Abdallah Benali - Academia.edu (original) (raw)

Papers by Abdallah Benali

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, May 1, 2001

-Modélisation mathématique de la perméation des gaz dans les polymères-Ce travail concerne la car... more -Modélisation mathématique de la perméation des gaz dans les polymères-Ce travail concerne la caractérisation des coefficients de transport de gaz dans les polymères à partir d'expériences de perméation. Dans un premier temps, la démarche de modélisation physique et mathématique est présentée. Deux modèles de dépendance en concentration sont utilisés pour décrire la diffusion des gaz dans le polymère. La démarche de modélisation mathématique aboutit à la construction d'un problème d'optimisation non classique. Un travail complémentaire à cette démarche concerne l'étude de sensibilité des paramètres qui caractérisent le coefficient de diffusion et la concentration maximale de gaz, inconnue dans les essais de perméation. Cette méthode d'optimisation ne dépend pas de l'initialisation des paramètres et permet de les déterminer de façon unique.

Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convectio... more Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convection qui rendent compte d'un certain nombre d'effets intervenant dans les procedes de filtration a travers une membrane. Le premier dit a resistance est lineaire. Le second appele modele osmotique est non lineaire. L'existence globale et l'unicite de la solution pour le modele a resistance reposent sur des arguments de compacite ainsi que sur l'injection continue de l'espace c o(0,t;l 2( l))l 2(0,t;h 1 l( l)) dans l 4(0,t;0). Pour le modele osmotique, l'existence locale en temps des solutions repose sur un theoreme de point fixe de type schauder. Apres cette analyse mathematique, des simulations numeriques sont effectuees. La discretisation en temps est etablie a l'aide de la methode d'euler implicite et celle en espace par une methode spectrale. La non linearite est traitee par un schema iteratif de type predicteur-correcteur. A partir des donnees experimentales, les simulations conduisent a de bons resultats numeriques et permettent de retrouver les profils physiques observes pour le modele osmotique.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 20, 2014

The invention is a method for exploiting a subterranean medium, according to an exploitation sche... more The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, May 1, 2001

HAL (Le Centre pour la Communication Scientifique Directe), Jan 18, 2012

HAL (Le Centre pour la Communication Scientifique Directe), Nov 27, 2013

The invention relates to a method for exploiting an underground environment, in which said underg... more The invention relates to a method for exploiting an underground environment, in which said underground medium is exploited according to an exploitation scheme defined from a representation of said medium, said representation of said medium being established from a grid two-dimensional representation representing said subterranean medium. The quality of the meshes of said grid is optimized by moving the nodes of said grid by a method of minimizing the deformation of said grid which comprises the following steps:(1) a reference grid is generated;(2) imposing a displacement of at least one node, said rigid node, of the reference grid on a corresponding node in the grid to be optimized; and(3) constructing an optimized two-dimensional grid by moving the other nodes of said reference grid, minimizing the displacement field of said nodes

HAL (Le Centre pour la Communication Scientifique Directe), Jan 20, 2011

A method having application for petroleum exploration or geological storage of generating a mesh ... more A method having application for petroleum exploration or geological storage of generating a mesh of a faulted underground medium, comprising generating a hex-dominant mesh from faults and horizons in a form of a 3D triangulated surfaces. Each 3D triangulated surface is converted to a 2D triangulated surface onto which the faults are projected by an isometric unfolding technique. A regular two-dimensional grid pattern is generated for each 2D triangulated surface. The faults are accounted for by deforming quadrilaterals of the grid pattern intersected by projected faults. The deformed regular grid pattern is then converted to a 3D gridded surface and each quadrilateral which is crossed by a fault is converted into two triangles at a level of a diagonal. Finally, after iterating for all the 3D triangulated surfaces, the mesh is generated by creating links between the nodes of neighboring three-dimensional gridded surfaces with respect to the faults

IOP conference series, Jun 1, 2010

Basin modeling aims to reconstruct the geological history of a basin and its oil system by means ... more Basin modeling aims to reconstruct the geological history of a basin and its oil system by means of fluid flow simulations, which is done by using a series of meshes describing basin geometry at each geological instant. These meshes are preferably hexahedral rather than tetrahedral in virtue for better numerical results. The basin can simply consist of geological layers delimited one from another by horizons. It can be geometrically complex with one or more faults interrupting the layers, which is barely studied but increasingly demanded. This paper exposes an automatic method which generates hex-dominant meshes for basin modeling with complex geometry. Firstly, based on their triangulations at the latest instant, 3D surface grids are generated with identical topology for all the horizons, and with some quadrilaterals being split across the diagonals to adapt to fault traces. Afterwards, all instants are iterated to generate corresponding meshes by firstly applying horizon and fault displacement on the mesh generated for precedent instant; the method then connects the bottom and top surface grids of the new layer along corresponding nodes, and splits certain cells along faults when necessary. Simulations have been carried out on generated meshes with satisfactory results.

HAL (Le Centre pour la Communication Scientifique Directe), May 21, 2012

International audienc

Engineering With Computers, Jul 8, 2011

Under the context of subterranean formation modeling using finite volume methods, the computation... more Under the context of subterranean formation modeling using finite volume methods, the computational domain is a basin, a reservoir, or an underground CO 2 storage site. Such a domain has a layered structure and is geometrically described by its layer limits called horizons and random disruption of layers called faults. Horizons and faults are both numerically represented by 3D triangulated surface meshes. Respecting the interface formed by horizons and faults, the volume mesh of the subterranean formation is required to be mainly hexahedral, with a few tetrahedrons, prisms or pyramids allowed along the faults, where mesh non-conformity is tolerated. A ''constrained grid'' approach is proposed to generate the so-desired mesh. Firstly, each horizon surface is unfolded with fault traces being sewn. Then, for each unfolded horizon, a regular grid with the same topology is generated from its boundary. Subsequently, node relocation and conditional grid refinement are applied to constrain fault traces to the grid. Afterwards, each grid is mapped back to its corresponding 3D horizon surface with fault nodes being split. Finally, a hex-dominant mesh is generated by connecting consecutive grids along corresponding nodes, with some elements cut into two by faults and degenerated into prisms, tetrahedrons, and pyramids. An optimization procedure is then applied to enhance the shape quality of the resulting 3D mesh.

The invention relates to a method for exploiting an underground environment, in which said underg... more The invention relates to a method for exploiting an underground environment, in which said underground medium is exploited according to an exploitation scheme defined from a representation of said medium, said representation of said medium being established from a grid two-dimensional representation representing said subterranean medium. The quality of the meshes of said grid is optimized by moving the nodes of said grid by a method of minimizing the deformation of said grid which comprises the following steps:(1) a reference grid is generated;(2) imposing a displacement of at least one node, said rigid node, of the reference grid on a corresponding node in the grid to be optimized; and(3) constructing an optimized two-dimensional grid by moving the other nodes of said reference grid, minimizing the displacement field of said nodes

Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convectio... more Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convection qui rendent compte d'un certain nombre d'effets intervenant dans les procedes de filtration a travers une membrane. Le premier dit a resistance est lineaire. Le second appele modele osmotique est non lineaire. L'existence globale et l'unicite de la solution pour le modele a resistance reposent sur des arguments de compacite ainsi que sur l'injection continue de l'espace c o(0,t;l 2( l))l 2(0,t;h 1 l( l)) dans l 4(0,t;0). Pour le modele osmotique, l'existence locale en temps des solutions repose sur un theoreme de point fixe de type schauder. Apres cette analyse mathematique, des simulations numeriques sont effectuees. La discretisation en temps est etablie a l'aide de la methode d'euler implicite et celle en espace par une methode spectrale. La non linearite est traitee par un schema iteratif de type predicteur-correcteur. A partir des donnees experi...

A method for generating a mesh of a faulted underground environment, comprising generating a hexa... more A method for generating a mesh of a faulted underground environment, comprising generating a hexa-dominant from faults and horizons as 3D triangulated surface mesh. It turns every triangulated 3D surface into a 2D triangulated surface, on which the flaws are projected, using a technique of isometric unfolding. a regular two-dimensional grid is generated for each triangulated surface 2D. Then, faults are taken into account by distorting the quadrilateral grid intersected by the projected gaps. the regular grid is then converted thereby deformed into a gridded surface 3D, and is converted into two triangles each quadrilateral crossed by a fault at a diagonal. Finally, after iterated for all 3D triangulated surfaces, the mesh is generated by creating links between the nodes of neighboring three-dimensional gridded surfaces, while respecting the faults. Applications to oil exploration or geological storage.

The method involves generating a hex-dominant mesh of an underground environment by generating ce... more The method involves generating a hex-dominant mesh of an underground environment by generating cells by creating connections between nodes of surface elements of three-dimensional gridded surfaces. The mesh is generated by detecting the nodes of the first gridded surface, by connecting each node of a detected non-gridded surface with the node in the second gridded surface having same coordinates, by connecting each node of the first gridded surface with a detected break portion and by regulating the cells with two vertices. An independent claim is also included for a method for operating an underground environment.

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, 2014

Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 ... more Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 pp. 507-766 et téléchargeable ici D o s s i e r DOSSIER Edited by/Sous la direction de : Z. Benjelloun-Touimi Geosciences Numerical Methods Modélisation numérique en géosciences

ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, 2012

To improve a dynamic hex-dominant mesh for basins, a particular optimization in shape is proposed... more To improve a dynamic hex-dominant mesh for basins, a particular optimization in shape is proposed in this article. The aim is to return a mesh as regular as possible on xyxyxy coordinates and align the zzz coordinates. This optimization must complete an existing approach generate a hex-dominant mesh to improve these generated elements. To do this optimization for the xyxyxy coordinate a Transformation called Smoothing Laplacian is applied. After, an iterative method which transforms some connections between layers in verticals. And it’s possible to conclude that this kind of optimization can be improved to have any shape wanted.

The invention is a method for exploiting a subterranean medium, according to an exploitation sche... more The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, May 1, 2001

-Modélisation mathématique de la perméation des gaz dans les polymères-Ce travail concerne la car... more -Modélisation mathématique de la perméation des gaz dans les polymères-Ce travail concerne la caractérisation des coefficients de transport de gaz dans les polymères à partir d'expériences de perméation. Dans un premier temps, la démarche de modélisation physique et mathématique est présentée. Deux modèles de dépendance en concentration sont utilisés pour décrire la diffusion des gaz dans le polymère. La démarche de modélisation mathématique aboutit à la construction d'un problème d'optimisation non classique. Un travail complémentaire à cette démarche concerne l'étude de sensibilité des paramètres qui caractérisent le coefficient de diffusion et la concentration maximale de gaz, inconnue dans les essais de perméation. Cette méthode d'optimisation ne dépend pas de l'initialisation des paramètres et permet de les déterminer de façon unique.

Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convectio... more Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convection qui rendent compte d'un certain nombre d'effets intervenant dans les procedes de filtration a travers une membrane. Le premier dit a resistance est lineaire. Le second appele modele osmotique est non lineaire. L'existence globale et l'unicite de la solution pour le modele a resistance reposent sur des arguments de compacite ainsi que sur l'injection continue de l'espace c o(0,t;l 2( l))l 2(0,t;h 1 l( l)) dans l 4(0,t;0). Pour le modele osmotique, l'existence locale en temps des solutions repose sur un theoreme de point fixe de type schauder. Apres cette analyse mathematique, des simulations numeriques sont effectuees. La discretisation en temps est etablie a l'aide de la methode d'euler implicite et celle en espace par une methode spectrale. La non linearite est traitee par un schema iteratif de type predicteur-correcteur. A partir des donnees experimentales, les simulations conduisent a de bons resultats numeriques et permettent de retrouver les profils physiques observes pour le modele osmotique.

HAL (Le Centre pour la Communication Scientifique Directe), Feb 20, 2014

The invention is a method for exploiting a subterranean medium, according to an exploitation sche... more The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, May 1, 2001

HAL (Le Centre pour la Communication Scientifique Directe), Jan 18, 2012

HAL (Le Centre pour la Communication Scientifique Directe), Nov 27, 2013

The invention relates to a method for exploiting an underground environment, in which said underg... more The invention relates to a method for exploiting an underground environment, in which said underground medium is exploited according to an exploitation scheme defined from a representation of said medium, said representation of said medium being established from a grid two-dimensional representation representing said subterranean medium. The quality of the meshes of said grid is optimized by moving the nodes of said grid by a method of minimizing the deformation of said grid which comprises the following steps:(1) a reference grid is generated;(2) imposing a displacement of at least one node, said rigid node, of the reference grid on a corresponding node in the grid to be optimized; and(3) constructing an optimized two-dimensional grid by moving the other nodes of said reference grid, minimizing the displacement field of said nodes

HAL (Le Centre pour la Communication Scientifique Directe), Jan 20, 2011

A method having application for petroleum exploration or geological storage of generating a mesh ... more A method having application for petroleum exploration or geological storage of generating a mesh of a faulted underground medium, comprising generating a hex-dominant mesh from faults and horizons in a form of a 3D triangulated surfaces. Each 3D triangulated surface is converted to a 2D triangulated surface onto which the faults are projected by an isometric unfolding technique. A regular two-dimensional grid pattern is generated for each 2D triangulated surface. The faults are accounted for by deforming quadrilaterals of the grid pattern intersected by projected faults. The deformed regular grid pattern is then converted to a 3D gridded surface and each quadrilateral which is crossed by a fault is converted into two triangles at a level of a diagonal. Finally, after iterating for all the 3D triangulated surfaces, the mesh is generated by creating links between the nodes of neighboring three-dimensional gridded surfaces with respect to the faults

IOP conference series, Jun 1, 2010

Basin modeling aims to reconstruct the geological history of a basin and its oil system by means ... more Basin modeling aims to reconstruct the geological history of a basin and its oil system by means of fluid flow simulations, which is done by using a series of meshes describing basin geometry at each geological instant. These meshes are preferably hexahedral rather than tetrahedral in virtue for better numerical results. The basin can simply consist of geological layers delimited one from another by horizons. It can be geometrically complex with one or more faults interrupting the layers, which is barely studied but increasingly demanded. This paper exposes an automatic method which generates hex-dominant meshes for basin modeling with complex geometry. Firstly, based on their triangulations at the latest instant, 3D surface grids are generated with identical topology for all the horizons, and with some quadrilaterals being split across the diagonals to adapt to fault traces. Afterwards, all instants are iterated to generate corresponding meshes by firstly applying horizon and fault displacement on the mesh generated for precedent instant; the method then connects the bottom and top surface grids of the new layer along corresponding nodes, and splits certain cells along faults when necessary. Simulations have been carried out on generated meshes with satisfactory results.

HAL (Le Centre pour la Communication Scientifique Directe), May 21, 2012

International audienc

Engineering With Computers, Jul 8, 2011

Under the context of subterranean formation modeling using finite volume methods, the computation... more Under the context of subterranean formation modeling using finite volume methods, the computational domain is a basin, a reservoir, or an underground CO 2 storage site. Such a domain has a layered structure and is geometrically described by its layer limits called horizons and random disruption of layers called faults. Horizons and faults are both numerically represented by 3D triangulated surface meshes. Respecting the interface formed by horizons and faults, the volume mesh of the subterranean formation is required to be mainly hexahedral, with a few tetrahedrons, prisms or pyramids allowed along the faults, where mesh non-conformity is tolerated. A ''constrained grid'' approach is proposed to generate the so-desired mesh. Firstly, each horizon surface is unfolded with fault traces being sewn. Then, for each unfolded horizon, a regular grid with the same topology is generated from its boundary. Subsequently, node relocation and conditional grid refinement are applied to constrain fault traces to the grid. Afterwards, each grid is mapped back to its corresponding 3D horizon surface with fault nodes being split. Finally, a hex-dominant mesh is generated by connecting consecutive grids along corresponding nodes, with some elements cut into two by faults and degenerated into prisms, tetrahedrons, and pyramids. An optimization procedure is then applied to enhance the shape quality of the resulting 3D mesh.

The invention relates to a method for exploiting an underground environment, in which said underg... more The invention relates to a method for exploiting an underground environment, in which said underground medium is exploited according to an exploitation scheme defined from a representation of said medium, said representation of said medium being established from a grid two-dimensional representation representing said subterranean medium. The quality of the meshes of said grid is optimized by moving the nodes of said grid by a method of minimizing the deformation of said grid which comprises the following steps:(1) a reference grid is generated;(2) imposing a displacement of at least one node, said rigid node, of the reference grid on a corresponding node in the grid to be optimized; and(3) constructing an optimized two-dimensional grid by moving the other nodes of said reference grid, minimizing the displacement field of said nodes

Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convectio... more Ce travail est une contribution au traitement mathematique de deux modeles de diffusion-convection qui rendent compte d'un certain nombre d'effets intervenant dans les procedes de filtration a travers une membrane. Le premier dit a resistance est lineaire. Le second appele modele osmotique est non lineaire. L'existence globale et l'unicite de la solution pour le modele a resistance reposent sur des arguments de compacite ainsi que sur l'injection continue de l'espace c o(0,t;l 2( l))l 2(0,t;h 1 l( l)) dans l 4(0,t;0). Pour le modele osmotique, l'existence locale en temps des solutions repose sur un theoreme de point fixe de type schauder. Apres cette analyse mathematique, des simulations numeriques sont effectuees. La discretisation en temps est etablie a l'aide de la methode d'euler implicite et celle en espace par une methode spectrale. La non linearite est traitee par un schema iteratif de type predicteur-correcteur. A partir des donnees experi...

A method for generating a mesh of a faulted underground environment, comprising generating a hexa... more A method for generating a mesh of a faulted underground environment, comprising generating a hexa-dominant from faults and horizons as 3D triangulated surface mesh. It turns every triangulated 3D surface into a 2D triangulated surface, on which the flaws are projected, using a technique of isometric unfolding. a regular two-dimensional grid is generated for each triangulated surface 2D. Then, faults are taken into account by distorting the quadrilateral grid intersected by the projected gaps. the regular grid is then converted thereby deformed into a gridded surface 3D, and is converted into two triangles each quadrilateral crossed by a fault at a diagonal. Finally, after iterated for all 3D triangulated surfaces, the mesh is generated by creating links between the nodes of neighboring three-dimensional gridded surfaces, while respecting the faults. Applications to oil exploration or geological storage.

The method involves generating a hex-dominant mesh of an underground environment by generating ce... more The method involves generating a hex-dominant mesh of an underground environment by generating cells by creating connections between nodes of surface elements of three-dimensional gridded surfaces. The mesh is generated by detecting the nodes of the first gridded surface, by connecting each node of a detected non-gridded surface with the node in the second gridded surface having same coordinates, by connecting each node of the first gridded surface with a detected break portion and by regulating the cells with two vertices. An independent claim is also included for a method for operating an underground environment.

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, 2014

Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 ... more Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 pp. 507-766 et téléchargeable ici D o s s i e r DOSSIER Edited by/Sous la direction de : Z. Benjelloun-Touimi Geosciences Numerical Methods Modélisation numérique en géosciences

ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery, 2012

To improve a dynamic hex-dominant mesh for basins, a particular optimization in shape is proposed... more To improve a dynamic hex-dominant mesh for basins, a particular optimization in shape is proposed in this article. The aim is to return a mesh as regular as possible on xyxyxy coordinates and align the zzz coordinates. This optimization must complete an existing approach generate a hex-dominant mesh to improve these generated elements. To do this optimization for the xyxyxy coordinate a Transformation called Smoothing Laplacian is applied. After, an iterative method which transforms some connections between layers in verticals. And it’s possible to conclude that this kind of optimization can be improved to have any shape wanted.

The invention is a method for exploiting a subterranean medium, according to an exploitation sche... more The invention is a method for exploiting a subterranean medium, according to an exploitation scheme defined on a representation of the medium based on a two-dimensional grid representing the subterranean medium. The quality of the mesh cells of the grid is optimized by displacing the nodes of the grid by a procedure for minimizing the deformation of the grid by generating a reference grid; imposing a displacement of at least one node, termed a rigid node, of the reference grid on a corresponding node in the grid to be optimized; and constructing an optimized two-dimensional grid by displacement of the other nodes of the reference grid, while minimizing the displacement field of the nodes