Boundary element techniques in petroleum reservoir simulation

Pecher, Radek; Stanislav, J.F.

doi:10.1016/s0920-4105(96)00066-6

Cited by 34 publications

(15 citation statements)

References 7 publications

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“…In this case, the inverse problem is to identify the rate of the outflow (see [17]). The first difficulty in the inverse source problems by boundary measurements concerns the unidentifiability of general sources, as shown in the following example:…”

Section: Introductionmentioning

confidence: 99%

On an inverse source problem for the heat equation. Application to a pollution detection problem

Badia

Ha-Duong

2002

Journal of Inverse and Ill-posed Problems

133

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We consider the problem of identification of a heat source in a bounded domain Ω. Assuming that the point sources became inactive after the time T * , we prove that they can be identified by measurements of the heat flux on Γ0 × (0, T ), where Γ0 is a part of the boundary of Ω, with non void interior, and T > T * . By a standard trandformation, we derive from these results a method to identify the polluting sources on the surface of a river, a lake . . .

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Section: Introductionmentioning

confidence: 99%

On an inverse source problem for the heat equation. Application to a pollution detection problem

Badia

Ha-Duong

2002

Journal of Inverse and Ill-posed Problems

133

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“…where q stands for the normal derivative of the pressure p q ¼ op [13]). The operators V , S, H , D are defined by:…”

Section: Integral Representation Of the Modelmentioning

confidence: 99%

“…They are generally limited to 2D problems [9,11,13,14]. In [10], Koh and Tiab have treated a 3D problem for homogeneous media.…”

Section: Introductionmentioning

confidence: 99%

Modelling of single-phase flow for horizontal wells in a stratified medium

et al. 2004

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“…BEM han been used in well tests in reservoir engineering [5,9] . As example, Pecher and Stanislas [9] proposed a resolution of a multi-domain integral methods to simulate well tests .…”

Section: Introductionmentioning

confidence: 99%

“…As example, Pecher and Stanislas [9] proposed a resolution of a multi-domain integral methods to simulate well tests . The main interest of the boundary integral method is its ability to describe complex geometry .…”

Section: Introductionmentioning

confidence: 99%

Coupling Finite Volume and Boundary Element Methods for Flow Modelling

Jeannin¹,

Basquet²,

Ding³

2002

ECMOR VIII - 8th European Conference on the Mathematics of Oil Recovery

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Abstrac tFlow modelling in heterogeneous media is a great challenge, especially in the presence of welk or hydraulic fracturen . The most used numerical scheme, finite volume method, allows taking heterogeneities into account . But finite volume meshes adapted to the geometry of welk or fracturen cannot be built efficiently . Conversely, Boundary element method (BEM) can be used to model complex geometries in homogeneous media . The use of BEM requires working on homogeneized area and accepting to loose the information about heterogeneities . In this paper, we propose an innovative method to solve this conflict and to use the combined advantages of both methods : we develop an approach using the coupling of finite volume scheme and boundary element method . The BEM is only used in reduced areas of complex geometries . The existence and uniqueness of the solution of our coupling scheme is mathematically proved and its performance is numerically studied . Finally, we show how our coupling scheme can bring a solution to the problem of modelling objects of complex geometry in heterogeneous media . Introductio nBEM han been used in well tests in reservoir engineering [5,9] . As example, Pecher and Stanislas [9] proposed a resolution of a multi-domain integral methods to simulate well tests . The main interest of the boundary integral method is its ability to describe complex geometry . So it seems to be tempted to use boundary element methods around objects of complex geometry such as advanced welk or fractures and to use more classical discrete numerical scheme far from the well . In this paper, we consider a steady-state problem . One application of such procedure is the calculus of well performance in an heterogeneous reservoir . Another application could be the homogeneization of geological objects . Moumas et al .[7] propose a method to discretize welk using integral methods . In this paper, we deal with the problem of coupling a finite volume scheme and a boundary integral representation of an intertor domaio . The first part describes the simplified problem considered and presents the discretization in space . In the second part, we generalize this approach to several bounded and simply connected domains, where the solution is given by an integral representation . Part 3 is devoted to numerical tests .

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Boundary element techniques in petroleum reservoir simulation

Cited by 34 publications

References 7 publications

On an inverse source problem for the heat equation. Application to a pollution detection problem

On an inverse source problem for the heat equation. Application to a pollution detection problem

Modelling of single-phase flow for horizontal wells in a stratified medium

Coupling Finite Volume and Boundary Element Methods for Flow Modelling

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