An implicit numerical model for multicomponent compressible two-phase flow in porous media

Zidane, Ali; Firoozabadi, Abbas

doi:10.1016/j.advwatres.2015.09.006

Cited by 28 publications

(7 citation statements)

References 31 publications

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“…Finite element and extended-finite element (XFEM) methods for embedded fractures into non-conforming meshes are presented in [21][22][23]. Mixed hybridized finite-element (MHFE) and discontinous Galerkin (DG) methods [10] are presented for multicomponent compressible flow in [24][25][26][27]. Other recent methods for discrete fracture model simulations include the mimetic finite-difference method [28] and the vertex-approximate-gradient (VAG) method [29,30].…”

Section: Introductionmentioning

confidence: 99%

CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations

Ahmed

Edwards

Lamine

et al. 2017

Journal of Computational Physics

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Two novel control-volume methods are presented for flow in fractured media, and involve coupling the controlvolume distributed multi-point flux approximation (CVD-MPFA) constructed with full pressure support (FPS), to two types of discrete fracture-matrix approximation for simulation on unstructured grids; (i) involving hybrid grids and (ii) a lower dimensional fracture model. Flow is governed by Darcy's law together with mass conservation both in the matrix and the fractures, where large discontinuities in permeability tensors can occur. Finite-volume FPS schemes are more robust than the earlier CVD-MPFA triangular pressure support (TPS) schemes for problems involving highly anisotropic homogeneous and heterogeneous full-tensor permeability fields. We use a cell-centred hybrid-grid method, where fractures are modelled by lower-dimensional interfaces between matrix cells in the physical mesh but expanded to equi-dimensional cells in the computational domain. We present a simple procedure to form a consistent hybrid-grid locally for a dual-cell. We also propose a novel hybrid-grid for intersecting fractures, for the FPS method, which reduces the condition number of the global linear system and leads to larger time steps for tracer transport. The transport equation for tracer flow is coupled with the pressure equation and provides flow parameter assessment of the fracture models. Transport results obtained via TPS and FPS hybrid-grid formulations are compared with the corresponding results of fine-scale explicit equi-dimensional formulations. The results show that the hybrid-grid FPS method applies to general full-tensor fields and provides improved robust approximations compared to the hybrid-grid TPS method for fractured domains, for both weakly anisotropic permeability fields and very strong anisotropic full-tensor permeability fields where the TPS scheme exhibits spurious oscillations. The hybrid-grid FPS formulation is extended to compressible flow and the results demonstrate the method is also robust for transient flow. Furthermore, we present FPS coupled with a lower-dimensional fracture model, where fractures are strictly lower-dimensional in the physical mesh as well as in the computational domain. We present a comparison of the hybrid-grid FPS method and the lower-dimensional fracture model for several cases of isotropic and anisotropic fractured media which illustrate the benefits of the respective methods.

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Section: Introductionmentioning

confidence: 99%

CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations

Ahmed

Edwards

Lamine

et al. 2017

Journal of Computational Physics

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“…Various types of numerical methods have been developed in literature to simulate two-phase flow in porous media. The fully implicit scheme [5,18,19,44,59,52,66,60,61,62,63] implicitly solves all the unknowns, and it thus could lead to unconditional stability and mass conservation for both of phases. The fully implicit scheme may need large time step size during the simulation and the difficulty of simulation lies in the resolution of nonlinear complex systems.…”

Section: Introductionmentioning

confidence: 99%

A new physics-preserving IMPES scheme for incompressible and immiscible two-phase flow in heterogeneous porous media

Chen

Sun

2021

Journal of Computational and Applied Mathematics

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“…In [36], decoupled DG methods with interior penalties and upwinding schemes were applied to the original formulation while the pressure equation is obtained by summing the discretized conservation equations of two phases. It is believed that the most stable scheme for subsurface multi-phase flows is the fully implicit method in which all the coupled nonlinear equations are solved simultaneously [16,42,56,65]. The first attempt to combine the implicit Euler method with coupled DG schemes for 2D two-phase flows was demonstrated in [20,21].…”

Section: Introductionmentioning

confidence: 99%

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

Luo

Liu

Cai

et al. 2020

Journal of Computational Physics

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An implicit numerical model for multicomponent compressible two-phase flow in porous media

Cited by 28 publications

References 31 publications

CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations

CVD-MPFA full pressure support, coupled unstructured discrete fracture–matrix Darcy-flux approximations

A new physics-preserving IMPES scheme for incompressible and immiscible two-phase flow in heterogeneous porous media

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids

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