Solution of axisymmetric hydraulic fracture problem for thinning fluids

Abstract

A problem of axisymmetric propagation of a penny-shaped crack driven by a thinning fluid is considered. 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, that serves the iterations in the opening to be properly organized 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 behaviour index of a thinning fluid. The results provide benchmarks for the accuracy control of 3D simulators. They are used for assigning an apparent viscosity when simulating the action of a thinning fluid by replacing it with an equivalent Newtonian fluid.