THE CRACK-TIP SOLUTION FOR HYDRAULIC FRACTURING IN A PERMEABLE SOLID

This paper extends previous work on self-similar analytical solutions fora hydraulically driven fracture propagating in a solid which is in a state of plane strain. In particular, we examine the effect of fluid loss to the formation modelled by the Carter leak-off mechanism. Our main new results are asymptotic solutions for arbitrary rock permeabil ity; it is shown how these may be represented by an expansion whose le ading term is the near-tip solution in the high permeability limit. Th is term gives an integrable singularity in the near-tip fluid pressure which is slightly stronger than the singularity which arises in the i mpermeable case; it follows that there is always a region immediately adjacent to the fluid front where the solution is dominated by fluid l oss. Our most important conclusion for applications is that the soluti on in the practical case of intermediate permeability may be construct ed as a series which starts from the loss dominated limit. We also pro vide a detailed comparison of our predictions with results from a nume rical model which includes a fluid lag zone. The results are found to be in good agreement in all of the various permeability regimes.