# The role of dissolution kinetics in the development of karst aquifers in limestone: a model simulation of karst evolution

#### Abstract

To model the development of karst aquifers from primary fissures in limestone rock, a numerical model of solutional widening of such fractures by calcite agressive water is suggested. The geological setting determines relevant geometrical parameters, i.e., length of the fracture, its initial width and the hydraulic gradient driving water from the input to the output. To simulate the solutional widening as it proceeds in time, the solution rates must be known as a function of concentration c of dissolved calcite. They are given as a first-order kinetic rate law for as . For close to equilibrium, a fourth-order rate law becomes dominant: . The parameters , and k depend on the chemistry of the carbonate system and rock chemistry. The saturation concentration, c_{eq}, with respect to calcite depends on the initial concentration of the inflowing solution, thus reflecting the influence of climate. The value of k for natural limestone ranges between 0.5 and 0.9. The results of the model show that the concerted action of both fast first-order kinetics and slow fourth-order kinetics is necessary to create early karst channels of several cm width in geologically reasonable times. At the beginning of the process the solutional widening occurs by slow fourth-order kinetics along the entire length of the fracture, because water reaches sufficiently high concentrations less than 1 m from the input. This widens the fissure slowly. As a consequence, increasing water flow rate increases the distance where first-order kinetics are operative. This region propagates through the length of the fracture with accelerating speed until it reaches the outlet. At the moment of breakthrough the flow rate increases dramatically by several orders of magnitude. From then on, further solutional widening is essentially constant along the entire length of the fracture, on the order of about . The breakthrough time is a significant measure in studies of karstification and has been calculated for a wide range of geometrical parameters. Expressions f

*This paper has been withdrawn.*