Bench-mark solution for a penny-shaped hydraulic fracture driven by a thinning fluid

Abstract

The paper presents a solution for axisymmetric propagation of a penny-shaped crack driven by a thinning fluid. The solution to the accuracy of four significant digits, at least, is obtained on the basis of the modified formulation of hydraulic fracture problem by employing the particle velocity, rather than conventionally used flux. This serves to properly organize iterations in the opening after reducing the problem to the self-similar form. Numerical results obtained show relatively small dependence of self-similar quantities (fracture radius, propagation speed, opening, particle velocity, pressure, flux) on the behavior index of a thinning fluid. The results provide bench marks for the accuracy control of truly 3D simulators and they serve for assigning an apparent viscosity when simulating the action of a thinning fluid by replacing it with an equivalent Newtonian fluid.