A unified finite element method for the simulation of hydraulic fracturing with and without fluid lag

Hydraulic fracturing with and without fluid lag has different flow boundary conditions at the fluid front, which always results in different simulation methods. In this paper, we extend a finite element method (Bao et al., 2015) to simulate hydraulic fracturing with and without fluid lag in a unified manner. A unified numerical boundary condition is imposed on the fluid front independent of fluid lag situations. No effort is needed to track the fluid front explicitly, and the burden of model re-meshing induced by fluid front advancement is avoided. The method is verified by comparing numerical simulations with some analytical solutions. The simulations cover hydraulic fracturing with constant fluid lag fraction, without fluid lag, and with vanishing fluid lag. Some factors governing the simulations are discussed.