This paper presents a mathematical model for simulating single-phase and multiphase flow through stress-sensitive formations using a conventional three-phase flow reservoir simulator. To incorporate the effect of rock deformation on flow in porous media, the proposed mathematical model formulation relies on (1) laboratory-determined correlations between permeability and effective stress and (2) an assumption that the in situ total stress in reservoirs is constant or a function of spatial coordinates and pressure. This assumption may provide a good approximation for flow through a thin layer in a deep formation, such as in most oil/gas and geothermal reservoirs. The proposed mathematical model is implemented into a multiphase, multidimensional black-oil reservoir simulator. In our numerical model specifically, a control-volume, integral finite-difference method is used for spatial discretization, and a first-order finite-difference scheme is adapted for temporal discretization of governing flow equations in deformable porous or fractured media. The resulting discrete nonlinear equations are solved fully implicitly by Newton iteration. The numerical scheme is verified against an analytical solution of flow through pressure-dependent permeability.


The permeability of porous and fractured media is dependent on pore pressures or the stress field within a formation. In most studies of fluid flow in porous or fractured media, however, it has been assumed that the influence of rock deformation on permeability is negligible, i.e., only fluid density and rock porosity are treated as functions of pressure. This assumption may be reasonable for slightly compressible fluid flow in high-permeability reservoirs, such as sandstone formations, under normal ranges of production and injection conditions. In such cases, the pore compressibility of the sandstone is usually very small and pressure disturbance is not very large compared with the original in situ conditions. Nevertheless, even for flow in fractured media or operational conditions with high-pressure injection or production, the same assumption of constant permeability has often been made. In practice, the potential influence of rock deformation on flow and transport in subsurface has in general been ignored in almost all reservoir characterizations and field simulation studies. While there exists a wealth of studies on coupled flow and rock deformation processes [10, 4, 16, 15, 22, 14, 9, 8, 17, 3], neglecting the effects of rock deformation on fluid mobility in permeable porous and fractured rock may introduce large errors, or result in faulty model predictions, when simulating flow in stress-sensitive reservoirs. However, because of the complexity and costs of coupled modeling, we often need to approximate these effects in conventional (uncoupled) reservoir simulators [17]. It has been long noticed that physical or chemical disturbances of in situ conditions in permeable formations-resulting from oil/gas production, CO2 sequestration, or geofluid withdraw in subsurface reservoirs-causes rock deformation. The fluid-flowinduced rock deformation, in turn, could have profound effects on poroelastic and transport properties in a lowpermeability reservoir, potentially impacting fluid flow and mass transport at various spatial scales. For example, permeability for pre-existing fractures may be enhanced significantly by the deformation of fractures in response to changes in stress fields and pore pressure.

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