Simplest Deformation Models for a Fluid-Saturated Poroelastic Medium
O. B. BOCHAROV1, V. YA. RUDYAK2, A. V. SERYAKOV1
1Baker Hughes Russian Science Center, pr. Kutateladze 4, Novosibirsk, 630128 Russia
2Novosibirsk State University of Architecture and Civil Engineering, ul. Leningradskaya 113, Novosibirsk, 630008 Russia
Keywords: poroelasticity, theory of mixtures, scaling method, saturated porous medium, compatibility model, unchanged volume medium, analytical solutions
Abstract
Under analysis is the compatibility model of two-phase flow in porous medium and deformation of the pore space. The model includes the equations of transfer of the medium components (fluid and porous matrix), derived from the conservation laws, the deformation consistency condition and the closing equations in the form of the generalized Hook law. It is shown that the system of the constitutive equations contains a series of small parameters, and the small parameter expansion allows a hierarchical sequence of models of certain deformation conditions. The null approximation and first approximation models are written in explicit form. It is found that if compact phases are incompressible, the first approximation equations go to the Buckley–Leverett model–like system with account for the change of the porous space. The zero approximation equations describe the porous medium behavior under condition of the unchanged volume. In this case, the equation of the pore pressure is separated from the equation of the elastic matrix. The analytical solutions derived for the zero approximation model in cylindrical coordinates feature shear stresses capable to cause failure.
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