The impact of fluid yield stress on hydraulic fracture propagation

Abstract

Summary We investigate the influence of fluid yield stress on propagation of a radial hydraulic fracture in a permeable reservoir. The hydraulic fracturing fluid rheology is governed by Herschel-Bulkley model including yield stress and non-linearity of the shear stress. The rock is linear elastic, and the fracture is formed due to fluid injection at a constant volumetric rate. The crack propagation criterion follows the theory of linear elastic fracture mechanics, and Carter’s leak-off law describes the fluid leak-off into formation. We developed two numerical approaches to compute the problem solution: fully numerical (Gauss-Chebyshev quadrature and Barycentric Lagrange interpolation techniques) and approximate (the global fluid balance equation combined with fracture tip asymptote). The presented simulations representing typical field cases demonstrate that the yield stress can lead to a fracture with a shorter radius and larger aperture compared to the radial fracture model with simpler power-law fluid. We derived limiting propagation regimes characterised by dominance of certain physical phenomena and built parametric maps showing their applicability domains. Such analysis enables one to identify whether the yield stress provides a substantial impact for any given problem parameters.