Solution and upscaling of compositional and immiscible displacements in composite media

Sathish K. Subramanian, Russell T. Johns, Birol Dindoruk

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The scale of heterogeneities in reservoirs is often smaller than the grid size used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the grid size in flow simulations. Thus, systems with fractional flow heterogeneities, i.e. relative permeability variations, have to be solved and effective relative permeability functions determined. In this paper, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different set of relative permeabilities, residual saturations and porosities. The analytical solutions show a significant discontinuity in the saturation and concentration profiles at the interface of the two media. Numerical results using several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture the discontinuity at the interface, whereas third-order TVD weighting requires much fewer. Lastly, the validity of the JBN method and harmonic averaging for determination of effective relative permeabilities and overall pressure drop is tested. Both the JBN method and harmonic averaging cannot reproduce the pressure drop across the composite media prior to water breakthrough.

Original languageEnglish (US)
Pages (from-to)287-291
Number of pages5
JournalPetroleum Geoscience
Volume5
Issue number3
DOIs
StatePublished - Aug 1999

Fingerprint

upscaling
Pressure drop
permeability
Flow simulation
Composite materials
Flow of fluids
pressure drop
Porosity
discontinuity
Water
saturation
simulation
fluid flow
porosity
water
method

All Science Journal Classification (ASJC) codes

  • Fuel Technology
  • Geology
  • Geochemistry and Petrology
  • Economic Geology
  • Earth and Planetary Sciences (miscellaneous)

Cite this

Subramanian, Sathish K. ; Johns, Russell T. ; Dindoruk, Birol. / Solution and upscaling of compositional and immiscible displacements in composite media. In: Petroleum Geoscience. 1999 ; Vol. 5, No. 3. pp. 287-291.
@article{ab6a3be5a1544a64afaa7ba6435db61e,
title = "Solution and upscaling of compositional and immiscible displacements in composite media",
abstract = "The scale of heterogeneities in reservoirs is often smaller than the grid size used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the grid size in flow simulations. Thus, systems with fractional flow heterogeneities, i.e. relative permeability variations, have to be solved and effective relative permeability functions determined. In this paper, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different set of relative permeabilities, residual saturations and porosities. The analytical solutions show a significant discontinuity in the saturation and concentration profiles at the interface of the two media. Numerical results using several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture the discontinuity at the interface, whereas third-order TVD weighting requires much fewer. Lastly, the validity of the JBN method and harmonic averaging for determination of effective relative permeabilities and overall pressure drop is tested. Both the JBN method and harmonic averaging cannot reproduce the pressure drop across the composite media prior to water breakthrough.",
author = "Subramanian, {Sathish K.} and Johns, {Russell T.} and Birol Dindoruk",
year = "1999",
month = "8",
doi = "10.1144/petgeo.5.3.287",
language = "English (US)",
volume = "5",
pages = "287--291",
journal = "Petroleum Geoscience",
issn = "1354-0793",
publisher = "Geological Society of London",
number = "3",

}

Solution and upscaling of compositional and immiscible displacements in composite media. / Subramanian, Sathish K.; Johns, Russell T.; Dindoruk, Birol.

In: Petroleum Geoscience, Vol. 5, No. 3, 08.1999, p. 287-291.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Solution and upscaling of compositional and immiscible displacements in composite media

AU - Subramanian, Sathish K.

AU - Johns, Russell T.

AU - Dindoruk, Birol

PY - 1999/8

Y1 - 1999/8

N2 - The scale of heterogeneities in reservoirs is often smaller than the grid size used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the grid size in flow simulations. Thus, systems with fractional flow heterogeneities, i.e. relative permeability variations, have to be solved and effective relative permeability functions determined. In this paper, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different set of relative permeabilities, residual saturations and porosities. The analytical solutions show a significant discontinuity in the saturation and concentration profiles at the interface of the two media. Numerical results using several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture the discontinuity at the interface, whereas third-order TVD weighting requires much fewer. Lastly, the validity of the JBN method and harmonic averaging for determination of effective relative permeabilities and overall pressure drop is tested. Both the JBN method and harmonic averaging cannot reproduce the pressure drop across the composite media prior to water breakthrough.

AB - The scale of heterogeneities in reservoirs is often smaller than the grid size used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the grid size in flow simulations. Thus, systems with fractional flow heterogeneities, i.e. relative permeability variations, have to be solved and effective relative permeability functions determined. In this paper, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different set of relative permeabilities, residual saturations and porosities. The analytical solutions show a significant discontinuity in the saturation and concentration profiles at the interface of the two media. Numerical results using several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture the discontinuity at the interface, whereas third-order TVD weighting requires much fewer. Lastly, the validity of the JBN method and harmonic averaging for determination of effective relative permeabilities and overall pressure drop is tested. Both the JBN method and harmonic averaging cannot reproduce the pressure drop across the composite media prior to water breakthrough.

UR - http://www.scopus.com/inward/record.url?scp=0033178198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033178198&partnerID=8YFLogxK

U2 - 10.1144/petgeo.5.3.287

DO - 10.1144/petgeo.5.3.287

M3 - Article

AN - SCOPUS:0033178198

VL - 5

SP - 287

EP - 291

JO - Petroleum Geoscience

JF - Petroleum Geoscience

SN - 1354-0793

IS - 3

ER -