Coupled fluid flow and geomechanics in reservoir study. I. Theory and governing equations

The purpose of this study is to examine Biot`s two-phase (fluid and rock), isothermal, linear poroelastic theory from the conventional porous fluid-flow modeling point of view. Not`s theory and the published applications are oriented more toward rock mechanics than fluid flow. Our goal is to preserve the commonly used systematic porous fluid-flow modeling and include geomechanics as an additional module. By developing such an approach, complex reservoir situations involving geomechanical issues (e.g., naturally fractured reservoirs, stress-sensitive reservoirs) can be pursued more systematically and easily. We show how the conventional fluid-flow formulations is extended to a coupled fluid-flow-geomechanics model. Consistent interpretation of various rock compressibilities and the effective stress law are shown to be critical in achieving the coupling. The {open_quotes}total (or system) compressibility{close_quotes} commonly used in reservoir engineering is shown to be a function of boundary conditions. Under the simplest case (isotropic homogeneous material properties), the fluid pressure satisfies a fourth-order equation instead of the conventional second-order diffusion equation. Limiting cases include nondeformable, incompressible fluid and solid, and constant mean normal stress are analyzed.