anwendung von umweltisotopen zur bestimmung hydrologischen … · 2015. 1. 19. · 1 h2 16o...
TRANSCRIPT
Anwendung von Umweltisotopen
zur Bestimmung hydrologischen Parametern
im Grundwasser
Piotr Maloszewski
Helmholtz Zentrum Muumlnchen
Institut fuumlr Grundwasseroumlkologie
85764 Neuherberg maloszewskihelmholtz-muenchende
TransAqua TP5 Workshop
bdquoAufbereitung von Wasserproben und Nachweis von Radionukliden in Wasserprobenldquo
KIT Karlsruhe 25-27 November 2014
Environmental tracers in the water cycle
Environmental
tracers
Environmental
tracers
Environmental
tracers
Environmental
tracers
Environmental
tracers Environmental
tracers
Environmental
tracers
Environmental tracers
Radioactive tracers
Tritium (3H) T12 = 124 a
Krypton-85 (85Kr) T12 = 108 a
Argon-39 (39Ar) T12 = 276 a
Carbon-14 (14C) T12 = 5730 a
Chlor-36 (36Cl) T12 =300000 a
Nonradioactive tracers (stable isotopes)
Oxygen-18 (18O)
Deuterium (2H)
Helium-3 (3He)
CFCs
Origin of tritium (3H)
A Natural production of tritium through cosmic radiation
HCnN 31
126
10
147
B Thermonuclear explosions (fusion)
eHHH 01
31
21
11
It yields mean concentration in precipitation 5-10 TU (06-12 Bql 16-32 pCil)
It has yield peak concentration in precipitation of ca 4000 TU in 1963 (480 Bql 2560 pCil)
)18(0
1
3
2
3
1 keVHeH
Tritium is radioactive (T12=124 years)
TRITIUM - INPUT FUNCTION
1E+01
1E+02
1E+03
1E+04
1950 1960 1970 1980 1990 2000
CALENDAR YEARS
TR
ITIU
M [
TU
]
Stable isotopes of water
1H1H16O 1H2H16O ndash 0032 1H1H18O ndash 0200
1H - 999844 2H - 00156 3H - 10-15
16O - 997630 17O - 00379 18O - 02005
permil1000
Standard
StandardSample
R
RRSample
H
Hor
O
ORwith
1
2
16
18
-values are relative values expressed in [permil] in the comparison
to the standard which is the mean ocean water V-SMOW
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Environmental tracers in the water cycle
Environmental
tracers
Environmental
tracers
Environmental
tracers
Environmental
tracers
Environmental
tracers Environmental
tracers
Environmental
tracers
Environmental tracers
Radioactive tracers
Tritium (3H) T12 = 124 a
Krypton-85 (85Kr) T12 = 108 a
Argon-39 (39Ar) T12 = 276 a
Carbon-14 (14C) T12 = 5730 a
Chlor-36 (36Cl) T12 =300000 a
Nonradioactive tracers (stable isotopes)
Oxygen-18 (18O)
Deuterium (2H)
Helium-3 (3He)
CFCs
Origin of tritium (3H)
A Natural production of tritium through cosmic radiation
HCnN 31
126
10
147
B Thermonuclear explosions (fusion)
eHHH 01
31
21
11
It yields mean concentration in precipitation 5-10 TU (06-12 Bql 16-32 pCil)
It has yield peak concentration in precipitation of ca 4000 TU in 1963 (480 Bql 2560 pCil)
)18(0
1
3
2
3
1 keVHeH
Tritium is radioactive (T12=124 years)
TRITIUM - INPUT FUNCTION
1E+01
1E+02
1E+03
1E+04
1950 1960 1970 1980 1990 2000
CALENDAR YEARS
TR
ITIU
M [
TU
]
Stable isotopes of water
1H1H16O 1H2H16O ndash 0032 1H1H18O ndash 0200
1H - 999844 2H - 00156 3H - 10-15
16O - 997630 17O - 00379 18O - 02005
permil1000
Standard
StandardSample
R
RRSample
H
Hor
O
ORwith
1
2
16
18
-values are relative values expressed in [permil] in the comparison
to the standard which is the mean ocean water V-SMOW
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Environmental tracers
Radioactive tracers
Tritium (3H) T12 = 124 a
Krypton-85 (85Kr) T12 = 108 a
Argon-39 (39Ar) T12 = 276 a
Carbon-14 (14C) T12 = 5730 a
Chlor-36 (36Cl) T12 =300000 a
Nonradioactive tracers (stable isotopes)
Oxygen-18 (18O)
Deuterium (2H)
Helium-3 (3He)
CFCs
Origin of tritium (3H)
A Natural production of tritium through cosmic radiation
HCnN 31
126
10
147
B Thermonuclear explosions (fusion)
eHHH 01
31
21
11
It yields mean concentration in precipitation 5-10 TU (06-12 Bql 16-32 pCil)
It has yield peak concentration in precipitation of ca 4000 TU in 1963 (480 Bql 2560 pCil)
)18(0
1
3
2
3
1 keVHeH
Tritium is radioactive (T12=124 years)
TRITIUM - INPUT FUNCTION
1E+01
1E+02
1E+03
1E+04
1950 1960 1970 1980 1990 2000
CALENDAR YEARS
TR
ITIU
M [
TU
]
Stable isotopes of water
1H1H16O 1H2H16O ndash 0032 1H1H18O ndash 0200
1H - 999844 2H - 00156 3H - 10-15
16O - 997630 17O - 00379 18O - 02005
permil1000
Standard
StandardSample
R
RRSample
H
Hor
O
ORwith
1
2
16
18
-values are relative values expressed in [permil] in the comparison
to the standard which is the mean ocean water V-SMOW
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Origin of tritium (3H)
A Natural production of tritium through cosmic radiation
HCnN 31
126
10
147
B Thermonuclear explosions (fusion)
eHHH 01
31
21
11
It yields mean concentration in precipitation 5-10 TU (06-12 Bql 16-32 pCil)
It has yield peak concentration in precipitation of ca 4000 TU in 1963 (480 Bql 2560 pCil)
)18(0
1
3
2
3
1 keVHeH
Tritium is radioactive (T12=124 years)
TRITIUM - INPUT FUNCTION
1E+01
1E+02
1E+03
1E+04
1950 1960 1970 1980 1990 2000
CALENDAR YEARS
TR
ITIU
M [
TU
]
Stable isotopes of water
1H1H16O 1H2H16O ndash 0032 1H1H18O ndash 0200
1H - 999844 2H - 00156 3H - 10-15
16O - 997630 17O - 00379 18O - 02005
permil1000
Standard
StandardSample
R
RRSample
H
Hor
O
ORwith
1
2
16
18
-values are relative values expressed in [permil] in the comparison
to the standard which is the mean ocean water V-SMOW
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Stable isotopes of water
1H1H16O 1H2H16O ndash 0032 1H1H18O ndash 0200
1H - 999844 2H - 00156 3H - 10-15
16O - 997630 17O - 00379 18O - 02005
permil1000
Standard
StandardSample
R
RRSample
H
Hor
O
ORwith
1
2
16
18
-values are relative values expressed in [permil] in the comparison
to the standard which is the mean ocean water V-SMOW
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
-90
-80
-70
-60
-50
-40
-30
-11 -10 -9 -8 -7 -6 -5 -4
18
O [permil]
2H
[permil
]
Origin of groundwater
GMWL from IAEA
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Obs well W1
Obs well W2
LAKE
(END MEMBER B)
LMWL
GW
(END MEMBER A)
Evaporation Line
Mixing of waters having different origin
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Altitude of recharge zone [m asl] (δ18O)
On which altitude (h) is its recharge area
Nr 7 has r a at (h) ap 2000m
from IAEA
In Central Europe the δ18O content decreases (01 ndash 05) [permil] per 100 m increased altitude
This information can be use to estimate the altitude of recharge
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
bull Peak-shift method
p
Z
t
dzz
q
p
0
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)δ2H [permil]
Precipitation stations
Kibi
Nsawan
sampling time in the depth profile
Δtp
z
2H
depth
pore water
zp
k
k
iiii
meanz
zz
11 )(
p
Zp
qmean = Zp Θmean Δtp
p
Z
t
dzz
q
p
0
Theory
That equation we can simplyfied to
Peak shift of δ2H for the estimation of recharge
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
0
1
2
3
4
5
6
7
0 005 01 015 02 025 03 035 04 045
water content adn porosity (msup3msup3)
dep
th (
m)
0
1
2
3
4
5
6
7
-40 -35 -30 -25 -20 -15
2H (permil)
dep
th (
m)
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
0
50
100
150
200
250
300
350
400
Jan 06 Jul 06 Jan 07 Jul 07 Jan 08 Jul 08
pre
cip
itati
on
(m
m m
on
th-1
)
-40
-35
-30
-25
-20
-15
-10
-5
0
2H
(permil
)
KibiNsawand2H (permil)
samplingt
qmean = zp mean Δtp = 075 m 023 1 a =017 ma 170 mma
Result from Peak Shift Method
Δtp = 1yr
Zp = 075m Θmean = 023
Peak shift of δ2H for the estimation of recharge
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
g(t)Cinp(t) Cout(t)
C t C t g dout inp( ) ( ) ( )exp
0
Properties of transit time distribution function
g d( )
10
g d T( )0
Q V
Mean transit time of water T = V Q
g()
Mathematical modelling of time-dependent
isotope concentrations
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
EM - Exponential-Model (T)
Transit time distribution functions
EPM - Combined Exponential-Piston Flow Model (T η)
PFM - Piston-Flow-Model (T) )()( Tg
T
Tg
)(exp)(
)1(exp)(
TT
g for gt ( - 1)T
g ( 0 for le ( - 1)T
TP
T
TPg
4
)1(exp
4
1)(
2
DM - Dispersion Model (T P)
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Transit time distribution functions
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
Pro
ba
bil
ity
[
]
DM
T=10 years
PD=001
PD=050
000
005
010
015
020
025
030
0 2 4 6 8 10 12 14 16 18 20
Transit time [years]
g(
) [
1y
ea
r ]
DM
T=10 years
PD=001
PD=050
37
5
20
P
ort
ion
[
]
Portion of water with different transit time
in the outflow from the system
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Karst catchment area
Schneealpe (Austria)
S= 23 km2
H= 900 m
Precipitation (INPUT)
P = 1050 mma (-1129 permil)
Outflow (OUTPUT)
Q = 510 Ls (690mma)
QSQ = 314 Ls ( -1204 permil)
QWQ = 196 Ls ( -1176 permil)
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
MOBILE
WATER
IMMOBILE
WATER
DRAINAGE CHANNELS
FISSURED-POROUS MASSIF
(DOUBLE POROUS)
PISTON FLOW MODEL (TC)
VC = QC TC
DISPERSION MODEL (TP)
T = (TP) = R TP
R = (nim + nm) nm
Vtotal = QP (TP)
g toc( ) ( )
g
P t
t
P tD op
op
D op
( )
exp
1
4
1
4
2T
T -
TC
Conceptual and mathematical model for the karst catchment
Tracer combined application
of O-18 and Tritium
Karst catchment
T
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Transit time through the massif ndash Tritium by base-flow
0
50
100
150
200
250
300
1970 1975 1980 1985 1990 1995
YEARS
TR
ITIU
M [T
U] DM
(TP)WQ = 26 years
(TP)SQ = 14 years
PD = 012
Karst catchment
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
0
50
100
150
200
250
300
0 36 72 108 144 180 216
MONTHS (1973-1990)
PR
EC
IPIT
AT
ION
[m
mm
on
th]
0
100
200
300
400
500
600
0 36 72 108 144 180 216
MONTHS (1973-1990)
DIS
CH
AR
GE
[L
s]
-21
-17
-13
-9
-5
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
-14
-13
-12
-11
-10
0 36 72 108 144 180 216
MONTHS (1973-1990)
OX
YG
EN
-18
CO
NT
EN
T [
o]
Channel flow O18 combined with rechargedischarge data
(TC)WQ=1month (TC)SQ=14months
Karst catchment
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Karst catchment
Final Results
Q=510Ls V=250times106 m3
Infiltrated water Q(t) Cin(t)
Karstic springQ(t)=Qc(t)+Qp(t)
Qc(t) Qp(t)
Cp(t)
Fissured-porous
aquifer (Tp=19 a)
Vp =246 106m3 (993)Qp=420 Ls (825)
Dra
ina
ge
ch
an
ne
ls
Tc=
1 m
on
th
Vc =16 106 m3 (065)
Qc = 90 Ls (175) C(t)
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
2223 km
DANUBE
2221 km o PS I o PS II 150m
River water
local ground water
Drinking water supply for PASSAU on the island
SOLDATENAU (03 km2) at Danube river
Production wells PS I and PS II with ca 105 Lsec
Bank filtration to the water supply
Transit time and portion of River water
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
-15
-14
-13
-12
-11
-10
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o] Local groundwater
Danube River
Bank filtration to the water supply
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
PUMPING WELL
C(t)=CPW(t)
DANUBE RIVER
Cin(t)=CDR(t)
LOCAL GROUNDWATER
CLG(t) = const
p Q
Q
(1-p) QT PD
Portion of Danube River water in the pumping well (mass balance equation)
LGDRPW OpOpO )()1()()( 181818
LGDR
LGPW
OO
OOp
1818
1818
Bank filtration to the water supply
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
LG
t
DRPW OpdtgCptC 18
0
)1()()()(
TP
T
TPg
4
)1(exp
4
1)(
2
Fitting-parameters T and P
Mathematical modelling of the bank filtration
-14
-13
-12
-11
0 6 12 18 24 30 36
MONTHS (Jan 90 - Dec 92)
OX
YG
EN
-18 I
N [
o]
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
0000
0002
0004
0006
0008
0010
0012
0014
0016
0018
0020
0 20 40 60 80 100 120
Transit time [days]
g(
) [
1d
ay
]
DM
T=60 days
PD=012
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100 110 120
Transit time [days]
Pro
ba
bil
ity
[
]
DM
T=60 days
PD=012
Bank filtration to the water supply
- portion of contaminated water
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
Deltaic Aquifer (unconfined Quaternary sediments sand and gravel)
Mean thickness 50 m
Glaciomarine with thickness of about 15-20 m
Silt Aquitard of 95 m thickness
Proglacial Aquifer
Issue quantifying of water velocity (hydraulic conductivity)
using 3H-3He method and numerical modeling
predicting of pollutant movement
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Applying of 3He3H method for bdquokldquo estimation
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
z=828m
hw=1665m
CT =1340 TU
CHe= 237 TU
x=900m
z=1168m
hw=1624m
CT =1270 TU
CHe= 865 TU
x=1260m
z=1042m
hw=1614m
CT =1440 TU
CHe=1173 TU
x=1930m
z=1008m
hw=1565m
CT =1250 TU
CHe=2065 TU
Letrsquos estimate now water age (assuming advective flow)
1ln
1
T
He
C
CT
T=173 years T=106 years T=92 years T=29 years
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Calculation of resulting parameters
Murphy et al (2010) Hydrogeology Journal 19 195-207
South Flow Path
x=0
T=29years
x=1930m
T=173years
Δx=1930m
ΔT=144years v=134 myear
i=ΔhΔx=(1665-1565)m1930m=00052 k=28610-4 ms for n=035
Applying of 3He3H method for bdquokldquo estimation
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Applying of 3He3H method for bdquokldquo estimation
Valley fill aquifer ldquoValcartierrdquo (Quebeck Canada) contaminated with TCE
v=195myear k=4710-4ms
v=134myear k=2910-4ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Leakage through Silt Aquitard to Proglacial Aquifer
Mean age above Silt T=15 years
Mean age below Silt T=27 years
Δz= 905 m (thickness of the Silt)
ΔT=12 years vz=075 myear
Δhz=302m (vertical hydraulic head difference) iz=ΔhzΔz=032 kz=2610-8 ms
Murphy et al (2010) Hydrogeology Journal 19 195-207
Applying of 3He3H method for bdquokldquo estimation
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Parameters for numerical modelling
Capture zone of the pumping well
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
NUMERICAL MODELING
OF WATER FLOW
FEFLOW
Region Case 1 Case 2
k [ms] k [ms]
Area (A) 12times10-4 4times10-4
Area (B) 50times10-4 15times10-4
Area (C) 15times10-4 8times10-4
Area (D) 19times10-4 12times10-4
Water flux [m3d] [m3d]
Inflow +18570 + 4840
Outflow -17620 - 3890
Recharge + 5900 + 5900
Pumping rate - 6850 - 6850
Balance 0 0
Error 0 0
bdquoClassicalldquo numerical modelling of water flow
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
O-18 Input data (Lake Leis)
-78
-74
-70
-66
-62
-58
0 13 26 39 52 65 78 91 104
WEEKS (111995 - 31121996)
OX
YG
EN
- 1
8 [
permil]
Determining of hydraulic conductivity using stable isotopes
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
x=37m
T=28days
PD=015
αL=55m
-78
-74
-70
-66
-62
-58
30 42 54 66 78 90 102
WEEKS (181995 - 15121996)
OX
YG
EN
- 1
8 [
permil]
P71
-78
-74
-70
-66
-62
-58
0 4 8 12 16 20 24
MONTHS (195-1296)
OX
YG
EN
- 1
8 [
o
]
x=187m
T=300days
PD=005
αL=94m
P75
comparison of results
between P75 divide P71
x=150m
ΔT=272days
v=055 md
known
i=0002
n=020
hydraulic conductivity k
k= (nv) i = 55 md
k = 6310-4 ms
Determining of hydraulic conductivity
using stable isotopes
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone
Region Case 3
k [ms]
Area (A) 6times10-4
Area (B) 20times10-4
Area (C) 15times10-4
Area (D) 19times10-4
Water flux [m3d]
Inflow + 8230
Outflow - 7280
Recharge + 5900
Pumping rate - 6850
Balance 0
Error 0
NUMERICAL MODELING
OF WATER FLOW AND TRACER TRANSPORT
with FEFLOW
Final result of the modelling of capture zone