(219d) Dissolution In Fractured and Porous Rocks – the Cave Formation Paradox and Other Instabilities

It has long been realized that limestone caves are solutional in origin; atmospheric CO₂ forms a weakly acidic solution which dissolves the surrounding limestone as it percolates through the fracture network. Under the simplest assumptions - uniform flow and linear kinetics - the concentration of reactant deacays exponentially with distance into the fracture, making it apparently impossible for long conduits to develop. Nevertheless, limestone caverns extend for kilometers; Mammoth cave in Kentucky has nearly 400 miles of passages. So how does the dissolution get so deep? The answer until recently has been described in terms of changes in chemical kinetics; in natural calcite the reaction rate decreases by orders of magnitude near saturation. Paradoxically this promotes dissolution since the undersaturated solution can penetrate deeper into the fractured rock.

Although this is an appealing and widely accepted resolution of the cave formation paradox, it turns out to be incomplete. About 12 years ago, Hanna and Rajaram^[1] showed by computer simulation that a fracture does not necessarily open uniformly across its width, but can develop localized regions of dissolution. This insight was subsequently confirmed by laboratory experiments^[2]. Recently, Piotr Szymczak and I realized that there is a universal instability in the equations for fracture dissolution, so that a dissolution front is always unstable^[3], even under the most idealized circumstances: i.e. a fracture modeled as two parallel plates, laminar flow, and linear reaction kinetics at the fracture surfaces. This generic instability provides a more effective means to promote dissolution than changes in chemical kinetics and has a profound effect on how long it takes for breakthrough (when the fracture opens along its whole length) to occur. Dissolutional breakthrough is an important component in assessing the safety of CO₂ sequestration sites.

In this presentation I will outline the equations governing the dissolution of fractures and also of a uniform porous media. They are similar to the standard equations for heat and mass transfer but because material dissolves there is an additional coupling to changes in permeability. A planar dissolution front in an entirely uniform fracture or porous matrix is unstable to infinitesimal perturbations and inevitably breaks up into highly localized regions of dissolution. Our results suggest that there is an inherent wavelength to the erosion pattern in dissolving fractures, which depends on the reaction rate and flow rate, but is independent of the initial roughness. I will compare the instability in fractured rocks with the better-known instability in dissolving porous media.

 

1. R. B. Hanna and H. Rajaram, Water Resources Res., 34:2843, 1998.
2. R. L. Detwiler, R. J. Glass and W. L. Bourcier., Geophys. Res. Lett., 30:1648 (2003).
3. P. Szymczak and A. J. C. Ladd, EPSL, 201:424-432, 2011.