simulation of dispersion in a heterogeneous aquifer: discussion of steady versus unsteady...
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Simulation of dispersion in a heterogeneous aquifer: discussion of steady versus unsteady groundwater flow
Gerard Uffink Amro ElfekiSophie Lebreton
Delft University of Technology, Netherlands
Demo 1: Steady Flow
Demo 2: Unsteady Flow (fluctuations)
Transport in steady or unsteady groundwater flow
0 4 0 0 8 0 0 1 2 0 0 1 6 0 0tim e (d ay s )
0
4 0 0
8 0 0
1 2 0 0
1 6 0 0 L o n g itu d in al V arian ceS te ad y flo wN o n S tea d y flo w
2x
Increase of variance in time
MADE-1 site
Literature:
Boggs et al. 1992Adams and Gelhar, 1992Rehfeldt et al. 1992Zheng and Jiao, 1998, etc
Available:
- measurement of tracer distribution- heads (contours) and fluctuations- hydraulic conductivities (several options)
Not available
- dispersivities
Depth-averaged bromide concentration distributions after 49, 279, and 503 days (Boggs et al., 1992).
Vertical position tracer plume
1 3 5 7 9 11 1 3 1 5 17 19 2 1 2 3 25 27 29 3 1t im e (m onth s)
0 .00 1
0 .00 2
0 .00 3
0 .00 4
0 .00 5
grad
ient
mag
nitu
de
m e as ured g rad ien tf itted season al com p o ne nt
Head data
Fluctuations head gradient Contours of head
0 50 100 150 200 250-100
-80
-60
-40
-20
0
0
4.3
43
430
0 20 40 60 80 100 120 140 160
-40
-20
0
0.781.323.561016264371116
Zheng & Jiao, 1998
(depth averaged)
Harvey & Gorelick, 2000(depth averaged)
Present Study (at 59 m depth)
Distribution of hydraulic conductivity according to various authors
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
49 days
279 days
503 days
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
0 20 40 60 80 100 120 140 160 180 200 220 240 260-100
-80
-60
-40
-20
0
0.1
1
10
100
49 days
279 days
503 days
Simulation tracer test (concentration in mg/L). K according to Zheng & Jiao
L= 1 m, T = 0.5 mL= 0.1 m, T = 0.01 m
Flow
Concentration distributions based on measurements
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
0.1
1
10
100
49 days
279 days
503 days
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
0 20 40 60 80 100 120 140 160-50
-40
-30
-20
-10
0
49 days
279 days
503 days
L= 0.1 m, T = 0.01 m L= 1 m, T = 0.5 m
Simulation tracer test (concentration in mg/L). K according to Harvey & Gorelick
49 days
279 days
503 days
0 50 100 150 200 250 300
-150
-100
-50
0
0 50 100 150 200 250 300
-150
-100
-50
0
0 50 100 150 200 250 300
-150
-100
-50
0
49 days
0 50 100 150 200 250 300
-150
-100
-50
0
0 50 100 150 200 250 300
-150
-100
-50
0
0 50 100 150 200 250 300
-150
-100
-50
0
279 days
503 days
0.1
1
10
100
L= 0.1 m, T = 0.01 m L= 1 m, T = 0.5 m
Simulation tracer test (concentration in mg/L). K as in present study
Comparison simulations and experiment
- head distribution good- tracer distribution poor
Possible explanation
- hydraulic conductivity field uncertain- velocity field uncertain
- ?? Steady versus unsteady flow ??
0 100 200 300 400 500 600tim e (days)
0
20
40
60
80m
ean
dis
plac
emen
t in
the
x-d
irect
ion
(m)
steady sta teseasonal trend fo r S=0.04 (cosine)m easured gradient for S =0.04 (dots)observed data
0 100 200 300 400 500 600tim e (days)
-35
-30
-25
-20
-15
-10
mea
n d
ispl
acem
ent
in t
he y
-dire
ctio
n (m
)
0 100 200 300 400 500 600tim e (days)
10
20
30
40
50
60
mea
n d
ispl
acem
ent
in t
he x
-dire
ctio
n (m
)
steady sta teseasonal trend for S=0 .04 (cosine )m easured gradien t fo r S=0.04 (dots)observed data
0 100 200 300 400 500 600tim e (days)
-35
-30
-25
-20
-15
-10
mea
n d
ispl
acem
ent
in t
he y
-dire
ctio
n (m
)
L= 0.1 m, T = 0.01 m
First Spatial Moments. K as by Harvey & Gorelick
L= 1 m, T = 0.5 m
L= 0.1 m, T = 0.01 m
Second Spatial Moments. K as by Harvey & Gorelick
L= 1 m, T = 0.5 m
0 100 200 300 400 500 600tim e (days)
0.0001
0.001
0.01
0.1
1
10
100
1000
10000lo
ngitu
dina
l va
rianc
e (m
2 )
steady s tateseasona l trend for S =0 .04 (co s ine )m ea su red g radien t fo r S=0.0 4 (d ots)observed da ta
0 100 200 300 400 500 600tim e (days)
0.1
1
10
100
late
ral
varia
nce
(m2 )
0 100 200 300 400 500 600tim e (days)
0.0001
0.001
0.01
0.1
1
10
100
1000
long
itudi
nal
varia
nce
(m2 )
0 100 200 300 400 500 600tim e (days)
0
20
40
60
80
late
ral
varia
nce
(m2 )
L= 0.1 m, T = 0.01 m
First Spatial Moments. K from present study
L= 1 m, T = 0.5 m
0 100 200 300 400 500 600tim e (days)
60
64
68
72
76
80m
ean
dis
plac
emen
t in
x-d
irect
ion
(m)
steady s ta teseasonal trend fo r S=0.04 (cosine)seasonal trend fo r S=0.1 (cosine)m easu re d grad ient fo r S=0.04 (do ts)observed da ta
0 100 200 300 400 500 600tim e (days)
-114
-112
-110
-108
-106
-104
mea
n d
ispl
acem
ent
in y
-dire
ctio
n (m
)
0 100 200 300 400 500 600tim e (days)
60
64
68
72
76
80
mea
n d
ispl
acem
ent
in x
-dire
ctio
n (m
)
steady s tateseasona l trend for S=0.04 (cosine)seasona l trend for S=0.1 (cos ine)m easu red grad ient for S=0.04 (dots)observed da ta
0 100 200 300 400 500 600tim e (days)
-116
-114
-112
-110
-108
-106
-104
mea
n d
ispl
acem
ent
in y
-dire
ctio
n (m
)
L= 0.1 m, T = 0.01 m
Second Spatial Moments. K from present study
L= 3 m, T = 1 m
0 100 200 300 400 500 600tim e (days)
0.001
0.01
0.1
1
10
100
1000
10000
long
itudi
nal
varia
nce
(m2 )
steady stateseasona l trend for S=0.04 (cosine)seasona l trend for S=0.1 (cos ine)m easured g radient fo r S=0.04 (do ts)observed data
0 100 200 300 400 500 600tim e (days)
1
10
100
late
ral
varia
nce
(m2 )
0 100 200 300 400 500 600tim e (days)
0.001
0.01
0.1
1
10
100
1000
10000
long
itudi
nal
varia
nce
(m2 )
steady s tateseasonal trend for S=0.04 (cos ine)seasonal trend for S=0.1 (cos ine)m ea sured grad ient fo r S=0.04 (do ts)observe d data
0 100 200 300 400 500 600tim e (days)
1
10
100
late
ral
varia
nce
(m2 )
Concluding remarks
- steady or unstead flow seems to have no effect on spreading of tracer
- good conductivity field is essential to reproduce realistic velocity field
- 2D versus 3D ??