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

地热能是最有前途的可再生能源之一，已被证明是可靠、清洁和安全的。在设计增强型地热系统（EGS）时，有必要了解影响增强型地热系统动态和产能的多尺度、多物理场、热-液压-机械（THM）过程。本项目旨在通过数值模拟，对控制EGS动力学的关键机制（固体位移、流体流动和传热）和EGS储层的可持续性有一个基本的认识。通过该项目建立的新型数值模拟框架将允许设计、管理和优化EGS的能源生产。EGS中的THM过程可以用Biot的热孔弹性模型来描述，这是一个非线性偏微分方程的耦合系统。任何理想的THM系统数值方法都应该保持基本的物理定律，例如质量和能量守恒，并且对于大范围的物理和模拟参数没有数值不稳定性。本项目旨在开发一个基于自适应富伽辽金（EG）方法的统一数值建模框架，以提供鲁棒性和物理保护的数值方法，其数值分析是可行的。所提出的EG格式具有质量保守性，并且不存在孔隙弹性和耦合流动输运问题中常见的数值不稳定性。本文将对所提方法的质量守恒性、稳定性和收敛性进行数学研究和数值验证。此外，还将推导基于残差的后验误差估计量，并将其用于设计动态网格自适应技术。开发的EGS算法将在有限元软件包中实现，以验证理论结果，并验证新的数值模型捕捉EGS动力学的能力。新的EG方法的性能将与最先进的数值方法进行比较。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.