Applications of Variational Fracture: Enhanced Geothermal Systems

BourdinDMS-0908267该奖项由2009年《美国复苏和再投资法案》(公法第111-5条)资助。强化的地热系统代表着一种几乎未开发的、清洁的、可再生的、经济上可行的和广泛可用的能源。它们依靠在深水干燥岩石中通过人工模拟的裂隙系统循环水来收集热量。该项目提供了对通常用于生成这些系统的机制的预测性理解：压力和温度驱动的压裂。建模和分析是基于一种变分裂缝公式，该公式是在过去十年左右发展起来的，具有坚实的数学和力学基础。本文将该公式推广到动态断裂问题，并改进了其在并行超级计算机上的实现。他通过研究和实施两种惩罚沿裂纹嘴唇的材料互穿的方法来扩大它的范围。他建立了压力和温度驱动的断裂问题的变分模型，使用Gamma收敛的思想对其进行逼近，在并行超级计算机上实现了正则化模型，并进行了大规模的实际验证实验，并与现有的工程文献进行了比较。这个项目是通过路易斯安那州立大学计算与技术中心推动的一项新的多学科倡议的第一步，涉及数学家、计算科学家和工程师。它每年支持两名本科生和一名研究生参加。随着国家努力减少碳足迹，保护经济不受油价波动的影响，并提高能源独立性，增强型地热系统(EGS)代表着一种几乎未开发、清洁、可再生、经济可行和广泛可用的能源。它们依赖于通过人工模拟的、高度相连的裂隙系统在深热干燥的岩石中通过循环水收集热量。美国能源部最近委托麻省理工学院领导的一个跨学科评估小组估计，即使没有重大的技术突破，到2050年，EGS也可以以经济可行的方式覆盖美国估计电力需求的20%，并且只有边际碳排放和土地利用。本报告确定的一个主要技术问题是建立充分连通的裂缝系统。研究人员根据过去十年发展出的力学上可靠的和数学上合理的裂缝变分公式，对通常用于产生这些系统的两种机制：压力驱动和温度驱动的裂缝进行了预测性的理解。该模型被扩展以解释EGS的特殊性，然后在并行超级计算机上实现。使用TeraGrid提供的网络基础设施进行大规模的数值模拟，使EGS设计者能够设计最大限度地提高新系统的效率和可持续性的估计模式。这个项目是通过路易斯安那州立大学计算与技术中心推动的一项新的多学科倡议的第一步，涉及数学家、计算科学家和工程师。它每年支持两名本科生和一名研究生参加。

BourdinDMS-0908267 This award is funded under the American Recovery andReinvestment Act of 2009 (Public Law 111-5). Enhanced geothermal systems represent a virtually untapped,clean, renewable, economically viable, and widely availablesource of energy. They rely on harvesting heat by circulatingwater through artificially stimulated fracture systems in deephot dry rocks. This project provides a predictive understandingof the mechanisms commonly used to generate these systems:pressure- and temperature-driven fracture. The modeling andanalysis are based on a variational fracture formulation, whichhas been developed over the last ten years or so and has strongmathematical and mechanical foundations. The investigatorextends this formulation to dynamic fractures and improves itsimplementation on parallel supercomputers. He extends its scopeby studying and implementing two approaches to the penalizationof material interpenetration along crack lips. He developsvariational models for the pressure- and temperature-drivenfracture problems, approximates them using the idea ofGamma-convergence, implements the regularized models on parallelsupercomputers, and conducts large scale realistic validationexperiments that are compared with existing engineeringliterature. This project is a first step in a nascentmulti-disciplinary initiative fostered through the Center forComputation and Technology at LSU, involving mathematicians,computational scientists, and engineers. It supports theparticipation of two undergraduates and one graduate student peryear. As the Nation strives to reduce its carbon footprint,protect its economy from fluctuating oil prices, and increase itsenergy independence, Enhanced Geothermal Systems (EGS) representa virtually untapped, clean, renewable, economically viable andwidely available source of energy. They rely on harvesting heatby circulating water through artificially stimulated, highlyconnected fracture systems in deep hot dry rocks. A recentMIT-led interdisciplinary assessment panel commissioned by theDepartment of Energy estimates that even without major technicalbreakthroughs EGS could cover 20% of the estimated US electricityneeds by 2050, in an economically viable way and with onlymarginal carbon emission and land use. A major technical issueidentified in this report is the creation of sufficientlyconnected fracture systems. The investigator develops apredictive understanding of two mechanisms commonly used togenerate these systems: pressure- and temperature-drivenfracture, based on a mechanically faithful and mathematicallysound variational formulation of fracture developed over the lastdecade. This model is extended to account for the specifics ofEGS, then implemented on parallel supercomputers. Large scalenumerical simulations are performed using the cyberinfrastructureprovided by the TeraGrid, to allow EGS designers to devisestimulation patterns maximizing the efficiency and sustainabilityof new systems. This project is a first step in a nascentmulti-disciplinary initiative fostered through the Center forComputation and Technology at LSU, involving mathematicians,computational scientists, and engineers. It supports each yearthe participation of two undergraduates and one graduate student.