Multiscale dual-continuum modelling of deformable porous media

Abstract

Within the geosciences, we are often challenged by how to model the coupling of physical phenomena across varying space and time scales, as well as between different phenomena themselves. As a result, we forgo accuracy and physical consistency/understanding, in favour of efficiency and practicality. To address these tradeoffs we can use multiscale and multiphysics modelling. In this work, we are concerned with multiscale behaviours owing to the coupling between a microscale model and a (macroscopic) dual-continuum model. For the multiphysics component, we consider the coupling between linear deformation and flow, referred to as poroelasticity. Accordingly, the goal of this thesis is to apply multiscale and multiphysics modelling concepts to the study of strongly heterogeneous (deformable) porous media, to better understand and represent the links between various scales of interest. We split this work into three main parts. Part one investigates the relations between microscopic and dual-continuum poroelastic constitutive models, including previously introduced phenomenological models. To do so, we use micromechanical approaches. Subsequently, starting from the microscale, we derive a fully anisotropic dual-continuum poroelastic constitutive model using homogenisation. We then show how the resulting model is related to constitutive models available in literature. For these previously introduced models, we use micromechanical considerations and analytical solutions to compare and contrast the various modelling concepts used in their derivation. We also investigate various simplifying assumptions made by past users of these models. On the basis of our studies we provide recommendations for how and when to use the various dual-continuum poroelastic constitutive modelling concepts and simplifications. Part two introduces a numerical framework for poroelastic dual-continuum modelling. We subsequently use this framework to further study the links between microscale and macroscale poroelastic materials. Our numerical framework considers anisotropy and uses a hybrid discretisation suited for the flow and deformation subproblems accordingly. We benchmark the resulting framework against analytical solutions and demonstrate its use on a complex geological grid. With the framework in-hand we compare and study dual-continuum behaviours against microscale representations given various modelling and material assumptions on the latter. We present a number of tests starting from isotropic cases, progressing to more complex anisotropic cases. Our results show that anisotropy can have measurable effects on coupled behaviours. However, for the tests considered, we show the dual-continuum approach is capable of capturing the global poroelastic behaviours of microscopic representations. Finally, part three establishes a computational multiscale approach based on machine learning to improve the accuracy of macroscopic approaches in subsurface modelling. Here the idea is to use data-driven modelling as a surrogate constitutive model within a hierarchical multiscale setting. Accordingly, we detail the framework, describing the key components and considerations therein. We then apply the framework to the problem of inter-continuum mass transfer, whilst considering an uncoupled (flow only) dual-continuum representation. We couple the resulting data-driven model to a physics-based model leading to a hybrid machine learning-physics-based approach. We show the resulting hybrid method to give high quality results with respect to a microscale model, without the computational expense of the latter.