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Computational Geosciences manuscript No will be inserted by the editor

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15 pages
Computational Geosciences manuscript No. (will be inserted by the editor) Vertex-centred Discretization of Multiphase Compositional Darcy flows on General Meshes R. Eymard · C. Guichard · R. Herbin · R. Masson Received: date / Accepted: date Abstract This paper concerns the discretization on general 3D meshes of multiphase compositional Darcy flows in heterogeneous anisotropic porous media. Ex- tending Coats' formulation [14] to an arbitrary number of phases, the model accounts for the coupling of the mass balance of each component with the pore volume conservation and the thermodynamical equilibrium, and dynamically manages phase appearance and disappear- ance. The spatial discretization of the multiphase com- positional Darcy flows is based on a generalization of the Vertex Approximate Gradient scheme (VAG), al- ready introduced for single phase diffusive problems in [18]. It leads to an unconditionally coercive scheme for arbitrary meshes and permeability tensors. The sten- cil of this vertex-centred scheme typically comprises 27 points on topologically Cartesian meshes, and the num- ber of unknowns on tetrahedral meshes is considerably reduced, compared with usual cell-centred approaches. The efficiency of our approach is exhibited on the near- well injection of miscible CO2 in a saline aquifer taking into account the vaporization of H2O in the gas phase as well as the precipitation of salt. R. Eymard University of Paris-Est, France, E-mail: robert.

  • phases ? ?

  • multiphase compositional

  • compact vertex-centred

  • centred finite

  • vag scheme

  • tri- phase darcy

  • vertex

  • darcy flow


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Computational Geosciences manuscript No. (will be inserted by the editor)
Vertex-centred Discretization of Multiphase Compositional Darcy flows on General Meshes R. Eymard C. Guichard R. Herbin R. Masson
Received: date / Accepted: date
Abstract This paper concerns the discretization on 1 Introduction general 3D meshes of multiphase compositional Darcy flows in heterogeneous anisotropic porous media. Ex- Many applications require the simulation of composi-tending Coats’ formulation [14] to an arbitrary number tional multiphase Darcy flow in heterogeneous porous of phases, the model accounts for the coupling of the media. In oil reservoir modelling, the compositional tri-mass balance of each component with the pore volume phase Darcy flow simulator is a key tool to predict and conservation and the thermodynamical equilibrium, and optimize the production of a reservoir. In sedimentary dynamically manages phase appearance and disappear- basin modelling, such models are used to simulate the ance. The spatial discretization of the multiphase com- migration of the oil and gas phases in a basin satu-positional Darcy flows is based on a generalization of rated with water at geological space and time scales. the Vertex Approximate Gradient scheme (VAG), al- The objectives are to predict the location of the po-ready introduced for single phase diffusive problems in tential reservoirs as well as the quality and quantity [18]. It leads to an unconditionally coercive scheme for of oil trapped therein. In CO 2 geological storage, com-arbitrary meshes and permeability tensors. The sten- positional multiphase Darcy flow models are used to cil of this vertex-centred scheme typically comprises 27 optimize the injection of CO 2 and to assess the long points on topologically Cartesian meshes, and the num- term integrity of the storage. Finally, two-phase com-ber of unknowns on tetrahedral meshes is considerably positional Darcy flow models are used to study the gas reduced, compared with usual cell-centred approaches. migration in nuclear waste repositories (which consist The efficiency of our approach is exhibited on the near- of porous media saturated with water), and to assess well injection of miscible CO 2 in a saline aquifer taking the safety of the storage. into account the vaporization of H 2 O in the gas phase as well as the precipitation of salt. The numerical simulation of such models first re-lies on a proper formulation which can account for the coupling of the mass and pore volume conservations together with the thermodynamical equilibrium. A ma-jor difficulty there is the management of phase appear-ance and disappearance induced by the change of phase reactions assumed to be at equilibrium. Many formula-tions have been proposed mainly in the oil industry (see [12] and the numerous references therein), and more recently for the modelling of gas migration in nuclear waste disposal (see for example [4], [9], [11]). In the following, we propose an extension to an ar-bitrary number of phases of Coats formulation [14] de-signed for reservoir simulation. This formulation, which is expressed in the natural variables of the thermody-
R. Eymard University of Paris-Est, France, E-mail: robert.eymard@univ-mlv.fr C. Guichard University of Paris-Est, France, E-mail: cindy.guichard@univ-mlv.fr R. Herbin University of Aix-Marseille, France, E-mail: raphaele.herbin@latp.univ-mrs.fr R. Masson University of Nice Sophia Antipolis, France, E-mail: roland.masson@unice.fr