Modeling the evolution of karst aquifers and speleogenesis. The step from 1-dimensional to 2-dimensional modeling domains

First models of karst evolution considered a single isolated fracture with no loss of flow along its entire length. Under conditions of constant head dissolution of limestone creates a positive feedback-loop of increase of aperture widths and flow until at breakthrough the flow and aperture width are enhanced dramatically. If a second dimension is added to this model domain, in the simplest case by an exit-tube connected to the isolated channel, water loss from the isolated channel occurs. We have investigated the influence of the water loss on the breakthrough time of the single channel. In all cases, when water loss is present, more aggressive solution enters at the input. The aggressive solutional activity penetrates deeper along the conduit. Therefore dissolutional widening at the exit is enhanced and breakthrough times are reduced. This is discussed in detail by investigating the profiles of hydraulic head, flow rates, aperture widths, and calcium concentrations along the conduit as they evolve in time and comparing them to those of the isolated 1-D conduit. In a further step the 1-D conduit is embedded into a net of fractures with smaller aperture widths. The conduit is located in the center of the rectangular domain and connected to the 2-D net at equally spaced nodes. By this way exchange flow from the conduit into the net can arise. But also flow from the net to the conduit is possible. We have studied the evolution of this aquifer considering dissolution also in the network of the narrow fissures. Flow from the main central fracture into the net again reduces breakthrough times. After breakthrough, however, a complex exit fan evolves in the net, which later on is overprinted by a net of entrance fans propagating down flow. These fans are related to flow from the net into the central fracture. The evolution of these fans resulting finally in a maze-like structure is significant for high hydraulic gradients (i30.1) as they exist at artificial dam sites. For such situations realistic modeling has to include dissolutional widening in the net. For low hydraulic gradients, i<0.03, the evolution in the net is slow compared to that of the central conduit and therefore the aquifer is dominated by the evolution of the central fracture.