Abstract
Convection-driven cooling in porous media influences thermo-poro-mechanical stresses, thereby causing deformation. These processes are strongly influenced by the presence of fractures, which dominate flow and heat transfer. At the same time, the fractures deform and propagate in response to changes in the stress state. Mathematically, the model governing the physics is tightly coupled and must account for the strong discontinuities introduced by the fractures. Over the last decade, and motivated by a number of porous media applications, research into such coupled models has advanced modelling of processes in porous media substantially. Building on this effort, this work presents a novel model that couples fracture flow and heat transfer and deformation and propagation of fractures with flow, heat transfer and thermo-poroelasticity in the matrix. The model is based on explicit representation of fractures in the porous medium and discretised using multi-point finite volume methods. Frictional contact and non-penetration conditions for the fractures are handled through active set methods, while a propagation criterion based on stress intensity factors governs fracture extension. Considering both forced and natural convection processes, numerical results show the intricate nature of thermo-poromechanical fracture deformation and propagation.
Highlights
For a porous medium, possibly containing fractures, the interplay between flow, thermal transport and deformation can be strong
The coupled dynamics are hypothesised to be crucial in heat transfer from the deep roots of geothermal systems by deepening natural convection through evolving fractures (Lister 1974; Bodvarsson 1982; Björnsson et al 1982; Björnsson and Stefánsson 1987)
Common to all of these applications is the limitation placed by tight coupling in the dynamics on the knowledge which can be gained from analysis of individual processes and mechanisms in isolation
Summary
Possibly containing fractures, the interplay between flow, thermal transport and deformation can be strong. Coupled thermo-hydro-mechanical (THM) processes in the intact porous medium interact with flow and thermal transport in fractures as well as fracture deformation and propagation. Deformation of existing fractures is modelled through contact mechanics relations based on a Coulomb friction criterion for slip along the fractures and a non-penetration condition (Hüeber et al 2008; Berge et al 2020) This is combined with a simple criterion for fracture propagation based on the mode I stress intensity factor, which we compute directly from the displacement jump in the vicinity of the fracture tip using a variant (Nejati et al 2015) of the displacement correlation method (Chan et al 1970). The finite volume approach combines the multi-point stress approximation method for Biot poroelasticity (Nordbotten 2016; Nordbotten and Keilegavlen 2021) with the multi-point flux approximation method for flow (Aavatsmark 2002) This combination has previously been applied for numerical modelling of fractured poroelastic media (Ucar et al 2018) with a simplified model for deformation along fractures.
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