Eric Flauraud - Academia.edu (original) (raw)

Papers by Eric Flauraud

Research paper thumbnail of A benchmark study on reactive two-phase flow in porous media: Part II -results and discussion

HAL (Le Centre pour la Communication Scientifique Directe), Dec 31, 2022

Research paper thumbnail of Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation

Journal of Computational Physics

In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in t... more In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in the numerical simulation of two-phase flows in porous media. The GOE, which occurs when using coupled finite volume schemes on structured grids, is well known to engineers. Several attempts, most of which are of empirical nature, have been put forward in order to alleviate this undesirable phenomenon. Here, our approach relies on a more rigorous notion of angular error for all directions, which in turn enables us-via integration and minimization-to single out the "least anisotropic" scheme within a given family of schemes depending on some tuning parameter(s). Numerical test problems testify to the improvement brought by the new construction.

Research paper thumbnail of A semi-implicit approach for the modeling of wells with inflow control completions

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

In the last two decades, new technologies have been introduced to equip wells with intelligent co... more In the last two decades, new technologies have been introduced to equip wells with intelligent completions such as Inflow Control Device (ICD) or Inflow Control Valve (ICV) in order to optimize the oil recovery by reducing the undesirable production of gas and water. To optimally define the locations of the packers and the characteristics of the valves, efficient reservoir simulation models are required. This paper is aimed at presenting the specific developments introduced in a multipurpose industrial reservoir simulator to simulate such wells equipped with intelligent completions taking into account the pressure drop and multiphase flow. An explicit coupling or decoupling of a reservoir model and a well flow model with intelligent completion makes usually unstable and non-convergent results, and a fully implicit coupling is CPU time consuming and difficult to be implemented. This paper presents therefore a semi-implicit approach, which links on one side to the reservoir simulation...

Research paper thumbnail of Méthodes de décomposition de domaine pour les écoulements en milieux poreux faillés

Research paper thumbnail of Study of compositional multiphase flow formulation using complementarity conditions

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

In this article, two formulations of multiphase compositional Darcy flows taking into account pha... more In this article, two formulations of multiphase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so-called natural variable formulation commonly used in reservoir simulation, the second has been introduced by Lauser et al. and uses the phase pressures, saturations and component fugacities as main unknowns. We will discuss how the Coats and the Lauser approaches can be used to solve a compositional multiphase flow problem with cubic equations of state of Peng and Robinson. Then, we will study the results of several synthetic cases that are representative of petroleum reservoir engineering problems and we will compare their numerical behavior.

Research paper thumbnail of A new fault model in geological basin modelling. Application of finite volume scheme and domain decomposition methods

We present in this paper a new approach to treat the faults in geological basin modelling. Indeed... more We present in this paper a new approach to treat the faults in geological basin modelling. Indeed the faults are not characterized as subdomains any more but as interfaces between sedimentary blocks. Numerically this new model is solved using finite volume scheme and domain decomposition method with generalized Robin type interface conditions.

Research paper thumbnail of Optimized interface conditions for sedimentary basin modelling

Research paper thumbnail of Ceres2d: a Numerical Prototype for Hc Potential Evaluation in Complex Area

Oil & Gas Science and Technology, 2002

Research paper thumbnail of Efficient Scheme for Chemical Flooding Simulation

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

and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la... more and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 pp. 507-766 et téléchargeable ici Re´sume´-Un sche´ma nume´rique performant pour la simulation des e´coulements d'agents chimiques dans les re´servoirs pe´troliers -Dans cet article, nous proposons un sche´ma nume´rique performant pour la simulation des proce´de´s de re´cupe´ration ame´liore´e utilisant des espe`ces chimiques. Dans un soucis de clarte´, seul le polyme`re est conside´re´dans le mode`le physique. Ainsi, nous conside´rons un mode`le black-oil ame´liore´par la prise en compte du polyme`re : une e´quation de conservation de sa masse et l'effet qu'il occasionne sur la phase eau. Nous supposons que le polyme`re est transporte´dans la phase eau uniquement ou adsorbe´sur la roche suivant une isotherme de Langmuir. Pour ce mode`le physique, nous proposons un sche´ma nume´rique base´sur une technique de pas fractionnaire. La premie`re e´tape consiste en la re´solution du sous syste`me constitue´des e´quations de conservation de la masse des composants lourd, volatile et eau et la deuxie`me e´tape est de´die´e a`la conservation de la masse du polyme`re. Les matrices issues des formulations implicites conservent une taille re´duite pre´servant ainsi l'efficacite´des solveurs line´aires. Cependant, le couplage entre les e´quations des constituants et du polyme`re n'est pas comple`tement re´solu. Pour montrer la validite´de ce sche´ma, nous avons de´veloppe´un sche´ma explicite pour le polyme`re. Son crite`re CFL (Courant-Friedrichs-Levy) contraint de prendre des petits pas de temps ce qui assure une bonne re´solution du couplage. Pour valider le sche´ma implicite, nous avons re´alise´quelques simulations utilisant du polyme`re: le balayage d'une carotte, un 5-spot en pre´sence d'ions et de surfactant et un cas re´el tridimensionnel. Des comparaisons sont effectue´es entre les sche´mas explicite et implicite du polyme`re. Elles montrent que le sche´ma implicite est efficace, robuste et reproduit bien la physqiue. Les de´veloppements et les simulations ont e´te´re´alise´s avec le logiciel PumaFlow [PumaFlow (2013) Reference manual, release V600, Beicip Franlab].

Research paper thumbnail of Optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients

Journal of Computational and Applied Mathematics, 2006

When the coefficients of a problem have jumps of several orders of magnitude and are anisotropic,... more When the coefficients of a problem have jumps of several orders of magnitude and are anisotropic, many preconditioners and domain decomposition methods (DDM) suffer from plateaus in the convergence due to the presence of very small isolated eigenvalues in the spectrum of the preconditioned linear system. One way to improve the preconditioner is to use a linear algebra technique called deflation, or very similarly coarse grid corrections. In both cases, it is necessary to identify and compute, at least approximately, all the eigenvectors corresponding to the "bad" eigenvalues. In the framework of DDM, we propose a way to design interface conditions so that convergence is fast and does not have any plateau. The method relies only on the knowledge of the smallest and largest eigenvalues of an auxiliary matrix. The eigenvectors are not used. The method relies on van der Sluis' result on a quasi-optimal diagonal preconditioner for a symmetric positive definite matrix. It is then possible to design Robin interface conditions using only one real parameter for the entire interface. By adding a second real parameter and more general interface conditions, it is possible to take into account highly heterogeneous and anisotropic media. Numerical results are given and compared with other approaches.

Research paper thumbnail of Domain decomposition for an asymptotic geological fault modeling

Comptes Rendus Mécanique, 2003

ABSTRACT We present in this paper a domain decomposition method to treat faults in geological bas... more ABSTRACT We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).

Research paper thumbnail of A benchmark study on reactive two-phase flow in porous media: Part II -results and discussion

HAL (Le Centre pour la Communication Scientifique Directe), Dec 31, 2022

Research paper thumbnail of Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation

Journal of Computational Physics

In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in t... more In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in the numerical simulation of two-phase flows in porous media. The GOE, which occurs when using coupled finite volume schemes on structured grids, is well known to engineers. Several attempts, most of which are of empirical nature, have been put forward in order to alleviate this undesirable phenomenon. Here, our approach relies on a more rigorous notion of angular error for all directions, which in turn enables us-via integration and minimization-to single out the "least anisotropic" scheme within a given family of schemes depending on some tuning parameter(s). Numerical test problems testify to the improvement brought by the new construction.

Research paper thumbnail of A semi-implicit approach for the modeling of wells with inflow control completions

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

In the last two decades, new technologies have been introduced to equip wells with intelligent co... more In the last two decades, new technologies have been introduced to equip wells with intelligent completions such as Inflow Control Device (ICD) or Inflow Control Valve (ICV) in order to optimize the oil recovery by reducing the undesirable production of gas and water. To optimally define the locations of the packers and the characteristics of the valves, efficient reservoir simulation models are required. This paper is aimed at presenting the specific developments introduced in a multipurpose industrial reservoir simulator to simulate such wells equipped with intelligent completions taking into account the pressure drop and multiphase flow. An explicit coupling or decoupling of a reservoir model and a well flow model with intelligent completion makes usually unstable and non-convergent results, and a fully implicit coupling is CPU time consuming and difficult to be implemented. This paper presents therefore a semi-implicit approach, which links on one side to the reservoir simulation...

Research paper thumbnail of Méthodes de décomposition de domaine pour les écoulements en milieux poreux faillés

Research paper thumbnail of Study of compositional multiphase flow formulation using complementarity conditions

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

In this article, two formulations of multiphase compositional Darcy flows taking into account pha... more In this article, two formulations of multiphase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so-called natural variable formulation commonly used in reservoir simulation, the second has been introduced by Lauser et al. and uses the phase pressures, saturations and component fugacities as main unknowns. We will discuss how the Coats and the Lauser approaches can be used to solve a compositional multiphase flow problem with cubic equations of state of Peng and Robinson. Then, we will study the results of several synthetic cases that are representative of petroleum reservoir engineering problems and we will compare their numerical behavior.

Research paper thumbnail of A new fault model in geological basin modelling. Application of finite volume scheme and domain decomposition methods

We present in this paper a new approach to treat the faults in geological basin modelling. Indeed... more We present in this paper a new approach to treat the faults in geological basin modelling. Indeed the faults are not characterized as subdomains any more but as interfaces between sedimentary blocks. Numerically this new model is solved using finite volume scheme and domain decomposition method with generalized Robin type interface conditions.

Research paper thumbnail of Optimized interface conditions for sedimentary basin modelling

Research paper thumbnail of Ceres2d: a Numerical Prototype for Hc Potential Evaluation in Complex Area

Oil & Gas Science and Technology, 2002

Research paper thumbnail of Efficient Scheme for Chemical Flooding Simulation

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

and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la... more and available online here Cet article fait partie du dossier thématique ci-dessous publié dans la revue OGST, Vol. 69, n°4 pp. 507-766 et téléchargeable ici Re´sume´-Un sche´ma nume´rique performant pour la simulation des e´coulements d'agents chimiques dans les re´servoirs pe´troliers -Dans cet article, nous proposons un sche´ma nume´rique performant pour la simulation des proce´de´s de re´cupe´ration ame´liore´e utilisant des espe`ces chimiques. Dans un soucis de clarte´, seul le polyme`re est conside´re´dans le mode`le physique. Ainsi, nous conside´rons un mode`le black-oil ame´liore´par la prise en compte du polyme`re : une e´quation de conservation de sa masse et l'effet qu'il occasionne sur la phase eau. Nous supposons que le polyme`re est transporte´dans la phase eau uniquement ou adsorbe´sur la roche suivant une isotherme de Langmuir. Pour ce mode`le physique, nous proposons un sche´ma nume´rique base´sur une technique de pas fractionnaire. La premie`re e´tape consiste en la re´solution du sous syste`me constitue´des e´quations de conservation de la masse des composants lourd, volatile et eau et la deuxie`me e´tape est de´die´e a`la conservation de la masse du polyme`re. Les matrices issues des formulations implicites conservent une taille re´duite pre´servant ainsi l'efficacite´des solveurs line´aires. Cependant, le couplage entre les e´quations des constituants et du polyme`re n'est pas comple`tement re´solu. Pour montrer la validite´de ce sche´ma, nous avons de´veloppe´un sche´ma explicite pour le polyme`re. Son crite`re CFL (Courant-Friedrichs-Levy) contraint de prendre des petits pas de temps ce qui assure une bonne re´solution du couplage. Pour valider le sche´ma implicite, nous avons re´alise´quelques simulations utilisant du polyme`re: le balayage d'une carotte, un 5-spot en pre´sence d'ions et de surfactant et un cas re´el tridimensionnel. Des comparaisons sont effectue´es entre les sche´mas explicite et implicite du polyme`re. Elles montrent que le sche´ma implicite est efficace, robuste et reproduit bien la physqiue. Les de´veloppements et les simulations ont e´te´re´alise´s avec le logiciel PumaFlow [PumaFlow (2013) Reference manual, release V600, Beicip Franlab].

Research paper thumbnail of Optimized interface conditions in domain decomposition methods for problems with extreme contrasts in the coefficients

Journal of Computational and Applied Mathematics, 2006

When the coefficients of a problem have jumps of several orders of magnitude and are anisotropic,... more When the coefficients of a problem have jumps of several orders of magnitude and are anisotropic, many preconditioners and domain decomposition methods (DDM) suffer from plateaus in the convergence due to the presence of very small isolated eigenvalues in the spectrum of the preconditioned linear system. One way to improve the preconditioner is to use a linear algebra technique called deflation, or very similarly coarse grid corrections. In both cases, it is necessary to identify and compute, at least approximately, all the eigenvectors corresponding to the "bad" eigenvalues. In the framework of DDM, we propose a way to design interface conditions so that convergence is fast and does not have any plateau. The method relies only on the knowledge of the smallest and largest eigenvalues of an auxiliary matrix. The eigenvectors are not used. The method relies on van der Sluis' result on a quasi-optimal diagonal preconditioner for a symmetric positive definite matrix. It is then possible to design Robin interface conditions using only one real parameter for the entire interface. By adding a second real parameter and more general interface conditions, it is possible to take into account highly heterogeneous and anisotropic media. Numerical results are given and compared with other approaches.

Research paper thumbnail of Domain decomposition for an asymptotic geological fault modeling

Comptes Rendus Mécanique, 2003

ABSTRACT We present in this paper a domain decomposition method to treat faults in geological bas... more ABSTRACT We present in this paper a domain decomposition method to treat faults in geological basin modeling. The particularity of this model is that the faults whose widths are very small in comparison with the basin size, are not characterized as subdomains any more but as interfaces between sedimentary blocks. The originality of this work lies in the formulation of this new fault model and in the definition and the computation of the interface conditions between the subdomains. To cite this article: E. Flauraud et al., C. R. Mecanique 331 (2003).