final_exam_2007 - Fall 2007 Final Examination Wed Dec 12...

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Unformatted text preview: Fall 2007 Final Examination Wed., Dec. 12, 2007 ENV 6002: Physical and Chemical Principles of Environmental Engineering University of South Florida Civil & Environmental Eng. J. A. Cunningham Instructions: 1. 10. 11. You may read the instructions on pages 1—3, but do not begin working on the problems until instructed to do so. Answer all questions in the exam booklet provided, and write your name conspicuously on the exam booklet. You are allowed two sheets of 8.5-by-11-inch paper (or A4 paper) with hand-written notes. You may write on both sides of those papers. However, mechanical reproductions (photocopying, laser printing, scanning, etc.) are not allowed; all notes must be hand— written. A calculator is recommended, but it may not be pre-programmed with formulae from the class. 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. Show all work and state all assumptions in order to receive maximum credit for your work. Make sure your answers include units if appropriate. Watch your units.’.’ This exam contains 3 questions, all with multiple parts. The total point value for the exam is 120 points -- one point per minute. Gauge your time accordingly! Use a reasonable number of significant digits when reporting your answers. You are likely to be graded down if you report an excessive number of significant digits. In some cases, the problem may indicate the precision to which you should report your answer. Don't cheat. Cheating will result in appropriate disciplinary action according to university policy. Pages 2 and 3 of this exam contain data, constants, and conversion factors that might be helpful to you as you complete the exam. 1/8 Potentially useful constants: Ideal gas constant, R: 8.314 Pa-m3-mol'1-K'1 = 82.06X10'6 atm-m3-mol'1-K'l Molecular weight of water, H20: 18.01 g/mole Density of water at 20°C: 0.998 g/mL Aqueous diffusivity of oxygen at 20°C, DozL: 2.0X10'9 mz/sec Henry’s constant for oxygen at 20°C, HCC: 30 Atomic Weights: C = 12.011 C1 = 35.453 H = 1.0079 N = 14.007 0 = 15.999 Potentially useful formulae: Volume of a sphere (radius r) = (4/3) 11 r3 Surface area of a sphere (radius r) = 4 TE r2 Specific surface area of a sphere (radius r) = 3/r Potentially useful conversion factors: Pressure: 1 atm = 760 mm Hg = 760 torr = 101325 Pa Mass: 1kg = 1000 g =1XlO6 mg Temperature: 25 °C = 298.15 K Volume: 1 m3 =1000 L 21x106 mL =1x106 cm3 2/8 The chemical tetrachloroethene (C2C14) is also called perchloroethene, or PCE. PCE is a solvent and it is a very common environmental contaminant. Often, PCE is found with another contaminant called 1,4-dioxane. Dioxane is a solvent stabilizer, so it is often added to PCB, and the two contaminants are therefore found together in many contaminated environments. Below is a table of the physical/chemical properties of these two contaminants at 22 OC: PCE 1,4-Dioxane Atomic formula C2 C14 C4 H3 02 Molecular weight (g/mol) 165.8 88.1 Liquid density, p (g/cm3) 1.4 1.02 Aqueous solubility, CSL (g/L) 0.15 Octanol-water coefficient, KOW 400 0.54 Vapor pressure, Psat (Pa) 1900 3600 Henry’s Constant, Hcc 2.0><1041 Aqueous diffusivity, D (mZ/sec) 0.73><10_9 1.1X10’9 An interesting thing about PCE is that it is does not undergo biodegradation under aerobic conditions. Imagine that a local doctoral student named Stuart Dent (called Stu by his friends) wanted to write his doctoral dissertation on the aerobic biodegradation of PCB. His advisor, Dr Pia Aichdee, told him that it is not a good dissertation topic, because PCE does not biodegrade under aerobic conditions. Stu is a bit stubborn and he did not listen to his advisor. To help Stu, in this exam you will answer questions about the behavior of PCB and dioxane in the environment. 3/8 Page 4 is left blank intentionally 4/8 (40 pts) Stu found out that PCB and dioxane were spilled into a river. The river is 0.5 m deep (on average) and flows with an average velocity of 0.3 m/sec. You can assume that the temperature in the river is about 22 °C. Where the PCB and dioxane were spilled, the concentration of each was about 15 mg/L in the river. About 10 km downstream, the concentration of 1,4-dioxane was still close to 15 mg/L, but the concentration of PCB was found to be less that 4 mg/L. Stu inferred from this information that PCE must have degraded aerobically during its travel down the river. However, Dr Aichdee did not agree with Stu’s conclusion. a. (5 pts) Why did Dr Aichdee not agree with Stu that the PCB had degraded? What other explanation could there be for the decrease in PCE concentration from 15 mg/L to less than 4 mg/L during this stretch of the river? b. (25 pts) Demonstrate mathematically that your answer to part (a) is consistent with the observed decrease in PCE concentration. In other words, find the concentration that you would expect to measure 10 km downstream of the spill, and verify that it is a little less than 4 mg/L. State any assumptions that you make as you proceed. c. (10 pts) How do you explain that the PCB concentration decreased by about 75%, but the concentration of dioxane barely decreased at all? Explain in terms of the relevant chemical properties, physical processes, and/or environmental characteristics. 5/8 (40 pts) Stu decided not to give up easily. He knew that soil contains bacteria capable of degrading many different types of contaminants. He thought maybe some soil from his back yard would contain bacteria capable of aerobically biodegrading PCE. He dug up some soil and sent it to a lab for analysis; it has a bulk density of pa = 1.8 g/cm3, it has a fraction of organic carbon foc = 2.0%, and many different species of bacteria are present. Stu got a 100 mL vial and he added 36 g (equivalent to 20 cm3) of the soil to the vial. He hoped that would contain enough bacteria to degrade the PCB. Then he added 60 mL of water, which was contaminated with both PCB and dioxane at concentrations of 3.0 mg/L. He left 20 mL of air in the vial to provide oxygen to the aerobic bacteria. Then he sealed the vial and left it alone for 5 days, in the hopes that the bacteria would aerobically degrade the PCB. At the end of 5 days, Stu measured the concentration of dioxane in the water and found that it was still very close to its initial concentration of 3.0 mg/L. However, the concentration of PCB in the water had decreased from 3.0 mg/L down to about 0.7 mg/L. Stu was delighted! He concluded that the PCB must have been biodegraded aerobically by the bacteria in the soil. However, Dr Aichdee did not agree with Stu’s conclusion. a. (5 pts) Why did Dr Aichdee not agree with Stu that the PCB had degraded? What other explanation could there be for the decrease in PCE concentration from 3.0 mg/L to 0.7 mg/L during this five-day span? b. (25 pts) Demonstrate mathematically that your answer to part (a) is consistent with the observed decrease in PCE concentration. In other words, find the concentration that you would expect to measure in the vial after 5 days, and verify that it is about 0.7 mg/L. State any assumptions that you make as you proceed. c. (10 pts) How do you explain that the PCB concentration decreased by about 75%, but the concentration of dioxane barely decreased at all? Explain in terms of the relevant chemical properties, physical processes, and/or environmental characteristics. 6/8 (40 pts) This question does NOT deal with PCE or 1,4-dioxane. Instead, imagine that you have to treat an industrial wastewater stream that contains some biodegradable contaminant. The concentration of the contaminant in the stream, expressed as oxygen demand, is L0. You build a completely-mixed flow reactor (CMFR) with volume V to treat the waste stream. The waste stream flows through the reactor with volumetric flow rate Q. The contaminant degrades in the reactor with first-order kinetics, and the first-order biodegradation rate constant is k1. The system is operated at steady state. The questions below will help you design the reactor to meet the engineering requirements. a. (5 pts) Based on the information above, what will be the concentration of waste, L, that exits the reactor? Note that L is the waste concentration expressed as oxygen demand. You should give an equation for L in terms of the other parameters of the problem, i.e., in terms of L0, V, Q, and k1. State any assumptions that you make as you proceed. Hint: the necessary formula was given in class, so it is possible to get this answer without any derivation; but if you don’t remember it, you should be able to derive it with an appropriate material balance. (3 pts) Suppose that the reactor volume is 500 m3, and the volumetric flow rate of the waste stream is 4><106 L/day (about equal to 1 million gallons per day). Find the average hydraulic residence time, in units of hours. (4 pts) Assume the same conditions as in part (b), and further suppose that L0 = 100 mg/L. The contaminant has Monod kinetic parameters kmx = 2.4 mg contaminant/(mg cells-hr) and K3 = 4.0 mg/L. What concentration of bacteria, X, must be present in the reactor if we require that the exit concentration L is no greater than 10 mg/L? (Hint: you need your answer from part (a) to answer this question.) Problem 3 continues 9 7/8 3. continued d. (10 pts) Now think about what happens to oxygen in this CMFR. Suppose the influent waste stream is saturated with respect to oxygen (i.e., the oxygen concentration in the influent stream is equal to C”). Also suppose that oxygen enters the reactor by mass transfer from the atmosphere, with overall mass transfer coefficient KL; the interfacial area between the reactor and the atmosphere is A. Consider the material balance for oxygen in the reactor: Accumulation = Flow in — Flow out + Sources — Sinks Write the appropriate mathematical expressions for each of the five terms in this material balance equation. State any assumptions that you deem necessary. (5 pts) Solve the equation that you wrote in part ((1) for the oxygen concentration in the reactor, C02. You should give an equation for C02 in terms of the other parameters of the problem, i.e., in terms ofLO, L, V, Q, k], C”, KL, and A. (8 pts) Identify the Stanton number and the Damkohler number in your answer from part (e). According to your equation, what happens to the oxygen concentration if St >> Da? What happens to the oxygen concentration if St << Da? Explain briefly (a few sentences) in terms of the relevant processes and the information that St and Da give you. (5 pts) Assume the same conditions as in parts (b) and (0), above. Also assume that the interfacial area A = 100 m2, and that the saturation oxygen concentration C” = 9.3 mg/L. How big must KL be in order to ensure that the concentration of oxygen in the reactor is at least 2 mg/L? (In practice, this number would then tell you something about how vigorously you have to mix the reactor to achieve your goal, but we won’t take the analysis that far in this examination.) END OF EXAMINATION 8/8 ...
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This note was uploaded on 06/12/2011 for the course ENV 6002 taught by Professor Staff during the Fall '08 term at University of South Florida.

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final_exam_2007 - Fall 2007 Final Examination Wed Dec 12...

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