multi-component matrix diffusion—Part II numerical algorithm and application examples

In part one of this study a matrix-fracture transfer function was presented for multi-species gas migration in dual-porosity media. This second part presents the numerical implementation of this transfer function. Since the transfer function proposed in Part I is of an integral form with history-dependency and the resultant flow equations become a set of integro-(partial) differential equations, an algorithm is developed here for these equations. The algorithm is formulated using a step-by-step finite difference procedure combined with a fully implicit quadrature scheme. The quadrature scheme is based on the modified trapezoidal method and is designed for variable time-step size. The transfer function and the algorithm developed are incorporated into the commercial gas reservoir simulator SIMED II, and three examples are illustrated here. Example 1 demonstrates the performance and feasibility of the algorithm in applications, and Example 2 discusses the effect of higher order terms as well as its influence on flow profiles. The impact of mutual-diffusivity to flow profiles and well performance is illustrated in Example 3.