Geometrical models for poroelastic behaviour

SUMMARY 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 formation 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 description 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 with an inclusion‐based model when one of these approximations is used. The connection is used to examine pore geometry effects on poroelastic behaviour by considering a simple model with identically shaped pores. The results of this modeling 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 condition. The following observations were made about specific poroelastic quantities. The Skempton ratio is relatively insensitive to porosites 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 condition grows as the pore aspect ratio decreases.