Particle velocity based hydrofracturing algorithm for a penny-shaped crack

TL;DR

This paper extends a particle velocity based hydraulic fracture simulation algorithm to penny-shaped cracks, capable of handling different regimes and providing accurate solutions with semi-analytical approximations.

Contribution

It introduces a novel extension of the particle velocity algorithm to penny-shaped cracks, enhancing simulation accuracy and applicability for various fracture regimes.

Findings

High-accuracy numerical solutions for penny-shaped cracks

Effective semi-analytical approximations for zero leak-off case

Successful validation against existing literature

Abstract

A universal particle velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of dealing with both the viscosity and toughness dominated regimes, with the fracture being driven by a power-law fluid. The computational approach utilizes two dependent variables; the fracture aperture and the reduced particle velocity. The latter allows for the application of a local condition of the Stefan type (the speed equation) to trace the fracture front. The obtained numerical solutions are carefully tested using various methods, and are shown to achieve a high level of accuracy. Simple, accurate, semi-analytical approximations of the solution are provided for the zero leak-off case. A comparison with other results available in the literature is undertaken.