HGS van Genuchten - FEFlow

2 nd
Well Vulnerability:
A Model Comparison
–
Issues and Pitfalls
E.O. Frind, M. Sousa, J.P.
Jones, and D.L. Rudolph,
University of Waterloo
International FEFLOW User Conference
September 14-18, 2009
Potsdam/Berlin, Germany

Wellhead
protection,
standard
approach
Apply particle
tracking,
delineate
capture zone
Possible
sources?

The Real
World:
Cape Cod
example
(USGS Circular
1174, 1998)
A: K=50 ft/d
B: K=150 ft/d
Small change
in head can
cause large
change in
particle tracks

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Key Issues
Sensitivity: Small changes in heads can cause large
changes in capture zone
Uncertainty:
–
–
Effect of heterogeneities
Stochastic approaches (mostly 2D)
Physical approach: represent small-scale heterogeneities by
macrodispersion (Gelhar and Axness 1983); large-scale by scenario
analysis (always 3D)
Determinism: Meaning of a source just inside vs. a source
just outside of capture zone boundary
Impact:
–
How critical will a contaminant source be?
Well Vulnerability Concept gives actual impact on well
Model performance:
against each other?
How do commercial models stack up

Illustrative Example: Mannheim Well Field
Grand River
Watershed
Chicago
Ontario
Detroit
Cleveland
Toronto
Grand River
Conservation Authority
Dundalk
Waterloo
Kitchener
Kitchener
Waterloo
50 km
Guelph
Cambridge
Brantford
• 6800 km2 drainage area
• 10% of Lake Erie
Local Drainage
• Population = 800,000
• 38 local/regional
Grand River
Watershed
governments
• Major reservoirs
regulate 27% of
watershed area
•82% of watershed residents
reliant on groundwater for
their drinking water supply.
Waterloo Moraine model
Mannheim
well field
Dunnville

Waterloo Moraine Model
N
Paul Martin,
1995
Mannheim
well field
Alder
Creek
watershed

Uncertainty due to Local Heterogeneities
N
Total Particles 1760
Reaching Limit 17.95 %
Reaching Top 82.05 %
Reaching Side 0.00 %
Well
K22
Mannheim North
K23
K93
K24
K94
K91
K92
K26
K21
K25
K29
Mannheim South
2km
Mannheim Well Field,
100-yr Capture Zone
by backward particle
tracking (older model)
Can draw envelope
curve around particle
end positions
But first consider
uncertainty due to
local heterogeneities

Uncertainty due to Local Heterogeneities
N
0.1
0.01
Well
0.3
0.5
0.9
0.7
K22
Capture probability
0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
K93
K23
K24
K94
K92
K91
K26
K21
K29
K25
2km
Transport parameters:
α L = 20 m, α Th = 5 m, α TV = 0.02 m, D m = 10 -10
(Frind et al., 2002)
100-yr Probability-of
Capture plume by
backward advectivedispersive
transport
modelling
Obtain capture zone
outline by mass balance
(not necessarily 0.5
contour)
m 2 /s

Particle Tracking vs Backward Transport Model
N
100-yr
Total Particles 1760
Reaching Limit 17.95 %
Reaching Top 82.05 %
Reaching Side 0.00 %
Well
K22
Mannheim North
K94 K21
K93
K92
K29
K91
K25
K23
Mannheim South
K24
K26
2km
Capture zone from
transport model is
larger due to
dispersion
- accounts for
uncertainty due to
local scale
heterogeneity
- more conservative
than particle tracking

N
100-yr
Source
Well
The Well Vulnerability Concept
K22
K23
K94 K21
K93 K92
K91
K29
K25
K24
K26
2km
(Frind et al., 2006)
Known source:
- Apply pulse at source
- Record breakthrough at
well (forward method)
Unknown source:
- Apply pulse at well
- Record breakthrough at
any point within capture
zone (backward method)
Forward and backward
breakthrough curves will be
the same (Adjoint theory)

Concentration (gm -3 )
Well Vulnerability: Forward Mode
5.0E-04
4.0E-04
3.0E-04
2.0E-04
1.0E-04
C
dws
C
peak
0.0E+00
0
Texceed
50
Tpeak
100 150
Time (days)
200
T
expo
Breakthrough curve
at well due to pulse
source within
capture zone:
• Max concentration
expected at well
• Time to reach max
concentration
• Time to breach
drinking water limit
• Time of exposure

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FEFLOW
–
–
Model Comparison:
Apply to Prediction of Well
Galerkin
Vulnerability
Finite Elements
requires specified recharge function
HydroGeoSphere (HGS) (Therrien
–
–
–
Control Volume Finite Elements
and Sudicky, 2003)
integrated groundwater / surface water model
distributes recharge by means of diffusion-wave
equation

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Model Functions Tested
Unsaturated flow/transport
–
1D column
3D homogeneous system
–
box model, average Mannheim aquifer properties
3D heterogeneous system
–
actual Mannheim aquifer, Alder Creek model

Recharge 200 mm/yr
Flux concentration 1 mg/L for 20 years
1 m 2
Water
Table
Unsaturated Flow/Transport
40m
Silty Sand:
K = 5 x 10-4 m/s
Porosity = 0.37
Residual Saturation = 0.049
Van Genuchten parameters:
A = 3.475, n = 1.746
Molecular diffusion = 1.2 x 10-9 m2 /s
Longitudinal dispersivity = 10 m
Transverse dispersivity = 1 m
Vertical discretization 20m

Van Genuchten vs Modified van Genuchten Model
δ = 5.4 δ = 4.0 δ = 1.1
VG
Improving
convergence
MVG
δ

Effect of van Genuchten δ
Changing δ from 5.4 to 1.1 will change the unsaturated
hydraulic conductivity by up to 7 orders of magnitude
This should have a big impact on travel time?
Not necessarily!
With a specified recharge boundary condition, the same flux
will enter the column, regardless of the K value
–
–
changing K will simply change the gradient
travel time and breakthrough curve will be the same

10m
20m
Breakthrough curve at water table
1m
FEFLOW
5m Modified van Genuchten
Effect of vertical
discretization
Solution converges for
Δz = 1m

Breakthrough curve at water table
1m
HGS
5m Modified van Genuchten
10m
20m
Effect of vertical
discretization
Solution converges for
Δz = 1m

10m
20m
1m
5m
FEFLOW vs. HGS
Modified van
Genuchten
FEFLOW
HGS

1m
5m
10m
20m
HGS
van Genuchten
HGS Solution
converges for
Δz = 1m
Feflow requires
Δz = 0.005m for
convergence
(not practical)

HGS
Van Genuchten vs
Modified van Genuchten
Mod. van Genuchten
Van Genuchten

HGS
Van Genuchten vs
Modified van Genuchten
Effect of unsat zone thickness
Van Genuchten
40m
5m
Mod. Van Genuchten
40m
5m

Findings: Unsaturated Flow/Transport
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Feflow works best with MVG
HGS works with both options
Difference between VG and MVG declines with
unsat zone thickness
δ
used with MVG does not affect results if flux
boundary is chosen
Overall, both models give equivalent results

3D Homogeneous System:
Box Model representing average
conditions for Mannheim aquifer
4km
Pumping Well
500 m 3 /day
1km
Top BC
Recharge 200 mm/yr
400m
25m
Default BC No-Flow
Side:
Constant Head 20m

Finite Element Model
Horizontal grid spacing: 15m

Source Conditions
Source centered within capture zone
Apply 1yr-pulse of specified recharge concentration of 1 g/m 3
Source outside capture zone (OCZ)
Apply 1yr-pulse of specified recharge concentration of 1 g/m 3
Well
Well

Inside Source
FEFLOW vs HGS,
Upwind vs No-Upwind
Upstream weighting
Feflow no-upwind option
provides best accuracy
Feflow full-upwind and
HGS upstream weighting
are equivalent

Outside Source FEFLOW vs HGS,
Upwind vs No-Upwind
Upstream weighting
Mass spread to outside
source by transverse
dispersion: upwind
options spread more
mass

FEFLOW, Plume at 8 years
No upwind
Some oscillations and
negative concentrations

FEFLOW, Plume at 8 years
Full upwind
Negligible oscillations but
significant smearing

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Findings: Homogeneous System
Feflow no-upwind option gives the best accuracy
Feflow full-upwind and HGS upstream weighting
give essentially the same results
Upwinding reduces oscillations, but increases
smearing
Transverse dispersion transfers mass to outside
source, upwinding increases the transfer
Overall, model results are comparable

3D Heterogeneous System
N
Waterloo
Moraine
model
Mannheim
well field
Alder
Creek
watershed

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Setup:
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3D Heterogeneous System:
Alder Creek Model
recharge distribution generated by HGS, transferred
to Feflow
MVG for Feflow and HGS
dispersive form for Feflow (mass flux specified)
Upwinding:
–
–
Feflow: full upwinding (no-upwind required very small
time step (0.1 day)
HGS: upstream weighting
Max time step:
–
–
10 days: 3 weeks execution time
100 days: 6 days execution time, same results

Alder Creek Watershed: Ground Surface Elevations

Alder Creek Watershed: Municipal Wells

Alder Creek Watershed: Recharge Distribution
Recharge distribution generated by HGS from DEM

87 layers (incl unsat zone)
7216 elements/layer
1204428 elements total
3D Finite
Element Grid
J.P. Jones, 2004
Study
Area
Elevation masl
Area 78 km 2

Alder Creek Watershed: Finite Element Grid
Study
Area

Sources for Vulnerability Study
2 nd
source
1 st
source
K22A
K23
K24
2 nd
source:
14m unsat
zone
1st source:
12m unsat
zone

2 nd
Recharge Distribution
source
1 st
source
K22A
K23
K24
Recharge distribution transferred from HGS to Feflow

Mannheim Well Field: Particle Tracks
N
Total Particles 1760
Reaching Limit 27.44 %
Reaching Top 65.91 %
Reaching Side 6.65 %
Well
K22
Mannheim North
K94 K21
K93
K92
K29
K91
K25
K23
K24
Mannheim South
K26
2km
From older
model,
uniform
recharge
100-year
particle tracks
2 nd
1 st
source
source

30 y
K24
K24
Other
wells
FEFLOW
HGS
1 st
Source
Mass at
300 yrs Feflow HGS
input (g) 9788 100% 9828 100%
K22A 4 0% 10 0%
K23 70 1% 382 4%
K24 1142 12% 1552 16%
K26 131 1% 281 3%
First arrival of critical conc ?
Arrival of max conc: ~30 years
Max concentration ?
Exposure time ?

60 y
K22A
K23
FEFLOW
HGS
Other
wells
2 nd
Source
Mass at
400 yrs Feflow HGS
input (g) 8597 100% 8327 100%
K22A 1697 20% 1396 17%
K23 2823 33% 4814 58%
K24 550 6% 289 3%
K26 404 5% 175 2%
First arrival of critical conc ?
Arrival of max conc: ~60 years
Max concentration ?
Exposure time ?

1 st
Source, Plume at 30 years
K22A
K23
K24
Feflow,
full
upwind
Plume
moves
south: -
this
explains
mass
loss

2 nd
Source, Plume at 75 years
K22A
K23
K24
Feflow,
full
upwind
Plume
moves
east and
south

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Why the smearing in Feflow?
Effect of heterogeneities?
–
smearing increases with Feflow when going to
heterogeneous system, less so with HGS
Upwinding?
–
both models use upwinding
Numerical approach?
–
–
Feflow uses Galerkin FE (globally mass conservative)
HGS uses Control Volume FE (locally and globally
mass conservative)
Increasing smearing with distance:
–
2nd source is twice as far away as 1st , so numerical
dispersion increases

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Findings: 3D Heterogeneous Model
Recharge distribution has controlling influence on flow
field
Placement of sources within capture zone does not
guarantee capture of input mass by wells
Upwinding seems to be a major factor in transverse
spreading of plume
Accuracy of well vulnerability measures is questionable
Max concentrations at well are all much lower than
source concentrations – dispersion plays a major role

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Reflections on Key Issues
Sensitivity: Recharge distribution has a major impact on
flow field and vulnerability functions
Uncertainty: Macrodispersion is useful, but other
sources of uncertainty may be controlling
Determinism: Sources both inside and outside of
capture zone can contribute to well contamination
Impact: Source location inside capture zone does not
mean that contamination will be critical
Model performance:
different results
Different models can give very

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What does it all mean?
Be aware of uncertainty and sensitivity in wellhead
protection work
Use the most complete data available
Use realistic recharge distributions and boundary
conditions
Use the best models available
Select model settings carefully
Consider scenario analyses (windows etc?)
Never take model results at face value
Remember that particle tracks only tell half the story
Use sufficient margins of safety in wellhead protection

Thanks, that’s it for now
We have come a long
way in this journey
Acknowledgements:
Hans-Joerg Diersch
Peter Schaetzl