Crack propagation in a geothermal energy reservoir

We consider the problem of the opening of pre-existing cracks with high pressure fluid in the case where changes in the fluid pressure are balanced predominantly by stresses due to the local crack asperity deformations. A model is proposed for this process using a particular choice of 'crack law' and 'flow law' which leads to a free boundary problem. A singular perturbation analysis reveals that, in the boundary layer, the motion of the free boundary is governed by a singular integro-differential equation