Name: Hydrogeology - HWR/GEOS 431/531 Final exam Dr. Marek Zreda 7 December :00-16:00 Closed books and notes; two cheat pages allowed

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1 Name: Hydrogeology - HWR/GEOS 431/531 Final exam Dr. Marek Zreda 7 December :00-16:00 Closed books and notes; two cheat pages allowed The test contains 10 problems on 10 pages; the total is 100 points (+ 10 extra points for problem 11). Read the entire exam first. In problems 1-7 use only the space provided. In problems 8-11 use separate sheets of paper. Problem 1. [10 points; 2 points each] Define the following terms (in words and using formulas, where applicable; give units; give typical values or example values). Describe where and how they are used. (a) equipotential line. (b) image well. (c) ion activity. (d) initial condition for radioisotope dating. (e) sorption. 1/11

2 Problem 2. [10 points; 2 each] Use simple graphs to show correlation between the following pairs of parameters/variables (in other words, show their mathematical relationships graphically). Explain briefly. (a) activity coefficient and total dissolved solids. (b) storativity and drawdown. (c) daughter nuclide and time. (d) water content and unsaturated hydraulic conductivity. (e) travel time and porosity. 2/11

3 Problem 3. [10 points; 5 each] Water at 20 C flows through a sand column of length 80 cm, diameter 6 cm, and at 45 angle. The median grain size of the sand d = 0.25 mm, the hydraulic conductivity K = 1 m/d and the porosity n = 0.2. The head at the lower end is 120 cm, at the upper end is 200 cm. (a) Calculate the specific discharge (q) and the average water velocity (v) through the column. (b) Calculate the intrinsic permeability of the soil. 3/11

4 Problem 4. [10 points; 5 points each] (a) You are conducting a pumping test in a confined aquifer which has transmissivity T = 10-4 m 2 / s and storativity S = The observation well is 100 m from the pumping well. How long will you have to pump before you can apply the Jacob semi-log analysis of drawdown with time? (b) A fully penetrating well is installed in a confined aquifer of thickness 12 m, hydraulic conductivity 10-4 m/s and storativity The well is pumped at a rate of 100 L/min for 10 hr. The pumps are then shut down. What is the drawdown 5 m from the well when the pumping is stopped? What is it four hours later? 4/11

5 Problem 5. [10 points; 5 points each] (a) Sketch a representative pore pressure - saturation (or pressure head - moisture content) curve for a sandy soil. On the same graph sketch a typical curve for a clayey soil. Label the curves and axes. On a separate graph sketch relative permeability - saturation (or hydraulic conductivity - moisture content) curves for the same two soils. The curves should be conceptually consistent. (b) 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? 5/11

6 Problem 6. [10 points, 5 points each] In an accident 25 years ago, a large quantity of nitrates (distribution coefficient K d =0) and an organic solvent (K d =0.5 ml/g) was dumped on the soil surface as a massive pulse. Rainfall and evaporation records indicate that about 1000 cm of water has infiltrated into the soil since that time. From soil coring, it was determined that the average water content of the soil profile is 0.25 and the bulk density is 1.5 g/cm 3. (a) Calculate the approximate positions of the nitrate and solvent pulses today. (b) If the water table depth is 50 m, calculate the arrival time for both pulses at the water table. What assumptions about long-term conditions do you have to make? 6/11

7 Problem 7. [10 points] (a) A radioactive nuclide (parent) decays, with the decay constant of y -1, to produce a daughter nuclide. If the measured concentration, in moles per liter, of the parent nuclide equals that of the daughter, what is the age of the sample? (b) If the nuclide in part (a) is 36 Cl, what is the age of the sample? What is the daughter nuclide? 7/11

8 Problem 8. The siege of Camelot [10 points] While most of his knights were upon the Quest for the Holly Grill, King Arthur and his remaining men stayed in the Castle of Camelot (see the figure). On the third day of June, the news came that the army of Mordred, Arthur's enemy, is swiftly approaching Camelot. Upon learning of Mordred's approach, Arthur ordered the moat surrounding the Camelot Castle to be flooded. Soon, the Mordred's army arrived and laid siege to the castle. Both sides fought for weeks, but Arthur was not yielding. On the ninth of July, Sir Mordred and his vile friends started hatching their sinister plots... One of the first ideas that came to their mind was thus: In the center of the Camelot Castle was the only well supplying water to all brave knights within. I say we pour a full barrel of our poison into the moat, said Sir Plug. Yeah, great idea! Let's poison those rats before the rescue comes, enthusiastically said the others. The object is to poison the water supply by Christmas, when the rescuers are expected. The news of Mordred's evil deed were soon brought to Arthur. Woe to us cried he, for there is no antidote for the poisons of Mordred! He is going to use his Tabute Cutri Esado poison! So he summoned his trusted sorcerer Merlin, and said, Merlin, men say that thou are the wisest man in all the world. Can't thou not find some means to help us? So Merlin retreated into his quarters to meditate upon this problem... (a) Evaluate the proposal of Sir Plug. Will the poison reach the castle well and kill Arthur and his knights? And if so, how soon will that happen? Be quantitative in your assessment. Clearly state all the assumptions you make. Make only necessary assumptions. Do not assume something that can be calculated. Describe in words what you are doing at every step of your work. Justify what you are doing. Note: Remember that flow to a well is different than flow in aquifer without any wells. These are some details copied from the secret charts of Merlin: 8/11

9 Depth of moat: 3.5 m. Radius of the moat: 25 m. The castle is underlain by glacial till and fluvioglacial sands. When the well was being planned, Merlin asked Monsieur Cydar, a famous waterologist from Dijon, to choose the location. Monsieur Cydar conducted laboratory experiments with soil samples from different depths. He loaded the samples, one at a time, into the same vertical cylinder (20 cm long, 5 cm in diameter) and connected the top to one bucket of water with the water level at 20 cm above the top of the cylinder, and the bottom to the other, lower bucket of water, whose water level was at 20 cm above the bottom of the column. He then measured how much water was flowing through the soil-filled cylinder. The results for different soils were (note different time units used in Monsieur Cydar's experiment): Soil # Depth (m) Flow rate ml/hr ml/min ml/min ml/min ml/day ml/day The castle has been occupied by 200 people for the last 60 years. It has been estimated that each person uses 200 liters of water per day. It is also known that before the castle was built, water levels in wells that penetrated the confined aquifer (at depth 4 to 7 m) were 1 m below the surface. We guess the storativity of the aquifer to be and the porosity 0.2. We also assume, for simplicity, that the aquifer is horizontal, of constant thickness and infinite laterally. 9/11

10 Problem 9. To dry or not to dry? This is the question! [10 points] Sir Mordred and his men are still laying siege to Camelot. Suppose that our poison trick does not work says Sir Ugly, what then? I says, I says, I says, let's stab them all in the chest, those demons, calls Sir Shrub, known for his rash temper. But how will we get through the moat? ask Sir John, Sir Paul, Sir George and Sir Ringo, all at the same time. I have a better idea, calls Sir Jacob. Listen... Sir Jacob proposes to dig 4 wells around the castle perimeter (see the figure), and pump water for some time. He thinks that this action will produce a cone of depression around Camelot and the castle well will dry out. (b) What are the chances that this plan will succeed? Assume that the four wells are 50 m apart and form a square as in the figure. What pumping rate should Mordred use so that the plan can be carried out successfully? Remember, the goal is to win as quickly as possible, and necessarily before Christmas. (c) Propose improvements to Sir Jacob's plan. Problem 10. The Unnoticed River [10 points] After the plan was ready to implement, Sir Leaky Roger discovered that 25 m to the west of the moat there is a river flowing from the north to the south. He reported this immediately to Sir Jacob. Sir Jacob had to take the new information into account and modify his plan, if deemed necessary. How will his plan proposed in Quest 2 change under these new conditions? Repeat the calculations in Quest 2 with the presence of the river. Assume the river fully penetrates the aquifer. The head in the river is 1 m below the land surface (the river cut 1 m into the soil). 10/11

11 Problem 11. [Extra credit: 10 points]: Damsel in Distress (a) In his life-long quest for adventure, Sir Duck A Lot arrived at the huge stone tower. In the tower, golden haired damsel Grisselda awaits in distress her rescuer. For years, she has been waving from the only window at the top of the tower, alas no knight has ever been able to rescue her from this plight. There are no ladders, not even trees in this desolate area. The only way to scale the tower is to climb on the long braid of Grisselda hanging from the window. By now, the braid is 2 m long, and Sir Duck A Lot cannot even reach it. From the incoherent shouting of Grisselda he learns that the golden hair grows at a rate of 3 cm/month. But he still has to estimate the tower's height to know how long until the braid reaches the ground. (*) Provide Sir Duck A Lot with a scheme (or schemes) for estimating the tower's height. (**) Assuming the tower's height (up to the window sill) is 25 m, calculate waiting time for the knight and damsel Grisselda and comment on the result. (b) A different damsel is in distress in a similar tower. Another knight, Sir Measured Well, comes to the tower. He wants to make a ladder in his castle and rescue the damsel, but first he has to measure the height of the tower. He is athletic and can climb the wall so that he can also reach the window at the top of the tower. However, he does not have any tape or string that he could use to measure the height. The only thing he has is a barometer shaped as in the figure. (This was a common weapon that knights carried with them at all times in those parts). Propose at least three possible methods to estimate the height of the tower using only the equipment at hand. You should know that Sir Measured Well did not get his name for nothing. He was knighted for measuring well in the kingdom of the King Arthur. 1 m Barometer 11/11