Matlab code to produce closed form solutions for radial and KGD hydraulic fractures

This file contains a Matlab code that is used to produce closed form solutions for a radial hydraulic fracture, whose behavior is determined by a simultaneous interplay of fracture toughness, fluid viscosity (Newtonian fluid), and leak-off (Carter's model). In addition to the radial geometry, there is an option to select a plane strain case (i.e. KGD fracture). The code also contains functions that produce the so-called vertex solutions, which are the limiting cases of the global solutions. In particular, there are four vertex solutions: viscosity-storage, viscosity-leak-off, toughness-storage, and toughness-leak-off. To get the results, launch "KGD_Rad_sol_main.m" in Matlab, select material parameters, and run the code. The output parameters are the fracture radius, aperture variation, pressure variation (note the pressure is less accurate, see paper), and efficiency.