Applications of Variational Fracture: Enhanced Geothermal Systems

Louisiana State University, Baton Rouge LA

Investigators

Abstract

Bourdin DMS-0908267 This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). Enhanced geothermal systems represent a virtually untapped, clean, renewable, economically viable, and widely available source of energy. They rely on harvesting heat by circulating water through artificially stimulated fracture systems in deep hot dry rocks. This project provides a predictive understanding of the mechanisms commonly used to generate these systems: pressure- and temperature-driven fracture. The modeling and analysis are based on a variational fracture formulation, which has been developed over the last ten years or so and has strong mathematical and mechanical foundations. The investigator extends this formulation to dynamic fractures and improves its implementation on parallel supercomputers. He extends its scope by studying and implementing two approaches to the penalization of material interpenetration along crack lips. He develops variational models for the pressure- and temperature-driven fracture problems, approximates them using the idea of Gamma-convergence, implements the regularized models on parallel supercomputers, and conducts large scale realistic validation experiments that are compared with existing engineering literature. This project is a first step in a nascent multi-disciplinary initiative fostered through the Center for Computation and Technology at LSU, involving mathematicians, computational scientists, and engineers. It supports the participation of two undergraduates and one graduate student per year. As the Nation strives to reduce its carbon footprint, protect its economy from fluctuating oil prices, and increase its energy independence, Enhanced Geothermal Systems (EGS) represent a virtually untapped, clean, renewable, economically viable and widely available source of energy. They rely on harvesting heat by circulating water through artificially stimulated, highly connected fracture systems in deep hot dry rocks. A recent MIT-led interdisciplinary assessment panel commissioned by the Department of Energy estimates that even without major technical breakthroughs EGS could cover 20% of the estimated US electricity needs by 2050, in an economically viable way and with only marginal carbon emission and land use. A major technical issue identified in this report is the creation of sufficiently connected fracture systems. The investigator develops a predictive understanding of two mechanisms commonly used to generate these systems: pressure- and temperature-driven fracture, based on a mechanically faithful and mathematically sound variational formulation of fracture developed over the last decade. This model is extended to account for the specifics of EGS, then implemented on parallel supercomputers. Large scale numerical simulations are performed using the cyberinfrastructure provided by the TeraGrid, to allow EGS designers to devise stimulation patterns maximizing the efficiency and sustainability of new systems. This project is a first step in a nascent multi-disciplinary initiative fostered through the Center for Computation and Technology at LSU, involving mathematicians, computational scientists, and engineers. It supports each year the participation of two undergraduates and one graduate student.