Hydrogeologic Assessment for CenTex Water Supply: Description of Methods and Procedures Part 1: Geotechnical Analysis of Aquifer Samples Bulk Density Weight of the sample divided by the volume of the sample. Porosity Method 1: Calculate the volume of water in the saturated sample (using the density of water and the weight of water in the sample) Divide volume of water in saturated sample by total sample volume Method 2: assume a specific gravity for the mineral fraction of the sample (~2.65), take the dry bulk density and the assumed specific gravity, and use the following equation… % volume min eral ρ bulk = ρ min eral x 100
rearranged to solve for % volume of the mineral phase… % volumemin eral ρ bulk = ρ min eral 100
… subtract percent volume of mineral phase from 1 to get percent volume of voids (i.e., porosity) Moisture content Use the data for the gravity-drained sample. Gravimetric moisture content is…
ω=
weight water weight solids
… while volumetric moisture content is…
θ=
volume water volume total
Degree of saturation Again, use the data for the gravity-drained sample. Calculate the volume of water in the sample and divide by the total volume of void space (or, by the volume of water in the saturated sample) Specific yield and specific retention Specific retention is the volume of water retained in the sample divided by the total volume of the sample; i.e.,
1
Sr =
volume retained volume total
Multiply the total porosity by the degree of saturation to get the specific retention. Subtract the specific retention from the total porosity to get the specific yield Grain-size distribution Use the worksheet provided (titled “GRAIN SIZE ANALYSIS DATA AND WORKSHEET”) to calculate the cumulative percentages, according to the following: % retained: retained weight divided by the total dry weight (at the bottom of the column % retained (cumulative): % retained summed from coarse to fine sieve size % finer: 1 - % retained (cumulative)
On the chart supplied, plot the % finer values versus the grain size of the sieve (in mm). Pencil in a best-fit curve to the data points on the graph (don’t connect all the points with a line; draw a smooth curve which best represents the distribution of data)
Part 2: Aquifer Permeability Estimation Empirical Equations The curves connecting the % finer grain size data represent the grain size distribution. Specific grain sizes on the grain size distribution curves can be notated as dx, where d is the grain diameter for percentage x (e.g., d50 is the grain size where 50% of the sample passes the sieve; this is also the mean grain size.). The Hazen method estimates hydraulic conductivity based on the effective grain size, or d10. The equation is:
K = C(d10)2 where: K = hydraulic conductivity (in cm/s) d10 = effective grain size (in cm) C = grain size coefficient, based on the following table: Very fine sand, poorly sorted
40-80
Fine sand with appreciable fines (clay & silt)
40-80
Medium sand, well sorted
80-120
Coarse sand, poorly sorted
80-120
Coarse sand, well sorted, clean
120-150
The samples from the CenTex site are fine to medium sand that are reasonably well sorted, so use C = 70. Note: Be careful with your units (mm, cm, m, etc.)! The Shepard method is based on the Hazen method. Shepherd found that hydraulic conductivity is generally proportional to some exponent of the mean grain size (d50) between 1.5 and 2. He noticed that the grain size coefficient (C) or ‘shape factor’, and the exponent increase as the sediments become more texturally mature (i.e., more well rounded, more uniform shape, etc.). He created an idealized graph that relates hydraulic
2
conductivity to mean grain diameter (Fetter, 2001, p 87). From this graph, he developed a set of empirical equations for sediments in various settings. Here are some of his equations: K = 40,000d502 (for glass spheres) K = 5,000d501.85 (for dune deposits) K = 1,600 d501.75 (for beach deposits) K = 450 d501.65 (for channel deposits) K = 1,000 d501.5 (for unconsolidated sediments) …where K = hydraulic conductivity in ft/day and d50 = mean grain size Use the grain size distribution data to determine the d50 for each sample. Assume that the sediments are channel deposits, and then use the appropriate equation and the d50 to determine K. Be careful with your units.
Constant Head Permeameter Test The equation for the constant head permeameter test is:
K=
QL Ah
where… K = hydraulic conductivity [L · t-1] Q = volumetric discharge of water [L3 · t-1] L = length of the sample [L] A = cross sectional area of the sample [L2] h = hydraulic head difference [L]
Falling Head Permeameter Test The equation for the falling head permeameter test is:
Ld 2t h o K = 2 ln td s h where… K = hydraulic conductivity [L · t-1] L = length of the sample [L] ho = initial head in the falling tube [L] h = final head in the falling tube [L] t = time for head to fall from ho to h [t] dt = inner diameter of the falling tube [L] ds = inner diameter of the sample chamber [L] and ln is the natural logarithm.
3
Part 3: Groundwater Maps 1. Log into the course BlackBoard site and navigate to the ‘Assignments’ area. Enter the folder marked “Problem Set 03 - CenTex Groundwater Map”. 2. Click on the < CenTex03_GroundwaterMap.pdf > link under ‘Base Map’ to open the base map file. Print out a hard copy. Feel free to save a copy to your disk, if you like. 3. Right-click on the < CenTex03_WaterLevelDataSpg2003.xls > link under ‘Water Level Data’ and select “Save Target As…” from the little pull-down menu. Save the file to your disk. 4. Open this file and your CenTex Master Workbook (i.e., the Excel Workbook that you created last time; the one that contains the results of the first two CenTex problem sets). Copy the worksheet from the Water Level Data workbook into your Master Workbook using the following procedure:
a. In the Water Level Data workbook, pull down the ‘Edit’ menu from the menu bar and select “Move or Copy Sheet”. b. A little window will pop up (Step-1). Pull down the little arrow under ‘To book:’ and select ‘CenTex_Master_Workbook…’ (Step-2). Then scroll down the list under ‘Before sheet:’ and select ‘(move to end)’ (Step-3). Hit the ‘OK’ button.
Step-1
Step-2
Step-3
.
At this point, the Water Level Data worksheet should now be in your CenTex Master Workbook located after the PERMEABILITY SUMMARY worksheet. 5. In cell F7, write an equation that subtracts the Depth to Water (cell E7) from the Land Surface Elevation (cell D7). Copy this formula to cells F8 through F19. At this point, you have hydraulic heads for all the wells in the study area. Print out a hard copy of this table.
4
On the hard copy of the map, write each hydraulic head value near the corresponding well. See the example at right. (Step-1) ÖÖ Contour these values by hand using a 30 meter contour interval (Step-2). On your map, indicate the general direction of groundwater flow with 3 or 4 arrows. Step-1
Step-2
You are required to turn in: 1. a hard copy of the table of water levels 2. an updated copy of your master spreadsheet (submitted via email) 3. your groundwater map
Part 4: Aquifer Tests and Transmissivity/Storativity Calculations 1. Go to the course Blackboard site, navigate to the ‘Assignments’ section, and click on the folder marked ‘Problem Set 04 – CenTex Aquifer Test’. Download and save to disk the file called < CenTex04_AquiferTestData(Spg2004).xls >. 2. Open the Excel workbook containing the aquifer test data and copy the data worksheet into your CenTex Master Workbook. Be sure to save your work. The Excel data worksheet contains aquifer test data from two wells in the study area. Each pumping well is shown on the well location map. Two separate tests were performed; one well (68-59-303) has data from only one observation well and the other well (68-51-701) has data from two observation wells. These data consist of pump rate at the pumping well (Q) distance to the observation well (r) time (t) and drawdown (s) data in the observation well over a 48 hour period
5
3. Using the graph paper provided, plot the data and match the resulting curve to the type curve (also provided). You will have three separate curves plotted – one for each set of data. You can plot these on separate graphs, or on the same graph (providing that you use different colors or some means of readily distinguishing between graphs). 4. Pick match points and calculate T (in m2/day) and S for each of the wells. A table of u and W(u) values is provided. Enter your values for t, s, 1/u, W(u), T, and S in the blanks at the bottom of the aquifer test data sheet. 5. Assuming that the saturated thickness of the aquifer (b) is 200 meters, use your values of T to calculate K for each of your wells. Enter the values in the blanks at the bottom of the data sheet. 6. Add a section on the DATA SUMMARY sheet of your CenTex Master Workbook for your aquifer test results. Your DATA SUMMARY sheet should look something like figure 1. Figure 1. Updated DATA SUMMARY sheet
Enter the values in the spreadsheet for each in the appropriate cells. Also, convert your hydraulic conductivity values to the same units as your other conductivity measurements so that you can compare the values.
Specific Methods and Procedures Steps 3 and 4: Specific details of the procedure for curve-matching with the Theis type curves are given in Domenico and Schwartz (1998, p 107). Step 5: Transmissivity (T) is equal to the hydraulic conductivity (K) times the saturated thickness (b); therefore:
K = T/b Step 6: The Theis equation, which calculates drawdowns in the aquifer in response to a pumping well, is:
s=
Q W (u ) 4πT
where
u=
r 2S 4Tt
and W(u) is the well function.
6
W (u ) = −0.5772 − ln u + u −
u2 u3 u4 u5 + − + − ... 2 ∗ 2! 3 ∗ 3! 4 ∗ 4! 5 ∗ 5!
where the variables are defined as follows: s = drawdown [L], defined as the initial head minus the head at time t Q = pumping rate from the well [L3/t]; assumed to be constant T = aquifer transmissivity (where T = Kb) [L2/t] r = radius (distance from pumping well) [L] S = storativity (where S = Ssb) [ - ] t = time after the start of pumping [t] A table of values of W(u) for values of u is provided below You will need to refer to this table to use the Theis equation. u
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
1.0E-00
0.219
0.049
0.013
0.0038
0.0011
0.00036
0.00012
0.000038
0.000012
1.0E-01
1.82
1.22
0.91
0.70
0.56
0.45
0.37
0.31
0.26
1.0E-02
4.04
3.35
2.96
2.68
2.47
2.30
2.15
2.03
1.92
1.0E-03
6.33
5.64
5.23
4.95
4.73
4.54
4.39
4.26
4.14
1.0E-04
8.63
7.94
7.53
7.25
7.02
6.84
6.69
6.55
6.44
1.0E-05
10.94
10.24
9.84
9.55
9.33
9.14
8.99
8.86
8.74
1.0E-06
13.24
12.55
12.14
11.85
11.63
11.45
11.29
11.16
11.04
1.0E-07
15.54
14.85
14.44
14.15
13.93
13.75
13.60
13.46
13.34
1.0E-08
17.84
17.15
16.74
16.46
16.23
16.05
15.90
15.76
15.65
1.0E-09
20.15
19.45
19.05
18.76
18.54
18.35
18.20
18.07
17.95
1.0E-10
22.45
21.76
21.35
21.06
20.84
20.66
20.50
20.37
20.25
1.0E-11
24.75
24.06
23.65
23.36
23.14
22.96
22.81
22.67
22.55
1.0E-12
27.05
26.36
25.96
25.67
25.44
25.26
25.11
24.97
24.86
1.0E-13
29.36
28.66
28.26
27.97
27.75
27.56
27.41
27.28
27.16
1.0E-14
31.66
30.97
30.56
30.27
30.05
29.87
29.71
29.58
29.46
1.0E-15
33.96
33.27
32.86
32.58
32.35
32.17
32.02
31.88
31.76
Values of W(u) for values of u You are required to hand in the following: 1. Three time-drawdown graphs with plotted drawdown data from each observation well (be sure to clearly mark each graph so that it is obvious which observation well it is from). 2. A hard copy of the ‘CenTex Drawdown Data’ sheet with your match points and results in the appropriate cells. 3. A hard copy of your latest ‘DATA SUMMARY’ sheet with all the values filled in and ready for comparison
7
Part 5: Analytical Model and Drawdown Calculations 1. Go to the course Blackboard site, navigate to the ‘Assignments’ section, and click on the folder marked ‘Problem Set 05 – CenTex Analytical Model’. Download and save to disk the file called < CenTex05_AnalyticalModel(Spg2004).xls >. 2. Open the Excel workbook containing the template for the analytical model and copy the worksheet into your CenTex Master Workbook. Be sure to save your work. The Excel worksheet contains a blank, pre-formatted template which you will use to create an analytical model that will simulate aquifer drawdowns in response to a hypothetical pumping well. I have already set it up and formatted it so that all you need to do is code in the appropriate equations, add the right input data, and then find out which pumping rate satisfies the following drawdown restrictions: at the end of 50 years, the maximum allowable drawdown at the property boundary is 10 meters, and the maximum allowable drawdown at any off-site well is 2.5 meters. The yellow cells with blue numbers are for the input values. The model will require a pumping rate (Q) in gallons per minute (GPM), a distance from the pumping well (r) in meters, a transmissivity (T) in square meters per day, a storativity (S), and a time (t) in years. The green cells will contain the equations which calculate the model results. The yellow cells currently contain dummy values; keep these values in the model until you have the equations correctly entered. Once the equations are correct, you will need to decide which values to put into the appropriate cells. 3. The first step is to enter the equations which convert the pumping rate and the time to the proper units for the equations. a. Time is entered in years; it will need to be converted to days for the calculations. To convert years to days, multiply the number of years by the number of days in a year. Enter an equation in cell D13 that multiplies the value in cell D12 by 365.25. (Using 365.25 days will account for the extra day in leap years that come around every 4 years.). Copy the cell and paste it into cells I13 and N13. b. The pumping rate is entered in GPM; it will need to be converted to m3/d for the calculations. To convert to m3/d; multiply the pumping rate in GPM by 5.450993. Enter an equation in cell D15 that multiplies the value in cell D6 by 5.450993. You will need to re-enter the equation in cells I15 and N15 (Note – you won’t be able to simply copy the cell contents from D15 to the other cells; you will have to rewrite it in the other cells.) 4. The next step is to enter the equations to calculate the drawdown. The equation which we will use to calculate drawdown is the Theis equation – the same one used in the previous part of the project to determine T and S values for the aquifer. The equation is
s=
Q W (u ) 4πT
where
u=
r 2S 4Tt
and W(u) is the well function.
W (u ) = −0.5772 − ln u + u −
u2 u3 u4 u5 + − + − ... 2 ∗ 2! 3 ∗ 3! 4 ∗ 4! 5 ∗ 5!
where the variables are defined as follows: s = drawdown [L], defined as the initial head minus the head at time t Q = pumping rate from the well [L3/t]; assumed to be constant
8
T = aquifer transmissivity (where T = Kb) [L2/t] r = radius (distance from pumping well) [L] S = storativity (where S = Ssb) [ - ] t = time after the start of pumping [t] For the purpose of this model, we will break the equation up into three parts – u, W(u), and the drawdown (s). a. In cell D19, enter the part of the equation that calculates u. Some hints on writing the equation:
- Be sure to refer to the appropriate cells in your equation - Use the value of time in days, not years (i.e., use the value in cell D13, not in D12) - To square the value in a cell (e.g., to square the value in cell A1), use the following format: (A1^2)
- To check your equation: if you leave the dummy values in the input cells, the correct
value for your equation should be 3.4E-08. Once you have the correct equation entered, you can copy and paste it into cells I19 and N19.
b. In cell D20, enter the equation that calculates W(u) based on the value of u calculated in cell D19. Since this part of the equation is an infinite series, you cannot enter the entire equation directly into Excel. However, if you truncate the series after the 5th factorial term, you will get a sufficiently good approximation of the final answer. Some hints on writing the equation:
- You will only need to refer to the value in cell D19 in the equation - ln u is the natural logarithm of u. The Excel function for calculating the natural log of a
number x (i.e., the ln in ln u) is =LN(x) So, for example, if u is in cell B14 you would calculate ln u with the following equation: =LN(B14) - The little exclamation point that shows up repeatedly in the equation is a factorial. 3! means 3x2x1, 4! means 4x3x2x1, 5! means 5x4x3x2x1, etc. To put this into an Excel equation: 3! would be (FACT(3), 4! would be (FACT(4), etc. - Be careful with your parentheses!!!! - To check your equation: if you leave the dummy values in the input cells, and have the correct equation in cell D19, the correct value for your equation in D20 should be 16.61315 Once you have the correct equation entered, you can copy and paste it into cells I20 and N20. c. In cell D22, enter the equation that calculates the drawdown based on the input values and the value of W(u) in cell D20. Some hints on writing the equation:
- The Excel function for calculating pi is PI(). Do not put anything in the parentheses. Alternately, you can enter a number for pi (3.1416).
- Be sure to use the pump rate in m3/day, not in GPM - To check your equation: if you leave the dummy values in the input cells, and have the
correct equation in cell D20, the correct value for your equation in D22 should be 7.21 Once you have the correct equation entered, you can copy and paste it into cells I22 and N22. 5. The next step is to enter the correct input values into the yellow cells. Leave the pump rate alone for now; that will be the last thing you will change. Start by entering the values for r, T, S, and t.
a. The values r1, r2, and r3, are the distances to the property boundary, well 68-51-701, and well 68-59303, respectively. Use the map titled ‘Analytical Model Setup: r-Values for Model Input’ (on the page following these instructions) to determine these values. b. Choose transmissivity and storativity values from the previous part of the project. The values you
9
choose will depend on which part of the aquifer you are simulating (hint: the part of the aquifer with a higher net sand percentage will most likely have a higher transmissivity). c. The time represents the end of the pumping period – in this case, 50 years 6. Once you have entered the appropriate input values, you are ready for the final step – determination of the largest pumping value that will satisfy the drawdown restrictions. Increase the pumping rate in cell D6 to 1000, and look at the drawdowns calculated by the model. If the drawdowns are greater that the limits (10 meters at the property boundary and 2.5 meters at either off-site well), then decrease the pumping limit and check again. If drawdowns are less than the limits, increase the pumping rate and check again. Keep increasing and decreasing until you find the largest pumping value that will keep the drawdowns within those limits. The final pumping value which you calculate is the final answer to the entire project – it represents the maximum yield of the aquifer, over a 50 year period, which will not cause an adverse impact to the aquifer outside of the property boundaries.
Due Date and What to Hand In The specific due date will be announced in class. You are required to turn in: a) a printout of your final model with all your input values and your final pumping value b) an updated copy of your master spreadsheet (submitted via email) that includes your model spreadsheet (NOTE: you are required to enter the equations on your spreadsheet, not just the numbers – you will not get credit if you do not submit a complete spreadsheet!) c) A short (1 paragraph) write up explaining which r, T, and S values you used in each part or your spreadsheet and why you used them. Your write up must have your name, the date, the name of the class, and the name of the exercise, and it must be typewritten/word processed.
10
Appendix 1: Data Worksheet Tables All of these tables are also included as Excel Spreadsheets.
Sample Data SAMPLE ID:
B-1
B-2
B-3
B-4 cm3
Sample Volume:
51.2
46.2
29.3
66.0
Sample Can Tare Wt:
0.7
0.7
0.7
0.7
g
Weight of can + sample:
112.2
106.1
66.1
143.9
g
Weight of can + sample:
100.1
97.2
59.4
131.0
g
Weight of can + sample:
97.3
96.1
58.8
123.4
g
(Saturated) (Gravity drained) (Oven dried)
Weight of sample:
g
(Saturated)
Weight of sample:
g
(Gravity drained)
Weight of sample:
g
(Oven dried)
Calculations SAMPLE ID:
B-1
B-2
B-3
B-4
Saturated bulk density:
g/cm3
Dry bulk density:
g/cm3
Porosity Estimate: Gravity drained moisture content:
(gravimetric)
Gravity drained moisture content:
(volumetric)
Degree of saturation:
(gravity drained)
Specific Yield: Specific Retention:
Grain Size Analysis SAMPLE ID:
B-1
B-2
B-3
B-4
(mm)
Retained (g)
Retained (g)
Retained (g)
Retained (g)
4
101.6
0.0
0.0
0.0
0.0
4
0.187
4.8
2.1
0.2
10.1
0.0
10
0.079
2.0
17.5
0.7
9.9
2.3
20
0.033
0.84
30.6
7.0
26.5
9.9
60
0.010
0.25
15.2
26.3
7.3
12.2
100
0.006
0.149
17.2
19.9
3.1
29.0
200
0.003
0.074
6.2
23.0
1.0
35.1
remainder:
7.8
18.3
0.2
34.2
Sieve #
Grain Size (in)
Table 1. Geotechnical data sheet for Part 1
% retained
% retained (cumulative)
% finer (cumulative)
34.2 122.7
0.2
58.1
remainder:
Total:
Table 2. Grain-size data sheet for Part 1
35.1
1.0
0.074
200
29.0
3.1
0.149
100
12.2
7.3
0.25
60
9.9
26.5
0.84
20
2.3
9.9
2.0
0.0
10.1
10
0.0
Retained (g)
0.0
Retained (g)
4.8
101.6
Grain Size (mm)
4
Sieve #
B-4
95.4
96.6
Total:
B-3
18.3
7.8
remainder:
SAMPLE ID:
23.0
6.2
0.074
200
19.9
17.2
0.149
100
26.3
15.2
0.25
60
7.0
30.6
0.84
20
0.7
2.0
10
17.5
Retained (g)
0.2
% finer (cumulative)
2.1
% retained (cumulative)
0.0
% retained
0.0
Retained (g)
B-2
4.8
101.6
Grain Size (mm)
B-1
4
Sieve #
SAMPLE ID:
% retained
% retained (cumulative)
% retained (cumulative)
% retained (cumulative)
% finer (cumulative)
% finer
Constant Head Permeameter Data Variables Sample length (L):
20 cm
Sample diameter:
5 cm
Cross-sectional area (A):
cm2
TEST 1
Data
B-1
B-2
B-3
B-4
Volume:
50
10
500
10 cm3
Time:
50
143
71
67 sec
Discharge:
1.00
0.07
7.04
0.15 cm3/sec
Head Loss (h):
12.6
12.6
12.6
12.6 cm
Calculation
K:
cm/sec
K:
m/sec
TEST 2
Data
B-1
B-2
B-3
B-4
Volume:
50
10
500
10 cm3
Time:
48
151
65
59 sec
Discharge:
1.04
0.07
7.69
0.17 cm3/sec
Head Loss (h):
12.6
12.6
12.6
12.6 cm
Calculation
K:
cm/sec
K:
m/sec Table 3. Constant head permeameter data sheet for Part 2
Fallling Head Permeameter Data Variables Sample length (L):
20 cm
Falling tube inner diameter (dt):
2 cm
Sample chamber inner diameter (ds):
5 cm
Initial head in falling tube (ho):
100 cm
TEST 1
Data
B-1
B-2
B-3
B-4
Final head (h):
52.1
92.7
9.8
88.1 cm
time (t):
30
60
15
60 sec
Calculation
K:
cm/sec
K:
m/sec
TEST 2
Data
B-1
B-2
B-3
B-4
Final head (h):
53.7
91.9
10
89.8 cm
time (t):
30
60
15
60 sec
Calculation
K:
cm/sec
K:
m/sec Table 4. Falling head permeameter data sheet for Part 2
Longitude
Latitude
Land Surface Elev
(DEG MIN SEC)
(DEG MIN SEC)
METERS
METERS
B-1
651.2
245.5
B-2
635.7
222.4
B-3
788.8
363.7
B-4
791.3
354.0
Boring ID or StateWell#
Depth to Water
Hydraulic Head METERS
68-50-603
98 45 50
29 11 13
655
165.7
68-51-602
98 37 46
29 10 13
786
363.9
68-51-701
98 43 42
29 08 48
798
368.9
68-59-303
98 39 10
29 06 49
612
241.0
68-58-302
98 47 29
29 06 09
650
313.1
68-59-312
98 35 46
29 04 06
580
248.8
68-59-501
98 42 25
29 04 06
545
238.9
68-59-602
98 47 04
29 03 10
534
280.6
68-59-804
98 42 12
29 00 29
496
263.7
Table 5. Groundwater level data sheet for Part 3
TEST #1
TEST #2 WELL ID PUMP RATE = r=
WELL ID PUMP RATE = r=
68-59-303 1000 GPM 8.1 m Obs. Well 1
t 0.083 0.25 0.5 0.75 1 2 3 4 5 10 15 30 45 60 120 180 240 300 600 900 1200 1440 1680 2400 2880 4320
Obs. Well 1
s
0.03 0.04 0.05 0.06 0.06 0.07 0.08 0.08 0.08 0.09 0.10 0.11 0.11 0.12 0.13 0.13 0.13 0.14 0.15 0.15 0.16 0.16 0.16 0.17 0.17 0.17
min min min min min min min min min min min min min min min min min min min min min min min min min min
68-51-701 300 GPM 6.5 m
t m m m m m m m m m m m m m m m m m m m m m m m m m m
0.083 0.25 0.5 0.75 1 2 3 4 5 10 15 30 45 60 120 180 240 300 600 900 1200 1440 1680 2400 2880 4320
min min min min min min min min min min min min min min min min min min min min min min min min min min
9.2
s
s
0.03 0.05 0.07 0.08 0.09 0.11 0.13 0.14 0.14 0.17 0.18 0.20 0.22 0.23 0.25 0.26 0.27 0.28 0.30 0.31 0.32 0.33 0.33 0.35 0.35 0.37
0.01 0.03 0.05 0.06 0.07 0.09 0.11 0.11 0.12 0.14 0.16 0.18 0.19 0.20 0.23 0.24 0.25 0.26 0.28 0.29 0.30 0.31 0.31 0.32 0.33 0.34
m m m m m m m m m m m m m m m m m m m m m m m m m m
m
Obs. Well 2
m m m m m m m m m m m m m m m m m m m m m m m m m m
MATCH POINTS AND RESULTS t:
min
t:
min
s:
m
s:
m
1/u:
1/u:
W(u):
W(u):
Transmissivity:
m2/d
Storativity: Sat. thickness: Hyd. Conductivity
Transmissivity:
m2/d
Storativity: m m/d
Sat. thickness: Hyd. Conductivity
Table 6. Aquifer test data sheet for Part 4
m m/d
0.01
0.1
1
10
100
Drawdown
0.1
1
10
Time 100
1000
10000
GRAPH PAPER FOR USE WITH THEIS NONEQUILIBRIUM TYPE CURVE (FULLY CONFINED)
100000
0.01
0.1
1
10
100
W(u )
0.1
1
10
1/u
100
1000
THEIS NONEQUILIBRIUM TYPE CURVE (FULLY CONFINED)
10000
100000
Appendix 2: Additional Maps and Illustrations
Appendix 2: Excel Tutorial Exercise Introduction The overall purpose of this exercise is to provide you with experience using a spreadsheet program (MS Excel) to solve simple equations and do calculations similar to those required by typical geology problems. I have found that Excel is an invaluable tool for performing scientific calculations, and in my academic and professional career I have probably spent more time using Excel (and received more benefit from it) than any other software package. It is worth your time to learn how to use it, as it has the potential to make things much easier for you in the future. The specific objective of this homework is to set up an Excel workbook that contains several sheets that solve the first two CenTex Problem Sets (Geotechnical Analysis and Aquifer Permeability Estimation). I have posted a workbook on BlackBoard that contains the data from those problem sets and is ready for equations. The instructions here will take you through the process of entering equations and performing the calculations required by these two problem sets. In the future, I will require that you use Excel to solve the CenTex problem sets and to manage the results of your work. These results will all be incorporated into your final project write-up.
Description of MS Excel General Microsoft Excel is a spreadsheet program that is capable of Tabulating and presenting data Performing calculations on lists and tables of data (e.g., adds values together, summarizes a column of data, find the average of a column of data, plug a series of values into an equation and return an answer, etc.) Generate graphs and charts with tables of data The basic idea behind the program is that the workspace is composed of a set of numbered rows (1, 2, 3…) and lettered columns (A, B, C…), forming a grid of cells (see figure 1). Each cell, therefore, has a columnrow address – for example, the cell in the upper left corner in figure 1 is cell A1; the cell to the right of it is B1, the cell below it is A2, etc. Data and text can be entered into each cell, and the cells can be formatted (e.g., bold, underline, italic, font size, etc.). Excel can be used to develop tables of data for printing and inclusion in a report. Equations can also be entered into the cells, and these equations can reference the data in other cells. For example, a column of ten cells (A1 to A10) could contain the height of ten people in the class. An equation can be entered into cell A11 to calculate the average height of these ten people.
Description of the Workspace Figure 1 shows the Excel workspace; this is what you see when you open up Excel. This is the area in which you enter data and formulas and format your data. The white grid in the middle of the image is the cells in which you can enter data and formulas. Above the grid are the menu bar, the formatting buttons, and the formula bar. Each Excel file is called a workbook; it is made up of a series of one or more worksheets. Figure 1 shows one worksheet; the tabs at the bottom of the workspace (marked worksheet tabs) allow you to access the other worksheets in the workbook. This example has three worksheets (Sheet1, Sheet2, and Sheet3); you can add as many as you like to your workbook and you can change the name on the tab by double-clicking the tab and typing in a new name. In this figure, cell A1 is highlighted and is the active cell. The content of this cell is the number 24. You can see that the formula bar above the grid also contains the content of the cell. Data and formulas can be entered into the active cell via the formula bar.
Figure 1. Excel worksheet
Assignment 1. Go to the Assignments section of BlackBoard and click on the folder marked “Excel Tutorial and CenTex Master Workbook”. Open the file called < CenTex_MasterWorkbook(NAME).xls >, and save it to a disk with your first and last name replacing the word NAME in the filename with your last name, a dash, and your first initial (for example, I would save it as < CenTex_MasterWorkbook(uliana-m).xls >). This file will be your personal summary file for all the data and calculations associated with the CenTex project. Be sure you put a copy of it on a disk and keep track of it; you will need it in the future 2. The open file should look something like this (Figure 2):
Figure 2. Blank Master Workbook
Select cell B4 and replace the words Firstname Lastname with your first name and last name. You are currently in the DATA SUMMARY sheet of the workbook. The workbook contains the following 5 sheets: 1. 2. 3. 4. 5.
DATA SUMMARY GEOTECH DATA GRAIN SIZE ANALYSIS PERMEAMETER CALCULATIONS PERMEABILITY SUMMARY
The first sheet is just as it says – a place to summarize all your results. The second sheet is the data and calculation sheet which contains the sample weight data from the Geotechnical Analysis Problem Set. The third sheet contains the grain size distribution data from the same problem set. The fourth sheet contains the Constant Head and Falling Head data from the Aquifer Permeability Estimation Problem Set. The last sheet contains a blank table which you will use to summarize your permeability measurements.
Geotech Data Calculations 3. Click on the tab marked GEOTECH DATA and click once on cell D12. In cell D12 type
=D6-D4
and hit Enter. This is an equation that calculates the weight of the saturated sample by subtracting the value in cell D4 (the weight of the can) from the value in cell D6 (the total weight of the can + the saturated sample). This first step illustrates the general format for Excel equations. The ‘equal’ sign (=) indicates that the cell contains a formula rather than a word or a piece of data. The ‘minus; sign (-) is the operator which tells the program to subtract the contents of D4 from the contents of D6. If you wanted to add those two cells together, you would put =D6+D4 in cell D12; to multiply, put =D6*D4 in cell D12, and to divide put =D6/D4 in cell D12. 4. Next, enter the appropriate equations into each of the cells in the column below cell D12 (i.e., cells D13, D14, D15, D16, D17, D18, D19, D20, and D21). The following table gives you the equations for each cell. D13
=D7-D4
D18
=(D13-D14)/D14
D14
=D8-D4
D19
=(D13-D14)/D3
D15
=D12/D3
D20
=(D13-D14)/(D12-D14)
D16
=D8/D3
D21
=D17-D22
D17
=((D12-D14)/1)/D3
D22
=D17*D20
You will notice that the equations in cells D17, D18, D19, and D20 contain parentheses. These are used just like the parentheses in a standard equation. For example, in D19, you need to subtract the contents of D13 from D14 before dividing by the contents of cell D3; if you didn’t have the parentheses, the program would divide D14 by D3 and subtract that from D13, giving an erroneous answer. BE CAREFUL WITH PARENTHESES!!! It is very easy to misplace your parentheses and result in an erroneous calculation. It is usually a good idea to check your answers on paper to see if your equations are entered correctly. 5. Once all of these values are entered, check the results in your spreadsheet with the results on your paper calculations to make sure that your equations are correct. 6. Now here is the cool part: Use the mouse to place the cursor over cell D12. Hold down the mouse button, and drag down the column to select cells D12 through D22. Your spreadsheet should look something like this:
Figure 3. Selecting a column of cells
Under Edit on the menu bar, select Copy. A flashing dotted line will appear around the selected cells.
7. Now select cells E12 to G22 the same way you selected cells D12-D22. Your spreadsheet should look like this:
Figure 4. Selecting an array of cells
8. Under Edit select Paste Special. A small dialog box should open up; in this box, select Formulas, and then hit OK. This will paste all of the formulas into the selected cells. The convenient thing about Excel is that copying and pasting formulas maintains the relative locations of the cells – in other words, if I copy and paste cell D12 into E12; it will automatically update the formula so that E12 contains the formula =E7-E4. Voila! You just completed the first part of the problem set.
Grain Size Distribution Calculations 9. Click on the tab marked GRAIN SIZE ANALYSIS to select the next worksheet. This sheet contains the data from the grain size distribution analysis. In cell D5, type the following equation:
=C5/C13 and hit Enter. This equation divides the weight of the retained fraction (the value in C5) by the total weight of the sample (the value in C13). (NOTE: I have set up the worksheet so that the values in these cells will automatically be calculated as percentages.) 10. The next step is to fill in the equations in cells D6 to D12. Each cell should have an equation that divides the value in the cell adjacent to the left by the value in C13. For example, in D6 type:
=C6/C13 and hit Enter. Note: if you try to copy and paste the equation in cell D5 to the other cells in the column (like we did in steps 7 and 8), the equations will not work. See if you can figure out why it won’t work. 11. The next step is to calculate the % retained cumulative values in column E. In cell E5, type
=D5 This will copy the value in cell D5 to cell E5. Then, in cell E6, type
=D6+E5 and hit Enter. This will add the value in cell D6 to the previous cumulative value. You can then select cell E6, copy, and paste it into cells E7 to E12.
12. The next step is to calculate the % finer cumulative values in column F. In F5, type
=1-E5 and hit Enter. You can then copy and paste this cell into cells F6-F12. 13. Next, select cells D5 to F12 (Figure 5).
Figure 5. Grain size table selection
Under Edit on the menu bar, select Copy. Select cell H5, then under Edit on the menu bar, select Paste. Do the same in cells D18 and H18. This will paste all the formulas to all of the calculation cells in the spreadsheet. At this point, you have done everything for the Geotechnical Analysis problem set except graph the grain size values.
Permeameter Calculations 14. Click on the tab marked PERMEAMETER CALCULATIONS to select that sheet. The first step is to calculate the cross-sectional area in cell F5, based on the sample diameter given in cell F4 (Figure 6). The equation for calculating the area of a circle is
A = πr 2 In Excel format, this equation is =PI()(F4/2)^2 Figure 6. Permeameter Calculations Sheet
PI() is the function for π, F4/2 is the diameter divided by 2 (i.e., the radius), and ^2 means that everything inside the parentheses is raised to the power of 2 (i.e., is squared).
15. The next step is to enter the equations for the Constant Head calculations. The equation for calculating permeability from the data given is:
K=
QL Ah
where K = hydraulic conductivity; Q = volumetric discharge of water; L = length of the sample; A = cross sectional area of the sample; and h = hydraulic head difference. The Excel format for this equation, in cell C13, is =(C10*F3)/(F5*C11) Type this equation into cell C13, hit Enter, and then type the appropriate version of it into cells D13 to F13 and cells C22 to F22. Note that, in each equation, F3 and F5 (L and A in the standard version of the equation) do not change, but C10 and C11 (Q and h in the standard equation) need to be updated based on cell location. For example… In cell D13, type equation =(D10*F3)/(F5*D11) In cell F22, type equation =(F19*F3)/(F5*F20) 16. Next, in cell C14 convert the value in cell C13 to m/s by dividing it by 100; in other words, type: =C13/100 and hit Enter. Copy this cell and paste it to cells D14 to F14 and cells C23 to F23. 17. The next step is to enter the equations for the Falling Head calculations. The equation for calculating permeability from the data given is:
Ld 2t h o K = 2 ln td s h where K = hydraulic conductivity; L = length of the sample; ho = initial head in the falling tube; h = final head in the falling tube; t = time for head to fall from ho to h; dt = inner diameter of the falling tube; and ds = inner diameter of the sample chamber. For this step, I will require that you figure out the proper Excel format for this equation and enter it into the spreadsheet. Some hints about generating Excel formulas: a) Start every equation with an equal sign (=). Excel will not recognize it as an equation without the equal sign. b) The multiplication symbol is an asterisk; division is a slash. Be sure to put the multiplication symbol between L and dt2 and between t and ds2. Also, the symbol for an exponent is ^; to square a value (e.g., a number like 25 or the value in a cell like D16), type =25ˆ2 or =D16^2. You can use any numerical exponent, or even a cell address, in an exponent (e.g., D16^E16; 25^3.1). c) The Excel function for calculating the natural log of a number x (i.e., the ln in ln(ho/h)) is =ln(x) So, for example, if ho is in cell B14 and h is in cell B12, you would calculate ln(ho/h) with the following equation: =ln(B14/B12)
d) Be especially careful of how you use your parentheses. In your Excel equation, put parentheses around L·dt2, then put parentheses around t·ds2, divide the two, then put parentheses around all of that before you multiply by ln(ho/h). You will probably have to use a little trial and error before you get it right.
Permeability Summary 18. Click on the tab labeled PERMEABILITY SUMMARY to switch to that sheet and enter the results of your permeability estimations. Select the units which you will use for reporting (either cm/s or m/s) an type that value in cell E3. Then type your values in the appropriate cells in the table. Print out a copy of this page to turn in with your other work. 19. Switch to the first sheet in the workbook (labeled DATA SUMMARY). Fill out the table with the appropriate values calculated on the other sheets. 20. Be sure to save your work. When you are finished with everything, email a copy of your workbook to me as an attachment. Be sure that your name is in the filename (see step 1).
