Correspondence principle for simulation hydraulic fractures by using pseudo 3D model
The original pseudo three-dimensional (P3D) model is extended to an arbitrary stress contrast on the basis of the correspondence principle suggested. The principle employs the similarity between solutions to plain-strain elasticity problems for (i) the crack, corresponding to the central cross-sections of the P3D model, and (ii) the crack of the Khristianovich-Geertsma-de Klerk (KGD) model, when the sizes and average openings of the cracks are the same. This suggests using the propagation speeds of the KGD problem for assigning the speed of the height growth of the P3D model. This approach is applicable in all the cases when the KGD problem may be accurately solved; specifically, when accounting for an arbitrary stress contrast.