Simulation of the hydraulic fracturing processes combining finite elements and lattice Boltzmann methods

Abstract

This research addresses hydraulic fracturing or hydro-fracking, i.e. fracture propagation process in rocks through the injection of a fluid under pressure, which generates cracks in the rock that propagate according to the amount of fluid injected. This technique leads to an increase of the permeability of the rock mass and consequently improve oil production. Several analytical and numerical models have been proposed to study this fracture mechanism, generally based in continuum mechanics or using interface elements through a known propagation path. In this work, the crack propagation is simulated using the PPR potential-based cohesive zone model [1,2] by means of an extrinsic implementation. Thus, interface cohesive elements are adaptively inserted in the mesh to capture the softening fracture process. The fluid pressure is simulated using the lattice Boltzmann model [3] through an iterative procedure. The boundaries of the crack, computed using the finite element method, are transferred to the lattice Bolztmann model as boundary conditions, where the force applied on these boundaries, caused by the fluid pressure, can be calculated. These forces are then transferred to the finite element model as external forces applied on the faces of the crack. The new position of the crack faces is then calculated and transferred to the lattice Boltzmann model to update the boundary conditions. This feedback-loop for fluid-structure interaction allows modeling of hydraulic fracturing processes. Examples will be provided to demonstrate the features of the proposed methodology.