Example Problem 1. Theis Solution

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Example Problem 2. Representation of Aquitards

A fully worked-out version of Example 1 is in the "Examples\example1" directory. The example is named "Theis1.mmb." Along with the example is another version named "Theis2.mmb". It has a more refined grid. There is also a set of density contours that you can import into the project if you want to do it a little faster.

 

Starting a New Project

To start a new MODFLOW model, select "New Modflow Project" from the "PIEs" menu. The Modflow Data Set dialog box will appear. You can get this box again at any time by selecting PIEs|Edit Project Info. You should assign a project name, date, description and project title. The project title will appear at the beginning of the MODFLOW output file. The other fields are for your use when editing the Argus ONE MODFLOW project but do not appear on the MODFLOW output.


Geology: Setting up the Layer Structure of the Model

Next switch to the Geology tab. You can set up two types of layers here; simulated layers and nonsimulated layers. You can "Yes" or "No" under "Simulated" to decide which. Usually, each aquifer will be a simulated layer and aquitards are nonsimulated layers. Sometimes, however, you may wish to divide an aquifer up into several simulated layers or to make aquitards simulated layers. You might wish to divide an aquifer into more than one layer if you wanted to simulate a partially penetrating well, for example. In MODFLOW, all wells are assumed to fully penetrate the layer so dividing an aquifer into two or more layers, allows you to have a well that only partially penetrates the aquifer. MODFLOW-96 allows you to have up to 200 simulated layers. (MODFLOW-88 allowed up to 80 layers.) Frequently there is no need to simulate the aquitards explicitly by setting them up as layers. Usually, you can assume that flow through the aquitards is vertical and there is no change in storage in the aquitard. By excluding the aquitards from a model, you make the model smaller which means it will run faster. That's why aquitards are often nonsimulated layers. You still have to specify the vertical hydraulic conductivity of nonsimulated layers of course. The vertical hydraulic conductivities of the nonsimulated layers are used to help calculate the vertical conductance between simulated layers.

In this case we will have only a single layer so we delete the aquitard and one of the aquifers that were set up automatically and rename the other aquifer to just "Aquifer". (You can name the layers anything you want.) Delete a layer by selecting it with the mouse and pressing the "Delete" button on the form. (Pressing the "Delete" button on the keyboard will do nothing.)


Stresses 1

We don't need to change anything on the Wetting tab so go directly to the Stresses 1 tab. We will be simulating a well so we need to check the WEL box. (All of the MODFLOW packages have three-letter abbreviations followed by a number to indicate which version of the package is being used. If there is only one commonly-used version, the number is often omitted. WEL is the abbreviation for the Well package.) We will be using a steady stress so we don't need to change anything else in the upper half of the page.


Time

Next change to the "Time" tab. Change "Steady-state flow (1)" to "Transient Flow (0)" and change the time units to "Seconds (1)". Next, in the lower half of the page, change Length to 86400, No. of steps to 100 and Multiplier to 1.1

You don't need to worry about the numbers in parentheses after "Transient flow" and "Seconds". The numbers are used in the MODFLOW input files. For example, if the variable ISS has a value of "1" the model will be a steady-state model and if ISS is "0" it will be a transient model. Argus ONE will prepare all the input files for you.

"Length" is the length of time that will be represented by the model, in this case 86400 seconds or 1 day. No. of steps is the number of time steps that the model will use to from the beginning of the stress period to the end.

The reason to have more than one time step in our stress period is that if we tried to solve this problem with MODFLOW using a single time step, we would get the wrong answer. The maximum size of the time step that will give acceptable accuracy depends on the grid size. See Anderson and Woessner (1992, Chapter 7.4) for a detailed discussion of the choice of time step length.) The multiplier is used to increase the length of each time step in the model by a specified factor. The length of the first time step can be calculated as DELT(1) = PERLEN(TSMULT-1)/(TSMULTNSTP-1). The length of any other time step is, DELT(i) = DELT(1)*TSMULT(i-1). In this case, the length of the first time step is 86400(1.1-1)/(1.1100-1) = 0.63 seconds. This value is calculated for you by the MODFLOW GUI. The reason for having the first time step so short is that at the beginning of the stress period, conditions are changing rapidly. You need a shorter time step when conditions change rapidly or the model will not be sufficiently accurate. later on, longer time steps are OK.


Output Files

Next change to the "Output Files" tab. Change the "Root name for MODFLOW simulation files" to "Theis" or any other name of your choice. The USGS version of MODFLOW-96 can not accept long file names so the root is limited to eight characters or less. It must also be different from the names of any subdirectories in the directory where you will run the model. The name you chose will be the root of all the files for this model. Different files in the same model will have different extensions. MODFLOW requires a separate input file for each of the packages and can produce several types of output files so there will be lots of files with this root. You can ignore most of them.

Change, the N's for head solution printed and drawdown solutions printed to 10, change the Overall Volumetric Budget to Every Nth time step and change the N for it to 1. Change the N's for head solution exported and drawdown solution exported to 5. We don't want the head printed for every time step because that would make the output file very large. However, we will need to check the water budget for every time step to make sure that the model is sufficiently accurate.


Solvers

Finally, go to the Solvers/Other Packages page. We will accept the default solver (Preconditioned Conjugate Gradient 2, PCG2). It is usually the best solver to use. Change the Maximum absolute change in head and Maximum absolute change in Residual to 0.0001. Finally click "OK" at he bottom of the dialog box.

The maximum absolute change in head (HCLOSE) and maximum absolute change in residual (RCLOSE) are the convergence criteria. A typical value of HCLOSE would be 0.01 feet (0.003 m). A typical value of RCLOSE would be 0.01 cfs (cubic feet per second). The table below shows that flow in other units.

Equivalent flows in various units
ft3 m3
/s 0.01 0.0002832
/min 0.6 0.0169901
/hr 36 1.0194065
/day 864 24.465755
/year 315576 8936.1172

MODFLOW uses an iterative technique to determine the groundwater flow. The convergence criteria tell it when the solution is sufficiently accurate. It compares the difference in head and flow in ever model cell between two iterations. If the difference is less than HCLOSE and RCLOSE respectively, it stops trying to improve the accuracy of the model. If the convergence criteria are too high, the model won't be sufficiently accurate. If the convergence criteria are too low, you may waste time trying to get a solution more accurate than you need.

This concludes entering the non-spatial data for the model. Click on OK to close the dialog box and enter spatial data.

Continue With Part 2 of Example 1.
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