Abstract
A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.
Highlights
Many natural and manufactured geomaterials exhibit strong heterogeneities in their material properties, owing to the existence of porous constituents at various length scales
We find a good match in both matrix and fracture pressure evolutions using coefficient models from Khalili and Valliappan (1996) and Berryman (2002) when the fracture is almost all void space
The goal of this paper was to formulate a set of recommendations for how and when to use different constitutive modelling concepts
Summary
Many natural and manufactured geomaterials exhibit strong heterogeneities in their material properties, owing to the existence of porous constituents at various length scales. Examples of multiscale systems that are commonly encountered in subsurface operations include fissured B Mark Ashworth. Doster or fractured rock and soil aggregates (Warren et al 1963; Kazemi et al 1976; Nelson 2001; Gerke 2006; Koliji 2008; Romero et al 2011). Modelling of such materials is invaluable in understanding how these systems behave in response to extraneous activities. Modelling can be done using either explicit (e.g. discrete fracture matrix models) or implicit methods (e.g. continuum approaches) (Berre et al 2018)
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