Collaborative Research: Physics-Preserving Adaptive Finite Element Methods for Thermo-Poroelasticity

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Geothermal energy is one of the most promising renewable energy sources and has proven to be reliable, clean, and safe. When designing enhanced geothermal systems (EGS), it is necessary to understand the multiscale, multiphysics, thermal-hydraulic-mechanical (THM) processes that impact the EGS dynamics and productivity. This project aims to gain a fundamental understanding of key mechanisms controlling the dynamics in EGS (solid displacement, fluid flow, and heat transfer) and sustainability of EGS reservoirs through numerical simulations. A novel numerical simulation framework to be built through this project will allow for designing, managing, and optimizing energy production from EGS. The THM processes in EGS can be described by Biot’s thermo-poroelasticity model, a coupled system of nonlinear partial differential equations. Any desirable numerical methods for THM systems should preserve the underlying physical laws, such as mass and energy conservation, and present no numerical instabilities for a wide range of physical and simulation parameters. This project seeks to develop a unified numerical modeling framework based on adaptive enriched Galerkin (EG) methods to provide robust and physics-preserving numerical methods whose numerical analysis is feasible. The proposed EG schemes are mass conservative and free of numerical instabilities commonly present in poroelasticity and coupled flow-transport problems. The mass conservation property, stability, and convergence behaviors of the proposed methods will be studied mathematically and confirmed numerically. Moreover, residual-based a posteriori error estimators will be derived and utilized for designing dynamic mesh adaptivity techniques. The developed EG algorithms will be implemented within finite element software packages to verify the theoretical results and validate the new numerical model's capabilities to capture the EGS dynamics. The performance of the new EG methods will be compared with that of state-of-the-art numerical methods.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.