Framework for Coupling Flow and Deformation of a Porous Solid

Abstract

In this paper, the flow of an incompressible fluid in a deformable porous solid is considered. A mathematical model using the framework offered by the theory of interacting continua is presented. In its most general form, this framework provides a mechanism for capturing multiphase flow, deformation, chemical reactions, and thermal processes, as well as interactions between the various physics, in a conveniently implemented fashion. To simplify the presentation of the framework, the results are presented for a particular model, which can be seen as an extension of Darcy’s equation (which assumes that the porous solid is rigid) and that takes into account the elastic deformation of the porous solid. The model also considers the effect of deformation on porosity. It is shown that by using this model identical results can be recovered as in the framework proposed in the literature. Some salient features of the framework are as follows: (1) it is a consistent mixture theory model, and adheres to the laws and principles of continuum thermodynamics; (2) the model is capable of simulating various important phenomena, such as consolidation and surface subsidence; and (3) the model is amenable to several extensions. Numerical coupling algorithms used to obtain a coupled flow-deformation response are also presented. Several representative numerical examples are presented to illustrate the capability of the mathematical model and the performance of the computational framework.