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

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