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.本文件包含一段Matlab代码，用于生成径向水力压裂（radial hydraulic fracture）的闭合形式解（closed form solutions）。该压裂体系的行为由断裂韧性（fracture toughness）、牛顿流体（Newtonian fluid）的粘度以及卡特滤失模型（Carter's model）描述的滤失效应三者的协同相互作用共同决定。除径向几何构型外，代码还支持选择平面应变工况（plane strain case，即KGD断裂，KGD fracture）。此外，代码内置了用于生成顶点解（vertex solutions）的函数，此类顶点解为全局解（global solutions）的极限情形，具体包含四类顶点解：粘性-储集主导解、粘性-滤失主导解、韧性-储集主导解以及韧性-滤失主导解。如需获取计算结果，可在Matlab中运行`KGD_Rad_sol_main.m`文件，选取材料参数后执行代码即可。程序的输出参数包括裂缝半径、裂缝开度分布、压力分布（注：压力计算精度有限，详见相关论文）以及压裂效率。