Remarks on application of different variables for the PKN model of hydrofracturing. Various fluid-flow regimes

TL;DR

This paper improves the PKN model for hydraulic fracturing by enhancing boundary conditions and introducing a new variable, leading to more accurate solutions across different fluid-flow regimes.

Contribution

It introduces an improved regularized boundary condition and a new physically meaningful dependent variable for the PKN model, enhancing numerical accuracy.

Findings

Enhanced solution accuracy for singular leak-off regimes.

Comprehensive analysis of numerical algorithms.

Comparison with existing numerical results confirms improvements.

Abstract

The problem of hydraulic fracture for the PKN model is considered within the framework presented recently by Linkov (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.