Wave dynamics and flow in multiple-porosity media

Abstract

The purpose of this paper is to describe the fluid flow and dynamics of wave propagation in multiple-porosity media (such as applied to porous rock with fissures of different sizes). Coupled partial differential equations for matrix deformation and Darcy flow with compressible mass conservation equations obtained from continuum mixture theory are developed. For the limiting case of a single porosity medium the transient response (pressure decay) solution for drilling into a gas saturated rock layer, for example, that is homogeneous and isotropic, will be derived exactly by transformation of the nonlinear diffusion equation describing the motions. Furthermore, a Burgers equation which admits solitons will be presented. Finally a generalization to the case of dual/triple continua will be treated.