Geometrical models for poroelastic behaviour

Abstract

Poroelasticity implicitly incorporates pore structure information through the use of empirically determined macroscopic parameters; hence, quantitative analysis of pore geometry effects on poroelastic behaviour cannot be performed. Analogues for poroelastic parameters with explicit dependence on pore structure are derived here by using an inclusion-based model where inclusions represent individual pores. The inclusion-based formulation used in this paper permits uniform pore fluid pressure throughout the pore space, a requirement of poroelasticity. When specific inclusion-based approximations resulting from different descriptions of inclusion interactions were considered, it was found that the analogue quantities obtained from the dilute volumetric average, Kuster-Toksöz and equivalent inclusion-average stress approximations replicated the relationships between poroelastic parameters predicted by poroelasticity. This equivalence implies that pore geometry information can be consistently incorporated into poroelastic parameters with an inclusion-based model when one of these approximations is used. This connection is used to examine pore geometry effects on poroelastic behaviour by considering a simple model with identically shaped pores. The results of this modelling study show that variations in pore shape significantly affect poroelastic parameters and that the nature of these effects is controlled by the specified applied stress-strain and fluid pressure conditions. The following observations were made about specific poroelastic quantities. The Skempton ratio is relatively insensitive to porosities below 0.1. Its minimum value for a given solid matrix, pore fluid and total porosity level is obtained when all pores are spherical; this value can be significantly greater than the theoretical lower limit of zero. Specific storage terms increase by several orders of magnitude as pores become more crack-like. The difference between the traditional definition of specific storage and that proposed by Green & Wang (1990) for 'normal' aquifer conditions grows as the pore aspect ratio decreases.