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

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

Well flow in layered aquifer systems

1979

Pumping test near Lexmond 1 2, 3 4

Analytical solutions for well flow in layered aquifer systems

1980

steady state well flow aquifer: T; aquitard: c recharge from the top (and base) 1 fully penetrating well drawdown s = f(layer number, r)

Analytical solutions for well flow in layered aquifer systems

1985

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)

Analytical solutions for well flow in layered aquifer systems

1987

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)

Analytical solutions for well flow in layered aquifer systems

1997

multi-screened well well radius, well storage s well , skin effect uniform gradient at well screens (layer no., t), s(layer no., r, t)

Analytical solutions for well flow in layered aquifer systems

1999

stratified aquifer well radius, well storage s well , skin effect partially penetrating well uniform drawdown at well screens (t), s(layer, r, t), flux well (layer, t)

MLU (DOS)

→

MLU for Windows

2007

theory → implementation 1 → 300 pumping/injection wells 1 → filters in any layer flux( 100 pumping periods

t

) for each filter + delayed observation well response

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

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.

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

MLU Interface

Input 1/4:

General info tab

Time units Length units

MLU Interface

Input 2/4:

Aquifer system tab

Upper and Lower boundary conditions Aquifer (Yellow) Aquitard (Orange)

MLU Interface

Input 3/4:

Pumping wells tab

Check boxes to temporarily exclude individual pumping wells and periods Pumping wells may be screened in any selection of layers

MLU Interface

Input 4/4:

Observation wells tab

Screened in one layer only

MLU Interface

Output 1/3:

Optimization results etc.

MLU Interface

Output 2/3:

Time graphs

MLU Interface

Output 3/3:

Contour plot

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

MLU Help MLU Interface

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 i s the result a proper solution ?

the accuracy

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.

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

Parameter optimization

What values can be optimized ?

Hydraulic properties + also: • r c , r w 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

Parameter optimization

Least squares solution: Residual error = difference between the computed and the measured drawdown Sum of squares of residuals is minimized linear: log: residual error = computed – measured drawdown 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 (ft 2 )

Parameter optimization

Non-linear regression Test case: Schroth.mlu Schroth & Narasimhan: GroundWater (35) 2, p.371-375 2 aquifers 1 pumping well 3 observation wells Log drawdown curve fitting

Parameter optimization

Analysis of the results

Has the optimization procedure been successful yet ? Two prerequisites: 1. Iterative process -> “parameters found” 2. 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 1 58.0 + 3.3 ( 6 % ) T 2 5.156E+00 c 2 248.6 S 1 4.865E-04 S 2 1.678E-05 S' 2 1.467E-04 rc 1 5.277E-02 + 6.381E-02 ( 1 % ) + 6.2 ( 3 % ) + 5.231E-05 ( 11 % ) + 1.030E-06 ( 6 % ) + 9.490E-06 ( 6 % ) + 4.385E-04 ( 1 % )

Analysis of the results

Tab “Optimization 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) 0.6031

Improvement last iteration 2.1E-12 Number of iterations Condition number 2.7390

0.0131

6 463.4

Correlation matrix (%) T 1 100 T 2 c 2 S 1 S 2 S' 2 rc 1 1 60 -82 -39 70 1 100 21 100 -14 53 3 -25 -78 100 -3 55 -6 43 100 -90 3 -67 100 -31 -1 100

Very high condition number (about 1e9 or higher) High correlations (near +/-100%) reduce the number of parameters

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

MLU for Windows Test cases 12 tests are available in the directory “examples”

layers pumping wells obs. wells 1 2 6 1 2 2 1 2 1 1 4 1 1 1 1 6 4 2 2 4 1 3 1 6 parameters 3 T1 c1 S1 6 T2 c2 S2 S’1 rc1 sk1 0 3 T1 S1 sk1 3 T1 S1 sk1 7 T1 T2 c2 S1 S2 S’2 rc1 2 T1 S1 7 T1 sk1

up to

sk6

Example 1: Pumping test The classical example “DALEM“ (Kruseman & de Ridder) Leaky aquifer Curve fitting: LOG-drawdown Linear-drawdown T 1780 ( 3 %) c 539 (36 %) S 1.6 10

-3

( 5 %) 1676 ( 3 %) 328 (22%) 1.8 10

-3

( 6%)

Example 2: Recovery test Pumping station Hardinxveld-Giessendam (Dec. 1981) pumping well radius = 0.155 cm LOG-drawdown curve fitting: without and with skinfactor T 854 ( 4%) S 6.1 10

-5

(10%) skin = sum of squares 1.5030 m

2

1321 ( 1%) 2.8 10

-4

(13%) 6.1 ( 4%) 0.0025 m

2

Example 3: Slug test Classical test example of “Cooper et al. 1967” Slug = 10.16 litre In MLU modeled as: for 0.1 sec a discharge of 0,1016 m

3

/s.

Cooper: T = 45 m

2

/d , S ~ 10

-3

MLU : T = 40,6 ( 4%) S = 1.9 10

-3

(29%)

Example 4: Step-drawdown test Classical test example “Clark 1977” Q increases from 1306 till 5019 m

3

/d in 6 steps (each 3 hr) Skinfactor increases with Q In MLU: 6 pumping wells, all at the same spot MLU : KD = 396 m 2 /d ( 1%) Sk 1 = 1.28 ( 7%) Q= Sk 2 = 1.69 ( 5%) Sk 3 = 2.07 ( 5%) Sk 4 = 2.42 ( 4%) Sk 5 = 2.77 ( 4%) Sk 6 = 3.19 ( 3%) 1306 m

3

/d 1693 2423 3261 4094 5019 + recov.

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

Design ATES Distance between Cold and Warm wells: larger: improves thermal operation smaller: reduces hydrological effects EXAMPLE

Properties ATES

Total capacity: Total volume: No. of wells: Filter depth:

Cross section

200 m³/hr 480.000 m³/season 8 (4 Cold and 4 Warm) 25 – 48 m

Single pumping well versus ATES Pumping well 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 of 200 m³/hr

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

Design ATES Hydrological effects (5 cm contours at filter depth)

A B

grid spacing 500 m

C

Large capacity site model: Agriport A7 Total capacity: 40.000 m³/hr Pumped volume: 190 million m³/yr

Benno

Conclusions

1 – 2 3

-

– 4

“New” analytical solution for non-steady state well flow in layered aquifer systems (publications available as pdf) Superposition in space and time Parameter optimization technique 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

MLU for Windows Version 2.25

A

MLU information + documentation www.microfem.nl/products/mlu.html

www.microfem.nl/download mlu-set.zip mlu.pdf mlu-user.pdf

= users guide mlu-tutorial.pdf = multilayer approach update.txt

= update history since 2008 mlu.pps

= MLU-LT software = fact sheet = powerpoint presentation

B

MLU office license, updates, support www.microfem.nl/order

C

Email: [email protected]