MLU for Windows User's Guide • Well flow modelling
Contents
1. Time units Days Length units Meters Only the drawdown contours of a single selected aquifer are displayed together with the location of pumping and observation wells Blue contour lines indicate a positive drawdown negative head red contour lines a negative drawdown Zero contours are not drawn Every fifth contour is black During animation a track bar indicates the course of time If the animation is halted by pressing the Pause button a single forward or backward time step can be done by pressing one of the arrow keys on the key board Clicking on the bar right or left of the indicator will cause the contours to jump two time steps or the indicator can be dragged to a specific time by left clicking and holding on the indicator itself You can save an ASCII file of the contour plot with the x and y coordinates and the drawdown values for all points that the contour plot is based on More details are presented below 19 Import Main menu Import image files Rectangular raster image maps can be imported and displayed as background in contour plots This includes raster files of the types bmp png tif or tiff jpg or jpeg and gif Some types of tif files are not supported only a grey rectangle will be displayed To georeference the image map an associated world file is required with the same file name and the extension bpw pgw tfw jgw or gfw respectively Further details can be found at http en wi2. MLU Help as well as lt F1 gt activate the Help system and display help texts corresponding with one of the following tabs Tabs 1 7 1 Data input General info 2 Data input Aquifer system 3 Data input Pumping wells 4 Data input Observation wells 5 Results Optimization results 6 Results Time graphs 7 Results Contour plot Start a new case by pressing the first left most button New and fill out the four input screen pages tabs 1 4 Or start a session by loading an existing MLU file File Open or press the second button Open MLU can handle many cases at the same time Data input 1 General info 4D MLU for Windows 1 16 G MLU examples for manual variant1 mlu 3 m ni xj D File Edit View Calculate Export Window Help l xl Aquifer system Pumping wells Observation wells Optimization results Time graphs Contour plot Project M General setup Name fvariantia Number of aquifers fs Test Liesbeth Number of pumping wells 24 Location IF Technalogy Number of observation wells ja zi Date december 2007 Remarks aquifer thermal energy storage 8 3 wells r File Parameter optimization 1 Data name 9 Relative stopping criterion o 0001 File name variant 1a Absolute stopping criterion o 0001 Date 19 12 2007 itti urve Fitting Remarks Fine example Log drawdown curve fitting to test all Contour plot Lin
3. S and S unaltered New input of Kv or Kh changes c or T New input and optimization of c or T changes Kv or Kh New input and optimization of S or S has no effect on other values in this table And in case of a zero thickness resistance layer 1 e within a stratified aquifer New input of thickness or base of a layer not only changes Kh of that layer but also Kv of the adjacent zero thickness layer s 10 Data input 3 Pumping wells aD MLU for Windows 1 16 G MLU examples for manualfourwells mlu ni xi 3 File Edit View Calculate Export Window Help la xl iui HY NO General info Aquifer system Pumping wells Observation wells Optimization results Time graphs Contour plot po froe fame pump ted layers C eene radus tae erem rs tmi Sen cer ci e o romero d D 100 5 v 0 1 0 05 D 5 mo Well A 10 2 pm WellB 1100 1100 5 6 30 1 0 05 o 5 3 m Wellc 100 1100 4 6 30 1 0 05 0 5 4 RW WellD 1100 100 135 01 0 05 0 5 Starting time d Discharge m3 d 2400 180 2400 360 2400 540 2400 720 2400 SI XXIX 4 Time units Days Length units Meters The upper blue table contains rows with information for all pumping and injection wells one row for each well The Include column contains checkboxes that are all checked by default When a pumping well is set to unchecked the well is ignored when computing time graphs contour plo
4. Confined system of two aquifers and one aquitard with storage One pumping well Drawdown measurements in the pumping well and the two piezometers estimated from published graphs Optimization parameters are T1 T2 c2 S1 S2 S 2 and rcl Next paragraph shows log drawdown curve fitting results slugtest mlu Classical Dawsonville slug test example of Cooper et al 1967 Table 3 Also used by e g Vedat Batu 1997 p 667 668 Slug of 10 16 liter modeled as a pumping rate of 0 1016 m sec during 0 1 sec Cooper s method T 45 m d S 10 3 Linear drawdown curve fitting T 40 6 4 S 0 0019 29 Log drawdown curve fitting T 47 3 4 96 S 0 00056 37 25 stepdrawdown mlu Classical step drawdown test example of Lewis Clark 1977 Table 1 Also used by e g Kruseman amp de Ridder 1994 p 203 205 The increasing skin is modeled with different pumping wells at the same location Results T 480 m d 7 Sk1 1 5 47 Q 1306 m3 d Sk2 2 2 35 1693 Sk3 2 6 30 2423 Sk4 3 0 27 3261 Sk5 3 4 24 4094 Sk6 4 0 22 5019 recovery Well face flux time Drawdown time 25 20 Drawdown m a o 0 0 2 04 0 6 0 8 1 Time d Time d vennebulten mlu Kruseman amp de Ridder 1994 p 104 106 Unconfined aquifer pumping test example Vennebulten Table 5 1 presents data of the deep and shallow piezometer at 90 m Fitting the shallow drawdown measurements requires an additional
5. for all wells and for all aquifers Times and discharges are saved in E format heads are saved in five decimals FTH files can be read by spreadsheets and by MicroFEM Export Save contours as XYZ When a contour plot is drawn a file can be saved that contains all computed drawdowns of the displayed contour plot Each of the approximately 14000 lines contains three numbers the x coordinate the y coordinate and the computed drawdown XYZ files can be read by various GIS CAD and similar mapping or graphics software Surfer Arcview 21 Export Save model as FEM Based on the MLU model data a finite element model can be created and saved as a FEM file ready for import by MicroFEM The number of aquifers is limited to 20 layers The model shape is always hexagonal while its length from West to East can be specified by the user The minimum length depends on the system hydraulic characteristics and the maximum length is set to 2 000 000 m or ft The number of nodes may vary between about 1000 and 50 000 for each layer It largely depends on the specified number for the grid density 1 lowest density 10 highest density and the number of wells Around each well the neighboring nodes are located at a distance equal to six times the screen radius Nodal distances gradually increase away from each well When the Preview button is pressed all nodes are positioned and their total number is displayed Subsequently the elements are b
6. Schematic diagram of a multiple screened thin skin finite diameter well skin in a leaky multiaquifer system with crossflow and aquitard storage Application The MLU characteristics allow for all sorts of tests including recovery tests variable discharge tests step drawdown tests complex tests in well fields and slug tests It also handles partially penetrating and large diameter wells bounded aquifers using image wells and double porosity systems MLU produces transient contour plots that may be helpful to design well fields e g as used for ATES aquifer thermal energy storage Simple examples of some of these tests and applications are demonstrated in the models supplied with the software These example models are briefly described hereafter Hydrogeologists have found MLU to be very useful for quickly estimating aquifer properties such as layer by layer transmissivity storativity and vertical resistance conductance based on aquifer testing data and efficiently incorporating these properties into numerical groundwater flow models for advanced subsurface flow evaluations As far as we know MLU is the only Windows tool for evaluating aquifer response to pumping in a multi layer aquifer system MLU versus numerical models MLU and numerical models like Modflow and MicroFEM can both model stratified aquifers and multi aquifer systems but there still is a number of differences that make an analytical model like MLU more favorable in man
7. fluxes place the cursor at any particular point or part of a curve A yellow pop up window displays the name of the series as in the legend the accurate time and corresponding y axis value of the selected point You can save the time graph by selecting in the Main menu Edit Copy chart as metafile or as Bitmap to copy a snapshot of the time graphs to memory Use Paste to reproduce the figure in your document Use Export Save curves as FTH File of Times and Heads to save an ASCII file with all the computed heads or fluxes used to construct the displayed curves on the graph The file can be opened by e g Excel spreadsheet and MicroFEM finite element model The times and the heads or fluxes for each curve are presented in columns 18 Results Contour plot QD MLU for Windows 1 10 D Documents and SettingsKick Hemker Bureaublad fourwells mlu E m Bi x File Edit View Calculate Export Window Help m 8 xl i H4 ANO General info Aquifer system Pumping wells Observation wells Optimization results Time graphs Contour plot Coordinates West 1500 East z600 North z600 South 1000 rAquifer Display aquifer E E Contours Min drawdown Min contour 0 3 Gontaur interval j0 05 Vv Max contour 0 55 Max Time Display time 570 Animation Starting time fo Final time 900 Intervals
8. professional version of MLU costs 450 about 650 US Order directly from the web site http www microfem com order index html or e mail the authors hemker microfem com Free updates and User support There are no yearly recurring costs Regular updates improvements and small extensions are free Customer login allows all licensed users to download the latest update anytime User support is provided by the developers free of charge support microfem com USER INSTRUCTIONS Installing and running MLU Installing Unzip the MLU zip file double click the exe file and follow the installation procedure Starting Double click the MLU icon The MLU window includes standard components Title bar Menu bar File Edit View Calculate Export Windows Help Tool bar with buttons New Open Save Cut Copy Paste Optimize Seven tabs to access the data input and result screens Status bar Menu commands File New start a new case Open load an existing MLU file Reopen Save Save as Close close the present case Exit close MLU Edit Cut Copy Paste Delete row s Insert row s Clear Select all View Status bar Toolbar Calculate Optimize Preferences Import Import image files Export Copy chart Copy contours Save curves as FTH Save contours as XYZ Save model as FEM Windows Cascade Tile horizontally Tile vertically Minimize all Arrange all Help MLU Help MLU on the web About
9. this software or the interpretation or misinterpretation of any results obtained from this software or for direct indirect special incidental or consequential damages resulting from the use of this software Specifically Hemker amp Post is not responsible for any costs including but not limited to those incurred as a result of lost profits or revenue loss of use of the computer program loss of data the costs of recovering such programs or data the costs of any substitute program claims by third parties or for other similar costs In no case shall the liability of Hemker amp Post exceed the amount of the license fee 30
10. 00000E 10 0 0 00000 0 3 00000 57 97095 49 4 861797E 04 52 3 00000 248 62465 50 1 467240E 04 53 3 00000 5 15558 51 1 677179E 05 54 100 00000 1 000000E 10 0 0 00000 0 Pumping Wells and Discharges n No of wells 1 X Y Casing x Screen x Skin x Periods Name 0 00000 0 00000 5 276889E 02 55 1 000000E 01 0 1 000000E 31 82 08000 1 000000E 08 0 00000 Well screens per layer for all pumping wells 1 Observation wells and Drawdowns No of observation wells 3 X Y Layer Casing x Screen x Skin x drawdowns Name 0 00000 0 00000 2 2 000000E 02 0 2 000000E 02 0 1 041670E 04 8 000000E 01 1 388890E 04 1 20000 2 083330E 04 1 80000 2 777780E 04 2 40000 3 472220E 04 3 00000 etc 2 083330E 01 2 400000E 01 2 777780E 01 2 700000E 01 Time graph settings Drawdown curves reserved for future use 0 Well face fluxes reserved for future use 0 Contour plot settings west east south north start steps final layer del 0 00000 0 2 Pumping well 1 0 00000 0 24 observation well 1 5000 00000 5000 00000 3000 00000 3000 00000 0 00000 50 10 00000 1 1 000000E 02 28 References The techniques used in MLU are based on the theory as described in the following publications Hemker C J 1984 Steady groundwater flow in leaky multiple aquifer systems Journal of Hydrology 72 355 374 Hemker C J 1985 Transient well flow in leaky multiple aquifer systems Jou
11. Checkboxes allow for temporarily ignoring individual measurements during optimization Unchecked measurements are disregarded when Time graphs are drawn The bar between the tables can be shifted upward and downward 13 Results Parameter optimization The parameter optimization process requires the setting of two stopping criteria General info tab The preset values of 0 0001 can be adopted in most cases The choice between Linear and Log drawdown curve fitting is subjective When it is assumed that errors of drawdown measurements are independent of their magnitude then Linear drawdown curve fitting should be selected On the other hand when it is supposed that small drawdowns have small measurement errors Log drawdown curve fitting may be more appropriate Parameter optimization automated calibration is started by clicking the Optimize button blue arrow or as a menu command Calculate Optimize Only aquifer system and well characteristics selected by a character in the columns will be optimized It is recommended to save your model before optimization is started The same character for more than one property means that these values are optimized as a single parameter using the same correction factor For example when a homogeneous aquifer consists of several layers i e model layers with the same conductivities their possibly different layer transmissivities should be optimized as a group to make sure that the aq
12. MLU example models were set up to demonstrate how some well known or otherwise interesting well flow problems can be simulated These example models are supplied with the MLU software and become available in a map example upon installation Example Bounded aquifer is used in S gol s Case 2 2 verification test Model Pumping Obs Optimization File name System layers wells wells parameters GRDUBMER Confined 1 187 13 0 verification aquifer Dalem u Leaky 1 1 4 3 T1 cl S1 incid Confined 2 1 1 3 Ta porosity Fourwells Phreatic 6 4 2 0 Moench Phreatic 6 1 4 0 verification MW slugtest Confined 1 1 2 3 T1 S1 ski Recovery Leaky 2 1 1 3 T1 S1 ski Schroth Confined 2 1 3 7 T1 T2 c2 S1 S2 S2rcl Slugtest Confined 1 1 1 2 T1 S1 Stepdrawn Confined 2 6 6 7 T1 ski up to sk6 Vennebulten Phreatic 3 1 2 4 T3 c3 S1 S3 Two aquifers Phreatic 6 1 6 0 verification 23 Main characteristics of the example models bounded aquifer mlu S gol 1994 Classic Groundwater Simulations page 49 51 Case 2 2 Alternative B Rectangular confined aquifer 9000 5000 m No flow boundaries at South and West side Fixed head boundaries at North and East side Solution uses 11 17 1 186 image wells See e g Kruseman amp de Ridder Chapter 6 for a discussion on the use of image wells to model well flow in bounded aquifers Drawdowns are obtained along southern boundary for 3 tim
13. ave model as FEM 4142 ated eO RR SR ACIER He 22 Verification tests and Example models sees eene 23 Main characteristics of the example models 0005 24 Optimization results Example Schroth mlu 000 27 MLU data file layout iuc 24d e aee ERE ROSA OR S Ree de e ee 28 Dioec Apa KR TEE RETE 29 License aBree melli a sou sanaaa dac D ace aa Ea Od aoac oq sates ake APP ad 30 INTRODUCTION MLU for Windows is a groundwater modeling tool to compute drawdowns analyze all sorts of well flow and aquifer test data and design well fields MLU for Windows is based on e An innovative analytical solution technique for well flow in layered aquifer systems e Stehfest s numerical method to convert the solution from the Laplace domain into the real domain e The superposition principle both in space multiple wells and time variable discharges e The Levenberg Marquardt algorithm for parameter optimization automated curve fitting This unique combination of techniques allows for all tests to be analyzed in a consistent way with a single user interface Results are printed in ASCII files and plotted as time drawdown graphs and animated contour plots Solution Method As a rule present day computer codes for aquifer and slug test analysis still use the same analytical solutions and techniques that were common several decades ago Each type of aquifer test characterized by a long list of conditions and assumpt
14. ch cases the parameters cannot be determined accurately together The ranges of their standard errors will be very wide while the condition number will be large When this happens one parameter the one best known to the user may be fixed to compute the remaining set of parameters or positively correlated parameters may be grouped Finally the normalized eigenvalues and eigenvectors of the covariance matrix are presented These eigenvectors are given for mathematical completeness only but are of little use for the practical interpretation of the optimization results 15 MODEL CONCEPT MODEL INPUT PARAMETER VALUES MEASUREMENTS UNKNOWN PARAMETERS PARAMETER OPTIMIZATION INTERNAL SEARCH PROCESS PARAMETER VALUES RESIDUALS STATISTICAL INFORMATION RESIDUAL ANALYSIS EXTERNAL SEARCH PROCESS SYSTEMATIC ERRORS YES NO Fitting model DHHCERTAIHTY ANALYSIS Above figure represents the full calibration process MLU takes care of the internal search process only Residual analysis allows the user to search for the best set of optimization parameters in order to obtain a fitting model 16 Results Time graphs QD MLU for Windows 1 88 D Documents and Settings Kick Hemker Bureaubladmoench mlu oj xj 2 File Edit View Calculate Export Window Help la xi General info Aquifer system Pumping wells Observation wells l Optimization results Time graphs contou
15. ckness and a Kv on the orange line The vertical resistance c value is computed as thickness upper sublayer thickness lower sublayer 2 Kv Used codes T1 T2 Transmissivities of aquifers or sublayers thickness Kh m day ft sec etc Kh horizontal hydraulic conductivity of an aquifer or aquifer layer cl c2 Vertical resistances inverse of conductance thickness Kv day sec etc Kv vertical hydraulic conductivity of an aquitard multi aquifer system or between the middles of two adjacent sublayers stratified aquifer S1 S2 Storativities of aquifers or sublayers S 1 9 2 Storativities of aquitards columns Use any non zero character A Z a z 1 9 to indicate that the current system property is a parameter to be optimized Two or more parameters that must be optimized as a group i e the same multiplication factor will be applied should be indicated by the same character If the entry is blank the current parameter will be kept constant during optimization Zero valued properties storativity cannot be optimized When entering new data in the table some other values in the table will be updated according to the following rules New input of thickness changes base New input of base 1f smaller that value above changes thickness It also changes the base of all lower layers New input of thickness or base changes Kv or Kh but leaves c T
16. der placement X axis Or y axis e g font scale X axis or y axis title e g font color Seres e g color and thickness of the selected curve Chart Options e g show legend titles The Reset options button sets all modified drawing options back to their default settings 17 By default only drawdown curves are plotted for included observation wells Similarly only well face fluxes are plotted for the screened aquifers of all pumping wells Use the cells in the Select curves table to remove individual curves right mouse click and to add curves or modify their colors left mouse click u Options Select curves j ix p a P a G 3 a PS1 PS2 Layer 1 ee Layer 3 Layer 4 NEN Layer 6 q Cancel The maximum number of curves drawn in the graph is 128 The accuracy of the calculated graphs can be improved by selecting higher values at the Main menu Calculate Preferences a Stehfest parameter default 10 options 6 16 Effects the accuracy of all computed drawdowns and fluxes A description of Stehfest s method and a comparison of results as a function of the chosen parameter is given in Hemker amp Maas 1987 b Number of computations per log cycle default 10 options 2 40 Calculation time increases more or less linearly with these numbers For point inspection of observed and calculated drawdowns and well face
17. eads with their differences cal obs By analyzing the sign of these residuals an impression can be obtained of how well the aquifer model simulates reality Generally speaking it can be said that positive and negative differences should occur randomly The same list of calculated and observed heads with their differences cal obs 1s also presented when no parameters are specified to be optimized Based on the analysis of the residuals one has to decide whether the model the curves fit the data observations When the model does not fit more or other parameters can be selected When no set of parameters can be found that produces a fitting model the model concept may need adjustment e g number of model layers or the field flow conditions are too complex to be modeled by MLU e g effects of heterogeneity lateral anisotropy Subsequently some numbers are given for the reduction of the sum of squares and the number of iterations The condition number may be regarded as an expression of the difficulty of finding the least accurate parameter Large numbers are unfavorable when the condition number is very large e g 1 000 000 at least one parameter cannot be determined properly MLU also presents a correlation matrix The correlation between all pairs of parameters is given as a percentage High correlations values near 100 or near 100 mean that a simultaneous change of both parameters will produce almost the same sum of squares In su
18. ear drawdown curve fitting features Time units Days ias Time units Days Length units Meters At a new start the text fields of Project and File are blank The text in the field File name determines the default file name when data are saved Time units is set to Days by default You may select here or after right clicking Time units at the Status bar other time units seconds minutes hours and years The alternative at the Status bar is always available The used conversion factor for days per year is 365 24 Length units may be set to either meters or feet You may change the Length units on the Status bar The conversion factor for meters per foot is 0 3048 The default setting can be changed for future sessions in the Calculate Preferences window General setup Specify the number of aquifers the number of pumping and injection wells and the number of observation wells piezometers In case of a layered stratified aquifer the number of aquifers should be read as the number of aquifer sub layers Parameter optimization the preset stopping criteria and linear curve fitting method can be adopted in most cases Data input 2 Aquifer system a gt MLU for Windows 1 10 D Documents and Settings Kick Hemker Bureaublad variantt mlu E ES Oj xj D File Edit View Calculate Export Window Help 81 x General info Aquifer system Pumping wells Observation wells Optimizat
19. es 0 05 0 15 and 2 days Comparison with analytical and numerical results see benchmark zip dalem u mlu Kruseman amp de Ridder 1994 p 83 84 Leaky aquifer 1 pumping well and 4 piezometers 51 observations Graphical solution T 1731 m d S 0 0019 c 468 d Linear drawdown curve fitting T 1676 m d 0 0018 c 328 d Log drawdown curve fitting T 1780 m d 0 0016 c 539 d double porosity mlu Kruseman amp de Ridder 1994 p 258 261 after Moench 1984 Modeled as a two aquifer confined system See e g Hemker amp Maas 1987 for a short discussion on the similarity between layered and fissured formations 72 observations in pumped well Graphical solution T2333 m d S 0 0016 Linear drawdown curve fitting T 334 m d S 0 0032 fourwells mlu Test example of a 4 wells square ATES Aquifer thermal energy storage configuration Alternating two wells discharging and two wells injecting in a yearly cycle Phreatic multi aquifer system 6 model layers Wells screened in 3rd aquifer 3 model layers 2 zero thickness resistance layers Contour plot animation verifies crosswise symmetric drawdown build up cone patterns moench mlu Moench 1997 Flow to a well of finite diameter in a homogeneous anisotropic water table aquifer Water Resources Research v 33 no 6 p 1397 1407 See also Paul M Barlow and Allen F Moench 1999 Water Resources Investigations Report 99 4225 WTAQ Sample Problem 2 http
20. esidual sum of squares is 0 0131 Residual sum of squares m 0 6031 Number of iterations 6 Condition number 463 4 Correlation matrix 96 T 1 100 T2 1 100 c 2 60 21 100 S 1 82 14 78 100 S2 39 53 3 43 100 S 2 70 3 55 90 67 100 rc 1 1 25 6 3 31 1 100 100 observation well 3 layer 1 observation well 1 layer 2 10 observation well 2 layer 2 e observation well 1 m observation well 2 ET 1 a observation well 3 i E amp 01 0 01 0 001 1E 04 0 001 0 01 0 1 1 Time d 27 MLU data file layout MLU data file c 2009 Kick Hemker amp Vincent Post Multilayer aquifer system Pumping test analysis MLU Version 1 54 00 www microfem nl products mlu html General Information Name Schroth amp Narasimhan Test 2 aquifers and 1 aquitard Loc Date Rem Ground water Vol 35 no 2 p 371 375 Measured drawdowns are Rem only estimatedfrom the graphs in the paper Rem Data parameters results of S amp N File schroth Date Rem cjh 24 sept 1997 change units to seconds Rem Rem Rem Parameter Optimization mE Rel 1 000000E 04 Abs 1 000000E 04 Linear drawdown curve fitting LIE Aquifer System TITEL P E LP EE ET EE E E EE E E Length m Time sec Top level 0 00000 No of sub aquifers 2 Top Aquitard Impervious Base Aquitard Impervious Thickness T c x S S x Name 46 00000 1 0
21. for Windows Well flow modeling in multilayer aquifer systems UNESCO edition Kick Hemker amp Vincent Post Amsterdam October 2010 www microfem com MLU for Windows CONTENTS Tntrod uot De uses uw e bx e AE eara e eee obs qe a pa aa ee PES VUE 3 SOMO Method 2 22 eo eS Ga eee RYE qu AA RRqSWESQRURESS 3 Application CRI 4 MLU versus numerical models 0 00 0 eee 4 Software CAPACI uas cevieoxs q UESOAXGG E RATERS RAST Eee RARE 5 Data p tt ee sah my Bm Walt ey C Gre wa ws BA Eee ems ere RS 5 Inverse modeling Data output Gr phical OutpU as ces oat Eu kh te aaa e dese Eo de a E arde 5 Free UNESCO edition 2 ioceasceo Rm RRR RE eS 6 Price and orders MD MN m 6 Free updates and User support 0 0 ccc eee eee 6 User instrucllotis esae de send Xe RYXTXAXRRARAJGR A RARO EES aR RAST RE T Installing and running MLU sseeeeee eee 7 Data input 1 General info n nunnana naana 8 Data input 2 Aquifer system llle 9 Data input 3 Pumping wells 0 0 0 cece cee eee 11 Data input 4 Observation wells llle 13 Results Parameter optimization 0 0 20 00 ce eee 14 Results Time frapis 1a s diu d ae e doe oe eoe hodie ORE 9 Wack ae ae 17 Results Contour plot scese sacer pe RECO YGORRAERRUS pA EROS ORC 19 Import Import image files 20 Export Save curves as FTH 220 2s3 cc ase edeeusg e RIDE E EAT TRE ER 21 Export Save contours as XYZ lessen 21 Export S
22. hs Contour plot 0 2 0 24 V observation well 1 0 02 0 02 2 v observation well 2 46 2 0 02 0 02 16 3 p observation well 3 52 o 1 0 02 0 02 0 n 77 Measurement data for observation well number 3 eene prse 7 1 0 01 0 025 sS lt l 0 05 0 08 0 11 0 13 0 18 0 21 0 24 0 27 SIX lt a 4 2 3 4 5 6 mv 7 8 9 5 a 4 Time units Seconds Length units Meters The upper green table contains rows with information for all observation wells piezometers one row for each well The Include column contains checkboxes that are all checked by default When an observation well is set to unchecked all measured drawdowns of this well are ignored during optimization Also unchecked wells will be disregarded when Time graphs are displayed It is recommended to use the same name for wells at the same location i e with same x and y coordinates The Layer column shows the number of the aquifer layer in which the well is open screened The casing radius well bore storage and skin factor of each observation well are used to compute the delayed observation well response The last column is used to indicate the number of drawdown observations in each observation well This number must be 1 or larger up to 100 and determines the number of rows in the lower table The lower table shows the measured drawdowns for each observation well selected in the upper table
23. icaties Downloadable publications 11 columns Well characteristics casing radius screen radius and skin factor may also be optimized Use any non zero character A Z a z 1 9 to indicate that the well property is a parameter to be optimized Two or more parameters that must be optimized as a group i e the same multiplication factor will be applied should be indicated by the same character Well characteristics cannot be grouped with aquifer system properties Zero valued well characteristics casing radius skin factor cannot be optimized The last column is used to indicate the number of constant discharge pumping periods This number must be 1 or larger up to 10 and determines the number of rows in the lower table The lower table shows how the pumping rate of the well selected in the upper table changes in time by specifying the starting time and the constant discharge rate of each period Injection rates are specified by negative discharges while the discharge rate of a recovery period is zero Checkboxes allow for temporarily ignoring particular pumping or injection periods The bar between the tables can be shifted upward and downward 12 Data input 4 Observation wells 4D MLU for Windows 1 16 G MLU examples for manual schroth mlu ni x File Edit Yiew Calculate Export Window Help laj xl General info Aquifer system Pumping wells Observation wells optimization results Time grap
24. ion results Time graphs Contour plot ayers oundary conditions Number of aquifers fF v Top aquitard present Impervious Leaky Elevation top layer fiz Bottom aquitard present Impervious C Leaky Tmaoesstm Winall owe ch efom St a tome Time units Days Length units Meters MLU always starts a new case with default values for all aquifer system properties Elevation top layer is the level of the top of the saturated system above reference level It is either the top of the upper fully confined aquifer or the water table level in a leaky top aquitard or phreatic aquifer The alternating yellow and orange rows of the table indicate aquifers yellow and aquitards orange in case of a multi aquifer system or the aquifer sublayers yellow and the intermediate resistances orange of a stratified aquifer The aquifers are numbered from top to bottom Aquitards can be present or absent at the top and at the base of the system When such a top or base aquitard is present the boundary condition can be specified as leaky indicated by a blue bar in the table In all other cases the system boundary is impervious In case of a phreatic aquifer the top aquitard 1s absent Within a stratified aquifer there are no aquitards but only aquifer sublayers The vertical resistance between two such sublayers depends on the thicknesses of these layers and their Kv In such cases MLU allows to enter a zero thi
25. ions is associated with a particular analytical solution e g Theis Hantush Neuman Boulton Papadopulos Moench for only one or sporadically two aquifer s The related procedures to determine the usually two or three aquifer properties often require straight line fitting or type curve matching with some part of the measured data Unlike such traditional aquifer test software MLU is based on a single analytical solution technique for well flow that handles e Layered aquifer systems i e multi aquifer systems aquifers and aquitards and or layered stratified aquifers Fig 1 e Confined leaky and delayed yield systems Effects of aquifer and aquitard storativities One or more pumping or injection wells One or more pumping periods for each well Finite diameter well screens in any selection of aquifer layers Well bore storage and skin effect for each pumping well Delayed observation well response Individual and grouped parameters to be determined in one run Theoretical background information on the applied analytical solution techniques for multiple aquifer systems has been published in e g Journal of Hydrology 90 p 231 249 1987 and 225 p 1 18 and p 19 44 1999 The non linear regression technique is described in Ground Water 1985 23 no 2 p 247 253 See the references for further details Fig 1 a Schematic diagram ofa partially penetrating thin skin finite diameter well in a horizontally layered aquifer b
26. kipedia org wiki World file To import a file use Main menu Import Import image files Add Several contiguous image maps can be displayed at the same time Piezometric surface build up drawdown D a bn y WA N o d J P i S R NS f e ey 4 M Kivette N TI VS DY S ALLE Right clicking in the contour plot Chart options Background allows adjustment of the brightness transparency Use Main menu View Background images Ctrl B to switch the background images on and off All information of loaded image files is saved with an MLU file to restore the images upon reloading of the project 20 Export Save curves as FTH When a time graph is drawn an ASCII file can be saved that contains all computed heads for all included observation wells from the upper displayed aquifer down to the lowest displayed aquifer FTH File of Times and Heads The file consists of the following parts The first three lines contain The header The number of aquifers the number of observation wells and 1 The actual numbers of these aquifers The next four lines show a number for each well the last part of their names and their x and y coordinates This is repeated for each aquifer The main part of the file consist of a number of up to 129 columns the first number on each line represents the time days while all the following numbers are calculated heads or discharges
27. layer between the pumped aquifer and the water table Two aquifers mlu Lebbe amp de Breuck 1995 use a synthetic pumping test for the validation of their numerical model The phreatic system is composed of two aquifers and an anisotropic aquitard which is discretized in three layers to model elastic storage Water is discharged from the lower aquifer Piezometers are installed in the aquitard and in the lower aquifer at three distances In two aquifers mlu the flow conditions of the numerical model are represented as good as possible by discretizing the aquitard in three layers with horizontal flow and elastic storage and four layers with vertical flow The largest drawdown differences occur after one minute of pumping numerically 0 286 and 0 042 m drawdown at 5 01 and 15 85 m distance respectively while MLU computes 0 298 and 0 050 m Of all 151 drawdowns most differences are 0 001 m or less 26 Optimization results Example Schroth mlu Results of Log drawdown curve fitting Parameter value Standard error T 1 58 0 3 3 6 9 Transm upper aquifer m d T 2 5 156 6 381E 2 1 Transm lower aquifer m d c2 248 6 6 2 3 Hydr resistance aquitard d S 1 4 865E 4 5 231E 5 11 Storativity upper aquifer S 2 1 678E 5 1 030E 6 6 Storativity lower aquifer S 2 1 467E 4 9 490E 6 6 Storativity aquitard rc 1 5 277E 2 4 385E 4 1 Radius of well casing m Initial sum of squares is 2 7390 R
28. low values can be used but they will remain positive This also explains why zero valued parameters cannot be optimized 14 When MLU for some reason doesn t succeed in finding a proper solution the optimization process is stopped The reason for stopping will be displayed When the calculation is broken off close the results window There are different ways to continue Just restart the optimization process First change some or all of the parameter values to be optimized and then restart the optimization process Reset all unrealistic properties and restart with a reduced number of parameters to be optimized When MLU has found a solution the computation is stopped parameters found In this case results are presented as a number of tables in the Optimization results tab window The first table shows the calculated optimal parameter values and their most probable ranges optimal value plus minus the standard error Of course the reliability of these results depends on several conditions The model should be capable of producing the proper values and all non optimized model values are supposed to be correct It is also assumed that there are no systematic errors in the observed heads and the random errors are normally distributed The percentage between brackets p is the ratio of the standard error to the parameter value The next table is a list of all calculated with the latest set of parameters and observed measured h
29. ma water usgs gov publications WRIR_99 4225 index htm Water table aquifer Partially penetrating pumping well of finite diameter 6 Layer MLU model simulates full 3D analytical solution 24 Drawdowns in a partial penetrating pumping well and 4 piezometers at different distances and different depths in a phreatic aquifer compared to 3D analytical results example Moench Drawdown time 10 PSI layer 2 PS2 layer 2 pumped well layer 5 PSI layer 5 1 PS2 layer 5 e pumped well m PSL a PS2 0 1 e PDL m PD2 o UO 8 45 0 01 0 001 1E 04 1 10 100 1000 10000 1E 05 1E 06 1E 07 1E 08 1E 09 Time s mw slugtest mlu Multiwell slug test pulse interference test Butler amp Liu 1997 Also J J Butler The Design Performance and Analysis of Slug Tests 1998 p 191 195 Lincoln County Site Multiwell slug test 2 Measurements is slugged well and in nearby observation well 138 Linear drawdown curve fitting T 10 4 m d 2 96 S 2 1 10 4 Skin 1 8 7 Log drawdown curve fitting T 11 4 m d 1 96 S 1 0 10 4 96 Skin 3 2 6 96 recovery mlu Well field research program Hardinxveld Giessendam 1981 Well B Well drawdown measured during 20 minutes pumping and 30 minutes recovery Log drawdown curve fitting T 1321 m d 1 96 S 0 00028 13 94 Skin 6 1 4 94 schroth mlu Schroth and Narasimhan 1997 Ground Water 35 p 371 375
30. ngng Geol 10 125 143 Cooper H H J D Bredehoeft and S S Papadopoulos 1967 Response of a finite diameter well to an instantaneous charge of water Water Resour Res 3 263 269 Kruseman G P and N A de Ridder 1990 Analysis and evaluation of pumping test data ILRI publication 47 Wageningen The Netherlands 377 pp Lebbe L and W De Breuck 1995 Validation of an inverse numerical model for interpretation of pumping tests and the study of factors influencing accuracy of results Journal of Hydrology 172 61 85 Moench A F 1984 Double porosity models for a fissured groundwater reservoir with fracture skin Water Resour Res 20 831 846 Moench A F 1997 Flow to a well of finite diameter in a homogeneous anisotropic water table aquifer Water Resour Research 33 6 1397 1407 Schroth B and T N Narasimhan Application of a numerical model in the interpretation of a leaky aquifer test Ground water 35 371 375 S gol G 1994 Classic groundwater simulations Proving and improving numerical models Prentice Hall 531 pp 20 License agreement MLU for Windows O 2008 2009 by C J Hemker amp V E A Post Amsterdam Hemker amp Post retain the ownership of all copies of the MLU software A copy is licensed to the purchaser for use under the following conditions 1 Copyright Notice This software is protected by both Dutch copyright law and international treaty provisions Hemker amp Post authorizes the p
31. r plot 4 Curve type Drawdown curves C Well face fluxes o 10 Starting time s 10 Stopping time s 1E 07 Time axis 34 1 Drawdown time PSI layer 2 PS2 layer 2 pumped well layer 5 P51 layer 5 PS2 layer 5 Logarithmic time axis e pumped well PS1 PS2 Linear time axis Value axis oe u E Logarithmic drawdown 0 1 PDi Linear drawdown 2 poz o Linear head E 0 01 L J Auto update a Drawing options Reset options 0 001 o E 04 d 1 10 100 1000 10000 1E 05 1E 06 1E 07 Time s Fr units Seconds Length units Meters y In the dialog box on the left one may choose between Drawdown curves and Well face fluxes When drawdown curves are plotted on a log scale absolute values are taken Well face flux curves show the time variant fluxes from the aquifer s into individual well screens taking account of well bore storage When the auto update box is not checked default setting graphs are only redrawn when the Update chart button is pressed Press the Drawing options button or right click in the graph window for a pop up menu with the following options Select curves select curves to be drawn and select their colors Chart area select color of area and border of graph Chart title e g font color Legend e g font bor
32. rnal of Hydrology 81 111 126 Hemker C J 1985 A General Purpose Microcomputer Aquifer Test Evaluation Technique Ground Water 23 247 253 Hemker C J and C Maas 1987 Unsteady flow to wells in layered and fissured aquifer systems Journal of Hydrology 90 231 249 Hemker C J and C Maas 1994 Comment on Multilayered leaky aquifer systems 1 Pumping well solutions by A H D Cheng and O K Morohunfola Water Resources Research Vol 30 No 11 p 3229 3230 Hemker C J 19992 Transient well flow in vertically heterogeneous aquifers Journal of Hydrology 225 1 18 Hemker C J 1999b Transient well flow in layered aquifer systems the uniform well face drawdown solution Journal of Hydrology 225 19 44 You may contact the author hemker microfem com for a PDF of the above publications References made in the description of the example models Barlow P M and A F Moench 1999 WTAQ A computer program for calculating drawdowns and estimating hydraulic properties for confined and water table aquifers U S Geol Survey Water Resources Investigations Report 99 4225 74 pp Butler J J Jr 1998 The Design Performance and Analysis of Slug Tests Lewis Publishers Boca Raton 252 pp Butler J J Jr and W Z Liu 1997 Analysis of 1991 1992 slug test in the Dakota aquifer of central and western Kansas Kans Geol Surv Open File Rep 93 1c Clark L 1977 The analysis and planning of step drawdown tests Quart J E
33. ting is based on the Levenberg Marquardt algorithm e Linear and log transformed least squares solutions e Statistical data output includes standard errors and correlation matrix e Parameter optimization and final output results in ASCII files Data output e Data exchange with spreadsheets copy amp paste MLU data file ASCII Optimization results including calculated and observed drawdowns ASCII Data file that contains computed heads of displayed time graph FTH file Data file that contains computed drawdowns of displayed contour map XYZ file Data file that contains a MicroFEM finite element model FEM file Graphical output Linear semi log and log log time graphs of drawdown or head Time variant aquifer discharge at a well screened over multiple aquifers Animated contour plots of drawdown and build up cones Clipboard bitmap output and vector based meta file output Free UNESCO edition The MLU UNESCO edition is a reduced version of MLU for Windows and is available for teaching testing and the analysis of one and two aquifers pumping tests The UNESCO edition is free but the application is limited with respect to the number of aquifers pumping and observation wells and the number of parameters to be optimized MLU UNESCO edition can handle e 2aquifers and 3 aquitards e 2pumping injection wells e 5 observation wells e 6 parameters to be optimized in one run Price and orders A site license for the Windows based
34. ts and when optimizing parameters The Layers column shows the numbers of the aquifers layers in which the well is screened To select a range of screens in adjacent layers for example layer 4 up to 6 type 4 6 To select nonadjacent layers type the numbers separated by a comma 3 5 Alternatively screened layers can be selected in a drop down list Casing radius code rc is the inside radius of the well in the interval where the water level is changing during pumping Actuality it should be smaller since the free water surface area is reduced by the e g the discharge pipe while in MLU this surface is computed as pi rc Screen radius code rw is the radius of the well screen or the screened interval of the well or open hole The drawdown along the well screen i e in the screened layer s at the screen radius is assumed constant in space at any time the UWD Uniform Well face Drawdown condition Hemker 1999b Based on this UWD condition individual well face fluxes can be computed and presented by MLU see Time graphs For a definition of the skin factor code Sk and more information on well performance tests step drawdown and recovery tests see e g Kruseman amp de Ridder Kruseman amp de Ridder 1990 Analysis and evaluation of pumping test data Chapter 14 ILRI publication 47 Wageningen The Netherlands 377 pp Also available from Internet http www alterra wur nl NL publicaties A Iterra ILRI publ
35. uifer remains homogeneous during optimization Hydraulic properties cannot be grouped with well properties The objective of the computations is to find that particular combination of parameters that minimizes the sum of squares of the residuals i e the differences between the measured and computed heads The applied iterative method is called the Levenberg Marquardt algorithm Intermediate results for each iteration are displayed in a separate window showing the iteration number and the set of parameter values When Log drawdown curve fitting is selected General info tab the logarithms of all measured and computed heads are taken before the sum of squares of the residuals is computed In this case the sum of squares is dimensionless The iterative process is terminated when a minimum sum of squares is reached i e when the values of the last and the one but last computed sum of squares SS are sufficiently close as defined by the Relative stopping criterion Rel and the Absolute stopping criterion Abs Improvement SS Rel SS Abs Abs Rel and Abs can be specified at the General info tab Rel is a dimensionless value while Abs is dimensionless in case of Log drawdown curve fitting but has a length unit m or ft in case Linear drawdown curve fitting is selected When optimizing hydraulic characteristics T c S and S values MLU uses the logarithms of these values internally So very high and very
36. uilt which is also displayed as an increasing number at the bottom line The total number of elements is always nearly twice as large as the number of nodes The element generation process can be interrupted with the Cancel button Once the grid is generated the Save button can be pressed to save the model A free version of MicroFEM is available from the MicroFEM site www microfem com This version is limited to two aquifers and 2500 nodes per layer Q9 MicroFEM model generator lol xl AZNB OON KONG DOOD ED S KAKA DESAI NR 7 c Jette ers Coe E QUOQOE RESO ALAA S A ATA TAVAT ATAYA OOGGNNSISOGGNSGGGC Mavavavavivivavivavavavvav d S AAA AV AVAVAVAN AVA ANANA ATA Sie LAUS NIA A vi Y X POOOOOO OY KPNI as vA Model length m eoo Grid density A 1705 nodes 3360 elements 22 VERIFICATION TESTS AND EXAMPLE MODELS Verification of MLU for Windows is based on comparison with analytical and numerical solutions of a large number of published test models e g the analytical moench model with a partially penetrating well in a phreatic aquifer and the numerical two aquifers model with piezometers in the aquitard between both aquifers Also the file benchmark zip available from the MicroFEM site contains five verification tests selected from S gol s book Classic Groundwater Simulations Cases 2 1A 2 1C 2 2 6 1 1 and 6 1 2 Furthermore a number of
37. urchaser to make archive copies of the software for the purpose of backing up the MLU software The purchaser of a license is also allowed to make copies of the software and use his backups of the software on more than one of his own machines on the strict condition that these backups are only used within the city of the purchaser s office or within the department of the university concerned Specifically the purchaser may not rent sub license or lease the software or documentation alter modify or adapt the software or documentation including but not limited to translating de compiling disassembling or creating derivative works without the prior written consent of Hemker amp Post 2 Warranty The MLU software has been used and tested since 1987 DOS version No software is completely error free however Should you encounter a bug Hemker amp Post will immediately work on it and supply you with a corrected version at no charge This warranty shall be limited to replacement and shall not encompass any other damages including but not limited to loss of profit and special incidental consequential or other similar claims 3 Disclaimer Except as specifically provided above neither the developer of this software nor any person or organization acting on behalf of him gives any warranty express or implied with respect to this software In no event will Hemker amp Post assume any liability with respect to the use or misuse of
38. y cases e Anumerical model with two or more wells requires a 3D model e Apumping well with multiple screens is a well known problem in numerical models e tis not easy to construct numerical models that allow for finite diameter well screens well bore storage skin effects and delayed observation well response in 3D models e When designing well fields e g for aquifer thermal energy storage relocating wells may be cumbersome in numerical models e When parameter optimization is the purpose of modeling an analytical model is more suitable and much faster since drawdowns can be computed immediately and more accurately for any point in space and time On the other hand MLU models have some important restrictions e All layers are assumed homogeneous isotropic and of infinite extent e Only groundwater flow as a result of pumping and injection wells can be modeled Software capacity The MLU software can handle e 40 aquifers layers and 41 aquitards 300 pumping injection wells e 10 pumping periods per well 50 observation wells 100 measured drawdowns per observation well e 16 parameters to be optimized in one run Data input e Interactive input e Data exchange with spreadsheets copy amp paste e Modify MLU input data file ASCIT e Time conversion seconds minutes hours days and years e Length conversion meters feet Inverse modeling e Individual and grouped parameters can be determined in one run e Automated curve fit
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