Universal hydrofracturing algorithm for shear-thinning fluids: particle velocity based simulation

TL;DR

This paper extends a particle velocity based hydraulic fracture simulation algorithm to shear-thinning fluids, offering a flexible, accurate, and universal computational scheme validated against analytical benchmarks.

Contribution

It introduces a universal particle velocity based algorithm for shear-thinning fluids, not limited by elasticity operators or crack regimes, enhancing simulation flexibility.

Findings

Validated accuracy against analytical solutions

Applicable to various elasticity operators and crack regimes

Flexible and modular numerical scheme

Abstract

A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.