Abstract
When it comes to geological storage of \(\hbox {CO}_{2}\), monitoring is crucial to detect leakage in the caprock. In our study, we investigated the wave speeds of porous media filled with \(\hbox {CO}_{2}\) and water in order to determine reservoir changes. We focused on deep storage sites where \(\hbox {CO}_{2}\) is in a supercritical state. In case of a leak, \(\hbox {CO}_{2}\) rises and eventually starts to boil as soon as it reaches temperatures or pressures below the critical point. At this point, there are two distinct phases in the pore space. We derived the necessary equations to calculate the wave speeds for unsaturated porous media and tested the equations for a representative storage scenario. We found that there are three modes of pressure waves instead of two for the saturated case. The new mode has a very small wave speed and is highly attenuated. This mode will most likely be very hard to detect in practice and therefore it may be necessary to use time-lapse seismic migration to detect leakage.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aki, K., Richards, P.G.: Quantitative Seismology, 2nd edn. University Science Books, Sausalito (2002)
Albers, B.: Analysis of the propagation of sound waves in partially saturated soils by means of a macroscopic linear poroelastic model. Transp. Porous Media 80(1), 173–192 (2009)
Biot, M.A.: Theory of elasticity and consolidation for a porous anisotropic solid. J. Appl. Phys. 26(2), 182–185 (1955)
Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956a)
Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. 28(2), 179–191 (1956b)
Brooks, R.H., Corey, A.T.: Hydraulic properties of porous media. Hydrology Papers 3, Colorado State University, Fort Collins (1964)
Carcione, J.M., Picotti, S., Gei, D., Rossi, G.: Physics and seismic modeling for monitoring \(\text{ CO }_{2}\) storage. Pure Appl. Geophys. 163(1), 175–207 (2006)
Coussy, O.: Poromechanics. Wiley, Chichester (2004)
Gor, G.Y., Prévost, J.H.: Modeling \(\text{ CO }_{2}\)-water leakage from geological storage involving phase transitions. Unpublished report, Department of Civil and Environmental Engineering, Princeton University (2014)
Jeffreys, H., Jeffreys, B.S.: Methods of Mathematical Physics, 2nd edn. Cambridge University Press, Cambridge (1950)
Kopp, A., Class, H., Helmig, R.: Investigations on \(\text{ CO }_{2}\) storage capacity in saline aquifers: Part 1. Dimensional analysis of flow processes and reservoir characteristics. Int. J. Greenh. Gas Control 3(3), 263–276 (2009)
Lo, W.C., Sposito, G., Majer, E.: Wave propagation through elastic porous media containing two immiscible fluids. Water Resour. Res. 41, W02025 (2005)
Morency, C., Luo, Y., Tromp, J.: Acoustic, elastic and poroelastic simulations of \(\text{ CO }_{2}\) sequestration crosswell monitoring based on spectral-element and adjoint methods. Geophys. J. Int. 185, 955–966 (2011)
Neumann, S.P.: Theoretical Derivation of Darcy’s Law. Acta Mech. 25(3–4), 153–170 (1977)
Pini, R., Krevor, S.C.M., Benson, S.M.: Capillary pressure and heterogeneity for the \(\text{ CO }_{2}\)/water system in sandstone rocks at reservoir conditions. Adv. Water Resour. 38, 48–59 (2012)
Plug, W.J., Bruining, J.: Capillary pressure for the sand-\(\text{ CO }_{2}\)-water system under various pressure conditions. Application for \(\text{ CO }_{2}\) sequestration. Adv. Water Resour. 30, 2339–2353 (2007)
Prévost, J.H.: Dynaflow: A Nonlinear Transient Finite Element Analysis Program (1981). http://www.blogs.princeton.edu/prevost/dynaflow/ (last update 2012)
Santos, J.E., Corber, J., Douglas Jr, J.: Static and dynamic behavior of a porous solid saturated by a two-phase fluid. J. Acoust. Soc. Am. 87(4), 1428–1438 (1990a)
Santos, J.E., Douglas Jr, J., Corber, J., Lovera, O.M.: A model for wave propagation in a porous medium saturated by a two-phase fluid. J. Acoust. Soc. Am. 87(4), 1439–1448 (1990b)
Span, R., Wagner, W.: A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25(6), 1509–1596 (1996)
van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980)
Wilmanski, K.: Thermodynamics of Continua. Springer, Berlin (1998)
Acknowledgments
This work was performed by Marc S. Boxberg while visiting Princeton University during the summer of 2013 as part of the REACH program sponsored by the Keller Center at Princeton University. This support is most gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Boxberg, M.S., Prévost, J.H. & Tromp, J. Wave Propagation in Porous Media Saturated with Two Fluids. Transp Porous Med 107, 49–63 (2015). https://doi.org/10.1007/s11242-014-0424-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-014-0424-2