On the application of simplified rheological models of fluid in the hydraulic fracture problems

TL;DR

This study compares simplified rheological models of non-Newtonian fluids in hydraulic fracture simulations, finding that power-law and truncated power-law models can effectively substitute the more complex Carreau model under certain conditions.

Contribution

It demonstrates that simplified rheological models like power-law and truncated power-law can reliably approximate complex Carreau fluid behavior in hydraulic fracture analysis.

Findings

Power-law rheology can substitute Carreau under specific conditions.

Truncated power-law model closely matches Carreau results.

Post-processing with shear rate averages verifies model credibility.

Abstract

In this paper we analyse a problem of a hydraulic fracture driven by a non-Newtonian shear-thinning fluid. For the PKN fracture geometry we consider three different rheological models of fluid: i) the Carreau fluid, ii) the truncated power-law fluid, iii) the power-law fluid. For each of these models a number of simulations are performed. The results are post-processed and compared with each other in order to find decisive factors for similarities/dissimilarities. It is shown that under certain conditions even the basic power-law rheology can be a good substitute for the Carreau characteristics. Although for a particular fluid such a conclusion cannot be made a priori, post-processing based on average values of the fluid shear rates is a very good tool to verify credibility of the results obtained for simplified rheological models. The truncated power-law rheology is a good alternative for the Carreau model. It always produces results that are very similar to those obtained with the equivalent Carreau fluid and simultaneously provides a relative ease of numerical implementation.