skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effective Pressure Law for the Intrinsic Formation Factor in Low Permeability Sandstones: EPL law for the formation factor

Abstract

The effective pressure law for the intrinsic formation factor of low permeability sandstones from the Ordos Basin (northwest of China) was studied experimentally by measuring the electrical resistivity of brine saturated rock samples while cycling the pore and confining pressures, pp and pc. We used a 100,000 ppm NaCl solution so that the results could be directly interpreted in terms of the intrinsic formation factor F. The Response Surface method was used to construct a quadratic function of pp and pc fitting the experimental data, from which the coefficient α of the effective pressure law, peff = pc – αpp, was determined. We found that the coefficient α generally had low values, mainly from 0.2 to 0.4, thus contradicting the theoretical prediction that α should be equal to 1 for scale-invariant properties, such as F, in linear elastic materials having a homogeneous solid matrix. Since the two underlying assumptions, linear elasticity and homogeneity of the solid matrix, are likely violated in reservoir rocks, we tried to assess their effects on α using simple analytical models, based on idealized geometries of the pore and solid phases. Analysis of these models suggests that non-linear elasticity associated with the formation of solid–solid contactsmore » in the compressed rocks (e.g., during closure of rough cracks or crack-like pores along the grain boundaries), may be more effective in producing the low α values observed than inhomogeneity of the solid matrix.« less

Authors:
 [1]; ORCiD logo [1];  [2];  [1];  [1];  [1];  [1];  [1]
  1. Southwest Petroleum Univ., Chengdu (China)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1537222
Grant/Contract Number:  
FG02-97ER14760
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Geophysical Research. Solid Earth
Additional Journal Information:
Journal Volume: 122; Journal Issue: 11; Journal ID: ISSN 2169-9313
Publisher:
American Geophysical Union
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; Geochemistry & Geophysics

Citation Formats

Chen, M., Li, M., Bernabé, Y., Zhao, J. Z., Zhang, L. H., Zhang, Z. Y., Tang, Y. B., and Xiao, W. L. Effective Pressure Law for the Intrinsic Formation Factor in Low Permeability Sandstones: EPL law for the formation factor. United States: N. p., 2017. Web. doi:10.1002/2017jb014628.
Chen, M., Li, M., Bernabé, Y., Zhao, J. Z., Zhang, L. H., Zhang, Z. Y., Tang, Y. B., & Xiao, W. L. Effective Pressure Law for the Intrinsic Formation Factor in Low Permeability Sandstones: EPL law for the formation factor. United States. doi:10.1002/2017jb014628.
Chen, M., Li, M., Bernabé, Y., Zhao, J. Z., Zhang, L. H., Zhang, Z. Y., Tang, Y. B., and Xiao, W. L. Fri . "Effective Pressure Law for the Intrinsic Formation Factor in Low Permeability Sandstones: EPL law for the formation factor". United States. doi:10.1002/2017jb014628. https://www.osti.gov/servlets/purl/1537222.
@article{osti_1537222,
title = {Effective Pressure Law for the Intrinsic Formation Factor in Low Permeability Sandstones: EPL law for the formation factor},
author = {Chen, M. and Li, M. and Bernabé, Y. and Zhao, J. Z. and Zhang, L. H. and Zhang, Z. Y. and Tang, Y. B. and Xiao, W. L.},
abstractNote = {The effective pressure law for the intrinsic formation factor of low permeability sandstones from the Ordos Basin (northwest of China) was studied experimentally by measuring the electrical resistivity of brine saturated rock samples while cycling the pore and confining pressures, pp and pc. We used a 100,000 ppm NaCl solution so that the results could be directly interpreted in terms of the intrinsic formation factor F. The Response Surface method was used to construct a quadratic function of pp and pc fitting the experimental data, from which the coefficient α of the effective pressure law, peff = pc – αpp, was determined. We found that the coefficient α generally had low values, mainly from 0.2 to 0.4, thus contradicting the theoretical prediction that α should be equal to 1 for scale-invariant properties, such as F, in linear elastic materials having a homogeneous solid matrix. Since the two underlying assumptions, linear elasticity and homogeneity of the solid matrix, are likely violated in reservoir rocks, we tried to assess their effects on α using simple analytical models, based on idealized geometries of the pore and solid phases. Analysis of these models suggests that non-linear elasticity associated with the formation of solid–solid contacts in the compressed rocks (e.g., during closure of rough cracks or crack-like pores along the grain boundaries), may be more effective in producing the low α values observed than inhomogeneity of the solid matrix.},
doi = {10.1002/2017jb014628},
journal = {Journal of Geophysical Research. Solid Earth},
number = 11,
volume = 122,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics
journal, December 1942

  • Archie, G. E.
  • Transactions of the AIME, Vol. 146, Issue 01
  • DOI: 10.2118/942054-G

The effective pressure law for permeability in Chelmsford granite and Barre granite
journal, June 1986

  • Bernabe, Y.
  • International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 23, Issue 3
  • DOI: 10.1016/0148-9062(86)90972-1

Water sensitivity of sandstones containing swelling and non-swelling clays
journal, June 1993

  • Mohan, K. Krishna; Vaidya, Ravimadhav N.; Reed, Marion G.
  • Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 73
  • DOI: 10.1016/0927-7757(93)80019-B

Effect of pore pressure on the velocity of compressional waves in low-porosity rocks
journal, July 1972


Laboratory‐determined transport properties of Berea sandstone
journal, May 1985


Electrical conductivity of brine‐saturated fractured rock
journal, August 1986


CO2 rock physics as part of the Weyburn-Midale geological storage project
journal, June 2013

  • Njiekak, Gautier; Schmitt, Douglas R.; Yam, Helen
  • International Journal of Greenhouse Gas Control, Vol. 16
  • DOI: 10.1016/j.ijggc.2013.02.007

Exact effective-stress rules in rock mechanics
journal, September 1992


Comparison of the effective pressure law for permeability and resistivity formation factor in Chelmsford granite
journal, January 1988

  • Bernabe, Yves
  • Pure and Applied Geophysics PAGEOPH, Vol. 127, Issue 4
  • DOI: 10.1007/BF00881747

Continuum percolation theory and Archie's law
journal, January 2004


Clay mineral elastic properties
conference, March 2012

  • Katahara, Keith W.
  • SEG Technical Program Expanded Abstracts 1996
  • DOI: 10.1190/1.1826454

Measurements of elastic and electrical properties of an unconventional organic shale under differential loading
journal, July 2015


Effective stress law for the permeability of clay-rich sandstones: EFFECTIVE STRESS LAW FOR PERMEABILITY
journal, April 2004

  • Al-Wardy, Widad; Zimmerman, Robert W.
  • Journal of Geophysical Research: Solid Earth, Vol. 109, Issue B4
  • DOI: 10.1029/2003JB002836

Effect of pore pressure and confining pressure on fracture permeability
journal, October 1981

  • Walsh, J. B.
  • International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 18, Issue 5
  • DOI: 10.1016/0148-9062(81)90006-1

Effective stress law for the permeability of a limestone
journal, February 2009

  • Ghabezloo, Siavash; Sulem, Jean; Guédon, Sylvine
  • International Journal of Rock Mechanics and Mining Sciences, Vol. 46, Issue 2
  • DOI: 10.1016/j.ijrmms.2008.05.006

The equivalent channel model for permeability and resistivity in fluid-saturated rock—A re-appraisal
journal, December 1983


Constitutive equations for coupled flows in clay materials: COUPLED FLOWS IN CLAYS
journal, May 2011

  • Revil, A.; Woodruff, W. F.; Lu, N.
  • Water Resources Research, Vol. 47, Issue 5
  • DOI: 10.1029/2010WR010002

Effect of Overburden Pressure and the Nature and Microscopic Distribution of Fluids on Electrical Properties of Rock Samples
journal, June 1989

  • Longeron, D. G.; Argaud, M. J.; Feraud, J. -P.
  • SPE Formation Evaluation, Vol. 4, Issue 02
  • DOI: 10.2118/15383-PA

Effective-stress rules for pore-fluid transport in rocks containing two minerals
journal, December 1993

  • Berryman, J. G.
  • International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 30, Issue 7
  • DOI: 10.1016/0148-9062(93)90087-T

Pore Space Connectivity and the Transport Properties of Rocks
journal, June 2016

  • Bernabé, Yves; Li, Min; Tang, Yan-Bing
  • Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Vol. 71, Issue 4
  • DOI: 10.2516/ogst/2015037

An exact effective stress law for elastic deformation of rock with fluids
journal, September 1971


Anisotropy of permeability and complex resistivity of tight sandstones subjected to hydrostatic pressure
journal, July 2009


An asperity-deformation model for effective pressure
journal, May 1996


Compressibility of porous rocks
journal, November 1986

  • Zimmerman, Robert W.; Somerton, Wilbur H.; King, Michael S.
  • Journal of Geophysical Research: Solid Earth, Vol. 91, Issue B12
  • DOI: 10.1029/JB091iB12p12765

Salinity dependence of the complex surface conductivity of the Portland sandstone
journal, March 2016


The mechanism of strong nonlinear elasticity in earth solids
conference, January 2000

  • Ostrovsky, Lev A.
  • 15th international symposium on nonlinear acoustics: Nonlinear acoustics at the turn of the millennium, AIP Conference Proceedings
  • DOI: 10.1063/1.1309181

Note on effective pressure
journal, May 1973


A simple derivation of the effective stress coefficient for seismic velocities in porous rocks
journal, March 2004


The effect of pressure on the electrical resistivity of water-saturated crystalline rocks
journal, November 1965

  • Brace, W. F.; Orange, A. S.; Madden, T. R.
  • Journal of Geophysical Research, Vol. 70, Issue 22
  • DOI: 10.1029/JZ070i022p05669

Electrical Resistivity Changes in Saturated Rock under Stress
journal, September 1966


Nature of surface electrical conductivity in natural sands, sandstones, and clays
journal, March 1998

  • Revil, A.; Glover, P. W. J.
  • Geophysical Research Letters, Vol. 25, Issue 5, p. 691-694
  • DOI: 10.1029/98GL00296

Effective stress for transport properties of inhomogeneous porous rock
journal, January 1992

  • Berryman, James G.
  • Journal of Geophysical Research, Vol. 97, Issue B12
  • DOI: 10.1029/92JB01593

Permeability and electrical conductivity changes due to hydrostatic stress cycling of berea and muddy J sandstone
journal, January 1986


Pore geometry and transport properties of Fontainebleau sandstone
journal, December 1993

  • Fredrich, J. T.; Greaves, K. H.; Martin, J. W.
  • International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Vol. 30, Issue 7
  • DOI: 10.1016/0148-9062(93)90007-Z

Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials
journal, April 1999

  • Guyer, Robert A.; Johnson, Paul A.
  • Physics Today, Vol. 52, Issue 4
  • DOI: 10.1063/1.882648

Effective pressure law for permeability of E-bei sandstones
journal, January 2009

  • Li, M.; Bernabé, Y.; Xiao, W. -I.
  • Journal of Geophysical Research, Vol. 114, Issue B7
  • DOI: 10.1029/2009JB006373

Elastic properties of solid clays
conference, March 2012

  • Wang, Zhijing (Zee); Wang, Hui; Cates, Michael E.
  • SEG Technical Program Expanded Abstracts 1998
  • DOI: 10.1190/1.1820064

Laboratory study of the electrical and hydraulic properties of rocks under simulated reservoir conditions
journal, April 1992


Electrical conductivity in shaly sands with geophysical applications
journal, October 1998

  • Revil, A.; Cathles, L. M.; Losh, S.
  • Journal of Geophysical Research: Solid Earth, Vol. 103, Issue B10
  • DOI: 10.1029/98JB02125

The effect of pressure on porosity and the transport properties of rock
journal, January 1984


A new non-Archie model for pore structure: numerical experiments using digital rock models
journal, July 2013

  • Yue, W. Z.; Tao, G.
  • Geophysical Journal International, Vol. 195, Issue 1
  • DOI: 10.1093/gji/ggt231

What is the cementation exponent? A new interpretation
journal, January 2009