===September 30, 2010===

===September 30, 2010===

The topic of this talk is to present a first step towards the predictive understanding of the mechanisms used in the creation of the highly connected crack networks required for Enhanced Geothermal Systems and oil shale mining. I will focus on thermal stimulation, where thermal stresses induced by a cold fluid circulating through a hot reservoir lead to nucleation of many short cracks. I will consider the limiting cases of purely diffusive and purely advective heat transfer, corresponding to extreme porosity limits in the reservoir. I  will present a mechanistically faithful yet mathematically sound model, based on Francfort and Marigo's generalization of Griffith's idea of competition between bulk and surface energies. I will discuss the virtues of the model, its approximation, and its numerical implementation. Finally, I will present some numerical experiments in 2 and 3 dimensions.

The topic of this talk is to present a first step towards the predictive understanding of the mechanisms used in the creation of the highly connected crack networks required for Enhanced Geothermal Systems and oil shale mining. I will focus on thermal stimulation, where thermal stresses induced by a cold fluid circulating through a hot reservoir lead to nucleation of many short cracks. I will consider the limiting cases of purely diffusive and purely advective heat transfer, corresponding to extreme porosity limits in the reservoir. I  will present a mechanistically faithful yet mathematically sound model, based on Francfort and Marigo's generalization of Griffith's idea of competition between bulk and surface energies. I will discuss the virtues of the model, its approximation, and its numerical implementation. Finally, I will present some numerical experiments in 2 and 3 dimensions.