Geochemical Self-Organization and the Evolution of Permeability

Abstract:

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 previously suggested that this instability may help 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. Numerical simulations suggest that dissolution may be a form of self-organization where patterns seem to develop in similar ways over a wide range of porosity distribution. If so, this offers the possibility of developing a theoretical understanding of the geomorphologies formed by dissolution-precipitation reactions independent (to some extent) of the initial conditions. We present numerical simulations of the dissolution of a porous matrix to indicate the insensitivity of key statistical markers to the initial distribution of porosity. Theory and simulations predict that a planar dissolution front breaks up into a number of competing fingers. Predictions from a linear stability analysis in porous and fractured rocks vary considerably depending on the underlying assumptions about flow rates and reaction rates. Once fingers develop, the nature of the competition is different in fractured and porous rocks. We are presently trying to understand the growth of individual fingers (see attached image), which numerical simulations show to be steadily propagating in time, much like the better-known phenomena of viscous fingering. We will indicate the difficulties that have so far prevented us from finding an explicit solution to the finger size, shape and velocity. Figure Caption Concentration profiles in a steadily-growing wormhole: Top - diffusion-dominated dissolution in a porous matrix; Center convection-dominated dissolution in a porous matrix; Bottom - convection-dominated dissolution in a fracture.