Anisotropic dual‐continuum representations for multiscale poroelastic materials: Development and numerical modelling

Abstract

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.

Multirate Mass Transfer Approach for Double‐Porosity Poroelasticity in Fractured Media

“…Note that here we consider a regular fracture network aligned with the direction of the applied load. Ashworth and Doster (2020) showed that the poroelastic response in fractures and matrix differ depending on the fracture orientation. While the orientation is expected to have an impact also for the disorder scenario under consideration here, we conjecture that the expected late time scaling will persist because it is caused by the broad distribution of matrix permeabilities.…”

Machine learning-based multiscale constitutive modelling: Development and application to dual-porosity mass transfer

“…Several investigations have shown use of the linear constitutive model in Eq. ( 42) to lead to measurable errors in flow behaviour (Zimmerman et al 1993;Ashworth and Doster 2020). One common way to alleviate these inaccuracies is to use multi-rate transfer models (Haggerty and Gorelick 1995;Geiger et al 2013).…”

“…Matrix G α is the coupling matrix arising from an inter-porosity flow expression such as the linear approximation in Eq. ( 42) (see Ashworth and Doster (2020) for details). Note, terms arising from the linear transfer approximation will also appear in the flow matrices.…”

“…These challenges necessitate simpler descriptions for inter-porosity exchange, leading to the commonly used linear description involving involving the difference between averaged pressures (Warren and Root 1963). However, this simplification is known to lead to measurable errors in flow behaviour, particularly at early-time (Zimmerman et al 1993;Ashworth and Doster 2020). Instead of making any such assumptions, we use a data-driven constitutive model learnt on time series data coming directly from the microscale.…”

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

“…Transverse isotropy is a common type of anisotropy in which the material properties are symmetric about a bedding plane and anisotropic in the direction normal to this plane 19–23 . The effect of anisotropy on the stiffness and strength of various transversely isotropic rocks has been extensively investigated in the literature 24–31 . The stiffness and strength of transversely isotropic rocks depend on the direction of the load with respect to the orientation of the bedding plane, and are often different in the bed‐normal (BN) and bed‐parallel (BP) directions.…”