Scale-Dependence of Dissolution Growth Rates in Variable-Aperture Fractures

We present results from a high-resolution computational study of dissolution of variable aperture fractures. Aperture variability is modeled as a stationary spatially correlated random field. Dissolutional growth of the fracture aperture is simulated by coupled solution of the fluid flow and mineral transport equations through a succession of quasi-steady states of aperture evolution. Dissolution kinetics is modeled using a nonlinear rate expression, corresponding to experimentally determined rates for natural limestones. Dissolution channels are initiated along preferential flow paths, leading to highly channelized growth patterns. A single dominant channel breaks through and spans the domain just prior to the onset of turbulent flow. The breakthrough time is an indicator of the time scale required for karstification, since the initial growth phase during laminar flow is the slowest. The dependence of the breakthrough time on aperture field statistics is investigated by carrying out simulations in 10 random field realizations for each set of statistical parameters. The breakthrough time is found to be relatively insensitive to changes in correlation length, while it is very sensitive to the coefficient of variation (cv) of the aperture field. An interesting scale-dependence was observed in the variation of breakthrough time with cv, with substantial differences between shorter (less than 15 correlation lengths) domains and longer ( greater than 20 correlation lengths) domains. This observation is fairly robuust across independent realizations of the random aperture field. We explain these differences by analyzing the nature of evolving preferential flow during dissolution growth, competition between channels and branching of the dominant channel.