The goal of this study is to compare two Perkins-Kern-Nordgren (PKN) hydraulic fracture models with non-local elasticity: the enhanced PKN (EPKN) model and the 2D Displacement Discontinuity Method (2D DDM). The elasticity equation in the EPKN model is obtained by substituting the elliptic vertical width profile into the elasticity integral for a planar crack. The 2D DDM elasticity equation is based on the plane strain solution and has a correction factor that is added to account for the finite height of the PKN fracture. Both approaches are implemented using a fixed mesh algorithm, where the tip asymptotic solution is used to advance the moving fracture front. To verify the accuracy of the algorithm, its plane strain version is tested against the reference solutions for the plane strain hydraulic fracture for different regimes of propagation. To evaluate the two non-local elasticity models, their predictions are compared to the reference numerical solution, obtained using a fully planar algorithm, for PKN fracture geometry. It is shown that the EPKN method has a better agreement with the reference solution, while the 2D DDM approach causes an approximately 20% error in the fracture length estimation for the considered cases.
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