Remarks on application of different variables for the PKN model of hydrofracturing: various fluid-flow regimes

摘要

The problem of hydraulic fracture for the PKN model is considered within the framework presented recently by Linkov (Doklady Phys 56(8):436-438, 2011). The modified formulation is further enhanced by employing an improved regularized boundary condition near the crack tip. This increases solution accuracy especially for singular leak-off regimes. A new dependent variable having clear physical sense is introduced. A comprehensive analysis of numerical algorithms based on various dependent variables is provided. Comparison with know numerical results has been given.