1. 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

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

3. 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 = +

4. 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

5. 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

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

7. Spring Creek swallow holes

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

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

11. Data and results

12. 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

13. 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)