The test contains 16 questions/problems on 8 pages. Each question is worth 5 points.

Transcription

1 University of Arizona Department of Hydrology and Water Resources Dr. Marek Zreda HWR431/531 - Hydrogeology Final exam - 13 December 2000 Open books and notes The test contains 16 questions/problems on 8 pages. Each question is worth 5 points. Problem 1. How many image wells are theoretically needed in the system that consists of one real well and two parallel straight line boundaries (figure)? Why? Are these pumping or injecting wells? How many wells will suffice in practice? Why? Show them on the graph. stream mountain front Problem 2. In a horizontal, confined aquifer, hydraulic conductivity changes linearly from K a =0.2 m/d at point A to K b =0.1 m/d at point B, and porosity changes linearly from n a =0.2 to n b =0.1 (A and B are along a typical flow path). Is the velocity of ground water constant along the flow path? Why or why not? Page 1 of 8

2 Problem 3. What does the figure show? What type of aquifer is it? What do the two dashed lines represent? Be complete, but do not overanalyze the information. 1 drawdown (m) observed time (d) Problem 4. For effective hydraulic conductivity, we can use arithmetic, harmonic or geometric mean. For the data in Table 1, order the three averages from smallest to largest. Is this relationship always valid? Why or why not? What assumption(s) regarding each layer did we make? Table 1: Data for problems 1d and 2d. Layer Thickness (m) K (m/d) Page 2 of 8

3 Problem 5. A sandy soil is in contact (horizontally) with a silty soil. If they have the same initial water content (and both are unsaturated) will there be a movement of water? Why or why not? If yes, in what direction? Why? Problem 6. A chemical tracer has been injected in a deep confined aquifer, and its concentrations monitored at observation wells. Expected arrival time was calculated based on advective velocity. Give at least one reason for each of the following cases: (i) the tracer arrived slightly earlier than expected; (ii) the tracer arrived much earlier than expected; (iii) the tracer arrived slightly later than expected; and (iv) the tracer arrived much later than expected. Page 3 of 8

4 Problem 7. On the graph, draw qualitative (but correct) contour plot of hydraulic conductivity as a function of the median grain size and the variability of the grain size (i.e., some measure of sorting). [Your plot should be a map with lines of equal values of hydraulic conductivity.] Explain briefly in the space below. Variance of grain size Median grain size Problem 8. A core sample from unsaturated zone is 10 cm long, 5 cm in diameter, weighs g before drying and g after drying. Calculate gravimetric water content, volumetric water content, porosity, void ratio, saturation percentage, and bulk density. Page 4 of 8

5 Problem 9. A perching layer of thickness b=0.5 m and hydraulic conductivity K=0.01 m/d supports a perched aquifer 1 m thick. Downward flux through the perching layer is 0.05 m/d. Calculate the pressure head at the bottom of the perching layer. (Assume that K of the aquifer above the perching layer is orders of magnitude higher than K of the perching layer). Problem 10. Five different isotropic horizontal layers (Table 1, in problem 4) separate a confined aquifer from ground surface. If the piezometric surface in the confined aquifer is at the bottom of layer 5, what is the recharge rate of the confined aquifer? (Assume that all layers are saturated, that the infiltration rate at the surface is sufficient to maintain any downward flow, and that no water is standing above the surface.) Page 5 of 8

6 Problem 11. Water at temperature 20 C is flowing through a sandy aquifer with average grain size of 0.5 mm. What is the upper velocity limit for laminar flow? If the hydraulic conductivity of sand is 20 m/d, what hydraulic gradient is necessary to produce turbulent flow? Problem 12. Consider the pumping history of a single well shown in the figure. Design an approach to analyze the pumping data. The objective is to determine drawdown (s) as a function of distance (r) from the pumping well and time (t). Do example calculations for the following conditions: transmissivity T=1000 m2/d, storativity S=0.005, r=50 m, and time t from 0 to 6 years. On the right graph, make a plot of drawdown as a function of time. Pumping rate (m 3 /d) Drawdown (m) Time (y) Time (y) Page 6 of 8

7 Problem 13. Write mass law expressions for the following equilibrium reactions: CaF 2 = Ca F - Mn 2+ + Cl - = MnCl + Cr OH - = Cr(OH) 3 CaMg(CO 3 ) 2 = Ca 2+ + Mg CO 3 - If the equilibrium constant for dissolution of dolomite (last reaction) is K= , what is the solubility of dolomite in water? Express in moles of Ca, Mg and CO 3 per liter of water. Problem 14. Use the Tamers equation to determine the age of a water sample having a total inorganic carbon content (C T ) of 16.7 mm (millimoles) and a HCO 3 - concentration of 997 mg/l. The measured 14 C activity is 2.7% modern carbon. Page 7 of 8

8 Problem 15. The concentration of CFC-11 in four groundwater samples was measured as 1.9, 76.9, 176.1, and pg/kg. Estimate the year in which recharge occurred. Problem 16. The equilibrium constant for the reaction 2Fe Cl - = 2Fe 2+ + Cl 2 is approximately Calculate the equilibrium ratio Fe 2+ /Fe 3+ for two sets of conditions: (a) Cl 2 = 1 atm. and Cl - = 1M; (b) Cl 2 = atm. and Cl - = 1M. Would you expect chlorine to oxidize Fe 2+ appreciably at ordinary temperatures? Would you expect to be able to smell Cl 2 over a solution of FeCl 3? Page 8 of 8