An enriched–FEM technique for numerical simulation of interacting discontinuities in naturally fractured porous media

Khoei, A.R.; Vahab, M.; Hirmand, M. Reza

doi:10.1016/j.cma.2017.11.016

Cited by 99 publications

(25 citation statements)

References 62 publications

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“…30 The X-FEM was applied in fracture growth simulation of deformable porous media; including: the fluid flow in fractured saturated and semi-saturated porous media by Réthoré et al 31,32 and Callari et al, 33 the cohesive crack propagation in multiphase porous media by Mohammadnejad and Khoei, 34 the crack growth simulation in saturated porous media by Khoei et al, 35 the hydraulic fracturing in deformable porous media by Mohammadnejad and Khoei, 36 the hydraulic cohesive fracture propagation in impermeable media with frictional natural faults by Khoei et al, 37 and the fracture growth simulation of interacting discontinuities in naturally fractured porous media by Khoei et al. [38][39][40] Basically, there are a few research works reported in literature for thermo-hydro-mechanical (THM) modeling of fractured porous media in which the fractures are taken explicitly into account. Khoei et al 41 applied the X-FEM in THM modeling of saturated porous media with impermeable discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

Khoei

Amini

Mortazavi

2021

Numerical Meth Engineering

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In this article, a computational model is presented for the analysis of coupled thermo-hydro-mechanical process with phase change (evaporation/condensation) in fractured porous media in order to model multiphase fluid flows, heat transfer, and discontinuous deformation by employing the extended finite element method. The ideal gas law and Dalton's law are employed to consider vapor and dry air as miscible gases. To take into account the phase change, latent heat and specific vapor enthalpy are incorporated into the physical model. The set of governing equations consists of linear momentum for the solid-phase, energy balance equation and mass conservation equations of water species (liquid and vapor) and dry air, which are derived within the framework of the generalized Biot's theory. The weak forms are presented in terms of the displacement, water pressure, capillary pressure, and temperature as the primary variables. The spatial and temporal discretizations are carried out applying the extended finite element method and the generalized Newmark scheme, respectively, resulting in the final system of fully coupled nonlinear equations. Finally, several numerical examples are solved to demonstrate not only the robustness of the proposed computational model but also the effect of the crack orientation, intrinsic permeability, and elastic modulus on the fluid flow patterns, relative humidity, and temperature distribution. Moreover, an edge-crack propagation is investigated under mode I fracture due to drying conditions.

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Section: Introductionmentioning

confidence: 99%

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

Khoei

Amini

Mortazavi

2021

Numerical Meth Engineering

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“…In these models, interfaces exhibit rigid‐cohesive behavior, ie, no displacement jump occurs until a certain traction criterion is reached. This affords the opportunity of adaptively inserting interface elements (or enrichment degrees of freedom in an extended FEM setting) during the simulation course whenever and wherever they are needed –. Alternatively, cohesive elements are placed everywhere in the mesh at the start of the simulation, and a zero opening constraint is imposed as in the work of Radovitzky et al Rigid‐cohesive models are also called extrinsic because, unlike with initially elastic or intrinsic models, the transition from the undamaged to the damaged state happens upon the satisfaction of an external criterion, namely that some effective interface traction reaches a critical value.…”

Section: Introductionmentioning

confidence: 99%

A continuation method for rigid‐cohesive fracture in a discontinuous Galerkin finite element setting

Hirmand

Papoulia

2018

Numerical Meth Engineering

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An energy minimization formulation of initially rigid cohesive fracture is introduced within a discontinuous Galerkin finite element setting with Nitsche flux.The finite element discretization is directly applied to an energy functional, whose term representing the energy stored in the interfaces is nondifferentiable at the origin. Unlike finite element implementations of extrinsic cohesive models that do not operate directly on the energy potential, activation of interfaces happens automatically when a certain level of stress encoded in the interface potential is reached. Thus, numerical issues associated with an external activation criterion observed in the previous literature are effectively avoided. Use of the Nitsche flux avoids the introduction of Lagrange multipliers as additional unknowns. Implicit time stepping is performed using the Newmark scheme, for which a dynamic potential is developed to properly incorporate momentum. A continuation strategy is employed for the treatment of nondifferentiability and the resulting sequence of smooth nonconvex problems is solved using the trust region minimization algorithm. Robustness of the proposed method and its capabilities in modeling quasistatic and dynamic problems are shown through several numerical examples. KEYWORDScohesive fracture, continuation method, discontinuous Galerkin method, initially rigid, nondifferentiable energy minimization, trust region method Int J Numer Methods Eng. 2018;115:627-650.wileyonlinelibrary.com/journal/nme

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“…This technique was then presented in the framework of an X-FEM by Belytschko and Black 18 and Moës et al 19 The X-FEM was exploited in various crack propagation problems, including the cohesive crack propagation by Moës and Belytschko, 20 fatigue crack initiation and propagation by Stolarska and Chopp, 21 three-dimensional crack growth by Areias and Belytschko, 22 and dynamic cohesive crack propagation by Remmers et al 23 A review on the X-FEM and its application was presented by Khoei. 24 The X-FEM was applied in modeling of fluid flow in saturated and semisaturated porous media by researchers; the shear band in saturated porous media by Réthoré et al, 25 the fluid flow in fractured saturated/unsaturated porous media by Réthoré et al, 26,27 the partially saturated porous domain with strong discontinuity by Callari et al, 28 the saturated porous media with weak discontinuity by Khoei and Haghighat, 29 the HM modeling of cohesive crack propagation in multiphase porous media by Mohammadnejad and Khoei,30 and the crack growth simulation in saturated porous media Khoei et al 31 The X-FEM was also implemented in simulation of HF in porous media; Mohammadnejad and Khoei 32 presented that the impermeability of the fracture faces, which is often assumed in analytical solutions, results in underestimating the crack mouth pressure (CMP), Khoei et al 33 modeled hydraulically driven cohesive fracture propagation in impermeable media with frictional natural faults, Khoei et al 34 performed HF modeling in fractured porous media using the X-FEM and an equivalent continuum model, and Khoei et al 35,36 presented X-FEM modeling of interacting discontinuities in naturally fractured porous media.…”

Section: Introductionmentioning

confidence: 99%

Thermo‐hydro‐mechanical modeling of fracturing porous media with two‐phase fluid flow using X‐FEM technique

Khoei

Mortazavi

2020

Num Anal Meth Geomechanics

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In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.

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An enriched–FEM technique for numerical simulation of interacting discontinuities in naturally fractured porous media

Cited by 99 publications

References 62 publications

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

A continuation method for rigid‐cohesive fracture in a discontinuous Galerkin finite element setting

Thermo‐hydro‐mechanical modeling of fracturing porous media with two‐phase fluid flow using X‐FEM technique

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