(97f) Reactive Infiltration Instabilities in Fractured and Porous Rocks

Reactive infiltration instabilities occur in a wide range of geophysical and geotechnical systems. The simplest such instability occurs when fluid flows between two soluble plates, which is an idealized model of fractured limestone. Even when the initial aperture is uniform at the nanoscale, an instability in the reaction front develops leading to the formation of pronounced solutional channels or “wormholes”. We have suggested that this instability may explain the onset of large underground caves systems, by allowing a much deeper penetration of reactant than is possible by uniform opening of the fracture [1].

Reactive infiltration in porous media has been investigated experimentally[2], numerically[3], and theoretically [4-6]. The predictions of the linear stability analysis vary considerably depending on the underlying model assumptions. In this talk I will outline how these different theoretical approaches can be viewed as limiting cases of a more general theory. Our results span the range of geologically feasible Peclet and Damkohler numbers [7-8]. In particular we show that the convective limit [5,6] is singular, with a wavelength selection and growth rate that is very sensitive to small amounts of diffusion. We also show that the opposite limit of diffusion-dominated dissolution [4] spans a much smaller parameter range than has been supposed.

In this talk I will briefly summarize some of our most important results and discuss their relevance to geophysical systems.

[1] Szymczak, P. & Ladd, A. J. C. 2011. The initial stages of cave formation: Beyond the

one-dimensional paradigm. Earth Planet. Sci. Lett. 301, 424-432.

[2] Fredd, C. N. & Fogler, H. S. 1998. Influence of transport and reaction on wormhole formation

in porous media. AIChE J. 44, 1933-1949.

[3] Hanna, R. B. & Rajaram, H. 1998. Influence of aperture variability on dissolutional growth

of fissures in karst formations. Water Resourc. Res. 34, 2843-2853.

[4] Chadam, D., Hoff, D., Merino, E., Ortoleva, P. & Sen, A. 1986. Reactive infiltration

instabilities. J. Appl. Math. 36, 207-221.

[5] Sherwood, J. D. 1987. Stability of a plane reaction front in a porous medium. Chem. Eng. Sci.

42, 1823-1829.

[6] Hinch, E. J. & Bhatt, B. S. 1990. Stability of an acid front moving through porous rock. J.

Fluid Mech. 212, 279-288.
[7] Szymczak, P. & Ladd, A. J. C. 2012. Reactive-infiltration instabilities in rocks. Fracture dissolution. J. Fluid Mech. To be Published.

[8] Szymczak, P. & Ladd, A. J. C. 2012. Reactive-infiltration instabilities in rocks. Dissolution of a porous matrix. In Preparation.