Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations

Beaude, Laurence; Brenner, Konstantin; López, Simón; Masson, Roland; Smaï, Farid

doi:10.1007/s10596-018-9794-9

Cited by 14 publications

(15 citation statements)

References 34 publications

(59 reference statements)

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“…We consider in this section the extension of the previous combined VAG-HFV discretization to the case of a non-isothermal compositional two-phase Darcy flow. This extension is based on the formulation of the model introduced in [5]. Its main advantages compared with the related Coats' variable switch formulation [9] is to be based on a fixed set of unknowns using extended phase molar fractions and to express the thermodynamical equilibrium as complementary constraints for both phases α ∈ P. Previous works have considered the VAG discretization of isothermal and of non-isothermal compositional two-phase Darcy flows in respectively [18] and [26].…”

Section: Combined Vag-hfv Discretization Of Non-isothermal Compositiomentioning

confidence: 99%

“…for ν ∈ V v D ∪ F h D and with the closure laws 3) by a Newton-Raphson algorithm adapted to the complementary constraints (see [5] for details). The size of the linear system to be solved at each Newton iteration can be considerably reduced by elimination of the Dirichlet d.o.f.…”

Section: Combined Vag-hfv Discretization Of Non-isothermal Compositiomentioning

confidence: 99%

“…Then, numerical tests investigate, on a 1D two-phase flow reference solution, the convergence and efficiency of the VAG-HFV schemes compared with the standalone VAG and HFV discretizations. Section 4 considers the extension of the VAG-HFV discretizations to non-isothermal compositional liquid gas Darcy flows based on the formulation introduced in [5]. Finally, the model and its VAG-TPFA discretization are tested on a simplified two dimensional cross-section of the Bouillante high temperature geothermal reservoir with an hybrid cartesian triangular mesh.…”

Section: Introductionmentioning

confidence: 99%

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Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems

et al. 2019

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In the last 20 years many discretization schemes have been developed to approximate the Darcy fluxes on polyhedral cells in heterogeneous anisotropic porous media. Among them, we can distinguished cell based approaches like the Two Point Flux Approximation (TPFA) or the Multi Point Flux Approximation (MPFA) schemes, face based approaches like the Hybrid Finite Volume (HFV) scheme belonging to the family of Hybrid Mimetic Mixed methods and nodal based discretizations like the Vertex Approximate Gradient (VAG) scheme. They all have their own drawbacks and advantages which typically depend on the type of cells and on the anisotropy of the medium. In this work, we propose a new methodology to combine the VAG and HFV discretizations on arbitrary subsets of cells or faces in order to choose the best suited scheme in different parts of the mesh. In our approach the TPFA discretization is considered as an HFV discretization for which the face unknowns can be eliminated. The coupling strategy is based on a node to face interpolation operator at the interfaces which must be chosen to ensure the consistency, the coercivity and the limit conformity properties of the combined discretization. The convergence analysis is performed in the gradient discretization framework and convergence is proved for arbitrary cell or face partitions of the mesh. For face partitions, an additional stabilisation local to the cell is required to ensure the coercivity while for cell partitions no additional stabilisation is needed. The framework preserves at the interface the discrete conservation properties of the VAG and HFV schemes with fluxes based on local to each cell transmissibility matrices. This discrete conservative form allows to naturally extend the VAG and HFV discretizations of two-phase Darcy flow models to the combined VAG–HFV schemes. The efficiency of our approach is tested for single phase and immiscible two-phase Darcy flows on 3D meshes using a combination of the HFV and VAG discretizations as well as for non-isothermal compositional liquid gas Darcy flows on a vertical 2D cross-section of the Bouillante geothermal reservoir (Guadeloupe) using a combination of the TPFA and VAG discretizations.

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Section: Combined Vag-hfv Discretization Of Non-isothermal Compositiomentioning

confidence: 99%

Section: Combined Vag-hfv Discretization Of Non-isothermal Compositiomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems

et al. 2019

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“…Our choice of the formulation of the compositional model is based on [38]. Like the Coats' formulation [39,40,41,22], it uses the phase pressures, phase saturations and phase molar fractions as set of principal unknowns.…”

Section: Introductionmentioning

confidence: 99%

“…The remaining of this article is outlined as follows. Section 2 describes the mf nonlinear hybrid-dimensional model using the formulation of the compositional two-phase Darcy flow introduced in [38]. Section 3 details the TPFA discretization of the hybrid-dimensional model including the definition of the porous volumes, the accumulation terms, the Darcy and Fick fluxes, as well as the thermodynamical equilibrium closure equations based on the complementary constraints.…”

Section: Introductionmentioning

confidence: 99%

A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

Aghili

Dreuzy

Masson

et al. 2021

Journal of Computational Physics

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes–Darcy flow problems

2023

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Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes–Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy’s law in the porous-medium domain and the classical interface conditions across the fluid–porous interface including the conservation of mass, the balance of normal forces and the Beavers–Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers–Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indices on the aMR-PC expansion and conduct the corresponding numerical simulations.

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Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations

Cited by 14 publications

References 34 publications

Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems

Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems

A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes–Darcy flow problems

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