(258d) Interacting Length Scales in a Reactive-Infiltration Instability

Reactive-infiltration instabilities occur in a wide range of geophysical and geotechnical systems where an incoming flow of reactant dissolves the surrounding solid matrix, leading to local increases in permeability. The enhanced permeability increases the local flow in that region leading to further dissolution. The reactive-infiltration instability is related to, but distinct  from, viscous fingering, where the permeability is constant but the viscosity of the fluid (and possibly its density) respond to variations in concentration.

The reactive-infiltration instability in porous materials contains two important length scales, unlike viscous fingering which only has one. In this presentation I will outline a linear stability analysis that simultaneously incorporates both scales. It shows that the commonly used ``thin-front'' model is a limiting case of a more general theory, which also includes convection-dominated dissolution as another special case. In contrast to the thin-front theory, the wavelength of the instability is bounded from below, and lies In the range 1mm to 1km for physically reasonable flow rates and reaction rates. We have obtained an explicit expression for the growth rate when the change in porosity is small.

 Theoretical investigations of the reactive-infiltration instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. However, this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We have shown that the "inlet'' instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g. carbonate cements) is small, the instability in the steady-state equations is dominant.