Influence of initial heterogeneities and recharge limitations on the evolution of aperture distributions in carbonate aquifers

Abstract. Karst aquifers evolve where the dissolution of soluble rocks causes the enlargement of discrete pathways along fractures or bedding planes, thus creating highly conductive solution conduits. To identify general interrelations between hydrogeological conditions and the properties of the evolving conduit systems the aperture-size frequency distributions resulting from generic models of conduit evolution are analysed. For this purpose, a process-based numerical model coupling flow and rock dissolution is employed. Initial protoconduits are represented by tubes with log-normally distributed aperture sizes with a mean μ₀ = 0.5 mm for the logarithm of the diameters. Apertures are spatially uncorrelated and widen up to the metre range due to dissolution by chemically aggressive waters. Several examples of conduit development are examined focussing on influences of the initial heterogeneity and the available amount of recharge. If the available recharge is sufficiently high the evolving conduits compete for flow and those with large apertures and high hydraulic gradients attract more and more water. As a consequence, the positive feedback between increasing flow and dissolution causes the breakthrough of a conduit pathway connecting the recharge and discharge sides of the modelling domain. Under these competitive flow conditions dynamically stable bimodal aperture distributions are found to evolve, i.e. a certain percentage of tubes continues to be enlarged while the remaining tubes stay small-sized. The percentage of strongly widened tubes is found to be independent of the breakthrough time and decreases with increasing heterogeneity of the initial apertures and decreasing amount of available water. If the competition for flow is suppressed because the availability of water is strongly limited breakthrough of a conduit pathway is inhibited and the conduit pathways widen very slowly. The resulting aperture distributions are found to be unimodal covering some orders of magnitudes in size. Under these suppressed flow conditions the entire range of apertures continues to be enlarged. Hence, the number of tubes reaching aperture sizes in the order of centimetres or decimetres continues to increase with time and in the long term may exceed the number of large-sized tubes evolving under competitive flow conditions. This suggests that conduit development under suppressed flow conditions may significantly enhance the permeability of the formation, e.g. in deep-seated carbonate settings.