Dispersion, retardation and scale effect in tracer breakthrough curves in karst conduits
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Characteristics of tracer breakthrough curves in karst conduits are examined and compared to results generated using well known equations applied to porous media. The equations of the turbulent dispersion lead to a transport equation similar to the classical advection–dispersion equation for porous media with a slightly different meaning for the dispersion and advection terms.For investigations at the meter length scale, we used a three-dimensional (3-D) computational fluid dynamics (CFD) code to simulate tracer transport in several conduit geometries. The simulations show that turbulent dispersion can be considered as Fickian at a meter length scale of observation and that turbulent dispersivity depends linearly on the average flow velocity in the range of observed velocities. The simulations show that pools induce retardation (tailing of the breakthrough curve) due to flow reversal in eddies. Retardation has a complex relationship with the pool dimensions. Irregularity of the conduit cross-section along the investigated section clearly produces retardation. This is obvious at the meter length scale but may still be visible 103 m downstream from the injection point. A transfer function (“black box”) approach is used for upscaling from a meter to a 103 m length scale. Before applying it to natural examples, the transfer function approach is tested by using the 3-D CFD code and appears to perform well. Several tests, based on numerical, laboratory and field experiments, of conduit segments which includes various dispersive features indicate that retardation tends to be transformed to symmetrical dispersion with distance. At large scale it appears that the dominant dispersion factor is the irregularity of the conduit geometry, which produces an increase in dispersivity with distance (“scale effect”), similar to that observed in porous media. In conclusion this suggests that retardation and high dispersion provide evidence of an irregular conduit, including either numerous dispersive features or large-scale ones (po