Identification of Poroelastic Constants of “Tight” Rocks from Laboratory Tests
Publication: International Journal of Geomechanics
Volume 6, Issue 3
Abstract
This paper discusses the identification of poroelastic constants and hydraulic conductivity from two transient laboratory tests performed on cylindrical core: drained isotropic confinement and pulse test. The combination of the two tests allows us to estimate all poroelastic parameters with the exception of the shear modulus. Despite the lack of analytical solutions for the fully coupled case, closed form solutions of the forward problems are obtained for a slender specimen. The validity of these solutions for a realistic aspect ratio of the core is assessed by a comparison with a finite element model. The identification problem is solved by minimizing a least square functional using an explicit gradient computed using the direct differentiation of the closed form solution and a Levenberg–Marquardt algorithm. The uniqueness of this inverse problem as well as the effect of noise on input data are fully discussed. The identification procedure is then applied to tests performed on a deep argillaceous rock (argillite of Meuse Haute–Marne).
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Acknowledgments
The authors would like to thank Professor E. Detournay and Dr. J. I. Adachi for the benefit of useful discussions. This research was funded by the French Agency for Radioactive Waste Management (ANDRA) through a Ph.D. Grant for B.L. The experimental campaign was run for ANDRA under Contract No. ANDRA UNSPECIFIED017079-Contract-cadre AQL. The experimental tests were performed at G3S, Ecole Poly Y technique, France by Serge Chanchole and François Coste.
References
Adachi, J. I., and Detournay, E. (1997). “A poroelastic solution of the oscillating pore pressure method to measure permeabilities of “tight” rocks.” Int. J. Rock Mech. Min. Sci., 34(3–4).
ANDRA, Direction Scientifique (1999). “Reférentiel géologique du site de l’est.” Rep. ANDRA ARP ADS 99-0 05, France.
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12, 155–164.
Brace, W. F., Walsh, J. B., and Frangos, W. T. (1968). “Permeability of granite under high pressure.” J. Geophys. Res., 73(6), 2225–2236.
Carslaw, H. S., and Jaeger, J. C. (1959). Conduction of heat in solids, Oxford Science Publications, Oxford, U.K.
CAST3M. (2005). ⟨www.cast3m.cea.fr⟩.
Cheng, A. H.-D., Sidauruk, P., and Abousleiman, Y. (1994). “Approximate inversion of the Laplace transform.” Mathematica, 4(2), 76–82.
Coussy, O. (2004). Poromechanics, Wiley, New York.
Detournay, E., and Cheng, A. H.D. (1993). Fundamentals of poroelasticity, in comprehensive rocks engineering, Vol. 2, Chap. 5, Pergamon, London, 113–171.
Escoffier, S., Homand, F., Giraud, A., and Su, K. (2001). “Mesure de la perméabilité et du coefficient de Biot dans les argilites de l’est (in French).” Proc., 15th Congrès Français de Mécanique, Nancy, France.
Gill, P. E., Murray, W., and Wright, M. H. (1982). Practical optimization, Academic, New York.
Hart, D. J., and Wang, H. F. (2001). “A single test method for determination of poroelastic constants and flow parameters in rocks with low hydraulic conductivities.” Int. J. Rock Mech. Min. Sci., 38, 577–583.
Hsieh, P. A., Neuzil, C. E., Bredehoeft, J. D., and Silliman, S. E. (1981). “Transient laboratory method for determining the hydraulic properties of tight rocks. I: Theory.” Int. J. Rock Mech. Min. Sci., 18, 245–252.
Lecampion, B. (2002). “Sur l’identification des paramètres des lois de comportements des roches argileuses.” Ph.D. thesis, Ecole Polytechnique, Palaiseau, France (in French).
Lecampion, B., and Constantinescu, A. (2005). “Sensitivity analysis for parameter identification in quasi-static poroelasticity.” Int. J. Numer. Analyt. Meth. Geomech., 29, 163–185.
Malinsky, L., Chanchole, S., and Coste, F. (2002). “Identification of poroelastic constants of deep argillaceous rocks. I: Experimental set up and qualitative analysis.” Proc., 2nd Biot Conf. on Poromechanics, Grenoble, France, J. L. Auriault et al., ed., Balkema, Rotterdam, The Netherlands.
Neuzil, C. E., Cooley, C., Silliman, S. E., Bredehoeft, J. D., and Hsieh, P. A. (1981). “Transient laboratory method for determining the hydraulic properties of tight rocks. II: Application.” Int. J. Rock Mech. Min. Sci., 18, 253–258.
Vincké, O., Longuemarre, P., Boutéca, M., and Deflandre, J. P. (1998). “Investigation of the poromechanical behavior of shales in the elastic domain.” SPE/ISRM 47589, 515–520.
Vogel, C. (2002). Computational methods for inverse problems, SIAM.
Wang, H. F., (2000). Theory of linear poroelasticity with applications to geomechanics and hydrogeology, Princeton University Press, N.J.
Zeynaldi-Andabily, E. M., and Rahman, S. S. (1995). “Measurement of permeability of tight rocks.” Meas. Sci. Technol., 6, 1519–1527.
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Published In
International Journal of Geomechanics
Volume 6 • Issue 3 • May 2006
Pages: 201 - 208
Copyright
© 2006 ASCE.
History
Received: Aug 24, 2004
Accepted: Jan 1, 2005
Published online: May 1, 2006
Published in print: May 2006
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