Influence of aperture variability on dissolutional growth of fissures in karst formations

The influence of aperture variability on dissolutional growth of fissures is investigated on the basis of two-dimensional numerical simulations. The logarithm of the fissure aperture before dissolution begins is modeled as a Gaussian stationary isotropic random field. The initial phase of dissolutional growth is studied up to the time when turbulent flow first occurs at a point within the fissure (the breakthrough time). The breakthrough time in variable aperture fissures is smaller than that in uniform fissures and decreases as the coefficient of variation of the aperture field (sigma/mu) increases. In comparing uniform and variable aperture fissures in limestone, the breakthrough time with sigma/mu = 0.1 is about a factor of 2 smaller than that in a uniform fissure. The breakthrough time is reduced by about an order of magnitude with sigma/mu = 2.0. The mechanism leading to reduced breakthrough times is the focusing of flow into preferential flow channels which are enlarged at a faster rate than the surrounding regions of slower flow. Dissolution channels are narrower and more tortuous as sigma/mu. increases. Investigations of the influence of reaction rate reveal that the influence of aperture variability is more pronounced in rapidly dissolving rock. In uniform fissures in rapidly dissolving minerals, breakthrough times are very long since water becomes saturated with respect to the mineral within a short distance of the entrance to the flow path. However, in variable aperture fissures, breakthrough occurs rapidly because of selective growth along preferential flow channels, which progressively capture larger fractions of the total flow. These results partly explain why conduits develop rapidly in gypsum, although previous one-dimensional studies suggest that conduit growth will not occur.