Tight gas reservoirs are characterized by single-phase (gas) or two-phase (gas and liquid) flow in extremely low-permeability, highly heterogeneous porous/fractured, and stress-sensitive rock. Gas flow in such tight formations is further complicated by other co-existing processes, such as Klinkenberg effect, non-Newtonian or non-Darcy flow behavior, due to strong interaction between fluid molecules and solid materials within tiny pores, or micro- and macro- fractures. Because of the low permeability in tight rock, the traditional double-porosity model may not be applicable for handling fracture-matrix interaction of gas flow in these reservoirs. In this work, we present a generalized mathematical model for simulating multiphase flow of gas in tight, porous/fractured reservoirs using a more general, multi-continuum modeling approach. The model incorporates the following processes: (1) Klinkenberg effect, (2) non-Newtonian behavior (i.e., threshold pressure gradient for flow to occur); (3) non-Darcy flow with inertial effects; and (4) rock deformation due to changes in the stress field. We propose to explicitly separate effects of rock mechanical deformation and molecular interaction between fluids and rock materials. The former effect is included using the intrinsic permeability and porosity relations, while the latter is accounted for by an apparent viscosity for non-Newtonian, non-Darcy's behavior, or a modified permeability for Klinkenberg effect

The proposed mathematical model has been implemented into a multiphase, multidimensional reservoir simulator. In the numerical model, specifically, a control-volume, integral finite-difference method is used for spatial discretization with an unstructured grid, and a first-order finite-difference scheme is adapted for temporal discretization of governing two-phase flow equations in tight gas reservoirs. The resulting discrete nonlinear equations are solved fully implicitly by Newton iteration. The numerical scheme has been verified against analytical solutions with Klinkenburg effect, non-Newtonian or non-Darcy flow, and flow in deformable fractured rock in our previous studies. The model's application to actual tight gas reservoirs is an on-going research project.

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