1. Well flow & Pumping tests
new techniques →
new possibilities → new software
MLU for Windows
MLU in broad outline
Development of the solution technique
Possibilities and limitations
Differences with similar software
How does MLU work (demonstration)
Multi-aquifer representation and data entry
Presentation of results
Calibration of analytical models
Pumping test analysis
Parameter optimization
Analysis of the results
Some practical cases
Recovery test, slug test, etc.
Aquifer thermal energy storage

2. 1 - Development of the solution technique
MLU in broad outline
Kick Hemker
1 - Development of the solution technique
Analytical solutions for well flow
in layered aquifer systems
1980 → NOW
2 - Possibilities and limitations
aquifers / systems
maximum model capacity
input and output
3 - Differences with similar software
with respect to classical p.test software
with respect to numerical models

3. in layered aquifer systems
Well flow
in layered aquifer systems
Pumping test near Lexmond 1
2, 3 4

4. Analytical solutions for well flow in layered aquifer systems
steady state well flow
aquifer: T; aquitard: c
recharge from the top (and base)
1 fully penetrating well
drawdown s = f(layer number, r)

5. Analytical solutions for well flow in layered aquifer systems
transient well flow
aquifer: T, S; aquitard: c
recharge from the top (and base)
1 fully penetrating well
drawdown s = f(layer number, r, t)

6. Analytical solutions for well flow in layered aquifer systems
aquitard storage
aquifer: T, S; aquitard: c, S’
top and base: no drawdown / no flow
1 fully penetrating well
drawdown s = f(layer number, r, t)

7. Analytical solutions for well flow in layered aquifer systems
multi-screened well
well radius, well storage, skin effect
uniform gradient at well screens
swell(layer no., t), s(layer no., r, t)

8. Analytical solutions for well flow in layered aquifer systems
stratified aquifer
well radius, well storage, skin effect
partially penetrating well
uniform drawdown at well screens
swell(t), s(layer, r, t), fluxwell(layer, t)

9. MLU (DOS) → MLU for Windows
theory → implementation
1 → 300 pumping/injection wells
1 → 100 pumping periods
filters in any layer
flux(t) for each filter
+ delayed observation well response

10. Features of MLU version 2.25
MLU for Windows
Features of MLU version 2.25
layered aquifers / aquifer systems
leaky, confined and unconfined
up to 40 aquifer layers
up to 300 pumping- and injection wells
up to 100 pumping periods for each well
up to 100 observation wells
up to 1000 measurements per obs. well
up to 16 parameters to be optimized
time conversion: sec, min, h, d and yr
copy & paste (spreadsheets)
time graphs (drawdown, head, flux)
contour plots (with animation)
bitmap and vector output
data output as fth, xyz and fem

11. MLU for Windows Limitations infinite areal extent
each layer homogeneous and isotropic
only well flow
only Darcy flow
superposition of wells
which means:
no drawdown cone in unconfined aquifer
no seepage face in phreatic well
no mutual effects of pumping wells
no sheet pile walls, etc.
and obviously also no:
Noordbergum effect.

12. Compared to classical pump.t.software
MLU for Windows
Compared to classical pump.t.software
Multi-layer
Multi-well
Multi-screen
Multi-Q (variable discharge)
Aquitard storage
Same interface for all tests:
pump, recovery, slug- and st-drawdown tests, etc.
Compared to 3D numerical models
No finite element or finite difference grid
No time steps
No multi-screen problem
Drawdown in pumping well (radius, storage, skin)
Delayed observation well response
Easy to design/adept well fields
More accurate results
Faster optimization

13. Input 1/4: General info tab
MLU Interface
Input 1/4: General info tab
Time units
Length units

14. Upper and Lower boundary conditions
MLU Interface
Input 2/4: Aquifer system tab
Upper and Lower boundary conditions
Aquifer (Yellow)
Aquitard (Orange)

15. Pumping wells may be screened in any selection of layers
MLU Interface
Input 3/4: Pumping wells tab
Pumping wells may be screened in any selection of layers
Check boxes to temporarily exclude individual pumping wells and periods

16. Screened in one layer only
MLU Interface
Input 4/4: Observation wells tab
Screened in one layer only

17. Output 1/3: Optimization results
MLU Interface
Output 1/3: Optimization results
etc.

18. MLU Interface
Output 2/3: Time graphs

19. MLU Interface
Output 3/3: Contour plot

20. MLU Interface Copy Time graph Copy contour plot Save curve data
Save contour data
Save model as FEM

21. MLU Interface
MLU Help

22. Calibration analytical model
Kick Hemker
1 – Pumping test analysis with MLU
differences with graphical methods
2 - Parameter optimization
the parameters
least-squares solution
non-linear regression
3 – Analysis of the results
is the result a proper solution ?
the accuracy

23. Pumping test analysis with MLU
Classical pumping test software
Based on graphical methods:
- curve-fitting or
Searching for a best-fit straight line
- limited to 1 – 4 parameters
- little information about the accuracy.
MLU → Calibration analytical model
Non-linear regression technique:
- parameter optimization
based on least-squares method
- graphical inspection of the model fit
- statistical information on the accuracy of
the results.

24. Parameter optimization
What values can be optimized ?
Make a selection of:
T- and S-values of all aquifers
c- and S’-values of all aquitards
using any code (1-9, a-z, A-Z) in the # column.
Use the same code to group two (or more) values
as a single parameter for optimization

25. Parameter optimization
What values can be optimized ?
Hydraulic properties + also:
rc, rw and skinfactor of all pumping wells
using any code (1-9, a-z, A-Z) in the # column.
Actual optimization parameters are dimensionless
0 : log (hydraulic property value/starting value)
1 : pumping well property/starting value
Starting values must be larger than zero.
Computed hydraulic property
= starting value * exp(parameter value)
Computed pumping well property
= starting value * parameter value

26. Parameter optimization
Least squares solution:
Residual error = difference between the computed and the measured drawdown
Sum of squares of residuals is minimized
linear: residual error = computed – measured drawdown
log: residual error = log (computed) – log (measured)
Least-squares solution is obtained iteratively
(Levenberg-Marquardt algoritm)
each iteration step the sum of squares is reduced
stopping-criterion:
improvement sum < Rel * sum + Abs * Abs (ft2)

27. Parameter optimization
Non-linear regression
Test case: Schroth.mlu
Schroth & Narasimhan: GroundWater (35) 2, p
2 aquifers
1 pumping well
3 observation wells
Log drawdown curve fitting

28. Parameter optimization

29. Analysis of the results
Has the optimization procedure been successful yet ? Two prerequisites:
Iterative process -> “parameters found”
Inspection of Time graphs -> “good fit”
Only if both OK -> See “Optimization results”
Values + accuracy
=====================================================
M L U A Q U I F E R T E S T A N A L Y S I S
For Unsteady-State Flow in Multiple-Aquifer Systems
THE CALCULATED LEAST SQUARES SOLUTION
Parameter value Standard deviation
T ( 6 % )
T E E-02 ( 1 % )
c ( 3 % )
S E E-05 ( 11 % )
S E E-06 ( 6 % )
S' E E-06 ( 6 % )
rc E E-04 ( 1 % )

30. Analysis of the results
=======================================================
M L U A Q U I F E R T E S T A N A L Y S I S
For Unsteady-State Flow in Multiple-Aquifer Systems ….
Initial sum of squares is
Residual sum of squares is
Residual sum of squares (m²)
Improvement last iteration E-12
Number of iterations
Condition number
Correlation matrix (%) T T c S S S' rc
Analysis of the results
Tab “Optimization results”
Very high condition number
(about 1e9 or higher)
High correlations
(near +/-100%)
reduce the number
of parameters

31. Kick Hemker, Benno Drijver
Some examples
Kick Hemker, Benno Drijver
1 – Different tests
pumping test
recovery test
slug test
step-drawdown test
2 – Aquifer thermal energy storage (ATES
differences with normal pumping well fields
design of ATES well fields
practical example

32. MLU for Windows Test cases
12 tests are available in the directory “examples”
layers
pumping wells
obs.-
wells
parameters 1 4 3
T1 c1 S1 2 6
T2 c2 S2 S’ rc1 sk1
T1 S1 sk1 7
T1 T2 c2 S1 S2 S’2 rc1
T1 S1
T1 sk1 up to sk6

33. Example 1: Pumping test
The classical example “DALEM“ (Kruseman & de Ridder)
Leaky aquifer
Curve fitting: LOG-drawdown Linear-drawdown
T ( 3 %) ( 3 %)
c (36 %) (22%)
S ( 5 %) ( 6%)

34. Example 2: Recovery test
Pumping station Hardinxveld-Giessendam (Dec. 1981)
pumping well radius = cm
LOG-drawdown curve fitting: without and with skinfactor
T ( 4%) ( 1%)
S (10%) (13%)
skin = ( 4%)
sum of squares m m2

35. Example 3: Slug test Classical test example of “Cooper et al. 1967”
Slug = litre
In MLU modeled as:
for 0.1 sec a discharge of 0,1016 m3/s.
Cooper: T = 45 m2/d , S ~ 10-3
MLU : T = 40, ( 4%)
S = (29%)

36. Example 4: Step-drawdown test
Classical test example “Clark 1977”
Q increases from 1306 till 5019 m3/d in 6 steps (each 3 hr)
Skinfactor increases with Q
In MLU: 6 pumping wells, all at the same spot
MLU : KD = m2/d ( 1%)
Sk 1 = ( 7%) Q= 1306 m3/d
Sk 2 = ( 5%) 1693
Sk 3 = ( 5%) 2423
Sk 4 = ( 4%) 3261
Sk 5 = ( 4%) 4094
Sk 6 = ( 3%) recov.

37. Aquifer thermal energy storage (ATES)
Discharge = infiltration (net discharge = zero) 
Area of influence much smaller than a “normal well field” 
Effects of major heterogeneities in area of influence small 
An analytical model is justified in most cases

38. Design ATES Distance between Cold and Warm wells:
larger: improves thermal operation
smaller: reduces hydrological effects
EXAMPLE
Properties ATES
Total capacity: 200 m³/hr
Total volume: m³/season
No. of wells: 8 (4 Cold and 4 Warm)
Filter depth: 25 – 48 m
Cross section

39. Single pumping well versus ATES
Drawdown cone after 50 days
of a continuous discharge
of 200 m³/hr
(grid spacing: 1 km)
ATES
Hydrological effects after 50 days of a continuous discharge and infiltration

40. Design ATES Some possible well configurations  configuration A:
relatively
unfavourable

41. Design ATES Hydrological effects (5 cm contours at filter depth) A B
grid spacing 500 m C

42. Benno Large capacity site model: Agriport A7
- Total capacity: m³/hr
- Pumped volume: 190 million m³/yr
Benno

43. Conclusions Analytical model 1 – “New” analytical solution
for non-steady state well flow
in layered aquifer systems
(publications available as pdf)
2 – Superposition in space and time
3 - Parameter optimization technique
4 - Simple interface
Analytical model
All sorts of aquifer tests
Design well fields
Graphical +
digital output
hydraulic heads
Statistical
results of
optimization
Transfer to
numerical
model

44. MLU for Windows Version 2.25
A MLU information + documentation - -
B MLU office license, updates, support - C
mlu-set.zip = MLU-LT software
mlu.pdf = fact sheet
mlu-user.pdf = users guide
mlu-tutorial.pdf = multilayer approach
update.txt = update history since 2008
mlu.pps = powerpoint presentation