An Open Source Numerical Framework for Dual-Continuum Geomechanical Simulation

Abstract

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.

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

“…In the dual continuum implicit approach, finite element method and finite volume or difference discretization schemes are typically used for discretization of the fluid flow process in fractured porous rocks. It is a practical approach to investigate and understand the behaviour of coupled mechanics of multiscale systems (Ashworth and Doster, 2019;Monteagudo and Firoozabadi, 2004). However, these models are limited to sugar cubic representations of a fractured system.…”

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

“…The discrete counterpart to Equations (59) to (61) is formulated using the finite‐volume method (FVM) for flow, the virtual‐element method (VEM) for mechanics 51,52 and the backward Euler method for time. This hybrid numerical approach to poroelasticity was originally developed using the Matlab Reservoir Simulation Toolbox (MRST) 53,54 by previous studies 55,56 for single‐continuum materials and later expanded in Ashworth and Doster 57 to DC materials. We use this hybrid framework in the current work due to its availability.…”

“…Finally, Equation (71) is solved using a fully coupled approach, 60 although extensions to sequential solution strategies for DC materials have been shown in Kim et al 48 and Ashworth and Doster 57 …”

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

“…( 59) to ( 61) is formulated using the finite-volume method (FVM) for flow, the virtual-element method (VEM) for mechanics (Beirão da Veiga et al 2013;Gain et al 2014), and the backward Euler method for time. This hybrid numerical approach to poroelasticity was originally developed using the Matlab Reservoir Simulation Toolbox (MRST) (Lie et al 2012;Lie 2019), by Andersen et al (2017a,b) for single-continuum materials and later expanded in Ashworth and Doster (2019a) to dual-continuum materials. We use this hybrid framework in the current work due to its availability.…”

“…Finally, Eq. ( 71) is solved using a fully coupled approach (Lewis and Schrefler 1998), although extensions to sequential solution strategies for DC materials have been shown in Kim et al (2012) and Ashworth and Doster (2019a).…”