Assessing the Fundamental Significance of the PKN Two-Dimensional Model in Hydraulic Fracture Modeling

In the field of petroleum engineering, substantial effort has been invested over decades in developing hydraulic fracture models with different levels of accuracy. This paper examines the critical role of the PKN (Perkins-Kern-Nordgren) two-dimensional model in the evolution of hydraulic fracture modeling. First, the analysis of its assumptions showed that the PKN model serves as a base for developing more complex pseudo-three-dimensional (P3D) models. The governing equations of the PKN model were then reformulated, leading to the analytical solutions for the two limiting cases of storage-dominated and leakoff-dominated regimes. A series of simulations were performed for the above analytical solutions for two cases of PKN in storage-dominated and leakoff-dominated regimes at both an early time and a late time. It was indicated that the storage-dominated regime happened at an early time of the hydraulic fracture propagation, and the leakoff-dominated regime happened at a late time of the process. The results also showed the effectiveness of using PKN analytical solutions to validate more complex P3D models.