The crack tip solution for hydraulic fracturing in a permeable solid
We present self-similar analytical solutions for a hydraulically driven fracture propagating in a solid which is in a state of plane strain. In particular, we examine the effect of fluid loss on the formation modelled by the Carter leak-off mechanism. Our main new results are asymptotic solutions for arbitrary rock permeability; it is shown how these may be represented by an expansion whose leading term is the near-tip solution in the high permeability limit. Our conclusion for applications is that the solution in the practical case of intermediate permeability may be constructed as a series which starts from the loss dominated limit. We also provide a detailed comparison of our predictions with results from a numerical model which includes a fluid lag zone.
scientific article; zbMATH DE number 1025642
scientific article