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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
ting G
roundw
ate
r A
ge
Dis
trib
uti
ons
from
Envir
onm
enta
l Tr
ace
r D
ata
, Te
chniq
ues
and M
eth
ods
4-F
3,
Jürg
ens,
Böhlk
e,
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.
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