Data from: An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off

This paper develops a closed-form approximate solution for a penny-shaped
hydraulic fracture whose behaviour is determined by an interplay of three
competing physical processes that are associated with fluid viscosity,
fracture toughness and fluid leak-off. The primary assumption that permits
one to construct the solution is that the fracture behaviour is mainly
determined by the three-process multiscale tip asymptotics and the global
fluid volume balance. First, the developed approximation is compared with
the existing solutions for all limiting regimes of propagation. Then, a
solution map, which indicates applicability regions of the limiting
solutions, is constructed. It is also shown that the constructed
approximation accurately captures the scaling that is associated with the
transition from any one limiting solution to another. The developed
approximation is tested against a reference numerical solution, showing
that accuracy of the fracture width and radius predictions lie within a
fraction of a per cent for a wide range of parameters. As a result, the
constructed approximation provides a rapid solution for a penny-shaped
hydraulic fracture, which can be used for quick fracture design
calculations or as a reference solution to evaluate accuracy of various
hydraulic fracture simulators.