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Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION
VERSUS TIME), ANNE ANDERSON ET AL. VERSUS W.R. GRACE ET
AL., WOBURN, MASSACHUSETTS
Nested monitoring wells at W.R. Grace (left) and "full strength" gallon of TCE (right).
Introduction
This assignment demonstrates how advection, diffusion, dispersion, and chemical retardation
influence the travel velocity and concentration of a TCE plume at Woburn, Massachusetts. Similar
to Problem #1 of this chapter, the Ogata and Banks (1961) analytical solution for one -dimensional
advective transport with dispersion is used (see Chapter 6 in the Reference Book). Using this
equation, you can calculate concentration breakthrough curves at given distances from the source
for TCE contamination.
Hydrogeologic data from the unconfined aquifer underlying the Aberjona River valley at
Woburn indicate that the aquifer has a hydraulic conductivity of 400 ft/d, an effective porosity of
30% (Metheny, 2004), and an average hydraulic gradient of 0.001 (Myette et al., 1982). The
longitudinal dispersivity (ax) is assumed to be 25 ft. and the coefficient of molecular diffusion is
assumed to be 1x10-6 ft2/d.
You will use these parameters to program the Ogata and Banks (1961) equation into the "C vs t"
worksheet to calculate the breakthrough curves of the TCE plume at 800, 1000, and 1200 feet.
Then these breakthrough curves are simulated assuming chemical retardation using a modified
form of the Ogata and Banks (1961) equation in the "C vs t with Retardation" worksheet.
Page 1 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Instructions - Part I
Determine the concentration of a non-reactive contaminant (no chemical retardation) at three
distances using the one-dimensional advection-dispersion equation developed by Ogata and Banks
(1961) (see Reference Book). To use the ERF and ERFC intrinsic function in EXCEL, you must
have the "Analysis ToolPak" installed as an Add-In. See EXCEL TIPS in the Reference Book for
more information.
1. Enter the values of the aquifer and contaminant parameters (K, i, n e, ax, and D*) in the table
provided on the "C vs t" worksheet.
2. Assume the TCE source at the Riley Tannery property is continuously releasing contaminants to
the groundwater flow system at a concentration of 1000 mg/L.
3. Use the "C vs t" worksheet to solve the Ogata-Banks equation in terms of concentration versus
time for specified distances of 800, 1000, and 1200 feet from the source.
4. Using the cells provided on the "C vs t" worksheet, solve for the average linear flow velocity
(vx) and the coefficient of hydrodynamic dispersion (D x) (see Reference Book equations 6-1 and 6-
2).
5. Use a time increment of 100 days between 100 and 2000 days in the first column of the
worksheet. [The smallest time variable is set to 1, instead of zero to avoid division by zero errors in
the worksheet.] The time increments (e.g., 100, 200, 300, etc.) will automatically be reflected into
the time columns for 1000 and 1200 feet.
- First, calculate the argument of the error function based on equation 6-3 in the Reference Book in
cells E16-E36, J16-J36, and O16-O36. The error function values then will change from the initial
values of 1.000 to the correct values based on the argument.
- Next, calculate the concentration (C) and then calculate the relative concentration (C/C 0) for each
of the time periods specified using equation 6-3 in the Reference Book.
6. Repeat the above two steps for the 1000 and 1200 feet portions of the worksheet.
7. Print the concentration versus time table and the breakthrough curves plotted on the " C vs t"
worksheet. Answer the Part I questions that appear on the "Questions" worksheet.
Page 2 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Instructions - Part II
Compute TCE concentrations in "C vs t" worksheet at the same distances and for the same times
using the same values of hydraulic parameters as in Part I, except use ax values of 10 and 50 feet.
Print the graphs of the breakthrough curves and calculation tables for each dispersivity value.
Answer the questions that appear under Part II of the "Questions" worksheet.
Instructions - Part III
Compute TCE concentrations in the same manner as in Parts I and II of this exercise but modify
the argument of the error function (cells E18-E38, J18-J38, and O18-O38) to account for chemical
retardation, as appears in equation 6-7 in the Reference Book. Use the same parameter values used
in Part I but compute the contaminant velocity (v c) and the retardation factor (R f) for
trichloroethylene (TCE) assuming the dry, bulk density of the soil is 2.00 g/cm 3, and a weight
fraction of organic carbon content equal to 0.60% or 0.006. The partition coefficient between
organic carbon and water (K oc) for TCE is 152 mg/g. Use the "C vs t with Retardation" worksheet
to determine the approximate time when the leading edge of the TCE plume (C/C 0= 0.005) travels
800 feet to well G. Use a starting time of 1 day then 400 days for the second time value and
subsequently at time intervals of 400 days to calculate the concentration curves. Answer the
questions in Part II of the "Questions" worksheet after printing your final breakthrough curve and
concentration versus time table.
References
Metheny, M. 2004. Evaluation of groundwater flow and contaminant transport at the Wells G & H
Superfund Site, Woburn, Massachusetts, from 1960 to 1986 and estimation of TCE and PCE
concentrations delivered to Woburn residences. Doctor of Philosophy, Ohio State University,
Geological Sciences. 367p.
Myette, C.F., D.G. Johnson, J.C. Olimpio. 1987. Area of influence and zone of contribution to
superfund site wells G and H, Woburn, Massachusetts. U.S. Geological Survey, Water -Resources
Investigations 87-4100. 86p.
Ogata, A. and R.B. Banks, 1961, A solution of the differential equation of longitudinal dispersion
in porous media, U.S. Geological Survey Professional Paper 411-A.
Page 3 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
ation of a TCE plume at Woburn, Massachusetts. Similar
am the Ogata and Banks (1961) equation into the "C vs t"
Page 4 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
annery property is continuously releasing contaminants to
set to 1, instead of zero to avoid division by zero errors in
in
) for each
Page 5 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
" worksheet at the same distances and for the same times
me manner as in Parts I and II of this exercise but modify
water flow and contaminant transport at the Wells G & H
Page 6 of 17 Introduction
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION
VERSUS TIME), ANNE ANDERSON ET AL. VERSUS W.R. GRACE ET
AL., WOBURN, MASSACHUSETTS
Questions - Part I (4 Total)
Question #1. Compare the concentration versus time curves (breakthrough curves) you calculated
in Part I of this problem (Woburn) with the concentration versus distance curves (concentration
profiles) you produced for Part I in problem 1 (Wooster) of this chapter. What are some of the
similarities and differences between these two types of curves?
Question #2. How long after the contaminant enters the flow system does it take for the leading
edge of the plume (C/C0 = 0.005) to travel from the Riley Tannery property to well G,
approximately 800 ft away? (Print the graph when complete.) [Suggestion: Adjust the time values
until the leading edge reaches 800 ft.]
Question #3. How long will it take the contaminant to travel the 800 feet to well G based solely on
advection? (Show your calculations or demonstrate with a concentration versus distance graph.)
Page 7 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Question #4. How long after the contaminant enters the flow system will it take for the
concentration at well G (800 feet downgradient) to be constant?
Questions - Part II (4 Total)
Question #1. How do differences in ax affect the shape of the breakthrough curves?
Question #2. How do differences in ax affect the arrival time of the leading edge of the
contaminant plume at well G?
Question #3. Compare the answers to the above two questions about the influence of ax to those
you gave for Problem 1, Part II, Questions #1 and #2 in this chapter.
Question #4. How does the change in dispersivity value impact advective front (C/C0 = 0.5) of the
breakthrough curves?
Page 8 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Questions - Part III (3 Total)
Question #1. What is the calculated retardation factor for TCE and how does accounting for
chemical retardation affect the shape of the breakthrough curves?
Question #2. Accounting for the chemical retardation of TCE, when does the leading edge of the
plume (C/C0 = 0.005) arrive at well G? When would the concentration at well G exceed the U.S.
EPA limit of 5 mg/L? [Suggestion: Adjust the time values until the leading edge reaches 800 ft.]
Question #3. Albert Einstein once said that "Everything should be made as simple as possible, but
no simpler." This is a telling quote in light of how one of the plaintiffs' expert witnesses in the
landmark "A Civil Action" trial used the Ogata-Banks equation to obtain arrival times for TCE at
wells G and H, as described in the problem setup material. Based on the geologic cross section you
constructed in Problem 1 in Chapter 1 and the potentiometric map you constructed in Problem 2 in
Chapter 1, what questions would you tell your attorney to pose to this expert on cross examination
if you were the expert witness representing the Riley Tannery, which was owned by Beatrice
Foods? What questions would you tell your attorney if you were the expert witness representing
the Cryovac Plant owned by W.R. Grace?
Page 9 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
e graph when complete.) [Suggestion: Adjust the time values
G based solely on
Page 10 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
= 0.5) of the
Page 11 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
blem setup material. Based on the geologic cross section you
Page 12 of 17 Questions
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION VERSUS TIME), ANNE
ANDERSON ET AL. VERSUS W.R. GRACE ET AL., WOBURN, MASSACHUSETTS
Input Parameters
K= 400 ft/day C0 = 1000 mg/L x1 = 800 feet
i= 0.001 ft/ft ax = 50 ft x2 = 1000 feet
n= 0.30 (decimal) D* = 1.00E-06 ft2/day x3 = 1200 feet
2
vx = 1.33 ft/day Dx = 67 ft /day
Calculations at 800 feet Calculations at 1000 feet Calculations at 1200 feet
t C/C0 C erfc argument t C/C0 C erfc argument t C/C0 C erfc argument
1 0.000 0.0 0.000 48.9081 1 0.000 0.0 0.000 61.1556 1 0.000 0.0 0.000 73.4030
100 0.000 0.0 0.000 4.0825 100 0.000 0.0 0.000 5.3072 100 0.000 0.0 0.000 6.5320
250 0.005 5.3 0.011 1.8074 250 0.000 0.1 0.000 2.5820 250 0.000 0.0 0.000 3.3566
300 0.023 22.8 0.046 1.4142 300 0.001 1.3 0.003 2.1213 300 0.000 0.0 0.000 2.8284
400 0.124 124.1 0.248 0.8165 400 0.022 21.7 0.043 1.4289 400 0.002 1.9 0.004 2.0412
500 0.303 302.8 0.606 0.3651 500 0.098 98.4 0.197 0.9129 500 0.019 19.4 0.039 1.4606
600 0.500 500.0 1.000 0.0000 600 0.240 239.8 0.480 0.5000 600 0.079 78.6 0.157 1.0000
700 0.669 668.7 1.337 -0.3086 700 0.414 413.6 0.827 0.1543 700 0.191 191.4 0.383 0.6172
800 0.793 792.9 1.586 -0.5774 800 0.581 580.9 1.162 -0.1443 800 0.342 341.5 0.683 0.2887
900 0.876 875.9 1.752 -0.8165 900 0.718 718.1 1.436 -0.4082 900 0.500 500.0 1.000 0.0000
1000 0.928 927.9 1.856 -1.0328 1000 0.819 819.3 1.639 -0.6455 1000 0.642 642.5 1.285 -0.2582
1100 0.959 959.1 1.918 -1.2309 1100 0.888 888.5 1.777 -0.8616 1100 0.757 756.9 1.514 -0.4924
1200 0.977 977.2 1.954 -1.4142 1200 0.933 933.2 1.866 -1.0607 1200 0.841 841.3 1.683 -0.7071
1300 0.988 987.5 1.975 -1.5852 1300 0.961 960.9 1.922 -1.2455 1300 0.900 899.9 1.800 -0.9058
1400 0.993 993.2 1.986 -1.7457 1400 0.978 977.6 1.955 -1.4184 1400 0.939 938.6 1.877 -1.0911
1500 0.996 996.4 1.993 -1.8974 1500 0.987 987.3 1.975 -1.5811 1500 0.963 963.2 1.926 -1.2649
1600 0.998 998.1 1.996 -2.0412 1600 0.993 992.9 1.986 -1.7351 1600 0.978 978.3 1.957 -1.4289
1700 0.999 999.0 1.998 -2.1783 1700 0.996 996.1 1.992 -1.8813 1700 0.987 987.5 1.975 -1.5842
1800 0.999 999.5 1.999 -2.3094 1800 0.998 997.9 1.996 -2.0207 1800 0.993 992.8 1.986 -1.7321
1900 1.000 999.7 1.999 -2.4351 1900 0.999 998.8 1.998 -2.1541 1900 0.996 996.0 1.992 -1.8732
2000 1.000 999.8 2.000 -2.5560 2000 0.999 999.4 1.999 -2.2822 2000 0.998 997.7 1.995 -2.0083
ADVECTIVE TRANSPORT WITH DISPERSION AND DIFFUSION TO WELL H
800 feet 1000 feet 1200 feet
1.0
0.9
0.8
0.7
0.6
C / C0
0.5
0.4
0.3
0.2
0.1
0.0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Page 13 of 17 C vs t
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
0.0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Time (days)
Page 14 of 17 C vs t
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Time (days)
Page 15 of 17 C vs t
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
1-D CONTAMINANT TRANSPORT OF TCE (CONCENTRATION VERSUS TIME), ANNE ANDERSON ET
AL. VERSUS W.R. GRACE ET AL., WOBURN, MASSACHUSETTS
Input Parameters
K= 400 ft/day C0 = 1000 mg/L rb = 2.00 g/cm3 Rf = 5.3 x1 = 800 feet
i= 0.001 ft/ft ax = 25 ft Koc = 152 mL/g vc = 0.3 ft/day x2 = 1000 feet
n= 0.30 (decimal) D* = 1.0E-06 2
ft /day foc = 0.006 (decimal) x3 = 1200 feet
vx = 1.3 ft/day Dx = 33 ft2/day Kd = 0.912 mL/g
Calculations at 800 feet Calculations at 1000 feet Calculations at 1200 feet
t C/C0 C erfc argument t C/C0 C erfc argument t C/C0 C erfc argument
1 0.000 0.0 0.000 158.984 1 0.000 0.0 0.000 198.743 1 0.000 0.0 0.000 238.502
400 0.000 0.0 0.000 6.946 400 0.000 0.0 0.000 8.934 400 0.000 0.0 0.000 10.922
800 0.000 0.0 0.000 4.200 800 0.000 0.0 0.000 5.606 800 0.000 0.0 0.000 7.011
1200 0.000 0.0 0.000 2.848 1200 0.000 0.0 0.000 3.996 1200 0.000 0.0 0.000 5.144
1680 0.005 5.1 0.010 1.818 1680 0.000 0.0 0.000 2.788 1680 0.000 0.0 0.000 3.758
2000 0.032 32.3 0.065 1.306 2000 0.001 1.0 0.002 2.196 2000 0.000 0.0 0.000 3.085
2400 0.134 134.4 0.269 0.782 2400 0.012 12.1 0.024 1.593 2400 0.000 0.3 0.001 2.405
2800 0.313 313.5 0.627 0.344 2800 0.061 60.7 0.121 1.095 2800 0.005 4.5 0.009 1.846
3200 0.519 519.3 1.039 -0.034 3200 0.172 172.2 0.344 0.669 3200 0.026 26.2 0.052 1.371
3600 0.698 698.4 1.397 -0.368 3600 0.338 338.3 0.677 0.295 3600 0.088 87.8 0.176 0.958
4000 0.827 827.2 1.654 -0.667 4000 0.522 521.6 1.043 -0.038 4000 0.202 201.9 0.404 0.590
4400 0.908 908.0 1.816 -0.939 4400 0.685 684.6 1.369 -0.340 4400 0.357 356.8 0.714 0.260
4800 0.954 953.8 1.908 -1.190 4800 0.808 808.1 1.616 -0.616 4800 0.524 523.6 1.047 -0.042
5200 0.978 977.8 1.956 -1.422 5200 0.891 890.9 1.782 -0.871 5200 0.674 674.2 1.348 -0.319
5600 0.990 989.8 1.980 -1.639 5600 0.941 941.4 1.883 -1.108 5600 0.793 792.6 1.585 -0.577
6000 0.995 995.4 1.991 -1.843 6000 0.970 970.0 1.940 -1.330 6000 0.876 876.0 1.752 -0.817
6400 0.998 998.0 1.996 -2.036 6400 0.985 985.3 1.971 -1.539 6400 0.930 929.8 1.860 -1.042
6800 0.999 999.2 1.998 -2.220 6800 0.993 993.0 1.986 -1.737 6800 0.962 962.1 1.924 -1.255
7200 1.000 999.6 1.999 -2.394 7200 0.997 996.8 1.994 -1.926 7200 0.980 980.3 1.961 -1.457
7600 1.000 999.9 2.000 -2.561 7600 0.999 998.5 1.997 -2.105 7600 0.990 990.1 1.980 -1.649
8000 1.000 999.9 2.000 -2.721 8000 0.999 999.4 1.999 -2.277 8000 0.995 995.2 1.990 -1.832
Advective Transport with Dispersion, Diffusion, and Retardation to Well H
800 feet 1000 feet 1200 feet
1.0
0.9
0.8
0.7
0.6
C / Co
0.5
0.4
0.3
0.2
0.1
0.0
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000
Time (days)
Page 16 of 17 C vs t with Retardation
Name ____________________ Practical Problems in Groundwater Hydrology Chapter 6 - Problem 2
Page 17 of 17 C vs t with Retardation
