A non-isothermal phase-field hydraulic fracture modeling in saturated porous media with convection-dominated heat transport

Abstract

This research aims to extend the isothermal continuum mechanical modeling framework of hydraulic fracturing in porous materials to account for the non-isothermal processes. Whereas the theory of porous media is used for the macroscopic material description, the phase-field method is utilized for modeling the crack initiation and propagation. We proceed in this study from a two-phase porous material consisting of thermomechanically interacting pore fluid and solid matrix. The heat exchange between the fluid in the crack and the surrounding porous environment through the diffusive fracture edges is carefully studied, and new formulations here are proposed. Besides, temperature-dependent solid and fluid material parameters are taken into account, which is of particular importance in connection with fluid viscosity and its effect on post-cracking pressure behavior. This continuum mechanical treatment results in strongly coupled partial differential equations of the mass, the momentum, and the energy balance of the thermally non-equilibrated constituents. Using the finite element method, two-dimensional initial-boundary-value problems are presented to show, on the one hand, the stability and robustness of the applied numerical algorithm in solving the emerged strongly coupled problem in the convection-dominated heat transport state. On the other hand, they show the capability of the modeling scheme in predicting important instances related to hydraulic fracturing and the role of the temperature field in this process. Additionally, they show the importance of using stabilization techniques, such as adding an artificial thermo-diffusivity term, to mitigate temperature fluctuations at high flow velocity.

A machine‐learning supported multi‐scale LBM‐TPM model of unsaturated, anisotropic, and deformable porous materials

“…Afterward, (2) the ML models are trained using the aforementioned datasets, before (3) testing the trained models with unseen data. Once a reliable ML-based model is developed, this can be integrated as an alternative to the conventional material models in a multiphase continuum mechanical framework within macroscopic poromechanics, see for example [16][17][18][19][20] for references and applications related to porous media mechanics.…”