Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

Abstract

We propose the generalization of the anisotropic poroelasticity theory. At a large scale, a medium is viewed as quasi‐static, which is the original assumption of Biot. At a smaller scale, we distinguish different sets of pores or fractures that are characterized by various fluid pressures, which is the original poroelastic extension of Aifantis. In consequence, both instantaneous and time‐dependent deformation lead to fluid content variations that are different in each set. We present the equations for such phenomena, where the anisotropic properties of both the solid matrix and pore sets are assumed. Novel poroelastic coefficients that relate solid and fluid phases in our extension are proposed, and their physical meaning is determined. To demonstrate the utility of our equations and emphasize the meaning of new coefficients, we perform numerical simulations of a triple‐porosity consolidation. These simulations reveal positive pore pressure transients in the drained behaviour of weakly connected pore sets, and these may result in the mechanical weakening of the material.

Multi‐porous extension of anisotropic poroelasticity: Linkage with micromechanics

“…The comprehensive, time-dependent considerations beyond expressions (1)-( 2), where varying permeabilities and interset fluid flows are taken into account, can be found in our parallel paper. 16…”

“…To account for the set connections and time factor leading to eventual pore pressure equilibration, additional coupling terms in expression (2) should appear. 16 Although, as noticed by researchers working on an isotropic extension of poroelasticity, 14,15,25 these coupling terms are very small and can therefore be neglected. (Also, the low permeability of interconnections implies a very long time required for pressure equilibration).…”

“…Note that the time-dependent multi-porous extension of anisotropic poroelasticity is discussed in our parallel article. 16 Note that (1)- (2), in contrast to the derivations of for example, Mehrabian, 15 allow material to be anisotropic and do not assume confining stress. The generalisation to anisotropy becomes crucial when coping with nonrandom pores or aligned cracks-common geological scenarios-that, in turn, may lead to fluid pressure variations at the pore scale or regional scale (the aforementioned polarisation).…”

“…Such a view underlines the dual-porosity extension of anisotropic poroelasticity studied by for example, Zhang and Borja, 11 Zhang et al 12 and the multi-porous (or multiple-porosity) generalisation of poroelasticity proposed by for example, Aifantis 13 Berryman, 14 Mehrabian 15 for isotropy and hydrostatic confining pressure. As depicted in our conceptual model from Figure 2 (discussed further in Adamus et al 16 ), the connections between pores continuously evolve over time and space. Consequently-at any F I G U R E 2 Schematic view of the conceptual model with scenarios described in the main text, where 𝑥 denotes the number of pores, 𝑛 stands for the number of pore sets, and 𝑡 denotes time.…”

“…given instant-some pores (and sets thereof) will be connected, and flow between them is possible, whereas othersat any given instant-will be isolated. In our parallel paper, 16 we derive expressions of multi-porous extension of anisotropic poroelasticity that describe the time-dependent deformation of a medium containing different pore sets, each with distinct fluid pressure. In this paper, however, we consider fundamental expressions of instantaneous poroelastic deformation.…”