in cooperation with west dakota water development district, city of rapid city,
DESCRIPTION
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. Limestone Open passages. - PowerPoint PPT PresentationTRANSCRIPT
U.S. Department of the InteriorU.S. Geological Survey
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
LimestoneOpen passages
Spring discharge
Conduit flow
Slow flow
0 0
qp p q p q t r q s p s
x x x
dTA x C mC T mC T h D x T T q xC T
dt
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
0
s
d mq
dx
0 2 2
4 4 4q qt s sr q x q s
p
T Th q x qT T T T
t D C D x D
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
02
4
d D d m
dx dx
Mixing of conduit and slow flow to a well
LimestoneOpen passages
The well is a binary mixture of conduit flow and local slow flow
(1 )d q lT T T
Tl
Tq
1+ dimensional model
Cross-section of Madison aquifer and conduit
Heat-transport equation is solved in each model cell by finite difference
0 2 2
4 4 4q qt s sr q x q s
p
T Th q x qT T T T
t D C D x D
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