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Step by Step instructions for applying the Theis method

Using Excel and PowerPoint 2007 (BAE450)

This handout goes through the Theis method for homework problem 4 of lesson 13/14.

Go to the class web page and download the lesson 13/14 homework problem set and the Theis data type curve excel spreadsheet.

The method is broken down into five main steps:

1. Creating the “Type chart”

2. Creating the “s curve chart”

3. Creating identical scales for the “s curve chart” and the “Type Chart”

4. Using PowerPoint to overlay the “s curve chart” and the “Type chart”

5. Calculating Transmissivity (T) and the Storage Coefficient (S) using the intersection point

Each of these steps will be described in detail below.

1. Creating the “Type” Chart

Step 1: Insert two header rows and column headings in the “u” and “W(u)” data worksheet. Select the “type curve” worksheet and insert two new rows at the top of the worksheet. (Select the “Home” tab then find the “Insert” button. Put the cursor in cell A1 and then from the pull down menu select “insert sheet rows”. Select this button twice to insert two rows). Add labels to each column heading. Type in the letter “u” in cell A2 and the letter “W(u)” in cell B2.

Step 2: Create the u vs W(u) “type” graph. First highlight the entire block of data A3:B146. Then select the main “Insert” tab and then select the “Scatter” button and from the pull down menu select the “scatter with straight lines and markers” graph. This should create a graph in your worksheet. Excel will always assume that the first column represents the horizontal “X” coordinates of the graph and the second column represents the vertical “Y” coordinates of the graph. This is the correct assumption for this data.

Step 3: It is important in the Theis problem to move this chart to its own separate sheet. To do this first select the graph with the left button on your mouse and then click the right button on your mouse and select the option called “Move chart”. Select the “New Sheet” button and type in a name such as “Type chart”.

Step 4: Convert the X and Y axis to logarithmic scale. First select the chart then select the “Layout” tab. Now you can right click on one of the axis and select “Format Axis” or go to the upper left corner of the Layout window where it has a pull down menu which probably says “Plot area”, click on the downward arrow then select either the “Horizontal (value) axis” or the “Vertical (value) axis”. Then click the “Format selection” option directly below this window. You should now have a window opened entitled “Format Axis”. Check the box in this window called “Logarithmic scale” then click “close”. Repeat this step for the other axis.

Step 5: Add gridlines. Select the chart, then select the “Layout” tab and click on the “Gridlines” pull down menu. In this menu select “Primary Horizontal Gridlines” then select “Major and Minor Gridlines”. Do the same thing again for the “Primary Vertical Gridlines”.

Step 6: Remove the chart legend. Do this by selecting the legend and then press delete.

2. Creating the “s curve chart”

Step 1: Create two continuous columns of time versus drawdown data. Select the “Data” worksheet. Highlight A1:I2 then press the right button on your mouse and select “copy”. Then select cell A12, press the right button on your mouse and select “Paste Special”. This will open up the “Paste Special” window. In this window check the “Transpose” box then click “ok”.

Step 2: Copy the remaining data and paste it below the data in Step 1. Highlight B3:I4, copy, and use the paste special transpose option again pasting the data below the previous block into cell A21. Repeat this same step for the last block of data B4:I6.

Step 3: Type in the pumping rate and the distance to the well information provided by the problem. In cell A8 type in “Pumping Rate (Q) =”. In cell B8 type in “500”. In cell C8 type in “gpm”. In cell A9 type in “Distance to well (r) =”. In cell B9 type in “200”. In cell C9 type in “ft”.

Step 4: The s curve in the Theis method plots “r2/t vs s” where r is the distance from the pump in feet units and t is time since pumping started in days. In this step you will create a column for r2/t in units of feet and days. Go to cell C12 and type in “r2/t (ft2/day)”. Go to cell C13 and type in the following formula “=($B$9^2)/A13*60*24” (Note: the 60*24 converts minutes to days). The value for this cell will show up as “#DIV/0!” since you are dividing by zero. You will ignore this value in your analysis. Next select cell C13 and double click on the little black box in lower right hand corner of the cell. This should copy this formula down to the end of the column.

Step 5: In this step you will create a column for “s”. Go to cell D12 and type in “s (ft)”. Then got to cell D13 and type in “=B13”. Next select D13 and double click on the lower right hand corner of the cell to copy down the formula as in Step 4.

Step 6: Now you have the data to create a “r2/t vs s” chart. Highlight block C14:D36 and follow steps 3 through 7 from the “Creating the Type Chart” instructions above. Name this chart “s curve chart”.

3. Creating identical scales for the “s curve chart” and the “Type Chart”

In the Theis method you are required to overlay the “S curve chart” on the “Type chart” and find a match point. It is essential that both these graphs are at the same scale in the x and y direction.

Step 1: Limit the range of the x-axis on the “s curve chart” so that chart focuses in on the data. In this problem the r2/t data ranges from 100,000 (1e5) to 100,000,000 (1e8) ft2/day. To focus the chart only on this range then select the axis then press the right button on the mouse and select “Format Axis”. Click the “Fixed” button next to the Minimum value. Type in “1e5” in this box. Next click the “Fixed” button next to the Maximum value. Type in “1e8” in this box. (note: we rounded this maximum value up to the nearest order of magnitude). It may be easier to read to convert the x-axis values to scientific notation by selecting the “Number” tab in the “Format Axis” window.

Step 2: The axis of the “Type Chart” should be formatted to match the same y-axis values as then s-curve chart and the x-axis should have the same scale (not necessarily the same values) as the x-axis in “s curve chart”. Right click each axis of the “Type chart” to get to the “Format axis” window. The y-axis should be set to range from 0.1 to 10 just like the “s chart curve” and the x-axis should be set to the four orders of magnitude where the W(u) values are within 0.1 to 10. For this problem this x-axis range is from 1e-3 and 1.

Step 3: In order to make this charts identical in scale select the x-axis, open the “format axis” window using the right button of the mouse, then select under the “Vertical Axis crosses:” option the “Axis Value:” button and enter in the value “1e-3” in the box.

At this point the size of the “s curve chart” and the “Type chart” should be identical. Now would be a good time to save the spreadsheet!

4. Using PowerPoint to overlay the “s curve chart” and the “Type chart”

Step 1: Before you overlay each chart you must first remove all background color from one of the charts. We will remove the background color of the “s curve chart”. Goto the “s curve chart” then right click the chart outside of the x and y axis and select “Format Chart Area”. Under the “Fill” tab select “No Fill” button and “close” the window. Next right click the plot area (inside the boundaries of the x and y axis) and select “Format Plot Area”. Again select the “No Fill” button and close the window.

Step 2: The actual overlay procedure will be conducted within power point. Open power point and remove all title formatting from the power point slide. You can do this by right clicking the slide then selecting “layout” and choosing the “Blank” option.

Step 3: Go back to excel and goto the “Type curve chart”. Right click the chart and select copy. Then go back to power point, select the “Home” tab, click the “Paste” pull down menu and select “Paste Special” then select “Picture (Enhanced Metafile)”

Step 4: Repeat step 3 for the “s curve chart”.

Step 5: You should now be able to see both charts on top of each other. At this point it is helpful to recolor the “s curve chart” picture so that you can better distinguish one chart from the other. Right click the “s curve chart” picture that you just pasted into power point and select “Format Picture”. Under the “Picture” tab select the drop down menu next to “Recolor”. Select one of the “Dark variations” then “close” this window.

Step 6: You should now check to make sure each picture is sized identically to each other. Select the “s curve chart” picture then use the arrow keys to line up the charts on top of each other. If the charts aren’t the exact same size then you will need to drag one or two sides of the picture to make them match. (Note: To make finer adjustments hold down the control key at the same time while moving the chart with the arrow keys.)

Step 7: Once you confirm that both charts are the same size you now should move the “s-curve chart” so that the “r2/t vs S” line completely covers the “u vs W(u)” line. This may take some fine tuning with the arrow keys to get them laid out just right.

Step 8: Once you have both lines overlapping each other you need to find an intersection point where you can read the coordinates of a point both in the “s curve chart” and in the “Type chart”. This point does not have to be on the line. One way to easily read off the coordinates is to use the drawing tool in power point to create a point right at this intersection point. Under the “Home” tab in PowerPoint select the oval shape and draw a small oval in the slide. Move this oval over the intersection point.

Step 9: You should now write down the (r2/t, s) and (u, W(u)) coordinates of this intersection point. It may be necessary to move one chart over while you read the other chart.

5. Calculating Transmissivity (T) and the Storage Coefficient (S) using the intersection point

Step 1: Go back to your excel spreadsheet where your data is located. Type in “u =” in cell F8, enter in your “u” coordinate in cell G8; type in “W(u) =” in cell F9, enter your “W(u)” coordinate in cell G9; type in “r2/t =” in cell F10, enter you “r2/t” coordinate in cell G10, type in “ft2/day” in cell H10; type in “s =” in cell F 11, enter your “s” coordinate in cell G11, and type in “ft” in H11.

Step 2: Calculate T and S. Type in “Transmissivity (T) =” in cell J10. Type in the formula “=114.6*B8*G9/G11” in cell K10; type in “gpd/ft” in cell L10. Type in “Storage coefficient (S) =” in cell J11. Type in the formula “=G8*K10/(1.87*G10)” in cell K11.

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