Abstract
Sedimentary rocks have complicated permeability patterns arising from the geological processes that formed them. We concentrate on pattern formation in one particular geological process, avalanches (grainflow) in windblown or fluvial sands. We present a simple experiment and numerical model of how these avalanches cause segregation in particle size that lead to characteristic laminated patterns. We also address the longstanding question of how such patterns are generated. We analyze data on two sandstone samples from different, but similar, geological environments, and find that the permeability fluctuations display long-range power-law correlations characterized by an exponent H. For both samples, we find H≈0.82–0.90. These permeability fluctuations significantly affect the flow of fluids through the rocks. We demonstrate this by investigating the influence of long-range correlation on percolation properties, like cluster morphology, and relate these properties to characteristics important for hydrocarbon recovery such as breakthrough time for injected fluids and recovery efficiency.
Preview
Unable to display preview. Download preview PDF.
References
Allen, J. R. L. Journal of Geology 78, 326–351 (1970).
Bagnold, R. A. The physics of blown sand and desert dunes (Chapman and Hall, London 1941).
Bagnold, R. A. Proc. Roy. Soc. London A 295, 219–232 (1966).
Borges, J. L. The book of sand (Emecé, Buenos Aires 1975).
Buck, S. G., Jour. Sed. Petrology 55, 895 (1985).
Bunde A. and Havlin, S., eds., Fractals in Science (Springer-Verlag, Berlin 1994).
Cheel, R. J. & Middleton, G. V. Journal of Geology 94, 489–504 (1986).
Coniglio, A., Nappi C., Russo L., and Peruggi F., J. Phys. A 10, 205–209 (1977).
Fryberger, S. G. & Schenk, C. Sedimentology 28, 805–821 (1981).
Halvorsen, C. and Hurst, A., in Advances in Core Evaluation Accuracy and Prediction, Edited by P. F. Worthington (Gordon and Breach, 1990).
Hele-Shaw, H. S. Nature 58, 34–36 (1898).
Hunter, R. E., Jour. Sed. Petrology 55, 886 (1985).
Jaeger, H. M. & Nagel S. R. Science 255, 1523–1531 (1992).
Jopling, A. V. & Walker, R. G. Journal of Sedimentary Petrology 38, 971–984 (1968).
Leschhorn H. and Tang L.-H., Phys. Rev. Lett. 70, 2973 (1993).
Makse, H. A. and Amaral, L. A. N., Europhys. Lett. 31, 379 (1995).
Makse, H. A., Davies, G., Havlin, S. Ivanov, P. Ch., King, P. R., and Stanley H. E., Phys. Rev. E 54, 3129 (1996a).
Makse, H. A., Havlin, S., King, P. R., and Stanley, H. E. (submitted, 1995b).
Makse H. A., Havlin, S., Stanley, H. E., and Schwartz, M. [1993 Int. Conf. Complex Systems in Computational Physics, Buenos Aires] Chaos, Solitons and Fractals 6, 295 (1995a).
Makse, H. A., Havlin, S., Schwartz, M., and Stanley, H. E., Phys. Rev. E 53, 5445 (1995c).
Makse H. A., Cizeau P., and Stanley, H. E. (submitted, 1996b).
McKee, E. D., Crosby, E. J. & Berryhill, H. L. JR. Journal of Sedimentary Petrology 37, 829–851 (1967).
Muzy, J.F., Bacry, E., and Arneodo, A., Phys. Rev. Lett. 67, 3515 (1991)
A. Arneodo, E. Bacry, P. V. Graves, and J. F. Muzy, ibid 74, 3292 (1995).
Peng, C. K., Havlin, S., Schwartz, M., and Stanley, H. E., Phys. Rev. A 44, 2239 (1991).
Peng C. K., Buldyrev S. V., Havlin, S., Simons, M., Stanley, H. E. and Goldberger, A. L., Phys. Rev. E 49, 1685–1689 (1994).
Prakash, S., Havlin S., Schwartz, M., Stanley, H. E., Phys. Rev E 46, R1724 (1992).
D. Saupe in The Science of Fractal Images, Peitgen, H.-O. and Saupe D., eds. (Springer-Verlag, New York 1988).
Feder J., Fractals (Plenum Press, New York 1988).
Vicsek, T., Fractal Growth Phenomena, 2nd ed., Part IV (World Scientific, Singapore, 1992).
Barabasi, A.-L. and Stanley, H. E., Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995).
Family, F. and Vicsek T., eds., Dynamics of Fractal Surfaces (World Scientific, Singapore 1991).
Weinrib, A., Phys. Rev. B 29, 387–395 (1984).
Author information
Authors and Affiliations
Editor information
Additional information
Dedicated to Professor W. Ebeling on the Occasion of his 60th Birthday.
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this paper
Cite this paper
Makse, H.A., Havlin, S., King, P.R., Stanley, H.E. (1997). Novel pattern formation in granular matter. In: Schimansky-Geier, L., Pöschel, T. (eds) Stochastic Dynamics. Lecture Notes in Physics, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105620
Download citation
DOI: https://doi.org/10.1007/BFb0105620
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62893-4
Online ISBN: 978-3-540-69040-5
eBook Packages: Springer Book Archive