Transcript Tracer Tests - Rice University

Tracers for Flow and
Mass Transport
Philip Bedient
Rice University
2004
Transport of Contaminants
• Transport theory tries to explain the rate and
extent of migration of chemicals from known
source areas
• Source concentrations and histories must be
estimated and are often not well known
• Velocity fields are usually complex and can
change in both space and time
• Dispersion causes plumes to spread out in x and y
• Some plumes have buoyancy effects as well
Transport of Contaminants
What Drives Mass Transport:
Advection and Dispersion
• Advection is movement of a mass of fluid at the
average seepage velocity, called plug flow
• Hydrodynamic dispersion is caused by velocity
variations within each pore channel and from one
channel to another
• Dispersion is an irreversible phenomenon by
which a miscible liquid (the tracer) that is
introduced to a flow system spreads gradually to
occupy an increasing portion of the flow region
Advection and Dispersion
in a Soil Column
Source Spill t = 0
Conc = 100 mg/L
Longitudinal Dispersion t = t1
n = Vv/Vt
porosity
Advection t = t1
C
t
Contaminant Transport in 1-D
Fx
Fx + (dFx/dx) dx
y
z
Fx = total mass per area transported in x direction
Fy = total mass per area transported in y direction
Fz = total mass per area transported in z direction
C
Fx  v x nC  nDx
x
C 
Inflow Outflow n  d xdydz
 t 
Substituting in Fx for the x direction only yields
2 

C
C
C
 D  2 V
t
x
x 

Accumulation Dispersion

Advection
C = Concentration of Solute [M/L3]
D = Dispersion Coefficient [L2/T]
V = Velocity in x Direction [L/T]
2-D Computed Plume Map
Advection and Dispersion

Analytical 1-D, Soil Column
•
•
•
•
Developed by Ogata and Banks, 1961
Continuous Source
C = Co at x = 0 t > 0
C (x,) = 0 for t > 0
  x  vt 


erfc 




2
Dt


C
 0.5

C0
vx 
 x  vt 
 exp
 erfc 



 D 
 2 Dt 

Error Function - Tabulated Fcn
Erf (x) 
Erf (0) = 0
Erf (3) = 1
Erfc (x) = 1 - Erf (x)
Erf (–x) = – Erf (x)
2

x
e
u 2
du
0
x

Erf
x
Erf(x) Erfc(x)
0
0
1
.25
.276
.724
.50
.52
.48
1.0
.843
.157
2.0
.995
.005
Contaminant Transport Equation
CB
 
C  
CW

BCVI  
BDIJ

t
x I 
x J  x I
n
C = Concentration of Solute [M/L3]
DIJ = Dispersion Coefficient [L2/T]
B = Thickness of Aquifer [L]
C’ = Concentration in Sink Well [M/L3]
W = Flow in Source or Sink [L3/T]
n = Porosity of Aquifer [unitless]
VI = Velocity in ‘I’ Direction [L/T]
xI = x or y direction
Analytical Solutions of Equations
Closed form solution, C = C ( x, y, z, t)
– Easy to calculate, can often be done on a spreadsheet
– Limited to simple geometries in 1-D, 2-D, or 3-D
– Limited to simple sources such as continuous or
instantaneous or simple combinations
– Requires aquifer to be homogeneous and isotropic
– Error functions (Erf) or exponentials (Exp) are usually
involved
Numerical Solution of Equations
Numerically -- C is approximated at each point of
a computational domain (may be a regular grid or
irregular)
– Solution is very general
– May require intensive computational effort to get the
desired resolution
– Subject to numerical difficulties such as convergence
problems and numerical dispersion
– Generally, flow and transport are solved in separate
independent steps (except in density-dependent or
multi-phase flow situations)
Domenico and Schwartz (1990)
• Solutions for several geometries (listed in Bedient
et al. 1999, Section 6.8).
• Generally a vertical plane, constant concentration
source. Source concentration can decay.
• Uses 1-D velocity (x) and 3-D dispersion (x,y,z)
• Spreadsheets exist for solutions.
• Dispersion = axvx, where ax is the dispersivity (L)
• BIOSCREEN (1996) is handy tool that can be
downloaded.
BIOSCREEN Features
•
•
•
•
Answers how far will a plume migrate?
Answers How long will the plume persist?
A decaying vertical planar source
Biological reactions occur until the electron acceptors in
GW are consumed
• First order decay, instantaneous reaction, or no decay
• Output is a plume centerline or 3-D graphs
• Mass balances are provided
Domenico and Schwartz (1990)
y
Vertical
Source
z
Plume at time t
x
Domenico and Schwartz (1990)
For planar source from -Y/2 to Y/2 and 0 to Z
Cx, y,z,t  1   x  vt 
  erfc

8  2 a x vt 
C0

y  Y 2 
 y  Y 2 

- erf

erf


2 a y x 

2 a y x 

 


 z  Z 
  z  Z 

- erf

erf


2 a z x 

2 a z x 

 

Y
Z
Flow x
Geometry
Instantaneous Spill in 2-D
Spill source C0 released at x = y = 0, v = vx
First order decay and release area A
C0 A
Cx, y,z,t  

1/ 2
4(t)(Dx Dy )
(x  vt)
y
exp[

 t]
4Dx t
4Dy t
2
2
2-D Gaussian Plume moving at velocity V
Breakthrough Curves
2 dimensional Gaussian Plume
Predicted Rice ECRS Tracer Test w/ acm
400
350
Concentration (mg/L)
300
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
250
200
150
100
50
0
0
10
20
30
40
50
Time (hours)
60
70
80
90
Tracer Tests
• Aids in the estimation of average hydraulic
conductivity between sampling locations
• Involves the introduction of a non-reactive
chemical species of known
concentration
Predicted Rice ECRS Tracer Test w/ acm
• Average seepage velocities
can be calculated from
resulting curves of
concentration vs. time
using Darcy’s Law
400
350
Concentration (mg/L)
300
C-1
C-2
C-3
C-4
C-5
C-6
C-7
C-8
250
200
150
100
50
0
0
10
20
30
40
50
Time (hours)
60
70
80
90
What can be used as a tracer?
• An ideal tracer should:
1. Be susceptible to quantitative determination
2. Be absent from the natural water
3. Not react chemically or be absorbed
4. Be safe in drinking water
5. Be inexpensive and available
• Examples:
– Bromide, Chloride, Sulfates
– Radioisotopes
– Water-soluble dyes
Tracer Test Results from Locations Down the Centerline in
Rice ECRS
900
Hour 14
Hour 43
800
Concentration (mg/L)
700
600
Line 21
Line 22
Line 23
Line 24
Line 25
Line 26
Line 27
Line 28
Hour 85
500
400
300
200
100
Hour 8
Hour 30
0
20
Hour 55
Hour 79
0
40
60
Time (hours)
80
100
120
Bromide Tracer Front - ECRS
Outlet
10
1
21
2
3
22
23
15
16
Inlet
13
11
9
14
12
4
5
24
25
6
26
17
18
7
8
27
28
19
20
Black Arrows @ t= 40 hrs
Red Arrows @ t= 85 hrs
New Experimental Tank
•
•
•
•
5000 mg/L Bromide tracer in advance of ethanol test
Pumped into 6 wells for 7 hour injection period
Pumping rate of 360 mL/min was maintained
Background water flow rate was 900-1000 mL/min
PLAN VIEW OF TANK
Flow
Line A Shallow
Line B Intermediate
New Tank Bromide Tracer Test July 2004
5000
1B
4500
2B
Bromide Concentration (mg/L)
4000
4B
3500
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
Tim e (Hours)
25
30
35
Line E Center
New Tank Bromide Tracer Test July 2004
5000
0.5E
4500
1E
Bromide Concentration (mg/L)
4000
2E
3500
4E
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
Time (Hours)
25
30
35
Line I Shallow
New Tank Bromide Tracer Test July 2004
5000
0.5I
4500
1I
2I
Bromide Concentration (mg/L)
4000
4I
3500
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
Tim e (Hours)
25
30
35
July 2004 New Tank prior to 95E test
(5.5 ft to 9.5 ft down tank)
Lines Time 2 Time 1 Distance (ft)
0.5A to 1A
4
3
0.5
1A to 2A
5
4
1
2A to 4A
13
5
2
Gradient Seepage Velocity (ft/hr) Vs (ft/day) Vs (m/day) K (ft/hr) K (ft/day) K (cm/sec)
0.027778
0.500
12.000
3.658
5.580
133.92 4.724E-02
0.027778
1.000
24.000
7.315
11.160 267.84 9.449E-02
0.027778
0.250
6.000
1.829
2.790
66.96
2.362E-02
0.5E to 1E
1E to 2E
2E to 4E
6
8
12
4
6
8
0.5 0.027778
1 0.027778
2 0.027778
0.250
0.500
0.500
6.000
12.000
12.000
1.829
3.658
3.658
2.790
5.580
5.580
66.96
133.92
133.92
2.362E-02
4.724E-02
4.724E-02
0.5I to 1I
1I to 2I
2I to 4I
8
10
14
6
8
10
0.5 0.027778
1 0.027778
2 0.027778
0.250
0.500
0.500
6.000
12.000
12.000
1.829
3.658
3.658
2.790
5.580
5.580
66.96
133.92
133.92
2.362E-02
4.724E-02
4.724E-02
1B to 2B
2B to 2B
10
17
5
10
1 0.027778
2 0.027778
0.200
0.286
4.800
6.857
1.463
2.090
2.232
3.189
53.57
76.53
1.890E-02
2.700E-02