Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T10:31:44.132Z Has data issue: false hasContentIssue false

6 - Mechanical Properties of Fluid-Bearing Rocks

Published online by Cambridge University Press:  19 November 2021

Nikolai Bagdassarov
Affiliation:
Goethe-Universität Frankfurt Am Main
Get access

Summary

Poroelastic problems are considered for drained and undrained rock conditions. The effective pressure coefficient a for bulk modulus is introduced to describe the effective pressure. The Skempton’s coefficient characterizes the relationship between pore pressure change and change in ambient pressure. The Gassman equation relates the bulk modulus of rock matrix, fluid and undrained rock with porosity and drained bulk modulus. Pore pressure follows the diffusion type equation: fluid transport and diffusion. Stress in rocks at depth may be estimated from hydraulic fracturing conditions. To calculate effective bulk and shear moduli of porous rocks, the differential Mori-Tanaka scheme is used. The effective bulk and shear moduli of a medium containing a family of identical-shaped pores can be expressed via the pore compressibility P and shear Q compliances. Focus Box 6.1: Elliptical coordinates and elliptical-shaped pores.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature

Berge, P. A., Wang, H. F. & Bonner, B. P. (1993). Pore pressure buildup coefficient in synthetic and natural sandstones. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 30(7), 11351141.Google Scholar
Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155164. https://doi.org/10.1063/1.1712886.Google Scholar
Brady, B. H. G. & Brown, E. T. (2004). Rock Mechanics. For Underground Mining. Kluwer Academic Press, Dordrecht, p. 628.Google Scholar
Carpenter, C. B. & Spencer, G. E. (1940). Measurements of compressibility of consolidated oil-bearing sandstones. Report of Investigations 3540, United States Department of The Interior – Bureau of Mines, Washington, DC.Google Scholar
David, E. C. & Zimmerman, R. W. (2011). Compressibility and shear compliance of spheroidal pores: Exact derivation via the Eshelby tensor, and asymptotic expressions in limiting cases. International Journal of Solids and Structures 48, 680686.CrossRefGoogle Scholar
David, E. C. & Zimmerman, R. W. (2012). Pore structure model for elastic wave velocities in fluid-saturated sandstones. Journal of Geophysical Research 117, B07210. doi: 10.1029/2012JB009195.Google Scholar
Geertsma, J. (1957). The effect of fluid pressure decline on volumetric changes of porous rock. Transactions of the AIME 210, 331339.CrossRefGoogle Scholar
Guéguen, Y., Dormieux, L. & Boutéca, M. (2004). Fundamentals of poromechanics. In: Guéguen, Y. & Boutéca, M. (Eds.) Mechanics of Fluid Saturated Rocks. Elsevier Academic Press, Amsterdam, Boston, International Geophysics Series 89, chapter 1: 154.Google Scholar
Guéguen, Y. & Palciauskas, V. (1994). Introduction to the Physics of Rocks. Princeton University Press, Princeton, NJ, p. 294.Google Scholar
Haimson, B. & Fairhurst, C. (1967). Initiation and extension of hydraulic fractures in rocks. Society of Petroleum Engineers 1710, 310318.CrossRefGoogle Scholar
Hantush, M. S. (1960). Modification of the theory of leaky aquifers. Journal of Geophysical Research 65(11), 37133725.CrossRefGoogle Scholar
Hart, D. J. (2000). Laboratory measurements of poroelastic constants and flow parameters and some associated phenomena, PhD thesis, University of Wisconsin, Madison, p. 122.Google Scholar
Hofmann, R., Xu, X., Batzle, M., et al. (2005). Effective pressure or what is the effect of pressure? The Leading Edge 24(12), 12561260.Google Scholar
Jaeger, J. C., Cook, N. G. & Zimmerman, R. W. (2009). Fundamentals of Rock Mechanics. J. Wiley & Sons, New York, 593 S.Google Scholar
Key, P. L. (1969). A relation between crack surface displacements and the strain energy release rate. International Journal of Fracture Mechanics 5, 287296.Google Scholar
Krumbein, W. C. & Sloss, L. L. (1953). Stratigraphy and Sedimentation. Freeman & Co., San Francisco, California, p. 218.Google Scholar
Kümpel, H.-J. (1991). Poroelasticity: parameters reviewed. Geophysical Journal International 105, 783799.CrossRefGoogle Scholar
Lan, Y., Moghanloo, R. G. & Davudov, D. (2017). Pore compressibility of shale formations. Society of Petroleum Engineers 22(6), SPE-185059-PA (12pp.). doi:10.2118/185059-PA.Google Scholar
Landau, L. D. & Lifschitz, E. M. (1986). Theory of Elasticity. Pergamon, Oxford.Google Scholar
LeRavalec, M. & Guéguen, Y. (1996). High- and low-frequency elastic moduli for a saturated porous/cracked rock – Differential self-consistent and poroelastic theories. Geophysics 61, 10801094.CrossRefGoogle Scholar
Luo, X., Were, P., Liu, J. & Hou, Z. (2015). Estimation of Biot’s effective stress coefficient from well logs. Environmental Earth Sciences 73, 70197028. doi: 10.1007/s12665-015-4219-8.Google Scholar
Marcussen, Ø., Maast, T. F., Mondol, N. H., Jahren, J. & Bjørlykke, K. (2010). Changes in physical properties of a reservoir sandstone as a function of burial depth – The Etive Formation, northern North Sea. Marine and Petroleum Geology 27, 17251735.CrossRefGoogle Scholar
Mavko, G., Mukerji, T. & Dvorkin, J. (1998). The Rock Physics Handbook. Cambridge University Press, Cambridge, p. 330.Google Scholar
Nur, A., Mavko, G., Dvorkin, J & Gal, D. (1995). Critical porosity: The key to relating physical properties to porosity in rocks. SEG Technical Program Expanded Abstracts 14(1), 878881.Google Scholar
Perras, M. A. & Diederichs, M. S. (2014). A review of the tensile strength of rock: Concepts and testing. Geotechnical and Geological Engineering 32, 525546. doi: 10.1007/s10706-014-9732-0.CrossRefGoogle Scholar
Pimienta, L., Fortin, J. & Guéguen, Y. (2016). Effect of fluids and frequency on Poisson’s ratio of sandstone samples. Geophysics 82(2), D35D47. doi:10.1190/GEO2015-0310.1.Google Scholar
Saberi, R. M. & Jenson, F. (2018). Determining dynamic Biot’s coefficient for unconventionals. www.hartenergy.com/exclusives/determining-dynamic-biots-coefficient-unconventionals–177102.Google Scholar
Salemi, H., Iglauer, S., Rezagholilou, A. & Sarmadivaleh, M. (2018). Laboratory measurement of Biot’s coefficient and pore pressure influence on poroelastic rock behaviour. The APPEA Journal 58(1), 182189. www.publish.csiro.au/aj/AJ17069.Google Scholar
Schmitt, D. R. & Zoback, M. D. (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 Sciences & Geomechanics Abstracts 26(6), 499506.Google Scholar
Sneddon, I. N. (1946). The distribution of stress in the neighborhood of a crack in an elastic solid. Proceedings of the Royal Society 187A, 229260. https://doi.org/10.1098/rspa.1946.0077.Google Scholar
Timoshenko, S. P. & Goodier, J. N. (1951). Theory of Elasticity. McGraw Hill, New York, p. 506.Google Scholar
Todd, T. & Simmons, G. (1972). Effect of pore pressure on the velocity of compressional waves in low-porosity rocks. Journal of Geophysical Research 77(20), 37313743. doi:10.1029/JB077i020p03731.CrossRefGoogle Scholar
Valkó, P. & Economides, M. J. (1994). Propagation of hydraulically induced fractures a continuum damage mechanics approach. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 31(3), 221229.Google Scholar
Vasquez, G. F., VargasJr., E. A., Ribeiro, C. J. B., Leão, M. & Justen, J. C. R. (2009). Experimental determination of the effective pressure coefficients for Brazilian limestones and sandstones. Revista Brasileira de Geofísica 27(1), 4353.CrossRefGoogle Scholar
Wang, H. F. (2000). Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton and Oxford.Google Scholar
Zimmerman, R. W. (1985). Compressibility of an isolated spheroidal cavity in an isotropic elastic medium. Journal of Applied Mechanics 52, 606608. doi: 10.1115/1.3169108.CrossRefGoogle Scholar
Zimmerman, R. W. (2017). Pore volume and porosity changes under uniaxial strain conditions. Transport in Porous Media 119, 481498. doi: 10.1007/s11242-017-0894-0.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×