The XFEM with an Explicit-Implicit Crack Description for Hydraulic Fracture Problems

Abstract

The Extended Finite Element Method (XFEM) approach is applied to the coupled problem of fluid flow, solid deformation, and fracture propagation. The XFEM model description of hydraulic fracture propagation is part of a joint project in which the developed numerical model will be verified against large-scale laboratory experiments. XFEM forms an important basis towards future combination with heat and mass transport simulators and extension to more complex fracture systems. The crack is described implicitly using three level-sets to evaluate enrichment functions. Additionally, an explicit crack representation is used to update the crack during propagation. The level-set functions are computed exactly from the explicit representation. This explicit/implicit representation is applied to a fluid-filled crack in an impermeable, elastic solid and compared to the early-time solution of a plane-strain hydraulic fracture problem with a fluid lag.

A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation

“…The coupling between fracture flow and mechanical model was achieved weakly through a successive procedure where the results of fracture flow were used to update the solution from the mechanical model and vice versa. Furthermore, the leak-off flow from the fracture to the porous media was ignored similar to the contributions of Lecampion [31], Weber et al [45] and Gordeliy and Peirce [22]. Furthermore, these models were developed for single-phase fracture flow.…”

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

“…This parameter is present in the leading terms of the power series representations for both the crack opening and the net fluid pressure, and thus in order to recreate the solution one needs to know its value. Moreover, the dimensionless crack half-length is employed in scaling when transforming the governing ODE from the formulation given in [17] to the formula (67). In fact, the scaling criterion relates this value to the crack propagation speedv(1).…”

“…In the recent paper by Lecampion et al [38] it was shown that the algorithms which utilize the appropriate multiscale hydraulic fracture tip asymptote perform much better than those that do not apply it. The advantages of employing enhanced asymptotic representation in the numerical algorithm have been demonstrated in [17,27,30] (special tip element), [2,8,21,22,23,37,67] (BEM and XFEM formulations).…”

An algorithm for the simulation of curvilinear plane‐strain and axisymmetric hydraulic fractures with lag using the universal meshes

“…Eschewing the need for a conforming mesh is the extended (or generalized) FEM (XFEM), which handles strong discontinuities such as cracks by enriching the standard FEM space with discontinuous shape functions. Because the mesh no longer conforms to the crack geometry, when applying XFEM to hydraulic fracture problems, special elements and treatment of elements intersected by the fracture are needed . Then, fluid flow in the crack may be accounted for using a separate surface mesh and appropriate coupling, or in cases such as poroelasticity, the fluid uses the same underlying discretization as the displacements but is enriched with shape functions to account for the discontinuity in the normal pressure gradients across the crack surface …”

“…Because the mesh no longer conforms to the crack geometry, when applying XFEM to hydraulic fracture problems, special elements and treatment of elements intersected by the fracture are needed. [27][28][29][30][31][32] Then, fluid flow in the crack may be accounted for using a separate surface mesh and appropriate coupling, or in cases such as poroelasticity, the fluid uses the same underlying discretization as the displacements but is enriched with shape functions to account for the discontinuity in the normal pressure gradients across the crack surface. 33,34 In contrast to FEM and XFEM, strategies, which utilize the boundary element method (BEM), require only the crack to be meshed.…”