Cargese Summer School on Flow and Transport in Porous and Fractured Media, Development, Protection, Management and Sequestration of Subsurface Fluids, July 20th - August 1st 2015

1. Large scale mixing and
GroundWater Age (GW Age)
Jean-Raynald de Dreuzy
Géosciences Rennes, CNRS, France

2. Residence Time
Transit Time
Renewal Time
GW Age

3. 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.

4. Transit Time
Renewal Time
http://pubs.usgs.gov/circ/2002/circ1224/html/understanding.html#winter
Vulnerability
Sustainability

5. 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

6. Tracer Concentrations &
GW Ages
0
200
400
600
1940 1960 1980 2000
CFC-12(pptv)
c(tw) (mol/l) →water
c(tw) (pptv) →air
tr
Apparent age A
tw
   )(1
winww tcCttA 

Tracer concentration c
 
/R
l
tA w 
Park, J., et al. (2002), Transport modeling applied to the interpretation of groundwater Cl-36 age, Water Resources Research, 38(5).

7. GW Age
Transit Time Distribution

8. 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

9. Continuous Stirred-Tank Reactor
http://en.wikipedia.org/wiki/Continuous_stirred-tank_reactor
 
 
Q
V
etP
tP
P
dt
dP
t













1
10
V: Volume
Q: Inflow=Outflow

10. Exponential TTD for
aquifers at wells
 




/
1
R
H
etP
t



H: Mean aquifer depth
: Aquifer porosity
R: Aquifer recharge
Haitjema, H. M. (1995), On the residence time distribution in idealized
groundwatersheds, Journal of Hydrology, 172(1-4), 127-146.

11. GW Age, Transit Time Distribution, Mixing
No mixing (piston-flow model) Full Mixing (exponential model)


/R
l
 

/R
H

     ttp   

t
etp


1
Hl

12. 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.
      S
t
p
pp
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.

13. 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

14. Crystalline aquifer
of Ploemeur
Illustration on a field case study

15. ▪ 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.

16. Hydrogeological model
Plœmeur granite
Guidel granite
N20 Fault
Contact zone
Micaschists
3 km
4 km
500 m

17. 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

18. Flow model
▪ Flow equation
▪ 3D flow, steady state with pumping Qw
▪ Unconfined, free surface flow

19. Flow model
▪ Calibration with head hw at the pumping well
▪ Recharge at its potential value

20. 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
sur0)).,(),((
sur0),(
0)0,(
0)()()),(
),(
.(
),(
*
"imposéCgrad"
*
imposée"C"
*
*
*
*
xxq
nxxq
x
x
x
xqx

21. Transport model

22. Transit Time Distribution
Approximate Lumped Parameter Model

23. Lumped Parameter Model
Worth in terms of predictions
▪ Prediction with ≠ conceptual models

24. Predictive relevance of
Lumped Parameter Models

25. Synthetic aquifer calibrated on Ploemeur site

26. Synthetic Tracer concentrations, TTD, Reference Predictions
TTD + atmospheric chronicles
+
Tracer concentrations: CFC-11, 85Kr et SF6.

27. Synthetic Apparent Ages

28. Calibration of LPM models on the synthetic ages

29. Prediction of 25% Renewal time

30. Prediction of 50% Renewal time

31. Accurate Predictions

32. Equivalence of some 2-parameters LPMs

33. Accurate Predictions

34. San Joaquin Valley’s Aquifer
Transit Time Distributions
Lumped 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

35. 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

36. Transit Time Distributions
Lumped Parameter Models
Flow patterns

37. LPMs & flow patterns
TracerLPM,2012:AnExcel®WorkbookforInterpretingGroundwaterAgeDistributionsfromEnvironmentalTracer
Data,TechniquesandMethods4-F3,Jürgens,Böhlke,Eberts

38. 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.

39. 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.