Mohammad Vahab

This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software package COMSOL Multiphysics for multi-field thermo-hydro-mechanical problems in discontinuous porous media. To this end, an exclusive enrichment strategy is proposed in compliance with the COMSOL modeling structure. COMSOL modules and physics interfaces are adopted to take account of the relevant physical processes involved in thermo-hydro-mechanical coupling analysis, namely: the mechanical deformation, fluid flow in porous media and heat transfer. Essential changes are made to the internal variables of the physics interfaces to ensure consistency in the evaluation of enriched solution fields. The model preprocessing, level-set updates, coupling of the relevant physics and postprocessing procedures are performed adopting a coherent utilization of the COMSOL built-in features along with the COMSOL LiveLink for MATLAB functions. The implementation process, remedies for the treatment of the enriched zones, XFEM framework setup, multiphysics coupling, numerical integration and numerical solution strategy are described in detail. The capabilities and performance of the proposed approach are investigated by examining several multi-field thermo-hydro-mechanical simulations involving single/multiple discontinuities in 2D/3D porous rock settings.

Traditional Hydraulic Fracturing (THF) treatments suffer difficulties such as high injection pressure, poor controllability and local stress concentration. In many cases, THF leads to the activation of relatively small number of perforations with limited contribution to the enhancement of the overall permeability of the reservoir. Alternatively, pulse water pressure may be exerted inside the borehole as a remedy to produce multiple macroscopic main cracks along the borehole axial and radial directions. To reach a better understanding of this technique so as to improve its efficiency in practice, the role of the contributing elements namely the fracturing fluid mean pressure, its amplitude, and frequency needs to be investigated in conjunction with the properties of the bulk. In this paper, an extended finite element framework is developed to study Pulse Hydraulic Fracturing (PHF) within a tight-low permeability reservoir. To this end, the momentum balance equation of the medium is solved in conjunction with the flow continuity equations of the fracturing fluid using the staggered Newton algorithm. In the context of X-FEM, the displacement field is enhanced by using the Heaviside enrichment function to account for the discontinuities due to crack body. The hydro-fracture inflow is modeled for both the laminar and/or turbulent flow regimes. The nonlinearities within the hydro-fracture tip are taken into account by using the potential based cohesive zone model, where the crack growth direction and increment are determined by taking advantages from the energy based cohesive stress functions. Using the developed computational framework, the performance of PHF treatments are in

In this paper, a computational algorithm based on the eXtended Finite Element Method (X-FEM) is developed to study the fluid-lag zone involved in hydraulic fracturing treatments. The fluid-lag zone, caused due to the high pressure gradient in the vicinity of the hydrofracture tip, is primarily treated by the imposition of the vapor pressure. The capillary action at the flow front is captured by inclusion of the surface tension effects. The overlap of the hydrofracture faces, particularly within the fluid-lag region, is prevented using an X-FEM penalty algorithm. The governing equations of the hydrofracture inflow and the surrounding domain are solved in a sequential order called the staggered Newton strategy. Finally, the performance and the accuracy of the proposed numerical approach are explored by means of numerical simulation.