On relative input of viscous shear into the elasticity equation at near-front, near-inlet and the major part of a hydraulic fracture

TL;DR

This paper estimates the influence of viscous shear traction on the elasticity equation in hydraulic fractures and finds it negligible in most regions, simplifying modeling assumptions.

Contribution

It provides a comprehensive estimation showing viscous shear effects are negligible across most of the fracture surface, reducing the need for their inclusion in models.

Findings

Viscous shear input is less than 10^-4 of the conventional term.

Negligible viscous shear effect except near the source and fluid front.

Applicable to both Newtonian and non-Newtonian fluids.

Abstract

The input of the hydraulically induced shear traction into the elasticity equation is estimated for the entire fracture surface. It is established that, except for negligibly small vicinities of a pointed source and of the fluid front, the relative input of the viscous shear does not exceed 10 - 4 of the input of the conventionally accounted term. The estimation is true for Newtonian, as well as non-Newtonian thinning fluids. This implies that there is no need to account for viscous shear not only in the form of conventional near-front asymptotics and fracture conditions, but also in factors entering them.