Software Spotlight/ Chunmiao Zheng, Software Editor

MLU: A Windows Application for the Analysisof Aquifer Tests and the Design of Well Fieldsin Layered Systemsreviewed by Fritz Carlson1 and Jeff Randall2

IntroductionUnlike other aquifer test analysis software supporting

a wide variety of different solution types for one andsometimes two aquifers (e.g., Theis, Hantush, Neuman,Boulton, Papadopulos, Moench, Bouwer-Rice), MLU isbased on a single analytical solution technique for wellflow that handles:

• Layered aquifer systems, that is, multi-aquifer systems(aquifers and aquitards) and single layered (stratified)aquifers

• Confined, leaky, and delayed yield aquifer conditions• Effects of aquifer and aquitard storativities• Up to 300 pumping or injection wells• Up to 50 pumping periods for each well• Up to 100 observation wells with 500 measured

drawdowns in each well• Wellbore storage and skin effect for each pumping well

and observation well• Partial penetration.

MLU can be used to analyze and simulate all sorts of tests,including variable discharge tests, recovery tests, step-drawdown tests, complex tests in multiple well fields andslug tests. It also handles partially penetrating and large-diameter wells, bounded aquifers, and double-porositysystems. In addition, MLU can also be used in forwardprediction mode to:

• Compute drawdowns at various times and locations ina well field—it is very easy to use multilayer aquifersimulator using known or assumed aquifer parameters

1Corresponding author: CH2M Hill, Redding, CA 96001;Fritz.Carlson@ch2m.com

2CH2M Hill, Seattle, WA 98004-4504; Jeff.Randall@ch2m.com

© 2012, The Author(s)Ground Water © 2012, National Ground Water Association.doi: 10.1111/j.1745-6584.2012.00945.x

• Assist in aquifer test design by “pre-simulating” teststo help determine which parameters can be measuredgiven a fixed array of monitoring and pumping wells.

MLU is subject to many of the same primary simplifyingassumptions used in most analytical groundwater flowsolutions:

• All layers are of infinite horizontal extent• All aquifer layers are homogeneous and isotropic with

respect to transmissivity• All aquifer layers are homogeneous with respect to

storativity• All aquitard layers are homogeneous with respect to

vertical resistance and storativity• A well is pumped at a constant or step-wise changing

rate• Darcy’s law is valid, except for turbulent flow near the

well screen.

Theoretical background information on the developed andapplied analytical solution techniques for multiple aquifersystems has been published by Hemker and Maas (1987;Hemker 1999a, 1999b). The applied nonlinear regressiontechnique is described by Hemker 1985.

How We TestedMLU version 2.25.38 was tested on a Dell Inspiron

E6500 laptop with an Intel Core2 Duo CPU P8700 @2.53 GHz and 4 GB of installed memory. The operatingsystem on this laptop is a 32 bit version of Windows 7Professional.

InstallationThe MLU installation file was downloaded from the

MLU website:http://www.microfem.com/

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After logging into the “customer login” section of thedownload page and entering the appropriate username andpassword, the 2-MB zipped installation file downloadedquickly. Although the full version of MLU was testedfor this review, a “light” version is available for free atthis site. Installation of MLU is very easy: just unzip theinstallation file and click on the “msetup22538.exe” file.

Test Example ProblemMLU comes with a number of test example problems

including a slug test, a step-drawdown test, a multiple welltest, and many of the pumping tests that are describedby Kruseman and de Ridder (1994). To illustrate the useof MLU to analyze an aquifer test, we developed a testproblem with a fully confined, three-layer aquifer witha 300-gpm well pumping from the uppermost layer 1.We used MLU to compute the drawdown in monitoringwells located in each aquifer layer at distances of 1, 10,100, 1000, and 10,000 feet and for 26 times from 1 to10,000 min. So in this example, we have 15 different mon-itoring wells with 26 data points each. After computingthese drawdowns with known aquifer properties, we thenused MLU to see how easily MLU could compute theaquifer parameters from initial property guesses nowherenear the “true” values.

What We Found

User InterfaceThe MLU user interface consists of six tabs and eight

pull-down menus. These will be illustrated using the testexample problem described above.

General InfoThe General info tab (Figure 1) is where one defines

the number of aquifers, the number of pumping wells,and the number of observation wells. The units for timeare defined on this tab; the length units (feet or meters)are defined in a pull-down menu (Calculate-options). Thestopping criteria are also defined on the General info tab.The default value of 0.0001 for both seems to work well.The user can also choose linear or log drawdown fitting.We have found that linear fitting works best in most cases.

Aquifer SystemThe Aquifer system tab for the test example is shown

in Figure 2. The most important part of this tab is theaquifer property matrix in which the user conceptualizesthe aquifer system. The properties of each aquitard areshown in the orange rows. The properties of the aquifersare shown in the yellow rows. To begin a run, the userdefines the thickness of each layer, and an initial guess forthe horizontal K and storativity for the aquifers and thevertical K and storativity for the aquitards. Note that thecolumn headings for columns 4 and 6 change dependingon whether the user is inputting Kh or Kv. In this example,we have chosen to simulate the three-layered aquifer

system as a stratified aquifer with no explicit aquitards.The user can choose a top and bottom aquitard is presentand whether these boundary conditions are impervious orleaky. In addition, there is a column that allows the userto name the various layers; this is very helpful for keep-ing track of the various aquifer names and zones that havebeen defined in an area.

In the aquifer property matrix, MLU automaticallycalculates the transmissivity for the aquifers on the basisof the Kh and thickness. For the implicit aquitards shownon the example tab, MLU calculates the vertical resistance“c” (which is the reciprocal of leakance) by dividingthe distance between the midpoints of the overlying andunderlying aquifer by the Kv of that interval. If an explicitaquitard (with a nonzero thickness) had been used, thevertical resistance would be calculated by the aquitardthickness divided by the Kv.

In the example tab shown in Figure 2, initial guessesof the parameter values have been entered. To instructMLU to compute the best values for an aquifer parameter(termed “optimizing” in MLU) the user inputs a uniqueletter or number in the “#” column. In the example,we have asked MLU to optimize the values for thetransmissivity and storativity in each layer and the verticalresistances between layers based on the data that is enteredon the Pumping wells and Observation well screens. Itis also possible to ask MLU to optimize parameters asa group. For example, if there are insufficient data todevelop unique values for each of the aquifer parameters,some of the parameters can be optimized together byentering the same letter in the “#” column. If there isno entry in the “#’ column, MLU will accept the enteredvalue for the parameter and not attempt to optimize it.

Pumping Well and Observation WellThe Pumping well tab is shown in Figure 3. In this

figure, the user enters the location, the screened layers, thecasing radius, the screen radius, and the skin factor. Thecasing radius is the inside radius of the well in the inter-val where the water level is changing during pumping,but adjusted to an effective radius to account for the pres-ence of the pump discharge pipe. The screen radius is theradius of the well screen or open hole. In the example tab,there is only one period listed. However, in a test wherethe pumping rate changes, additional pumping periods canbe inserted to approximate the changing pumping rate ina step-wise fashion.

The Observation well tab is shown in Figure 4. Thereare two parts to the Observation well tab. The upper partis a table listing the observation wells, their coordinates,screened layer, casing screened layer, skin factor, and thenumber of observations from that well. The lower part ofthe tab has the observed time-drawdown data for the wellhighlighted in well table in the upper part of the tab. Thetime-drawdown data can be pasted from ascii data sets orfrom a spreadsheet. Because there is a limit of 500 datapoints per observation well, large data sets collected bya transducer are not appropriate for direct input to MLU.In our experience, reducing the number of data points

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Figure 1. General info tab.

Figure 2. Aquifer system tab with initial guesses of aquifer parameters.

to those needed to define the drawdown curve will makeMLU run much faster. One way of doing this is to plot allthe data on a semi-log or log-log graph and then manuallydigitize 20 to 30 points that define the curve. Alternatively,this process may be automated using a cubic-spline add-into Excel to generate interpolated data points every, say,0.2 log cycles during the duration of the test.

The Pumping well and Observation well tabs bothhave “include” check boxes that allow the user to ignoreentire observation wells or pumping wells or selections ofdata that may be anomalous or inconsistent with the restof the data set.

Optimization ResultsAfter entering the observed data, the pumping rates

and initial guesses of the aquifer properties, the user

can instruct MLU to begin the optimization process bypushing the red “optimize” button at the top of the tab.Figure 5 shows the comparison of observed and simulateddrawdown data based on the initial guesses of the aquiferparameters, in other words, with no optimization. Then,by putting a letter in the “#” column of the Aquifer sys-tem tab, we asked MLU to optimize the values for thetransmissivities of layers 1, 2, and 3, the storativities oflayers 1, 2, and 3, and the vertical resistance betweenlayers 1 and 2 and between layers 2 and 3. After pushingthe red “optimize” button, optimization began and MLUreported the iteration-by-iteration progress. For the 61 iter-ations in this example, MLU took less than 1 min to run.If the optimization appears to be satisfactory, push the“accept results” button at the bottom of the progress tab.At this point, MLU then shows updated aquifer parameters

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Figure 3. Pumping wells tab.

Figure 4. Observation wells tab.

in the Aquifer system tab (Figure 6). Figure 7 shows theexcellent correlation between the observed and calculateddrawdown data.

After performing optimization, the top of theOptimization results tab shows the computed aquifer

parameters and the standard deviation of the estimatewhich gives an indication of just how good and howconstrained the estimate is. Next, the Optimization resultstab gives a list of the observed and calculated drawdown.The user can use this information to help determine if

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Figure 5. Comparison of observed and calculated data based on initial guesses of aquifer parameters.

Figure 6. Aquifer system tab showing optimized parameter values.

any data point or perhaps an entire set of data from awell yields anomalous or possibly erroneous results. Afterlisting the calculated and observed data, MLU presentsa correlation table that shows the degree of correlationamong the parameters. High correlations (values near100% or near −100%) mean that simultaneous changeof both parameters will produce almost the same sum ofsquares. In that case, those parameters cannot be deter-mined independently.

Documentation and HelpMLU has a pull-down help menu that addresses the

common questions the user may have on running MLU. In

addition, there are an extensive user’s manual and tutorialavailable for free on the website. The tutorial in particularis very useful because it includes a test-by-test discussionof all the example tests included in the installation files.Many of these examples are classic tests reported byKruseman and de Ridder (1994). Other examples showhow MLU can be used to analyze slug tests and step-drawdown tests.

Software SupportThe author of MLU is very responsive to e-mail

questions and comments about MLU. There is typically aresponse to a question within a day or so.

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Figure 7. Comparison of observed and calculated data based on optimized values of aquifer parameters.

What We Liked• MLU offers a powerful, yet easy to use, method

of aquifer test analysis that takes into account allof the monitoring wells in the test. Too frequently,aquifer test analysis proceeds on a well-by-well basiswith different aquifer properties computed from eachdrawdown curve. Then there is some sort of averagingof the test results from a number of monitoring wellsthat result in some reported values of the aquiferparameters. On the other hand, MLU gives a single setof aquifer parameters based on the best fit of all the testdata. However, MLU also offers the option includingonly a single well or a group of wells in an analysis.

• Developing an MLU analysis is hydrogeology-based inthat it assists the user to define aquifer layers basedon stratigraphy. Because of this, the computed aquiferproperties are more easily translated into numericalmodels where the results of the MLU evaluation wouldbe used to solve problems.

• The ability of MLU to quickly generate a finiteelement model for use in MicroFEM allows the userto conveniently assess the reasons for anomalous datain the aquifer test. For example, the effects of aquiferheterogeneity (which would violate the assumptionsinherent in MLU) can easily be tested in MicroFEM.

• Technical documentation and support.• Price.

What We Did Not Like• Although MLU is powerful, there is a tendency

among new users to have MLU compute more aquiferparameters than is really possible from the data.Although the MLU optimization results tab has infor-mation on which parameters cannot be determined inde-pendently, this information is hard to find and inter-pret for beginning users. It would be nice if the MLUwould warn the users about trying to compute too manyparameters.

• Graphic output is excellent for assisting the user inanalysis but not of high quality for presentations.

OverallMLU is a powerful analytical tool for aquifer test

analysis and forward modeling of an aquifer system’sresponse to pumping. Although limited by many of thetypical assumptions inherent in analytical solutions, MLUprovides an almost unique ability to compute aquiferresponses in multilayer, multi-well situations. Most typicalanalytical solutions include only one or two layers; MLUoffers a generalized solution technique that handles upto 40 layers. As such, it is a valuable tool for anygroundwater professional working in thick, multilayeraquifer systems.

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RankingsThe reviewed ranked the software’s capability,

reliability, ease of use, and technical support on a scaleof 1(worst) to 5(best)

Capability 4.8Reliability 4.5Ease of use 4.0Tech support 5.0

How to Obtain the SoftwareMLU is available from the following website:http://www.microfem.com/. The current cost for an

“office license” of the software is 450 Euros (about $600).According to the website, the purchaser of an “Officelicense” is allowed to make copies of the software anduse his backups of the software on more than one of hisown machines, on the strict condition that these backupsare only used within the city of the purchaser’s office orwithin the department of the university concerned.

All licenses are perpetual. There are no (yearly) recur-ring costs. Regular updates (improvements and small

extensions) are free. The “Customer login” link at theDownload page allows all licensed users to download thelatest versions anytime.

User support is provided by the developers free ofcharge: support@microfem.com.

ReferencesHemker, 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 Hydrology90, 231–249.

Hemker, C.J. 1999a. Transient well flow in vertically heteroge-neous aquifers. Journal of Hydrology 225, 1–18.

Hemker, C.J. 1999b. Transient well flow in layered aquifersystems: the uniform well-face drawdown solution. Journalof Hydrology 225, 19–44.

Kruseman, G.P., and N.A. de Ridder. 1994. Analysis and Eval-uation of Pumping Test Data. ILRI publication 47, 377.The Netherlands: Wageningen. http://www2.alterra.wur.nl/Internet/webdocs/ilri-publicaties/publicaties/Pub47/Pub47.pdf (accessed April 27, 2012).

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