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**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

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**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

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**in layered aquifer systems**

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

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**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)

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**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)

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**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)

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**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)

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**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)

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**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

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**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

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**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.

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**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

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**Input 1/4: General info tab**

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

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**Upper and Lower boundary conditions**

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

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**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

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**Screened in one layer only**

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

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**Output 1/3: Optimization results**

MLU Interface Output 1/3: Optimization results etc.

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MLU Interface Output 2/3: Time graphs

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MLU Interface Output 3/3: Contour plot

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**MLU Interface Copy Time graph Copy contour plot Save curve data**

Save contour data Save model as FEM

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MLU Interface MLU Help

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**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

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**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.

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**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

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**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

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**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)

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**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

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**Parameter optimization**

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**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 % )

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**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

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**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

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**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

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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%)

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**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

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**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%)

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**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.

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**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

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**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

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**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

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**Design ATES Some possible well configurations configuration A:**

relatively unfavourable

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

grid spacing 500 m C

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**Benno Large capacity site model: Agriport A7**

- Total capacity: m³/hr - Pumped volume: 190 million m³/yr Benno

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**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

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**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

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