This website uses cookies to improve your experience. If you continue without changing your settings, you consent to our use of cookies in accordance with our cookie policy. You can disable cookies at any time.

×

Within the Biot poroelasticity theory, the effective pressure coefficient for the bulk volume of a fluid-saturated rock and the Biot coefficient are one and the same quantity. The effective pressure coefficient for the bulk volume is the change of confining pressure with respect to fluid-pressure changes when the bulk volume is held constant. The Biot coefficient is the fluid volume change induced by bulk volume changes in the drained condition. However, there is experimental evidence showing a difference between these two coefficients, arguably caused by microinhomogeneities, such as microcracks and other compliant pore-scale features. In these circumstances, we advocate using the generalized constitutive pressure equations recently developed by Sahay wherein the effective pressure coefficient and the Biot coefficient enter as distinct quantities. Therein, the difference is attributed to the porosity effective pressure coefficient that serves as a measure for the deviation from the Biot prediction and accounts for microinhomogeneities. We have concluded that these generalized constitutive pressure equations offer a meaningful alternative to model observed rock behavior.

REFERENCES

  • Al-Tahini, A. M., Y. N. Abousleiman, and J. L. Brumley, 2005, Acoustic and quasi-static laboratory measurement and calibration of the pore pressure prediction coefficient in the poroelastic theory: Presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, SPE 95825.CrossrefGoogle Scholar
  • Altmann, J., T. M. Müller, B. I. R. Müller, M. R. P. Tingay, and O. Heidbach, 2010, Poroelastic contribution to the reservoir stress path: International Journal of Rock Mechanics and Mining Science, 47, 1104–1113, doi: 10.1016/j.ijrmms.2010.08.001.IRMGBG0148-9062CrossrefWeb of ScienceGoogle Scholar
  • Berryman, J. G., 1992, Effective stress for transport properties of inhomogeneous porous rock: Journal of Geophysical Research, 97, 409–417, doi: 10.1029/92JB01593.JGREA20148-0227CrossrefWeb of ScienceGoogle Scholar
  • Berryman, J. G., and G. W. Milton, 1991, Exact results for generalized Gassmann’s equation in composite porous media with two constituents: Geophysics, 56, 1950–1960, doi: 10.1190/1.1443006.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Biot, M. A., 1941, General theory of three-dimensional consolidation: Journal of Applied Physics, 12, 155–164, doi: 10.1063/1.1712886.JAPIAU0021-8979CrossrefGoogle Scholar
  • Biot, M. A., and D. G. Willis, 1957, The elastic coefficients of the theory of consolidation: Journal of Applied Mechanics, 24, 594–601.JAMCAV0021-8936Google Scholar
  • Bishop, A. W., and G. E. Blight, 1963, Some aspects of effective stress in saturated and partly saturated soils: Géotechnique, 13, 177–197, doi: 10.1680/geot.1963.13.3.177.CrossrefGoogle Scholar
  • Blöcher, G., T. Reinsch, A. Hassanzadegan, H. Milsch, and G. Zimmermann, 2014, Direct and indirect laboratory measurements of poroelastic properties of two consolidated sandstones: International Journal of Rock Mechanics and Mining Sciences, 67, 191–201, doi: 10.1016/j.ijrmms.2013.08.033.IRMGBG0148-9062CrossrefWeb of ScienceGoogle Scholar
  • Brown, R. J. S., and J. Korringa, 1975, On the dependence of the elastic properties of a porous rock on the compressibility of a pore fluid: Geophysics, 40, 608–616, doi: 10.1190/1.1440551.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Cheng, A. H.-D., and Y. Abousleiman, 2008, Intrinsic poroelasticity constants and a semilinear model: Int. J. Numer. Anal. Meth. Geomech., 32, 803–831, doi: 10.1002/nag.647.GPYSA70016-8033CrossrefWeb of ScienceGoogle Scholar
  • de la Cruz, V., and T. J. T. Spanos, 1985, Seismic-wave propagation in porous medium: Geophysics, 50, 1556–1565, doi: 10.1190/1.1441846.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Gassmann, F., 1951, Über die Elastizität poröser Medien: Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, 96, 1–23.Google Scholar
  • Hart, D. J., and H. F. Wang, 2010, Variation of unjacketed pore compressibility using Gassmann’s equation and an overdetermined set of volumetric poroelastic measurements:Geophysics , 75, no. 1N9–N18., doi: 10.1190/1.3277664.SPTJAJ0037-9999AbstractGoogle Scholar
  • Hettema, M. H. H., and C. J. de Pater, 1998, The poromechanical behaviour of Felser sandstone: Stress- and temperature-dependent: SPE/ISRM Rock Mechanics in Petroleum Engineering, Society of Petroleum Engineers, SPE/lSRM 47270, 347–355, doi: 10.2118/47270-MS.SPTJAJ0037-9999CrossrefGoogle Scholar
  • Jaeger, J. C., N. G. W. Cook, and R. W. Zimmerman, 2007, Fundamentals of rock mechanics (4th ed.): Blackwell, 475.Google Scholar
  • Klimentos, T., A. Harouaka, B. Mtawaa, and S. Saner, 1998, Experimental determination of the Biot elastic constant: Applications in formation evaluation (sonic porosity, rock strength, Earth stresses, and sanding predictions): SPE Reservoir Evaluation and Engineering, 1, 57–63, doi: 10.2118/30593-PA.CrossrefWeb of ScienceGoogle Scholar
  • Landau, L. D., and E. M. Lifshitz, 1980, Statistical physics (3rd ed.): Pergamon Press.Google Scholar
  • Laurent, J., M. J. Bouteca, J. P. Sarda, and D. Bary, 1993, Pore-pressure influence in the poroelastic behavior of rocks: Experimental studies and results: SPE Formation Evaluation, 8, 117–122, doi: 10.2118/20922-PA.SPTJAJ0037-9999CrossrefGoogle Scholar
  • Lopatnikov, S. L., and A. H. -D. Cheng, 2002, Variational formulation of fluid infiltrated porous material in thermal and mechanical equilibrium: Mech. Mater., 34, no. 11, 685–704, doi: 10.1016/S0167-6636(02)00168-0.CrossrefWeb of ScienceGoogle Scholar
  • Mavko, G., T. Mukerji, and J. Dvorkin, 2009, The rock physics handbook: Tools for seismic analysis of porous media (2nd ed.): Cambridge University Press, 511.CrossrefGoogle Scholar
  • Miskimins, J. L., B. A. Ramirez, and R. M. Graves, 2004, The economic value of information and Biot’s constant: How important are accurate measurements?: Presented at the 6th North America Rock Mechanics Symposium (NARMS): Rock Mechanics Across Borders and Disciplines, 1–9.Google Scholar
  • Müller, T. M., and P. N. Sahay, 2013, Porosity perturbations and poroelastic compressibilities: Geophysics, 78, no. 1, A7–A11, doi: 10.1190/geo2012-0129.1.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Müller, T. M., and P. N. Sahay, 2014, Solid-phase bulk modulus and microinhomogeneity parameter from quasistatic compression experiments: Geophysics, 79, no. 6, A51–A55, doi: 10.1190/geo2014-0291.1.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Müller, T. M., and P. N. Sahay, 2016, Generalized poroelasticity framework for micro-inhomogeneous rocks: Geophysical Prospecting, doi: 10.1111/1365-2478.12392.GPPRAR0016-8025CrossrefGoogle Scholar
  • Nur, A., and J. D. Byerlee, 1971, An exact effective stress law for elastic deformation of rocks with fluid: Journal of Geophysical Research, 76, 6414–6419, doi: 10.1029/JB076i026p06414.JGREA20148-0227CrossrefWeb of ScienceGoogle Scholar
  • Omdal, E., M. Madland, H. Breivik, K. Naess, R. Korsnes, A. Hiorth, and T. Kristiansen, 2009, Experimental investigation of the effective stress coefficient for various high porosity outcrop chalks: Presented at the 43rd US Rock Mechanics Symposium and 4th U.S.-Canada Rock Mechanics Symposium, 1–4.Google Scholar
  • Sahay, P. N., 2013, Biot constitutive relation and porosity perturbation equation: Geophysics, 78, no. 5, L57–L67, doi: 10.1190/geo2012-0239.1.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Sahay, P. N., T. J. T. Spanos, and V. de la Cruz, 2001, Seismic wave propagation in inhomogeneous and anisotropic porous media: Geophysical Journal International, 145, 209–222, doi: 10.1111/j.1365-246X.2001.00353.x.GJINEA0956-540XCrossrefWeb of ScienceGoogle Scholar
  • Schmitt, D. R., and M. D. Zoback, 1989, Poroelastic effects in the determination of the maximum horizontal principal stress in hydraulic fracturing tests: A proposed breakdown equation employing a modified effective stress relation for tensile failure: International Journal of Rock Mechanics and Mining Science, 26, 499–506, doi: 10.1016/0148-9062(89)91427-7.IRMGBG0148-9062CrossrefWeb of ScienceGoogle Scholar
  • Sulem, J., and H. Ouffroukh, 2006, Hydromechanical behaviour of Fontainebleau sandstone: Rock Mechanics and Rock Engineering, 39, 185–213, doi: 10.1007/s00603-005-0065-4.RMREDX1434-453XCrossrefWeb of ScienceGoogle Scholar
  • Terzaghi, K., 1923, Die Berechnung der Durchlässigkeitsziffern des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen: Akademie der Wissenschaften in Wien. Sitzungsberichte. Mathematisch naturwissenschaftliche Klasse, Abt. 2A, 132, 125–138.Google Scholar
  • Terzaghi, K., 1926, Principles of soil mechanics: McGraw-Hill.Google Scholar
  • Wang, H. F., 2000, Theory of linear poroelasticity: Princeton University Press.Google Scholar
  • Wu, B., 1999, Evaluation of the Biot effective stress coefficient by different experimental methods and implication in sand production prediction: Proceedings of the International Symposium on Coupled Phenomena in Civil, Mining and Petroleum Engineering, 59–75.Google Scholar