A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

Samimi, Soodeh; Pak, Ali

doi:10.1016/j.enganabound.2013.10.011

Cited by 19 publications

(13 citation statements)

References 37 publications

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“…The applications of PFM to hydraulic fracturing can be found in, 12–15 though approximation of crack width for calculating permeability of the fractured domain within the diffuse fracture is far from trivial. Other continuous‐based approaches for simulating fluid‐driven fractures can be found in 16,17 using boundary element method and element‐free method, among many others. Discontinuity can be treated naturally in a discrete manner, and thus discrete‐based method, such as the discrete element method (DEM), 18 discontinuous deformation analysis (DDA) 19 and finite‐discrete element method (FDEM), 20 have been successfully applied for studying complex hydraulic fractures.…”

Section: Introductionmentioning

confidence: 99%

Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Sun

Fish

2021

Num Anal Meth Geomechanics

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In the present manuscript fracture propagation in a saturated porous medium is modeled based on the classical Biot theory, where solid skeleton and fluid flow are represented by separate two layers. The non‐ordinary state‐based peridynamics (NOSBPD) layer is employed to capture deformation including fracturing of the solid skeleton, while the fluid flow is controlled by the finite element method (FEM) layer. The interaction between the layers is realized by considering the effects of pore pressure from the FEM layer on the NOSBPD layer and, vice versa, the effect of the volumetric strain, porosity, and permeability variations from the NOSBPD layer on the FEM layer. The coupling terms retain their parent characteristics, that is, the interaction term in the momentum balance equation is approximated by the local FEM formulation whereas the interaction term in the mass balance equation is approximated by the nonlocal NOSBPD formulation. By doing so, the model retains the flexibility of coupling two independent discretizations. The coupled system is solved by a fully implicit solution scheme. The accuracy of the proposed method has been verified against available closed‐form solutions and published numerical approaches for the pressure‐ and fluid‐driven facture propagation problems.

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Section: Introductionmentioning

confidence: 99%

Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Sun

Fish

2021

Num Anal Meth Geomechanics

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“… ψ = d( χs )/d s is the incremental effective stress parameter, with χ being the effective stress parameter, and s = p a − p w is the matric suction, which will be simply referred to as suction in this article hereon. The distinction between the total and incremental forms of the effective stress relationship is often overlooked in the literature, although it is essential to obtain the correct form of the deformation model . A constitutive equation in an incremental form and the strain‐displacement relationship for small strains of the solid skeleton are also employed to complement the equilibrium equation, as stated in Equations and , respectively.…”

Section: Governing Equationsmentioning

confidence: 99%

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

Ghaffaripour

Esgandani

Khoshghalb

et al. 2019

Num Anal Meth Geomechanics

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Summary This paper presents the first application of an advanced meshfree method, ie, the edge‐based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro‐mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three‐point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton‐Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state‐of‐the‐art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.

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“…). The wetting-phase pressure-saturation profiles along the x-axis after 180 and 360 days, are plotted in Figure 5, where the results of two other The pressure (left) and saturation(right) profiles along the x-axis at 180 and 360 days , results of proposed model compared to Grüninger (2012) and Samimi and Pak (2014) 296 HFF 26,1 models, namely DUNE-PDELAB a software with interior DG method without H(div) projection (Grüninger, 2012), and a 3D fully implicit model using a different formulation (P w − P n ) (Samimi and Pak, 2014) are also super imposed. It should be noted that the later has used a different numerical scheme, namely element free Galerkin (EFG) method.…”

Section: Backley-leverett Problemmentioning

confidence: 99%

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

Jamei

Ghafouri

2016

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose – The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme. Design/methodology/approach – The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings – Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media. Research limitations/implications – The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible. Practical implications – The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers. Originality/value – The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

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A novel three-dimensional element free Galerkin (EFG) code for simulating two-phase fluid flow in porous materials

Cited by 19 publications

References 37 publications

Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media

Fully coupled elastoplastic hydro‐mechanical analysis of unsaturated porous media using a meshfree method

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

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