A comparative study of explicit high-resolution schemes for compositional simulations

Mojtaba Moshiri, Mehrdad T Manzari

Research output: Contribution to journalArticle

1 Citation (Scopus)
5 Downloads (Pure)

Abstract

In this paper, compositional flow of two- and three-phase
fluids in one dimensional porous media is studied numerically and a comparison is made between several upwind and central numerical schemes.
Implicit Pressure Explicit Composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly while the mass conservation equations are solved explicitly using different Upwind (UPW) and Central (CEN) numerical schemes. These include Classical Upwind (UPW-CLS), Flux-based Decomposition Upwind (UPW-FLX), Variable-based Decomposition Upwind (UPW-VAR), Roe's Upwind (UPW-ROE), Local Lax Friedrichs (CEN-LLF), Dominant
Wave (CEN-DW), Harten-Lax-van Leer (HLL), and newly proposed Modied Dominant Wave (CEN-MDW)
schemes. To achieve higher resolution, high-order data generated by either MUSCL or WENO reconstructions
are utilized.
It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme utilizes most of the information in
flux function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e., degenerate, umbilic, and elliptic points, which require to apply correction procedures to produce physically acceptable (entropy) solutions.
This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids while gravity and capillary effects are neglected.
The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.
A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.
Original languageEnglish
Pages (from-to)94-131
Number of pages38
JournalInternational Journal of Numerical Methods for Heat & Fluid Flow
Volume29
Issue number1
DOIs
Publication statusPublished - 31 Jan 2019

Fingerprint

High-resolution Schemes
Explicit Scheme
Comparative Study
Central Schemes
Porous materials
Simulation
Decomposition
Numerical Scheme
Multiphase flow
Flow in Porous Media
Computational efficiency
Compressibility
Costs
Conservation
Gravitation
Entropy
Solubility
Computational Cost
Fluxes
Fluids

Keywords

  • compositional
  • porous media
  • conservation laws
  • MUSCL
  • WENO
  • wave structure
  • Conservation laws
  • Porous media
  • Wave structure
  • Compositional
  • WENO SCHEMES
  • GENERAL SYSTEMS
  • DECOMPOSITION
  • 2-PHASE
  • PART II
  • RIEMANN PROBLEM
  • 3-PHASE FLOW
  • ONE-DIMENSION
  • CONSERVATION
  • 4-COMPONENT GAS/WATER/OIL DISPLACEMENTS

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics
  • Computer Science Applications

Cite this

A comparative study of explicit high-resolution schemes for compositional simulations. / Moshiri, Mojtaba; Manzari, Mehrdad T.

In: International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29, No. 1, 31.01.2019, p. 94-131.

Research output: Contribution to journalArticle

@article{e8c12636073f42fca56d751007946644,
title = "A comparative study of explicit high-resolution schemes for compositional simulations",
abstract = "In this paper, compositional flow of two- and three-phasefluids in one dimensional porous media is studied numerically and a comparison is made between several upwind and central numerical schemes.Implicit Pressure Explicit Composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly while the mass conservation equations are solved explicitly using different Upwind (UPW) and Central (CEN) numerical schemes. These include Classical Upwind (UPW-CLS), Flux-based Decomposition Upwind (UPW-FLX), Variable-based Decomposition Upwind (UPW-VAR), Roe's Upwind (UPW-ROE), Local Lax Friedrichs (CEN-LLF), DominantWave (CEN-DW), Harten-Lax-van Leer (HLL), and newly proposed Modied Dominant Wave (CEN-MDW)schemes. To achieve higher resolution, high-order data generated by either MUSCL or WENO reconstructionsare utilized.It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme utilizes most of the information influx function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e., degenerate, umbilic, and elliptic points, which require to apply correction procedures to produce physically acceptable (entropy) solutions.This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids while gravity and capillary effects are neglected.The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.",
keywords = "compositional, porous media, conservation laws, MUSCL, WENO, wave structure, Conservation laws, Porous media, Wave structure, Compositional, WENO SCHEMES, GENERAL SYSTEMS, DECOMPOSITION, 2-PHASE, PART II, RIEMANN PROBLEM, 3-PHASE FLOW, ONE-DIMENSION, CONSERVATION, 4-COMPONENT GAS/WATER/OIL DISPLACEMENTS",
author = "Mojtaba Moshiri and Manzari, {Mehrdad T}",
year = "2019",
month = "1",
day = "31",
doi = "10.1108/HFF-08-2017-0333",
language = "English",
volume = "29",
pages = "94--131",
journal = "International Journal of Numerical Methods for Heat & Fluid Flow",
issn = "0961-5539",
publisher = "Emerald Group Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - A comparative study of explicit high-resolution schemes for compositional simulations

AU - Moshiri, Mojtaba

AU - Manzari, Mehrdad T

PY - 2019/1/31

Y1 - 2019/1/31

N2 - In this paper, compositional flow of two- and three-phasefluids in one dimensional porous media is studied numerically and a comparison is made between several upwind and central numerical schemes.Implicit Pressure Explicit Composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly while the mass conservation equations are solved explicitly using different Upwind (UPW) and Central (CEN) numerical schemes. These include Classical Upwind (UPW-CLS), Flux-based Decomposition Upwind (UPW-FLX), Variable-based Decomposition Upwind (UPW-VAR), Roe's Upwind (UPW-ROE), Local Lax Friedrichs (CEN-LLF), DominantWave (CEN-DW), Harten-Lax-van Leer (HLL), and newly proposed Modied Dominant Wave (CEN-MDW)schemes. To achieve higher resolution, high-order data generated by either MUSCL or WENO reconstructionsare utilized.It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme utilizes most of the information influx function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e., degenerate, umbilic, and elliptic points, which require to apply correction procedures to produce physically acceptable (entropy) solutions.This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids while gravity and capillary effects are neglected.The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.

AB - In this paper, compositional flow of two- and three-phasefluids in one dimensional porous media is studied numerically and a comparison is made between several upwind and central numerical schemes.Implicit Pressure Explicit Composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly while the mass conservation equations are solved explicitly using different Upwind (UPW) and Central (CEN) numerical schemes. These include Classical Upwind (UPW-CLS), Flux-based Decomposition Upwind (UPW-FLX), Variable-based Decomposition Upwind (UPW-VAR), Roe's Upwind (UPW-ROE), Local Lax Friedrichs (CEN-LLF), DominantWave (CEN-DW), Harten-Lax-van Leer (HLL), and newly proposed Modied Dominant Wave (CEN-MDW)schemes. To achieve higher resolution, high-order data generated by either MUSCL or WENO reconstructionsare utilized.It was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme utilizes most of the information influx function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e., degenerate, umbilic, and elliptic points, which require to apply correction procedures to produce physically acceptable (entropy) solutions.This paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids while gravity and capillary effects are neglected.The proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.A new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.

KW - compositional

KW - porous media

KW - conservation laws

KW - MUSCL

KW - WENO

KW - wave structure

KW - Conservation laws

KW - Porous media

KW - Wave structure

KW - Compositional

KW - WENO SCHEMES

KW - GENERAL SYSTEMS

KW - DECOMPOSITION

KW - 2-PHASE

KW - PART II

KW - RIEMANN PROBLEM

KW - 3-PHASE FLOW

KW - ONE-DIMENSION

KW - CONSERVATION

KW - 4-COMPONENT GAS/WATER/OIL DISPLACEMENTS

UR - http://www.scopus.com/inward/record.url?scp=85057627763&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/comparative-study-explicit-highresolution-schemes-compositional-simulations

U2 - 10.1108/HFF-08-2017-0333

DO - 10.1108/HFF-08-2017-0333

M3 - Article

VL - 29

SP - 94

EP - 131

JO - International Journal of Numerical Methods for Heat & Fluid Flow

JF - International Journal of Numerical Methods for Heat & Fluid Flow

SN - 0961-5539

IS - 1

ER -