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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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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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Well flow in layered aquifer systems 1979 Pumping test near Lexmond 1 2, 3 4

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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)

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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)

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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)

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Analytical solutions for well flow in layered aquifer systems 1997 multi-screened well well radius, well storage, skin effect uniform gradient at well screens s well (layer no., t), s(layer no., r, t)

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Analytical solutions for well flow in layered aquifer systems 1999 stratified aquifer well radius, well storage, skin effect partially penetrating well uniform drawdown at well screens s well (t), s(layer, r, t), flux well (layer, t)

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MLU (DOS) → MLU for Windows 2007 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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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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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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Time units Length units MLU Interface Input 1/4: General info tab

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

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

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

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

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MLU Help MLU Interface

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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 i s 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 ? Use the same code to group two (or more) values as a single parameter for optimization 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.

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Parameter optimization What values can be optimized ? 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 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.

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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 (ft 2 )

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Parameter optimization Non-linear regression Test case: Schroth.mlu Schroth & Narasimhan: GroundWater (35) 2, p 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: 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 ( 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 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) Improvement last iteration 2.1E-12 Number of iterations 6 Condition number Correlation matrix (%) T 1100 T c S S S' rc Very high condition number (about 1e9 or higher) High correlations (near +/-100%) reduce the number of parameters

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

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Example 1: Pumping test The classical example “DALEM“ (Kruseman & de Ridder) Leaky aquifer Curve fitting: LOG-drawdown Linear-drawdown T 1780 ( 3 %) 1676 ( 3 %) c 539 (36 %) 328 (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 854 ( 4%) 1321 ( 1%) S (10%) (13%) skin = 6.1 ( 4%) sum of squares m m 2

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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 m 3 /s. Cooper: T = 45 m 2 /d, S ~ MLU : T = 40,6 ( 4%) S = (29%)

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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=1306 m 3 /d Sk 2 = 1.69 ( 5%)1693 Sk 3 = 2.07 ( 5%)2423 Sk 4 = 2.42 ( 4%)3261 Sk 5 = 2.77 ( 4%)4094 Sk 6 = 3.19 ( 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 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

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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) grid spacing 500 m AB C

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

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Conclusions 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 Transfer to numerical model Statistical results of optimization

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A MLU information + documentation B MLU office license, updates, support - C MLU for Windows Version 2.25 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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