Reduced Models for Description of Invasion Zone Geomechanics

摘要

This paper presents a coupled poroelastic model describing rock matrix deformation and two-phase filtration flow. The model has been derived based on mechanical principles of interpenetrated continuum and includes conservation laws written for the mixture components and constitutive equations in a form of the generalized Hook's law. The system has at least two spatial scales that define small quantity - scales ration. The small parameter decomposition has been utilized to obtain a series of approximate model corresponding to the special deformation condition. The zero-order approximation describes porous media with invariant volume. One also has obtained and analyzed an analytical solution in cylindrical coordinates for the zero volumetric deformation. The periodicity along radius stresses and pore pressure distribution in this solution demonstrate a possibility of disruption zones appearances not only at the borehole wall but also at some distance deeper in the rock. Its first-order approximation under a compact phase incompressibility assumption produces a generalization of the Buckley-Leverett two-phase filtration model with porous space deformations taken into account. The reduced poroelastic models presented enables a quick solution for mechanics and fluids-dynamics problems of invasion zone.