Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

Feng, Xiaobing; Masson, Roland; López, Simón

doi:10.1016/j.jcp.2017.05.043

Cited by 11 publications

(26 citation statements)

References 41 publications

(114 reference statements)

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“…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]. The HFV discretization of isothermal two component two-phase Darcy flows is also derived in [3] and the related Mixed-Hybrid Finite Element discretization of three-phase Darcy flows in [2].…”

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

confidence: 99%

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%

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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“…This section recalls, in the particular case of a non-isothermal single-component single-phase Darcy flow model, the hybrid-dimensional model introduced in [42].…”

Section: Hybrid-dimensional Non-isothermal Single-phase Discrete Fracmentioning

confidence: 99%

“…To focus on the implementation aspects related to well modeling, the physics of the fluid is kept relatively simple and we refer to [42] for a compositional multiphase non-isothermal modeling of reservoir flow. The fluid is monophasic and is described by its thermodynamical variables X = (P, T ) where P is the pressure and T the temperature.…”

Section: Non-isothermal Single-phase Flow Modelmentioning

confidence: 99%

“…This has motivated the development of a new geothermal simulator based on unstructured meshes and adapted to parallel distributed architectures with the ability to represent fractures as co-dimension 1 surfaces connected to the surrounding matrix domain. The current version of this simulator is described in [42]. The objective of this Cemracs project is to bring the development of this simulator to a level where operational use is possible and real geothermal test cases can be considered.…”

Section: Introductionmentioning

confidence: 99%

“…In section 1, the hybrid-dimensional model presented in [42] is recalled. Although the implementation has been done for the multi-phase compositional model defined in [42], we focus here on the particular case of a non-isothermal single-component single-phase Darcy flow model in order to simplify the presentation. Section 2 introduces the space and time discretization of the model.…”

Section: Introductionmentioning

confidence: 99%

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Parallel Geothermal Numerical Model with Fractures and Multi-Branch Wells

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Brenner³

et al. 2018

ESAIM: ProcS

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To answer the need for an efficient and robust geothermal simulation tool going beyond existing code capabilities in terms of geological and physical complexity, we have started to develop a parallel geothermal simulator based on unstructured meshes. The model takes into account complex geology including fault and fracture networks acting as major heat and mass transfer corridors and complex physics coupling the mass and energy conservations to the thermodynamic equilibrium between the gas and liquid phases. The objective of this Cemracs project was to focus on well modeling which is a key missing ingredient in our current simulator in order to perform realistic geothermal studies both in terms of monitoring and in terms of history matching. The well is discretized by a set of edges of the mesh in order to represent efficiently slanted or multi-branch wells on unstructured meshes. The connection with the 3D matrix and the 2D fracture network at each node of the well is accounted for using Peaceman’s approach. The non-isothermal flow model inside the well is based on the usual single unknown approach assuming the hydrostatic and thermodynamical equilibrium inside the well. The parallelization of the well model is implemented in such a way that the assembly of the Jacobian at each Newton step and the computation of the pressure drops inside the well can be done locally on each process without MPI communications.

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