USING A MULTI-TRACER EXPERIMENT TO ESTIMATE FLOW PATH GEOMETRY

In karst aquifers, flow and transport are predominantly controlled by conduits, but their location and geometry are largely unknown. To provide constraints on this uncertainty, karst hydrologists frequently estimate an upper bound on conduit volume by summing discharge between hydraulic and chemical or thermal responses for fully submerged conduits or by summing discharge between injection and detection of a tracer. If a good estimate of flow path distance is available, then estimates of conduit cross-sectional area and diameter are also possible.

We propose a new, complementary method which enables estimates of flow path geometry using a modified temperature signal at a spring. We conducted a multi-tracer experiment where we dumped a pool with approximately 13,000 L of water and several tracers into a sinkhole near Freiheit Spring, MN. Flow peaked first at the spring and was followed by a suspended sediment peak; then essentially identical uranine, chloride, and δD peaks; and finally a temperature peak. By summing discharge between the time of the initial increase in stage produced by a pressure pulse and the time of the chloride peak, the conduit volume is estimated as 51 m³. With an estimate of flow path distance, the conduit cross-sectional area and diameter for a circular conduit are 0.36 m² and 0.68 m, respectively. Water temperature interacted with the aquifer as it moved along the flow path, producing a damped, lagged thermal signal at the spring. We used heat transport simulations to reproduce the observed thermal breakthrough curve. Our best fits in both cylindrical conduit and planar fracture simulations required a hydraulic diameter of < 0.1 m, much less than the estimate using the traditional method. Our best fit occurred with a planar fracture simulation with a hydraulic diameter of 0.07 m. This corresponds to a flow path height of 0.035 m for a low, wide flow path. If combined with the cross-sectional estimate using the traditional method, then the flow path width is 10 m, in agreement with the observed spring geometry. Multiple tracers permit a flow path to be probed in many ways, and the combination of parameters provides more powerful constraints on flow path geometry.