A two-phase flow simulation of a fractured reservoir using a new fissure element method

Granet, S.; Fabrie, Pierre; Lemonnier, P.; Quintard, Michel

doi:10.1016/s0920-4105(01)00146-2

Cited by 63 publications

(24 citation statements)

References 11 publications

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“…That version takes into account the high fluid compressibility via a pseudo-pressure, and the non-Darcy flow near the wellbore via a rate-dependent skin. Granet et al (1998Granet et al ( , 2001 developed a 2-D discrete model of fractures and matrix to simulate single-phase and two-phase flow on the realistic geological images of fractured reservoirs generated by a stochastic fracture modeling software. They used an unstructured grid made of two kinds of elements, linear elements for the fissure network and triangular elements for the matrix with an appropriate finite volume scheme.…”

Section: Alternative Approaches In Fractured Reservoir Simulationmentioning

confidence: 99%

Simulation of Naturally Fractured Reservoirs. State of the Art

Lemonnier

Bourbiaux

2010

Oil Gas Sci. Technol. – Rev. IFP

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Résumé -Simulation des réservoirs naturellement fracturés. État de l'art : Partie 1 -Mécanismes physiques et formulation des simulateurs -L'utilisation des simulateurs de réservoir fracturé aide l'ingénieur de réservoir à mieux comprendre les principaux mécanismes physiques, à choisir le procédé de récupération le mieux adapté et à l'optimiser. Des progrès sensibles ont été réalisés depuis les premières publications sur le concept double-milieu dans les années soixante. Cet article présente les techniques actuelles de modélisation utilisées dans les simulateurs industriels. Après une description des procédés de récupération et des principaux mécanismes physiques associés, suit un historique de la simulation des réservoirs. La formulation mathématique générale des simulateurs double-milieu est ensuite décrite. L'article se termine sur une présentation de la simulation numérique de l'écoulement dans les fractures et les failles et de la modélisation des puits. La formulation des échanges matrice-fracture ainsi que les techniques d'analyse des incertitudes et de calage d'historique contraint par la géologie et l'écoulement sont traitées dans un second article, associé à celui-ci, Partie 2 : Échanges matrice-fracture et spécificités des études numériques. Abstract

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Section: Alternative Approaches In Fractured Reservoir Simulationmentioning

confidence: 99%

Simulation of Naturally Fractured Reservoirs. State of the Art

Lemonnier

Bourbiaux

2010

Oil Gas Sci. Technol. – Rev. IFP

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“…Different aspects of flow in fractured porous media, especially in the contexts of petroleum reservoirs, have been investigated by different numerical methods such as Finite Elements [1,2,3], Finite Volume [4,5,6] and Discrete Fracture Network [7,8] among many others. In many problems related to flow in fractured geological formations or in micro-cracked porous rocks, one is interested in the steady state flow that takes place under given farfield conditions.…”

Section: Introductionmentioning

confidence: 99%

“…It can be noticed that in many works fractures intersections have been simply excluded to avoid conceptual and numerical difficulties. In some works, dealing with 2D flow, the mass balance at fracture intersection points is expressed only in the numerical model: Granet et al [5] impose some relations on nodal velocities in elements adjacent to an intersection point in order to assure the mass balance. But concerning the 3D intersecting fractures, we could not find any expression of mass balance conditions on intersection lines and points.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional flow in fractured porous media: A potential solution based on singular integral equations

Pouya

2012

Advances in Water Resources

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Governing equations for flow in three-dimensional heterogeneous and anisotropic porous media containing fractures or cracks with infinite transverse permeability are described. Fractures are modeled as zero thickness curve surfaces with the possibility of multiple intersections. It is assumed that flow obeys to an anisotropic Darcy's law in the porous matrix and to a Poiseuille type law in fractures. The mass exchange relations at fractures intersections are carefully investigated as to establish a complete mathematical formulation for the flow problem in a fractured porous body. A general potential solution, based on singular integral equations, is established for steady state flow in an infinite fractured body with uniform and isotropic matrix permeability. The main unknown variable in the equations is the pressure field on the crack surfaces, reducing thus from three to two the dimension of the numerical problem. A general transformation lemma is then given that allows extending the solution to matrices with anisotropic permeability. The results lead to a simple and efficient numerical method for modeling flow in three-dimensional fractured porous bodies.

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“…However, even due to the robustness of this type of approach, any advantages are quickly diminished by the inherent computational inefficiency. A cost-effective alternative to single-porosity modeling is the discrete-fracture modeling approach (see, e.g., [14,17,24]). A discrete-fracture model may be viewed as a modified single-porosity model where specialized elements are used to portray the fractures within a porous medium [14,24].…”

Section: Introductionmentioning

confidence: 99%

“…A cost-effective alternative to single-porosity modeling is the discrete-fracture modeling approach (see, e.g., [14,17,24]). A discrete-fracture model may be viewed as a modified single-porosity model where specialized elements are used to portray the fractures within a porous medium [14,24]. For example, in [14] a "fissure element" method was proposed to handle the fractures within a porous medium.…”

Section: Introductionmentioning

confidence: 99%

Application of the two-stage Markov chain Monte Carlo method for characterization of fractured reservoirs using a surrogate flow model

et al. 2011

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In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves sampling from a representation of a fracture's permeability that has been suitably adjusted to the dynamic tracer cut measurement data. We propose to use a type of dual-porosity, dualpermeability model for tracer flow. This model is built into the Markov chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model. With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate. A number of numerical examples are presented to illustrate the performance of the method.

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A two-phase flow simulation of a fractured reservoir using a new fissure element method

Cited by 63 publications

References 11 publications

Simulation of Naturally Fractured Reservoirs. State of the Art

Simulation of Naturally Fractured Reservoirs. State of the Art

Three-dimensional flow in fractured porous media: A potential solution based on singular integral equations

Application of the two-stage Markov chain Monte Carlo method for characterization of fractured reservoirs using a surrogate flow model

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