An efficient numerical model for incompressible two-phase flow in fractured media

Hoteit, Hussein; Firoozabadi, Abbas

doi:10.1016/j.advwatres.2008.02.004

Cited by 272 publications

(162 citation statements)

References 42 publications

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“…In order to represent the fractures explicitly in fractured porous media, we use the discrete-fracture model (DFM) [16,27]. In the DFM, fracture gridcells are simplified as matrix gridcell interfaces and fractures are surrounded by matrix blocks.…”

Section: Discrete Fracture Modelmentioning

confidence: 99%

“…The dual-continua models, such as dual-porosity/dual-permeability model [13,17,19,22,24] treat matrix and fractures as two separated domains, that are theoretically in-terconnected by fluid mass transfer across their interfaces. In the discrete-fracture-model (DFM) [13,16,20,21,27], fractures dimension is taken n-1 when the matrix dimension is n.…”

Section: Introductionmentioning

confidence: 99%

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A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

El-Amin

Kou

Sun

2017

Day 3 Wed, April 26, 2017

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Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy's law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.

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Section: Discrete Fracture Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

El-Amin

Kou

Sun

2017

Day 3 Wed, April 26, 2017

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“…Such interface models have been studied extensively in the engineering literature, e.g. see [4,25,24,32,26,22], as well as in the mathematical literature, e.g. see [30,3,29,16,20,34,27,12,11], to name just a few.…”

Section: Introductionmentioning

confidence: 99%

First-order indicators for the estimation of discrete fractures in porous media

Ameur

Chavent

Fatma

et al. 2017

Inverse Problems in Science and Engineering

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Abstract:Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.

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“…Removing this assumption will thus require the derivation of more general coupling conditions and will be the subject of future works. Finally, we point out that a large variety of method is available in literature for the simulation of underground flows in presence of fractures, using discrete fracture models with conforming meshes [11,12].…”

Section: Introductionmentioning

confidence: 99%

An Efficient XFEM Approximation of Darcy Flows in Arbitrarily Fractured Porous Media

Fumagalli

Scotti

2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Re´sume´-Une approximation efficace par XFEM pour e´coulements de Darcy dans les milieux poreux arbitrairement fracture´s -Les e´coulements souterrains sont fortement influence´s par la pre´sence de failles et de grandes fractures qui modifient la perme´abilite´du milieu agissant comme des barrie`res ou des conduits pour l'e´coulement. Une description pre´cise des proprie´te´s hydrauliques des fractures est donc essentielle pour la mode´lisation de la migration du pe´trole ou de l'exploitation de ressources non conventionnelles. Toutefois, la largeur de fractures est souvent petite par rapport a`la taille typique des e´le´ments du maillage. Pour re´soudre le proble`me par une approximation nume´rique obtenue sans raffinement du maillage, on remplace les fractures par des surfaces immerge´es dans la matrice poreuse. Par ailleurs, on veut permettre aux surfaces d'eˆtre inde´pendantes par rapport a`la structure du maillage, en manipulant les discontinuite´s à l'inte´rieur des e´le´ments par la me´thode des e´le´ments finis e´tendus (XFEM Extended Finite Element Method). On utilise une technique similaire pour obtenir un outil plus flexible, apte a`la re´solution du proble`me dans les re´gions d'intersection potentielles entre les fractures.Abstract -An Efficient XFEM Approximation of Darcy Flows in Arbitrarily Fractured Porous Media -Subsurface flows are influenced by the presence of faults and large fractures which act as preferential paths or barriers for the flow. In literature models were proposed to handle fractures in a porous medium as objects of codimension 1. In this work we consider the case of a network of intersecting fractures, with the aim of deriving physically consistent and effective interface conditions to impose at the intersection between fractures. This new model accounts for the angle between fractures at the intersections and allows for jumps of pressure across the intersection. This latter property permits to describe more accurately the flow when fractures are characterised by different properties, than other models that impose pressure continuity. The main mathematical properties of the model, derived in the two-dimensional setting, are analysed. As concerns the numerical discretization we allow the grids of the fractures to be independent, thus in general non-matching at the intersection, by means of the Extended Finite Element Method (XFEM), to increase the flexibility of the method in the case of complex geometries characterized by a high number of fractures.

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An efficient numerical model for incompressible two-phase flow in fractured media

Cited by 272 publications

References 42 publications

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

A Multiscale Time-Splitting Discrete Fracture Model of Nanoparticles Transport in Fractured Porous Media

First-order indicators for the estimation of discrete fractures in porous media

An Efficient XFEM Approximation of Darcy Flows in Arbitrarily Fractured Porous Media

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