Numerical Modelling of Convection-Driven Cooling, Deformation and Fracturing of Thermo-Poroelastic Media

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.

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

“…Recently, the coupled THM‐fracturing processes have been simulated numerically for large‐scale single and multiple vertical natural fracture(s) embedded in formations under thermal gradient (Patterson & Driesner, 2021; Stefansson et al., 2021). Initially, there is no water flow under hydrostatic pressure that corresponds to variable water density with in situ temperature variation in the vertical direction.…”

Crustal Conditions Favoring Convective Downward Migration of Fractures in Deep Hydrothermal Systems

“…We consider propagation due to tensile forces, modeled by the stress intensity factor (Stefansson, Keilegavlen, et al., 2021; se also Nejati et al., 2015), $$${\text{SI}}_{I}=\sqrt{\frac{2\pi }{{R}_{d}}}\left(\frac{\mu }{\kappa +1}{\lBrack \mathbf{u}\rBrack }_{n}\right),$$$ where R d is the distance between the point where the displacement jump is evaluated and the fracture tip, μ is the shear modulus of the rock, and κ is the Kolosov constant for plain strain described as a function of the shear and the bulk moduli of the rock (see Supporting Information ). The fracture tip propagates when SI I exceeds a critical value, $$${\text{SI}}_{I}\ge {\text{SI}}_{I\text{crit}},$$$ which can be viewed as the rock toughness.…”

“…In the following, key components of the model are reviewed. A full description of the mathematical model, including coupling between variables in the rock matrix and the fracture (Jaffré et al., 2011; Martin et al., 2005; Stefansson, Keilegavlen, et al., 2021), is provided in the Supporting Information of this paper.…”

“…Expanding on the conceptual model by Lister (1974) and Axelsson (1985), Stefansson, Keilegavlen, et al. (2021) present a fully coupled numerical approach for fracture propagation and deformation that allow for multiple fractures in a thermo‐poroelastic medium. The effect of thermo‐poroelastic stresses on fracture transmissivity is incorporated through a fracture contact mechanics model.…”

“…In the work of Stefansson, Keilegavlen, et al. (2021), the downward migration of fractures due to convective cooling is considered for a test case with a set of smaller fractures ( H = 200 m, L = 200 m, W = 2 mm) at the bottom of a geothermal system. The study applied parameters which are representative for a geothermal system in a geological setting with a high geothermal gradient of 150°C/km.…”