Assume That the Retardation Factor of a Contaminant Is Equal to 2

GEOLOGY 727 Spring 2004 QUIZ (50 points)

Note: Each question is worth 10 points. Since this is a quiz, you are expected to work on these problems independently. Due date is midnight,Wednesday, March 3nd. Please contact me by email if you have any questions about the quiz.

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?

2. Answer the following questions or fill in the blanks with the correct answer. (a) In its most general form the dispersion coefficient tensor has _____ components. (b) Under what conditions does the dispersion coefficient tensor reduce to the 3 principle components along the center diagonal? (c) List the non-zero components of the dispersion coefficient tensor when there is horizontal two-dimensional flow (i.e., vz = 0).

3. Use the Domenico analytical solution for a continuous patch source in an infinitely extensive aquifer with a uniform 1D flow field with the parameters from Problem Set #1. (Remember that the Domenico solution is available as one of the Illinois suite of solutions available on the Illinois web site. See the course homepage for the Illinois web address.) Generate the concentration profile along the centerline of the plume at t=150 days. a) What is the x coordinate of the edge of the plume, along the plume centerline, for a conservative plume (no chemical reactions), if we assume the edge of the plume is defined by a concentration of 0.01 mg/l? b) Where is the edge of the plume along the centerline if the retardation factor is 2 but there is no decay? c) Where is the edge of the plume if there is no retardation but the half life of the contaminant is 50 days? d) Where is the edge of the plume if there is both retardation and decay with R= 2 and half life is 50 days? e) Write the algebraic equations that define the boundary conditions used in the Domenico model.

4. 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 solve the 1D advection-dispersion equation with a uniform flow field (constant velocity) and longitudinal dispersion with retardation and 1st order decay: C  2C C R  D  v  RC t x 2 x Use an explicit approximation with upstream weighting. Write down 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.

5. Solve the spreadsheet model developed in #4 above for t = 20 days using the following set -1 of parameter values:  = 0.6 m; v = 0.1 m/day; R = 2;  = 0.1 d , 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 chemical reactions 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 [email protected].