Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

doi:10.1016/j.jcp.2017.12.003

Cited by 57 publications

(84 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thanks to this additional robustness and to the efficiency of nodal discretizations on tetrahedral meshes, the HU VAG scheme makes possible the simulation of large and highly heterogeneous DFM models as exhibited in the numerical section. In perspective, we plan to investigate the efficiency of the HU VAG scheme for the simulation of two-phase Darcy flow discontinuous pressure DFM models accounting for fractures acting both as barrier or drains for which the PPU VAG scheme has been introduced in [14].…”

Section: Discussionmentioning

confidence: 99%

“…These discontinuities play a major role and should be accurately captured in many important processes such as capillary driven imbibition in oil recovery or capillary barrier effects in oil migration and gas storage. This is particularly enhanced in the case of Discrete Fracture Matrix (DFM) models which exhibit highly contrasted permeabilities and capillary pressure curves between the fracture network and the surrounding matrix domains [9,35,42,38,34,12,13,2,31,14,1,3,45,4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media

Brenner

Masson

Quenjel

2020

Journal of Computational Physics

View full text Add to dashboard Cite

In this article, a new nodal discretization is proposed for two-phase Darcy flows in heterogeneous porous media. The scheme combines the Vertex Approximate Gradient (VAG) scheme for the approximation of the gradient fluxes with an Hybrid Upwind (HU) approximation of the mobility terms in the saturation equation. The discretization in space incorporates naturally nodal interface degrees of freedom (d.o.f.) allowing to capture the transmission conditions at the interface between different rock types for general capillary pressure curves. It is shown to guarantee the physical bounds for the saturation unknowns as well as a nonnegative lower bound on the capillary energy flux term. Numerical experiments on several test cases exhibit that the scheme is more robust compared with previous approaches allowing the simulation of 3D large Discrete Fracture Matrix (DFM) models. 1 discretizations like the Mixed Hybrid Finite Element (MHFE) method [34,2] or the Hybrid Finite Volume scheme [1]. The additional asset of nodal discretizations compared with cell centered discretizations is to include d.o.f. at rock type interfaces as long as the mesh is conforming with the heterogeneities of the porous medium. These nodal pressures and saturations unknowns will be used to enforce the Darcy normal flux continuity equations combined with the saturation jump condition [16,11,27]. In this work, we will consider the Vertex Approximate Gradient (VAG) discretization developed in [27,12,13] for two-phase Darcy flows in heterogeneous media. The VAG scheme is based on nodal d.o.f. like Control Volume Finite Element (CVFE) methods but it also includes the cell d.o.f. which are eliminated at the linear algebra level at each Newton iteration without any fill-in. These cell d.o.f. provide an additional flexibility in the choice of the control volumes in order to avoid mixing different rock types at nodal control volumes. It has been shown in [27] to be more accurate than usual CVFE discretizations.The time integration will be chosen implicit to avoid severe time step restrictions in high velocity regions such as fractures. It will be also fully coupled to account for the strong coupling between the pressure and saturation unknowns in the transmission conditions at different rock type interfaces. As noticed in [5], the pressure and saturation unknowns cannot be decoupled at such different rock type interfaces to preserve the stability of the discretization.The selected numerical method should also provide a robust nonlinear convergence of the Newton type solver to allow for large time steps, typically at the time scale of the matrix in DFM simulations. Let us refer to [41,37] for alternative linearization schemes to the Newton method which aim to the improvement of the nonlinear solver. In this work, the additional nonlinear solver robustness will be first achieved by extension of the Hybrid Upwind (HU) transport scheme to the VAG discretization framework. The HU transport scheme has been introduced in [24,28] as an alternative to the Phase Pot...

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media

Brenner

Masson

Quenjel

2020

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…An alternative approach is proposed in [31] for two-phase flows in order to capture the jump of the saturations at the matrix fracture interface Γ due to discontinuous capillary pressure curves. These two choices are compared in [32] to a reference solution provided by an equi-dimensional model in the fractures. It is shown that the second choice provides a better solution as long as the matrix acts as a barrier since it captures the saturation jump.…”

Section: Hybrid-dimensional Compositional Non-isothermal Darcy Flow Mmentioning

confidence: 99%

“…They could be included following the usual phase based upwinding approach as in [25] or recent ideas developed in [31] for two-phase flows. Let us refer to [32] for a comparison of both approaches in the case of an immiscible two-phase flow using a reference solution provided by the equi-dimensional model in the fractures. All the underlying assumptions of our reduced model will be carefully stated.…”

Section: Introductionmentioning

confidence: 99%

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

Feng

Masson

López

2017

Journal of Computational Physics

View full text Add to dashboard Cite

International audienceThis paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence

show abstract

“…This approach has been successfully applied to different kind of physics, ranging from advection of a passive scalar, heat transport, multi-phase flow. An incomplete list of references is the following [31,35,23,3,32,26,12,19,18,33,22,37,30,38,13,1,10,27,8,4,39,17,7,9,34].…”

Section: Introductionmentioning

confidence: 99%

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

Fumagalli

Scotti

2020

Comput Geosci

View full text Add to dashboard Cite

In this work we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structure where the high strain core is surrounded by the so called damage zones, characterized by the presence of smaller fractures which enhance the permeability of the medium. To obtain reliable simulation outcomes these damage zone, as well as the fault, have to be accurately described. The new model proposed in this work considers both these two regions as lower dimensional and embedded in the rock matrix. The model is presented, analyzed, and tested in several configurations to prove its robustness and ability to capture many important features, such as hight contrast and heterogeneity of permeability.

show abstract

Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

Cited by 57 publications

References 35 publications

Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media

Vertex Approximate Gradient discretization preserving positivity for two-phase Darcy flows in heterogeneous porous media

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

A multi-layer reduced model for flow in porous media with a fault and surrounding damage zones

Contact Info

Product

Resources

About