ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING. University of South Florida Civil & Environmental Eng.

Transcription

1 ENV 4001: ENVIRONMENTAL SYSTEMS ENGINEERING Fall 2016 Quiz #1 Wednesday, September 28 University of South Florida Civil & Environmental Eng. Prof. J.A. Cunningham Instructions: 1. You may read these instructions, but do not turn the page or begin working until instructed. 2. This quiz contains three questions. Answer any two. 3. If, for some reason, you attempt all three questions, please indicate clearly which two I should grade. If it is not clear, then I will choose which questions I feel like grading. 4. Some questions might have multiple parts. In those cases, the point value of each part is indicated. The total number of points possible is Unit conversion factors and other potentially useful information is provided on the back of this page. 6. Answer each question in the space provided. If you need more space, you can attach additional pages as needed, but make sure to put your name on them. 7. Show your work and state any important assumptions you make. I cannot award partial credit if I can t follow what you did. 8. Report a reasonable number of significant digits in your answers. 9. Include units in your answers as appropriate. An answer without proper units is not correct! 10. You are allowed to use your text book, your course notes, or other printed materials. You may not receive help from another person. 11. A hand-held calculator is recommended. Other electronic devices are not permitted. 12. Time limit: 60 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. 13. Don t cheat. Cheating will result in appropriate disciplinary action according to university policy. More importantly, cheating indicates a lack of personal integrity. 14. Please print your name legibly in the space provided below, and turn in this quiz at the end of the period. 15. 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. Name: p 1/9

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 25 C: g/ml = 997 kg/m 3 Viscosity of water at 25 C: Pa sec Density of air at 25 C: 1.18 kg/m 3 Viscosity of air at 25 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 5 cm = 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 Al = g/mole K = g/mole Ca = g/mole Fe = g/mole Cu = g/mole p 2/9

3 This page is left blank intentionally. p 3/9

4 1. (30 pts) A water stream contains Chemical X,which is known to be hazardous. We have designed a completely mixed flow reactor (CMFR) to treat the stream, converting Chemical X into Chemical Z. The good news is that Chemical Z is known to be harmless. The bad news is that the conversion of Chemical X to Chemical Z proceeds through Chemical Y, which is the worst of all: X Y Z The volumetric flow rate of the stream is Q. The volume of the reactor is V. The conversion of Chemical X to Chemical Y is first-order with respect to the concentration of Chemical X, with first-order rate coefficient kx. The conversion of Chemical Y to Chemical Z is first-order with respect to the concentration of Chemical Y, with first-order rate coefficient k Y. The stream flowing into the reactor has a known concentration of Chemical X, C X influent. The stream flowing into the reactor does not contain any Chemical Y or Chemical Z. The system is operating at steady state. a. (5 pts) What is the concentration of Chemical X, C X, in the reactor? Hint: you can derive it with a material balance, but the solution is pretty much already in your notes, with maybe just some very minor modification. b. (15 pts) Derive an expression for the concentration of Chemical Y in the reactor s effluent stream. Show the steps of your derivation you will be graded on your procedure, not just the final equation that you derive. problem 1 continues p 4/9

5 1. continued b. more space to work on part b c. (10 pts) Suppose kx = 3.0 hr 1, k Y = 24 hr 1, and the influent concentration of Chemical X is 100 mg/l. We want to be sure that the effluent concentrations Chemical X is no greater than 10 mg/l, and the effluent concentration of Chemical Y is no greater than 1 mg/l. How much hydraulic residence time is required in the reactor? Hint #1: use your solutions from part a and part b. Hint #2: If you do not get an exact value, make a pretty close estimate, and that is probably good enough for today the algebra can get kind of ugly. p 5/9

6 2. (30 pts) Power plants that burn coal to generate electricity contribute to acid rain, because burning coal emits the gaseous chemical sulfur dioxide, SO2. We will learn more about that later this semester. When SO2 dissolves in rain droplets, it is converted to sulfurous acid (H2SO3) and then oxidized to sulfuric acid (H2SO4). We never got to oxidation chemistry this semester, so don t worry about H2SO4 we will only consider H2SO3. SO2 dissolves in water according to the following: SO2 (g) + H2O H2SO3 (aq) KH = 1.3 mol/(l atm) H2SO3 is a diprotic acid that dissociates as follows: H2SO3 <==> H + + HSO3 pka1 = 1.88 HSO3 <==> H+ + SO3 2 pka2 = 7.18 Now suppose we are wondering about the ph of the rain water in the vicinity of a particular power plant. Here is what we know. The concentration of SO2 in the air near the power plant is 50 µg/m 3. The air temperature is 15 C. The rain droplets contain a concentration of sulfite, SO3 2, equal to 5.3 µg/l. Estimate/calculate the ph of the rain droplets in the air near the power plant. (It actually would be worse if we considered H2SO4, because H2SO4 is a stronger acid than H2SO3, but don t worry about that for today.) Hint: you have five chemical species SO2 (g), H2SO3, HSO3, SO3 2, and H +. Therefore you need five equations, which have all been given to you in some form. problem 2 continues p 6/9

7 2. continued more space to work on problem 2 p 7/9

8 3. (30 pts) (Based on a problem from the book Environmental Engineering Science by Nazaroff and Alvarez-Cohen) Suppose we are growing bacteria in a batch reactor in the laboratory. The conditions are such that the bacteria are following exponential growth, with specific growth rate µ. For the purposes of this problem, ignore bacterial death or decay assume that the bacteria grow but do not die. It is not a great assumption, but it is OK for today. a. (7 pts) Define td to be the time required for the biomass concentration to double. Derive an expression for td in terms of the specific growth rate µ. b. (10 pts) Suppose that we know the bacteria follow Monod kinetics for their growth. In our experiment, the substrate concentration S is held constant in the reactor. We ran the experiment twice, with two different values of S. When S = 10 mg/l, the bacteria take 32 hr to double their biomass. When S = 100 mg/l, the bacteria take only 8 hr to double their biomass. Based on this, estimate/calculate the maximum specific growth rate coefficient (µmax) and the half-saturation constant (KS). Make sure to provide the proper units. problem 3 continues p 8/9

9 3. continued b. more space to work on part b c. (6 pts) What would be the minimum time in which the bacteria could double their biomass? What conditions would you provide to make this happen? d. (7 pts) If we conducted an experiment with a substrate concentration S = 30 mg/l, how long would it take for the bacteria to reach 10 times their initial biomass concentration? END OF QUIZ p 9/9