Temperature: A useful tracer for separating conduit and diffuse flow in the karstic Madison aquifer In cooperation with West Dakota Water Development District, City of Rapid City, South Dakota School of Mines and Technology Andy Long Patrick Gilcrease

Model shown conceptually Inflow from sinking stream Limestone Open passages Spring discharge Slow flow Conduit flow

Ts Tq Tr - = + Heat transport equation for flow in pipe Heat accumulation Heat flow in Convective heat from conduit wall Heat from slow inflow Heat flow out = +

Inflow from small openings Change in mass flow rate from slow inflow qs Change in velocity due to change in mass flow rate Final heat transport equation for the conduit

Mixing of conduit and slow flow to a well Limestone Open passages The well is a binary mixture of conduit flow and local slow flow Tq Tl 1+ dimensional model

Black Hills Model application Study area is dominated by streamflow recharge (~90%)

Spring Creek swallow holes

Temperature sensor Omega RTD class A ±0.03°C at 0°C Spring Creek Well house

Cross-section of Madison aquifer and conduit Heat-transport equation is solved in each model cell by finite difference

Data and results

Summary The model is useful for estimating the conduit flow fraction to a well or spring Conduit flow to the well varied temporally from 2 to 31% of total flow Conduit velocity ranged from 44 to 353 m/d Changes in temperature for the well were influenced by conduit velocity and the changing relative pressures of the conduit and surrounding aquifer

ht = heat transfer coefficient D = conduit diameter qs = flow rate of slow flow Ts = temperature of slow flow Tq = temperature of rocks Td = temperature of water at discharge point = conduit flow fraction (weighted by head)