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

Abstract

In this paper we analyse a problem of a hydraulic fracture driven by a non-Newtonian shearthinning 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, postprocessing 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.

On the influence of fluid rheology on hydraulic fracture

“…The KGD fracture geometry (Wrobel & Mishuris, 2015) is considered in a formulation that accounts for the hydraulically induced tangential tractions on the crack flanks (Wrobel et al, 2017(Wrobel et al, , 2018Papanastasiou & Durban, 2018). The paper is in a sense complementary to the previous report by Wrobel (2020a), where it was shown among other things that: i) the truncated power-law is a good alternative for the Carreau model, ii) the fluid flow inside the fracture evolves from the high shear rate Newtonian regime at initial times towards the intermediate shear rate regimes at later stages. As the PKN geometry does not reflect properly the near-tip region of a planar fracture, it is the present research that provides relevant information on the spatial distribution of flow regimes inside the crack, including the near-tip zone.…”

“…As the PKN geometry does not reflect properly the near-tip region of a planar fracture, it is the present research that provides relevant information on the spatial distribution of flow regimes inside the crack, including the near-tip zone. Moreover, in Wrobel (2020a) it was found that the range of shear rates over which the viscosity gradation takes place is equally important for the HF process as the magnitudes of cut-off viscosities themselves. Now, with the truncated power-law we will quantify precisely this influence.…”

A plane‐strain hydraulic fracture driven by a shear‐thinning Carreau fluid

“…12 In what follows, we extend the work of Moukhtari and Lecampion 13 who studied the asymptotic case of a steadily moving semi-infinite fracture. Very recently, as we finalize this work, the propagation of a plane-strain hydraulic fracture driven by a truncated power-law rheology (which is an approximation of the Carreau model 14 ) has been investigated numerically. 15 Our analysis using the complete Carreau rheology goes in more details regarding the different regimes of the solution.…”

A simplified modelling of hydraulic fractures in elasto-plastic materials

“…It comes from the fact that, although geometrically simplified, they reflect properly the inherent features of the underlying physical processes. For example, by analyzing the classical 1D models the crack propagation regimes have been identified and categorized (Detorunay, 2004;Garagash, 2009), the influence of the non-Newtonian fluid rheology has been recognized (Adachi & Detournay, 2002;Wrobel, 2020a;Wrobel et al, 2021) or power requirements for simultaneous propagation of multiple fractures have been established (Bunger, 2013). Moreover, these simplified HF models can be successfully used in construction and verification of advanced computational algorithms.…”

“…To this end we consider three variants of the HF problem: i) hydrofracturing in an elastic solid, ii) hydraulic fracture in elastic solid but with the plastic deformation effects localized in the near-tip zone only, iii) fully elasto-plastic model of hydraulic fracture. The solution to the first variant of the problem is obtained in the framework of LEFM with the numerical algorithm introduced by Wrobel & Mishuris (2015) and enhanced further to account for additional features of the HF phenomenon (Perkowska et al, 2016;Wrobel et al, 2017Wrobel et al, , 2018Wrobel, 2020a;Wrobel et al, 2021). As the algorithm proved to be efficient and versatile we modify it to account for the plasticity effects.…”