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EGS动态和生产力的多尺度，多物理场，热-水力-机械（THM）过程。该项目旨在通过数值模拟对控制EGS（固体驱替，流体流动和传热）动态和EGS油藏可持续性的关键机制进行基本了解。通过该项目建立的一个新的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过程可以用毕奥的热-孔隙弹性模型来描述，这是一个耦合的非线性偏微分方程组。THM系统的任何理想的数值方法都应该保持基本的物理定律，如质量和能量守恒，并且在广泛的物理和模拟参数范围内不会出现数值不稳定性。该项目旨在开发一个统一的数值建模框架的基础上，自适应丰富的Galerkin（EG）方法，提供强大的和物理保持的数值方法，其数值分析是可行的。建议的EG格式是质量守恒的，并且没有通常存在于多孔弹性和耦合流动输运问题中的数值不稳定性。所提出的方法的质量守恒性质，稳定性和收敛行为将进行数学研究和数值证实。此外，残差为基础的后验误差估计将推导和用于设计动态网格自适应技术。所开发的EG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获EGS动态的能力。新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NSF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.