Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

Devloo, Philippe R.B.; Teng, Wenchao; Zhang, Chen-Song

doi:10.32604/cmes.2019.04812

Cited by 9 publications

(8 citation statements)

References 27 publications

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“…Since it is possible to combine discrete models with multiscale methods [49,50,51,52], the final goal of the improved MRCM proposed here is to allow a unified treatment of fractured karst reservoirs in which the modeling of the fractures is shared, depending on the fracture's size, between the volumetric grid and the discrete models. For this reason, we consider here permeability fields containing multiple narrow and relatively straight features (channels, barriers) that mimic the largest structures of a fractured porous medium, and refer to them as "fractured-like" fields.…”

Section: Introductionmentioning

confidence: 99%

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

Rocha,

Sousa,

Ausas

et al. 2021

Preprint

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It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability) and barriers (low permeability) for flows in heterogeneous porous media. We propose here new interface spaces, which are based on physics, to deal with permeability fields in the simultaneous presence of fractures and barriers, accommodated respectively, by the pressure and flux spaces. Existing multiscale methods based on mixed formulations can take advantage of the proposed interface spaces, however, in order to present and test our results, we use the newly developed Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], which generalizes most well-known multiscale mixed methods, and allows for the independent choice of the pressure and flux interface spaces. An adaptive version of the MRCM [Rocha, et al., J. Comput. Phys., 409 (2020), 109316] is considered that automatically selects the physics-based pressure space for fractured structures and the physics-based flux space for regions with barriers, resulting in a procedure

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Section: Introductionmentioning

confidence: 99%

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

Rocha,

Sousa,

Ausas

et al. 2021

Preprint

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“…For instance, numerical verification tests presented in [18] revealed locally conservative, robust, and accurate results for the simulation of 2D and 3D Darcy's problems. These properties have also been demonstrated by MHM-H(div) flow simulations in 2D porous media with fractures [34], showing flexibility in the enforcement of the required coupling of two-dimensional matrix flow with the one-dimensional fracture flow. Moreover, the MHM-H(div) method can also be coupled with geomechanical deformations [35], where the elastic material properties are defined at the fine geocellular scales.…”

Section: Introductionmentioning

confidence: 73%

A multiscale mixed finite element method applied to the simulation of two-phase flows

Durán

Devloo

Gomes

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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The multiscale hybrid mixed finite element method (MHM-H(div)), previously developed for Darcy's problems, is extended for coupled flow/pressure and transport system of two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is combined with an implicit transport solver in a sequential fully implicit (SFI) manner. The MHM-H(div) method is designed to cope with the complex geometry and inherent multiscale nature of the phenomena. The discretizations are based on a general domain partition formed by polyhedral subregions, where a hierarchy of meshes and approximation spaces are considered. The multiscale approach is applied to the flux/pressure kernel making use of coarse scale normal fluxes between subregions (trace variable). The fine-scale features inside each subregion are determined by resolving completely independent local Neumann problems, the boundary conditions being set by the trace variable, by the mixed finite element method using fine flux and pressure representations. These properties imply that the MHM-H(div) can be interpreted as a classical mixed formulation of the model problem in the whole domain, based on a H(div)conforming space with normal components over the macro-partition interfaces constrained by the trace space, and showing divergence compatibility with the pressure space. Consequently, local mass conservation is observed at the micro-scale elements inside the subregions, an essential property for flows in heterogeneous media, and divergence-free constraint strongly enforced for incompressible flows. The efficient use of static condensation leads to a global system to be solved only in terms of primary degrees of freedom associated with the trace variable and of a piecewise constant pressure for each subregion. This procedure allows a substantial reduction of the dominant computational costs associated with the flux/pressure kernel embedded in the numerical model. An iterative coupling technique is adopted to solve the two-phase flow equations using a shared integration point memory implementation model. At each SFI time step, the efficiency iterative method for the transport equations is improved using a Quasi-Newton method with a simple but effective nonlinear acceleration. The numerical examples show that the proposed scheme is able to solve challenging coupled flow and transport problems.

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“…Since it is possible to combine discrete models with multiscale methods (BOSMA et al, 2017;TENG;ZHANG, 2019;XIA et al, 2018), the final goal of the improved MRCM proposed here is to allow a unified treatment of fractured karst reservoirs in which the modeling of the fractures is shared, depending on the fracture's size, between the volumetric grid and the discrete models. For this reason, we consider here permeability fields containing multiple narrow and relatively straight features (channels, barriers) that mimic the largest structures of a fractured porous medium.…”

Section: Chapter 4 Interface Spaces Based On Physicsmentioning

confidence: 99%

Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

Rocha¹

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Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

Cited by 9 publications

References 27 publications

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media

A multiscale mixed finite element method applied to the simulation of two-phase flows

Enhanced multiscale mixed methods for two-phase flows in high-contrast porous media

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