ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING. University of South Florida

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1 ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING Fall 2017 Final Examination Monday, December 4, 2017 University of South Florida Civil & Environmental Engineering Prof JA Cunningham Instructions: 1. You may read these instructions, but do not turn the page or begin working until instructed to do so. 2. This exam contains 5 questions. Answer any 3. Each question has multiple parts. 3. The total number of points possible is 120. Point values for each question are indicated. 4. Answer the exam questions on separate sheets of paper (i.e., not on these exam sheets). Make sure your name is on each piece of paper, and that you submit all pages you want graded. At the end of the exam period, staple your papers together in the proper order. You may use as many sheets of paper as you need (though, in the spirit of ENV 4001, I encourage you not to be wasteful). 5. To maximize your partial credit, show all your work and state your assumptions clearly. I can only assign you partial credit if I can follow what you are doing. 6. Report your answers to a reasonable number of significant digits and with proper units. 7. You are allowed to use your text book, your course notes, or other printed materials. You may not receive help from another person. 8. The back of this page contains some constants and unit conversions that you might find helpful. I am also including two additional pages, scanned from a previous year s text book, that have some helpful tables on them. 9. A hand-held calculator is recommended. Other electronic devices are not permitted. 10. Time limit: 120 minutes. Stop working when asked. If you continue working after time has been called, you will be penalized at a rate of 1 point per minute. 11. Don t cheat. Cheating will result in appropriate disciplinary action according to university policy. More importantly, cheating indicates a lack of personal integrity. 12. Hints: Read each question carefully and answer the question that is asked. Watch your units. If you take good care of your units, they will take good care of you. Work carefully and don t rush. 1

2 Potentially useful constants: Ideal gas constant, R: Pa m 3 mol 1 K 1 = atm m 3 mol 1 K 1 Gravitational acceleration, g: 9.81 m/s 2 Molecular weight of water, H2O: g/mole Density of water at 18 C: g/ml = kg/m 3 Viscosity of water at 18 C: Pa sec Density of air at 18 C: 1.21 kg/m 3 Viscosity of air at 18 C: Pa sec Potentially useful conversion factors: Pressure: 1 atm = 760 mm Hg = 760 torr = Pa 1 Pa = 1 N/m 2 = 1 kg/(m sec 2 ) Mass: 1 kg = 1000 g = 10 6 mg = 10 9 µg 1 kg = lbmass 1 t (metric tonne) = 1000 kg = 2207 lbmass 1 ton (English ton) = 2000 lbmass Length: 1 km = 1000 m = 10 6 mm = 10 9 µm 1 ft = 12 in = cm = m Temperature: 25 C = K Volume: 1 m 3 = 1000 L = 10 6 ml = 10 6 cm 3 1 gal = L Work/Energy: 1 BTU = kj Power: 1 MW = 10 6 W = 10 6 J/s = 10 6 N m/s Area : 1 ha = 10 4 m 2 Atomic Masses: H = g/mole C = g/mole N = g/mole O = g/mole P = g/mole S = g/mole Cl = g/mole Br = g/mole Na = g/mole Mg = g/mole Ca = g/mole Fe = g/mole 2

3 from Principles of Environmental Engineering and Science, 2nd edition, by Davis and Masten 3

4 from Principles of Environmental Engineering and Science, 2nd edition, by Davis and Masten 4

5 1. (40 pts) biochemical oxygen demand; oxygen depletion in a river A particular river has a temperature of 20 C and flows at a velocity of 0.05 m/s. Some nearby residents are concerned about the health of the river because it is known to contain some organic pollution from an industrial discharge. a. (15 pts) The concerned residents set out to measure the biochemical oxygen demand (BOD) in the river at a couple different locations. Just a little bit downstream of the discharge point, they measured the BOD5 and found it to be 16.0 mg/l. At another spot 21.6 km downstream, they got confused and measured the BODult instead of the BOD5. The BODult was 8.0 mg/l. Based on this information, estimate/calculate the apparent first-order rate coefficient for degradation of organic pollutants in the river. b. (25 pts) The concerned residents floated down the river in a canoe, starting just downstream of the discharge point. As they floated downstream, they used a probe to measure the concentration of dissolved oxygen (DO) in the river. After they got 3.0 km downstream, they had to turn around and start paddling home. The data they collected are shown below. Assuming that the rate coefficient for oxygen reaeration is 0.6 d 1, estimate/calculate the downstream distance at which the dissolved oxygen concentration would be the lowest. What would be the concentration of dissolved oxygen at that location? What do you think about the health of the river? 5

6 2. (40 pts) risk assessment; environmental biology; material balances Dieldrin is an insecticide that was used in the 1950s through the 1970s. According to Wikipedia ( it is an extremely persistent organic pollutant; it does not easily break down. Furthermore, it tends to biomagnify as it is passed along the food chain. Let s suppose dieldrin is still present in the sediment of a particular lake, even though it has not been applied there for over 40 years. (That is actually possible for persistent compounds of this type.) A person who lives nearby the lake likes to fish in the lake. Each week, he eats about 200 g of fish that he has caught from the lake. The best estimate I could find for the bioaccumulation factor (BAF) of dieldrin is 576,000 L/kg (New York State, Human Health Fact Sheet, 1998). a. (15 pts) Imagine that the fisherman has been fishing in the lake for 30 years. The fisherman now wonders how much he has increased his risk of contracting cancer by eating the fish. If we consider an acceptable risk level to be , what aqueous concentration (i.e., concentration in the water) is acceptable for the lake? Report your answer in units of µg/l. The fisherman is 48 years old and has a body mass of 80 kg. Hint: your answer should be a very low aqueous concentration because dieldrin bioaccumulates pretty strongly and is also pretty carcinogenic. Now let s see if we think the concentration of dieldrin in the lake will exceed the acceptable level you found. Suppose the volume of the lake is L, and it is has one inlet stream and one outlet stream, both flowing at a rate L/d. Dieldrin is released from the lake sediment into the lake water at a rate R = krelease*(1.0 µg/l C), where C is the concentration of dieldrin in the lake, and krelease is a first-order rate coefficient. Also, in the lake, dieldrin biodegrades according to first-order kinetics, with a biodegradation rate coefficient of 0.01 d 1. b. (15 pts) Write a material balance for the mass of dieldrin in the lake water. Then derive an equation for C as a function of krelease. Clearly state any assumptions. c. (5 pts) What value of krelease would result in an acceptable aqueous concentration for fishing in the lake? d. (5 pts) Compare the value of krelease to the value of the biodegradation rate coefficient. W/hat does this tell you about the acceptable value of krelease? Based on this, what do you think about fishing in a lake where dieldrin was applied in the past? 6

7 3. (40 pts) drinking water treatment, reactor theory Suppose a drinking-water treatment plant is treating L/d of water. One of the steps in the treatment process is conventional sedimentation. The sedimentation basin has a depth of 3.0 m, a width of 6.0 m, and a length of 12.0 m. The temperature of the water is 18 C. a. (6 pts) Estimate/calculate the average hydraulic residence time in the sedimentation basin, in units of hr. Also estimate/calculate the overflow rate, in units of m/s. b. (12 pts) For this sedimentation basin, estimate/calculate the fractional removal of spherical particles that have a diameter of 0.01 mm and a particle density of 2500 kg/m 3. c. (9 pts) Suppose the length of the sedimentation basin is doubled to 24.0 m. What happens to the average hydraulic residence time you found in part (a)? What happens to the fractional removal you found in part (b)? Also calculate these parameters if the length of the sedimentation basin is tripled to 36.0 m. d. (8 pts) Draw a graph. On the x-axis, put average hydraulic residence time. On the y- axis, put fraction of particles remaining in the water after sedimentation. (Hint: you calculated the fraction removed, so it is easy to calculate the fraction remaining.) Use the three data points that you calculated above to draw your graph. You can also pretty easily include a data point at θ = 0. e. (5 pts) What type of reaction kinetics does this graph describe: zero-order, first-order, second-order, or Monod? How can you tell? Explain briefly. (no credit for a lucky guess) f. BONUS -- up to 8 points -- derive an equation for the reaction rate coefficient k as a function of the particle settling velocity, the dimensions of the sedimentation basin, and the influent concentration of particles in the water. (This one is somewhat tricky; if you don t see how to get it, then probably it is best to just skip it.) 7

8 4. (40 pts) wastewater treatment; air pollution A wastewater treatment plant is treating 1600 m 3 /hr of municipal wastewater. The plant uses a conventional activated sludge process for secondary treatment. Effluent from the secondary clarifier is discharged to a nearby river. Under their current operation, the average hydraulic residence time in the aeration basin is 1.0 hr, and the solids retention time (SRT) is 20 d. The plant is successfully meeting all of their effluent discharge limits; the liquid effluent contains 3.0 mg/l of suspended solids and 3.2 mg/l of soluble BOD5. However, when waste activated sludge is sent to anaerobic digestion (at a current rate of about 125 kg/d), the digester is not generating much methane. The plant engineers think the SRT is too long and the sludge is too old to be digested properly. The plant engineers are going to ask the plant operators to waste sludge at a faster rate (i.e., to increase the flow rate of the waste activate sludge) to reduce the SRT. a. (12 pts) At what rate (in units of kg/d) should the plant operators waste the sludge if they want to reduce the SRT from 20 d to 10 d? Assume that the MLVSS concentration in the aeration basin does not change. We want to make sure that the new SRT will be acceptable for the plant effluent. We can assume that the suspended solids concentration does not change, but we are not so sure about the soluble BOD concentration. Suppose we know that the bacteria in the aeration basin grow and degrade organic contaminants according to Monod kinetics. The maximum specific growth rate coefficient is 3.0 d 1, the yield coefficient is 0.6 mg/mg, and the bacterial death rate coefficient is 0.1 d 1. b. (12 pts) Will the proposed SRT of 10 d still produce an acceptable concentration of soluble BOD5 in the effluent? The plant s discharge limit is 5.0 mg/l of soluble BOD5. A battery processing facility will be built next to the wastewater treatment plant. It is estimated that the new facility will emit 10 kg/d of lead (Pb). A busy urban area is 3.0 km directly downwind of the planned incinerator. c. (16 pts) Estimate/calculate the necessary height of the stack so that the Pb concentration at ground level will remain below the federal standard of 0.15 µg/m 3. For the purposes of this problem, assume a wind speed of 4.0 m/s and neutral (class D) stability. 8

9 5. (40 pts) environmental chemistry A beaker contains 1.0 L of water. It also contains 10 mg of CaCO3 solid precipitate; you can assume that the water and the CaCO3 are in equilibrium. The ph of the water is 9.3 and the water contains 20 mg/l of bicarbonate (HCO3 ). a. (15 pts) Estimate/calculate the concentration of calcium ion, [Ca 2+ ], in the water. Report your answer in units of mg/l. b. (4 pts) Estimate/calculate the number of moles of calcium present in the CaCO3 precipitate. Suppose we start adding a solution of sulfuric acid, H2SO4, to the beaker of water. As we add the acid solution, the CaCO3 dissolves. c. (6 pts) Briefly explain why the precipitate dissolves when acid is added. A few sentences will probably be sufficient. We observe that if we add 0.2 L of the acid solution, it is just enough acid so that all the CaCO3 dissolves. The water is therefore just at the saturation point for CaCO3. d. (6 pts) What is the molar concentration of calcium in the beaker now? Hint: the precipitate dissolved, which released Ca 2+ into solution; also, the volume changed. e. (3 pts) What is the molar concentration of carbonate, CO3 2? Hint: the water is just at the saturation point for CaCO3. I was going to have you calculate the bicarbonate concentration, [HCO3 ], in the system after the acid is added. But it is a bit tricky and beyond the scope of ENV So I will just tell you that the bicarbonate concentration [HCO3 ] is 26.9 mg/l. f. (6 pts) Estimate/calculate the ph after the acid is added. I actually had more that I wanted to add to this problem, but it is long enough already. I was thinking that if you keep adding H2SO4, eventually you might start to form a new precipitate, in the form of CaSO4. I was wondering how much acid you would have to add for this to happen. I will just have to keep wondering for a little while longer, because this problem is long enough already. END OF EXAMINATION 9