Incorporating pore geometry and fluid pressure communication into modeling the elastic behavior of porous rocks

Abstract

Inclusion‐based formulations allow an explicit description of pore geometry by viewing porous rocks as a solid matrix with embedded inclusions representing individual pores. The assumption commonly used in these formulations that there is no fluid pressure communication between pores is reasonable for liquid‐filled rocks measured at high frequencies; however, complete fluid pressure communication should occur throughout the pore space at low frequencies. A generalized framework is presented for incorporating complete fluid pressure communication into inclusion‐based formulations, permitting elastic behavior of porous rocks at high and low frequencies to be described in terms of a single model. This study extends previous work by describing the pore space in terms of a continuous distribution of shapes and allowing different forms of inclusion interactions to be specified. The effects of fluid pressure communication on the elastic moduli of porous media are explored by using simple models and are found to consist of two fundamental elements. One is associated with the cubical dilatation and governs the effective bulk modulus. Its magnitude is a function of the range of pore shapes present. The other is due to the extensional part of the deviatoric strain components and affects the effective shear modulus. This element is dependent on pore orientation, as well as pore shape. Using sandstone and granite models, an inclusion‐based formulation shows that large differences between high‐ and low‐frequency elastic moduli can occur for porous rocks. An analysis of experimental elastic wave velocity data reveals behavior similar to that predicted by the models. Quantities analogous to the open and closed system moduli of Gassmann‐Biot poroelastic theory are defined in terms of inclusion‐based formulations that incorporate complete fluid pressure communication. It was found that the poroelastic relationships between the open and closed system moduli are replicated by a large class of inclusion‐based formulations. This connection permits explicit incorporation of pore geometry information into the otherwise empirically determined macroscopic parameters of the Gassmann‐Biot poroelastic theory.