Abstract
Pore pressure changes in a geothermal reservoir, as a result of injection and/or production of water, result in changes of stress acting on the reservoir rock and, consequently, changes in the mechanical and transport properties of the rock. Bulk modulus and permeability were measured at different pressures and temperatures. An outcropping equivalent of Rotliegend reservoir rock in the North German Basin (Flechtinger sandstone) was used to perform hydrostatic tests and steady state fluid flow tests. Permeability measurements were conducted while cycling confining pressure; the dependence of permeability on stress was determined at a constant downstream pressure of 1 MPa. Also, temperature was increased stepwise from 30 to 140 °C and crack porosity was calculated at different temperatures. Although changes in the volumes of cracks are not significant, the cracks control fluid flow pathways and, consequently, the permeability of the rock. A new model was derived which relates microstructure of porosity, the stress–strain curve, and permeability. Porosity change was described by the first derivative of the stress–strain curve. Permeability evolution was ascribed to crack closure and was related to the second derivative of the stress–strain curve. The porosity and permeability of Flechtinger sandstone were reduced by increasing the effective pressure and decreased after each pressure cycle.
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References
Bear, J. (1988). Dynamics of Fluids in Porous Media. Dover Books on Physics and Chemistry. Dover.
Bernabe, Y. (1986). The effective pressure law for permeability in chelmsford granite and barre granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 23(3):267–275.
Bernabe, Y. (1987). The effective pressure law for permeability during pore pressure and confining pressure cycling of several crystalline rocks. J. Geophys. Res., 92:649–657.
Biot, M. (1956). General solutions of the equations of elasticity and consolidation for a porous material. Journal of Applied Mechanics, 78:91–96.
Biot, M. A. (1941). General theory of three-dimensional consolidation. J. Appl. Phys., 12(2):155–164.
Biot, M. A. (1973). Nonlinear and semilinear rheology of porous solids. Journal of Geophysical Research, 78:4924–4937.
Blöcher, G., Zimmermann, G., and Milsch, H. (2009). Impact of poroelastic response of sandstones on geothermal power production. Pure and Applied Geophysics, 166(5–7):1089–1106.
Brace, W. (1980). Permeability of crystalline and argillaceous rocks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 17(5):241–251.
Brace, W. F. (1978). Volume changes during fracture and frictional sliding: A review. Pure and Applied Geophysics, 116:603–614.
Carman, P. (1956). Flow of gases through porous media. Butterworths Scientific Publications.
Carroll, M. (1980). Mechanical response of fluid suturated porous materials. In Theoretical and Applied Mechanics, Proc. 15th Int. Congress of Theoretical and Applied Mechanics, Toronto, August 1723, F. P. J. Rimrott and B. Tabarrok, eds., North-Holland, Amsterdam, pages 251–262.
Carroll, M. M. and Katsube, N. (1983). The role of terzaghi effective stress in linearly elastic deformation. Journal of Energy Resources Technology Transactions of the Asme, 105(4):509–511.
David, C., Menendez, B., Zhu, W., and Wong, T. F. (2001). Mechanical compaction, microstructures and permeability evolution in sandstones. Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 26(12):45–51.
David, C., Wong, T.-F., Zhu, W., and Zhang, J. (1994). Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust. Pure and Applied Geophysics, 143:425–456.
David, E. C., and Zimmerman, R. W. (2012). Pore structure model for elastic wave velocities in fluid-saturated sandstones. Journal of Geophysical Research: Solid Earth, 117:2156-2202.
Detournay, E. and Cheng, A. H.-D. (1993). Fundamentals of poroelasticity. In Comprehensive Rock Engineering: Principles, Practice and Projects, volume 2, chapter 5, pages 113–171. Pergamon Press.
Fortin, J., Schubnel, A., and Guéguen, Y. (2005). Elastic wave velocities and permeability evolution during compaction of bleurswiller sandstone. International Journal of Rock Mechanics and Mining Sciences, 42(78):873–889.
Guéguen, Y., Gavrilenko, P., and Le Ravalec, M. (1996). Scales of rock permeability. Surveys in Geophysics, 17:245–263.
Guéguen, Y., and Dienes J. (1989). Transport properties of rocks from statistics and percolation. Mathematical Geology, 21(1):1–13.
Guéguen, Y. and Palciauskas V. (1994). Introduction to the Physics of Rocks. Princeton University Press.
Hassanzadegan, A., Blöcher, G., Milsch, H., Urpi, L. and Zimmermann G. (2013). The Effects of Temperature and Pressure on the Porosity Evolution of Flechtinger Sandstone Rock Mechanics and Rock Engineering, doi:10.1007/s00603-013-0401-z.
Hassanzadegan, A., Blöcher, G., Zimmermann, G., and Milsch, H. (2012). Thermoporoelastic properties of Flechtinger sandstone. International Journal of Rock Mechanics and Mining Sciences, 49(0):94–104.
Hassanzadegan, A., Blöcher, G., Zimmermann, G., Milsch, H., and Moeck, I. (2011). Induced stress in a geothermal doublet system. In Thirty-Sixth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, SGP-TR-191, pages 1–1.
Jaeger, J., Cook, N., and Zimmerman, R. (2007). Fundamentals of Rock Mechanics. Blackwell Pub.
Morlier, P. (1971). Description de l’ètat de fissuration d’une roche à à partir d’essais non-destructifs simples. Rock Mechanics and Rock Engineering, 3:125–138.
Rice, J. R. and Cleary, M. P. (1976). Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents. Reviews of Geophysics and Space Physics, 14(2):227–241.
J. Sarout (2012). Impact of pore space topology on permeability, cut-off frequencies and validity of wave propagation theories. Geophysical Journal International 189: 481–492
Scheidegger, A.E. (1974). The physics of flow through porous media. University of Toronto Press.
Sisavath, S., Jing, X., and Zimmerman, R. (2000). Effect of stress on the hydraulic conductivity of rock pores. Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 25(2):163–168.
Walsh, J. B. (1965). The effect of cracks on the compressibility of rock. J. Geophys. Res, 70(2):381–389.
Walsh, J. B. (1980). Static deformation of rock. Journal Of The Engineering Mechanics Division, 106:1005–1019.
Zimmerman, R. (1991). Compressibility of Sandstones. Developments in Petroleum Science. Elsevier.
Zoback, M. and Byerlee, J. (1975). Permeability and effective stress. American association of petroleum geologists bulletin, 59:154–158.
Acknowledgments
The authors would like to gratitude Liane Liebeskind for Laboratory assistance. Moreover, the authors would like to thank the reviewers for their constructive and valuable comments that helped to improve the manuscript. This work has been performed in the framework of the GeoEn-Phase 2 project and funded by the Federal Ministry of Education and Research [BMBF, 03G0767A].
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Hassanzadegan, A., Zimmermann, G. A Poroelastic Description of Permeability Evolution. Pure Appl. Geophys. 171, 1187–1201 (2014). https://doi.org/10.1007/s00024-013-0714-6
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DOI: https://doi.org/10.1007/s00024-013-0714-6