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 1 arXiv:1903.11361v2 [physics.geo-ph] 25 Oct 2019 end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromehcanical 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.

Modelling multiscale-multiphysics geology at field scales is non-trivial due to computational resources and data availability. At such scales it is common to use implicit modelling approaches as they remain a practical method of understanding the first order processes of complex systems. In this work we introduce a numerical framework for the simulation of geomechanical dual-continuum materials. Our framework is written as part of the open source MATLAB Reservoir Simulation Toolbox (MRST). We discretise the flow and mechanics problems using the finite volume method (FVM) and virtual element method (VEM) respectively. The result is a framework that ensures local mass conservation with respect to flow and is robust with respect to gridding. Solution of the coupled linear system can be achieved with either fully coupled or fixed-stress split solution strategies. We demonstrate our framework on an analytical comparison case and on a 3D geological grid case. In the former we observe a good match between analytical and numerical results, for both fully coupled and fixed-stress split strategies. In the latter, the geological model is gridded using a corner point grid that contains degenerate cells as well as hanging nodes. For the geological case, we observe physically plausible and intuitive results given the boundary conditions of the problem. Our initial testing with the framework suggests that the FEM-VEM discretisation has potential for conducting practical geomechanical studies of multiscale systems.

Summary Dual‐continuum (DC) models can be tractable alternatives to explicit approaches for the numerical modelling of multiscale materials with multiphysics behaviours. This work concerns the conceptual and numerical modelling of poroelastically coupled dual‐scale materials such as naturally fractured rock. Apart from a few exceptions, previous poroelastic DC models have assumed isotropy of the constituents and the dual‐material. Additionally, it is common to assume that only one continuum has intrinsic stiffness properties. Finally, little has been done into validating whether the DC paradigm can capture the global poroelastic behaviours of explicit numerical representations at the DC modelling scale. We address the aforementioned knowledge gaps in two steps. First, we utilise a homogenisation approach based on Levin's theorem to develop a previously derived anisotropic poroelastic constitutive model. Our development incorporates anisotropic intrinsic stiffness properties of both continua. This addition is in analogy to anisotropic fractured rock masses with stiff fractures. Second, we perform numerical modelling to test the DC model against fine‐scale explicit equivalents. In doing, we present our hybrid numerical framework, as well as the conditions required for interpretation of the numerical results. The tests themselves progress from materials with isotropic to anisotropic mechanical and flow properties. The fine‐scale simulations show that anisotropy can have noticeable effects on deformation and flow behaviour. However, our numerical experiments show that the DC approach can capture the global poroelastic behaviours of both isotropic and anisotropic fine‐scale representations.

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