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

合作研究：热多孔弹性的物理保持自适应有限元方法

基本信息

批准号：
2208426
负责人：
Son-Young Yi
金额：
$ 25.05万
依托单位：
University of Texas at El Paso
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208426&HistoricalAwards=false
关键词：
Collaborative Research Physics Preserving Adaptive

项目摘要

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.

地热能是最有前景的可再生能源之一，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力学和生产率的多尺度、多物理、热-水力-机械(THM)过程。该项目旨在通过数值模拟对EGS(固体驱替、流体流动和热传递)的动力学和EGS油藏的可持续性的关键控制机制有一个基本的了解。通过该项目将建立一个新的数值模拟框架，以设计、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，这是一个耦合的非线性偏微分方程组。对于THM系统，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，并且对于大范围的物理和模拟参数不存在数值不稳定性。本项目旨在开发一个基于自适应丰富伽辽金(EG)方法的统一数值模拟框架，以提供稳健和物理保持的数值方法，其数值分析是可行的。所提出的EG格式是质量守恒的，并且没有在孔隙弹性和流动-输运耦合问题中常见的数值不稳定性。对所提出方法的质量守恒性、稳定性和收敛行为将进行数学研究和数值验证。此外，还将导出基于残差的后验误差估计器，并将其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中实现，以验证理论结果和新的数值模型捕捉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。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。