Large scale mixing and GroundWater Age (GW Age)Jean-Raynald de DreuzyGéosciences Rennes, CNRS, France

Residence Time Transit Time

Renewal Time GW Age

Residence time in the compartments of the water cycle

Aeschbach-Hertig, W., and T. Gleeson (2012), Regional strategies for the accelerating global problem of groundwater depletion,

Nature Geoscience, 5(12), 853-861.

Transit Time Renewal Time

http://pubs.usgs.gov/circ/2002/circ1224/html/understanding.html#winter

VulnerabilitySustainability

Tracer Concentrations &GW Ages

Hinsby K (2001): Freshwater – our most important resource. – In: Hinsby and Binzer “Freshwater our most important resource – Geology and groundwater models”, special issue of Geologi – Nyt fra GEUS, nr.1 – 2001

Tracer Concentrations &GW Ages

1940 1950 1960 1970 1980 1990 2000 20100

200

400

600

CF

C-1

2 (

pp

tv)

c(tw) (mol/l) →water

c(tw) (pptv) →air

trApparent age A

tw

)(1winww tcCttA

Tracer concentration c

/Rl

tA w

Park, J., et al. (2002), Transport modeling applied to the interpretation of groundwater Cl-36 age, Water Resources Research, 38(5).

GW AgeTransit Time Distribution

GW Age, Transit Time Distribution, Mixing

No mixing (piston-flow model) Full Mixing (exponential model)

TracerLPM, 2012: An Excel® Workbook for Interpreting Groundwater Age Distributions from Environmental Tracer

Data, Techniques and Methods 4-F3, Jürgens, Böhlke, Eberts

ttp

t

etp

1

Continuous Stirred-Tank Reactor

http://en.wikipedia.org/w

iki/Continuous_stirred-tank_reactor

Q

V

etP

tP

P

dt

dP

t

1

10

V: Volume Q: Inflow=Outflow

Exponential TTD for aquifers at wells

http://www.amiadini.com/NewsletterArchive/100507-NL135/envEnl-135.html

/

1

R

H

etPt

H: Mean aquifer depthf: Aquifer porosityR: Aquifer recharge

Haitjema, H. M. (1995), On the residence time distribution in idealized groundwatersheds,

Journal of Hydrology, 172(1-4), 127-146.

GW Age, Transit Time Distribution, Mixing

No mixing (piston-flow model) Full Mixing (exponential model)

/R

l

/R

H ttp

t

etp

1

Hl

Transit Time Distribution and Transport

Ginn, T. R. (1999), On the distribution of multicomponent mixtures over generalized

exposure time in subsurface flow and reactive transport…, Water Resources Research, 35(5),

1395-1407.

St

ppp

t

p

u

Dv

Cornaton, F. J. (2012), Transient water age distributions in environmental flow systems:

The time-marching Laplace transform solution technique, Water Resources Research, 48.

Infering Transit Time Distribution from GW Age

▪ Apparent age A

▪ Direct problem

▪ Inverse problem

▪ Use of multiple tracers (multiple GW ages)

▪ Simplify the model of transit time distributions?

▪ Dirac, Exponential,…, Lumped Parameter Models

▪ Broad variety of natural distributions?▪ Geological conditions, old versus young GW

▪ Sampling conditions

▪ Hydrological conditions

▪ Reduce the distribution to the mean, standard deviation, shape?

0

11 )()()( dttpttCCttcCttA wininwwinww

Crystalline aquifer of Ploemeur

Illustration on a field case study

▪ Fully-heterogeneous 3D models

Methodology

PhD S. Leray (2012), Caractérisation des aquifères de socle cristallin et de leur ressource en eau- Apport des données d’ « âge » de l’eau, University of Rennes 1.

Hydrogeological model

Plœmeur granite

Guidel granite

N20 Fault

Contact zone

Micaschists

3 km

4 km

500 m

Hydrogeological model

▪ Parameters

▪ Topography

▪ R = 200 mm/an

▪ TCZ = 2 - 3 10-3 m2/s

▪ KMS = 10-8 – 5 10-6 m/s

▪ H = 180 – 280 m

▪ φ = 2 – 6%

Hydraulic calibration Head hw

Age CFC-12

At pumping

well

Flow model

▪ Flow equation

▪ 3D flow, steady state with pumping Qw

▪ Unconfined, free surface flow

Flow model

▪ Calibration with head hw at the pumping well

▪ Recharge at its potential value

Transport model

▪ Advection, no diffusion

▪ Diffusion/dispersion vs pumping, heterogeneity

▪ Backward-time from the pumping well

ttdΓtp

Γ

Γ

x

w

sΓ

s

w

& ),(),()( avec

sur 0)).,(),((

sur 0),(

0)0,(

0)()()),(),(

.(),(

*

"imposé C grad"*

imposée" C"*

*

**

xxq

nxxq

x

x

xxqx

Transport model

Transit Time Distribution Approximate Lumped Parameter Model

Lumped Parameter ModelWorth in terms of predictions

▪ Prediction with ≠ conceptual models

Predictive relevance of Lumped Parameter Models

Synthetic aquifer calibrated on Ploemeur site

Synthetic Tracer concentrations, TTD, Reference Predictions

TTD + atmospheric chronicles

+Tracer concentrations: CFC-11, 85Kr et SF6.

Synthetic Apparent Ages

Calibration of LPM models on the synthetic ages

Prediction of 25% Renewal time

Prediction of 50% Renewal time

Accurate Predictions

Equivalence of some 2-parameters LPMs

Accurate Predictions

San Joaquin Valley’s Aquifer

Transit Time DistributionsLumped Parameter Models

Green, C. T., et al. (2014), Accuracy of travel time distribution (TTD) models as affected by TTD

complexity, observation errors, and model and tracer selection, Water Resources Research(50),

6191 - 6213.

Predictions of Nitrate

concentrations

Conclusions▪ Large variety of Transit Time Distributions

▪ Sensitive to geological, hydrological, topographical constraints

▪ Limited number of Lumped Parameter Models

▪ Effective for bulk predictions on renewal times, nitrate concentrations

▪ Restrictions in the use of Lumped Parameters Models

▪ High influence of sampling (largely unknown)

▪ Tracer concentrations may be affected by reactivity, contamination,….

▪ Relating parameters to flow structures, hydraulic parameters

▪ Modification of boundary conditions, transient state

▪ Spatial variations in contaminant sources

▪ Combination of hydraulic and geochemical information

▪ Hydraulic Model give the shape of the distribution

▪ Tracers give the right order of magnitude

Transit Time DistributionsLumped Parameter Models

Flow patterns

LPMs & flow patterns

Trace

rLPM

, 2

01

2:

An E

xcel®

Work

book f

or

Inte

rpre

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roundw

ate

r A

ge

Dis

trib

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ons

from

Envir

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enta

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ace

r D

ata

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eth

ods

4-F

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Jürg

ens,

Böhlk

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Ebert

s

TTDs & flow patterns

Eberts, S. M., et al. (2012), Comparison of particle-tracking and lumped-parameter age-distribution models for evaluating vulnerability of production

wells to contamination, Hydrogeology Journal, 20(2), 263-282.

TTDs & flow patterns

Eberts, S. M., et al. (2012), Comparison of particle-tracking and lumped-parameter age-distribution models for evaluating vulnerability of production

wells to contamination, Hydrogeology Journal, 20(2), 263-282.