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

Chen, Huangxin; Sun, Shuyu

doi:10.1016/j.cam.2020.113035

Cited by 12 publications

(5 citation statements)

References 61 publications

(71 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the MSD model demands that the local mass conservation law holds for both phases. To guarantee the local mass conservation law for both phases, the upwind strategy for mobilities has been applied in References 13, 58‐60. However, the upwind mobilities could destroy Onsager's reciprocal principle.…”

Section: Introductionmentioning

confidence: 99%

“…For simulations of various scientific and engineering problems, the positivity preserving numerical methods are often strongly recommended to guarantee the physical reasonability of numerical solutions 5‐7,20,41,59‐70 . There have been several excellent approaches to devise such schemes, such as the nonlinear convex splitting approach, 41,61,62 the cut‐off approach, 63 the post‐processing approach, 70 the variational approach, 5,64 and the Lagrange multiplier approach, 67,68 and we refer to References 67, 68 for a up‐to‐date review on the existing approaches.…”

Section: Introductionmentioning

confidence: 99%

“…For simulations of various scientific and engineering problems, the positivity preserving numerical methods are often strongly recommended to guarantee the physical reasonability of numerical solutions. [5][6][7]20,41,[59][60][61][62][63][64][65][66][67][68][69][70] There have been several excellent approaches to devise such schemes, such as the nonlinear convex splitting approach, 41,61,62 the cut-off approach, 63 the post-processing approach, 70 the variational approach, 5,64 and the Lagrange multiplier approach, 67,68 and we refer to References 67, 68 for a up-to-date review on the existing approaches. Nevertheless, the MSD model has the high nonlinearity and fully coupling relationship between pressure and saturations, so it remains quite challenging to preserve this property while ensuring the other key physical properties.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media

Kou

Chen

et al. 2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Numerical modeling of two-phase flow in porous media has extensive applications in subsurface flow and petroleum industry. A comprehensive Maxwell-Stefan-Darcy (MSD) two-phase flow model has been developedrecently, which takes into consideration the friction between two phases by a thermodynamically consistent way. In this article, we for the first time propose an efficient energy stable numerical method for the MSD model, which can preserve multiple important physical properties of the model. First, the proposed scheme can preserve the original energy dissipation law. This is achieved through a newly-developed energy factorization approach that leads to linear semi-implicit discrete chemical potentials. Second, the scheme preserves the famous Onsager's reciprocal principle and the local mass conservation law for both phases by introducing different upwind strategies for two phase saturations and applying the cell-centered finite volume method to the original formulation of the model. Third, by introducing two auxiliary phase velocities, the scheme has ability to guarantee the positivity of both saturations under proper conditions. Another distinct feature of the scheme is that the resulting discrete system is totally linear, well-posed and unbiased for each phase. Numerical results are also provided to show the excellent performance of the proposed scheme. K E Y W O R D S energy stability, Maxwell-Stefan-Darcy model, Onsager's reciprocal principle, two-phase flow in porous media 546

show abstract

Section: Introductionmentioning

confidence: 99%

“…For simulations of various scientific and engineering problems, the positivity preserving numerical methods are often strongly recommended to guarantee the physical reasonability of numerical solutions 5‐7,20,41,59‐70 . There have been several excellent approaches to devise such schemes, such as the nonlinear convex splitting approach, 41,61,62 the cut‐off approach, 63 the post‐processing approach, 70 the variational approach, 5,64 and the Lagrange multiplier approach, 67,68 and we refer to References 67, 68 for a up‐to‐date review on the existing approaches.…”

Section: Introductionmentioning

confidence: 99%

“…For simulations of various scientific and engineering problems, the positivity preserving numerical methods are often strongly recommended to guarantee the physical reasonability of numerical solutions. [5][6][7]20,41,[59][60][61][62][63][64][65][66][67][68][69][70] There have been several excellent approaches to devise such schemes, such as the nonlinear convex splitting approach, 41,61,62 the cut-off approach, 63 the post-processing approach, 70 the variational approach, 5,64 and the Lagrange multiplier approach, 67,68 and we refer to References 67, 68 for a up-to-date review on the existing approaches. Nevertheless, the MSD model has the high nonlinearity and fully coupling relationship between pressure and saturations, so it remains quite challenging to preserve this property while ensuring the other key physical properties.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media

Kou

Chen

et al. 2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…The applications of nonlocal models have been reported in various research areas, such as groundwater flow in heterogeneous porous media [5], heat conduction in composite materials [6], and the deformations of heterogeneous materials [7]. Numerical discretization of a traditional local model usually yields many degrees of freedom, which leads to excessive calculations and increases the computational complexity, despite providing low accuracy [8,9]. Therefore, nonlocal models have been proposed to facilitate numerical analysis [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A Nonlocal Fractional Peridynamic Diffusion Model

et al. 2021

View full text Add to dashboard Cite

This paper proposes a nonlocal fractional peridynamic (FPD) model to characterize the nonlocality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the peridynamic (PD) model. The main idea is to use the fractional Euler–Lagrange formula to establish a peridynamic anomalous diffusion model, in which the classical exponential kernel function is replaced by using a power-law kernel function. Fractional Taylor series expansion was used to construct a fractional peridynamic differential operator method to complete the above model. To explore the properties of the FPD model, the FDM, the PD model and the FPD model are dissected via numerical analysis on a diffusion process in complex media. The FPD model provides a generalized model connecting a local model and a nonlocal model for physical systems. The fractional peridynamic differential operator (FPDDO) method provides a simple and efficient numerical method for solving fractional derivative equations.

show abstract

“…Numerical simulation for subsurface flows has been extensively applied in industry, such as in the management of groundwater energy and waste pollutants, petroleum engineering, and exploitation of geothermal energy [1][2][3][4][5][6][7][8][9][10][11][12][13]. The main numerical methods in the simulation include the Fully Implicit scheme (FI) [14][15][16][17] and the IMplicit EXplicit scheme (IMEX) [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media

et al. 2021

Self Cite

View full text Add to dashboard Cite

In this work, an improved IMplicit Pressure and Explicit Saturation (IMPES) scheme is proposed to solve the coupled partial differential equations to simulate the three-phase flows in subsurface porous media. This scheme is the first IMPES algorithm for the three-phase flow problem that is locally mass conservative for all phases. The key technique of this novel scheme relies on a new formulation of the discrete pressure equation. Different from the conventional scheme, the discrete pressure equation in this work is obtained by adding together the discrete conservation equations of all phases, thus ensuring the consistency of the pressure equation with the three saturation equations at the discrete level. This consistency is important, but unfortunately it is not satisfied in the conventional IMPES schemes. In this paper, we address and fix an undesired and well-known consequence of this inconsistency in the conventional IMPES in that the computed saturations are conservative only for two phases in three-phase flows, but not for all three phases. Compared with the standard IMPES scheme, the improved IMPES scheme has the following advantages: firstly, the mass conservation of all the phases is preserved both locally and globally; secondly, it is unbiased toward all phases, i.e., no reference phases need to be chosen; thirdly, the upwind scheme is applied to the saturation of all phases instead of only the referenced phases; fourthly, numerical stability is greatly improved because of phase-wise conservation and unbiased treatment. Numerical experiments are also carried out to demonstrate the strength of the improved IMPES scheme.

show abstract

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

Cited by 12 publications

References 61 publications

An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media

An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media

A Nonlocal Fractional Peridynamic Diffusion Model

Improved IMPES Scheme for the Simulation of Incompressible Three-Phase Flows in Subsurface Porous Media

Contact Info

Product

Resources

About