A thermo-flow-mechanics-fracture model coupling a phase-field interface approach and thermo-fluid-structure interaction

TL;DR

This work addresses fracture behavior in geothermal reservoirs under temperature changes by coupling a thermo-hydro-mechanical model with a phase-field fracture approach. A four-step algorithm alternates between thermo-fluid-structure interaction on a reconstructed sharp fracture geometry and a diffuse phase-field fracture problem to update fracture width and propagation. The approach demonstrates temperature-induced modulation of fracture opening and cracking, validated through mesh-convergence studies and multiple propagating-crack scenarios. The resulting THM-TFSI-PFF framework advances permeability prediction in Enhanced Geothermal Systems and opens paths for future 3D extensions and multi-physics extensions.

Abstract

Geothermal energy, a promising renewable source, relies on efficiently utilizing geothermal reservoirs, especially in Enhanced Geothermal Systems (EGS), where fractures in hot rock formations enhance permeability. Understanding fracture behavior, influenced by temperature changes, is crucial for optimizing energy extraction. To address this, we propose a novel high-accuracy phase-field interface model integrating temperature dynamics into a comprehensive hydraulic-mechanical approach, aiming for a thermo-fluid-structure interaction representation. Therein, the key technical development is a four-step algorithm. This consists of computing the fracture width, reconstructing the sharp interface geometry, solving the thermo-fluid-structure interaction (TFSI) problem, and employing a phase-field approach coupled to the temperature and pressure from the TFSI problem. By coupling temperature-hydraulic-mechanical processes with our newly proposed high-accuracy phase-field interface approach, we investigate how temperature impacts fracture width values, which are crucial for permeability in EGS reservoirs. Through this model and three different numerical simulations, we aim to provide an approach to deepen understanding of the complex interplay between temperature, mechanical deformation, and permeability evolution. Therein, we substantiate our formulations and algorithms through mesh convergence results of crack width and total crack volumes for static fractures, and crack lengths in the case of propagating fractures.

Figures (16)

• Figure 1: (a) Setup for the thermo-fluid-structure interaction (TFSI) problem and (b) the change of $\Omega_f$ due to the fracture propagation problem from the phase-field fracture (PFF) approach
• Figure 2: Classical phase-field approach utilizes the diffusive fracture and propagate directly by solving the phase-field problem.
• Figure 3: Illustration of different types of fractures
• Figure 4: Sketch of the presented algorithm.
• Figure 5: Sketch of re-meshing procedure. The dashed line represents the known center line of the crack, the blue points the computed crack opening displacements on the crack interface, which are connected by the green line segments to form the reconstructed geometry approximation.

Theorems & Definitions (10)

• Remark 1
• Definition 1
• Definition 2
• Remark 2: Linearization
• Remark 3: Penalty method
• Remark 4: Temperature influence on fracture aperture and propagation
• Remark 5: Biot's coefficient $\alpha_B$
• Remark 6
• Definition 3: Stationary thermo-fluid-structure interaction
• Definition 3: Stationary thermo-fluid-structure interaction