GEOLOGY 727

Spring 2007

QUIZ (50 points)

Note: Since this is a quiz, you are expected to work on these problems independently. Due date is 2:25 PM March 8th. Please contact me by email if you have any questions about the quiz.Each question is worth 10 points.

  1. Assume that the retardation factor of a contaminant is equal to 2.0 and the concentration in solution in groundwater is 10 mg/l.

(a)Calculate the total amount of contaminant in grams (including both dissolved and adsorbed) in a cubic meter of porous material. Assume porosity is equal to 30 percent. (Assume that 1 mg/l = 1 gm/m3.)

(b)Assume uniform flow with specific discharge, q = 1 ft/day. What is the effective velocity of the contaminant?

  1. Answer the following questions.

(a) List the non-zero components of the dispersion coefficient tensor when there is

horizontal two-dimensional flow (i.e., vz = 0).

(b) Explain why sorption, simulated as a linear isotherm (i.e.,c = cKd), does not

affect the long term value of the breakthrough concentration. See graph below.

(c) Explain why sorption, simulated as a linear isotherm as in (b) above does affect the long term value of the breakthrough concentration when the contaminant is subject to first order decay. In the graph below compare the gold and blue lines. (Assume the governing equation is of the form in question #4 below.)

  1. Use the ATRANS analytical solution for a patch source in a bounded aquifer with a uniform

1D flow field with parameter values from Problem Set #1a (i.e., with dispersion but no retardation and no decay). However, now assume that the patch source is present only for a period of 10 days(i.e., the source concentration is 100 mg/l for 10 days and 0 mg/l after 10 days).

(a)If the regulatory limit for the concentration of the contaminant is 1 mg/l, then, for regulatory purposes, what is the minimum distance(reported to the nearest meter) from the source that is not contaminated at any time? (HINT: Solving this problem is best done with the ATRANS spreadsheet rather than running in dos.)

(b)Present a breakthrough curve (concentration vs. time) at the distance along the centerline reported in part (a).

(c)Explain why the breakthrough curve has a steep rising limb at early times and a long tail at later times.

  1. Recall that we used a spreadsheet to develop a numerical solution for the 1D “Ogata and Banks” form of the advection dispersion equation using an explicit finite difference approximation with upstream weighting. Modify the spreadsheet (which you can download from the course homepage) to include retardation and 1st order decay. That is, solve this governing equation:


Use an explicit approximation with upstream weighting for the advection term and central differences for the dispersion term. Write the finite difference expression you used in your spreadsheet model as your answer to this question. Also consult p. 4-20 in the MT3DMS manual and develop stability criteria for your spreadsheet model. Include the expressions for the stability criteria in your answer to this question. Include these new stability criteria in your spreadsheet model.

  1. Solve the spreadsheet model developed in #4 above for t = 20 days using the following set of parameter values:  = 0.6 m; v = 0.1 m/day; R = 2;  = 0.1 d-1, t = 2 d, x = 1 m, Co = 1 mg/l. Plot your finite difference solution with retardation and decay on a graph that shows the solution for the same problem without retardation or decay using the Ogata and Banks analytical solution (which does not include retardation and decay). Send me your Excel spreadsheet as an attached email document. Send it to .