Numerical Simulation of Reservoir Stimulation - a Variational Approach

We present recent results on the modeling and numerical simulation of reservoir stimulation in Hot Dry Rocks. Our approach is based on a mechanistically faithful yet mathematically sound model, generalizing Griffith's idea of competition between bulk and surface energies. At each time increment, the fracture and displacement configuration of a reservoir is sought as the minimizer of a global energy. In doing so, the variational approach allows full crack path identification, interaction between multiple cracks, crack initiation and branching in two and three space dimensions. The numerical approach is based on building a regularized energy where cracks are represented by a smooth function, similar in spirit to a phase-field approach. In this paper, we focus on thermal stimulation.