CEE ENVIRONMENTAL QUALITY ENGINEERING PROBLEM SET #5

Transcription

1 CEE ENVIRONMENTAL UALITY ENGINEERING PROBLEM SET #5 Problem 1. (adapted from Water uality by Tchobanoglous and Schroeder) A stream has a nearly uniform cross section, although it passes through a number of curves. The average width is 20 m and the average depth is 1.5 m. A slug of rhodamine dye tracer is added over an interval of 10 seconds to the stream when the flow rate is 30 m 3 /s and the tracer concentration is measured 2 km downstream. The slug of tracer is added in a manner that provides rapid lateral mixing and the measured initial concentration is 0.5 g/l (i.e., 500 g/m 3 ). The downstream results are shown below: Concentration of dye Time in seconds in river, g/m a) Using the above data, calculate the average residence time in the river. Compare this value to the theoretical value for reactor θ. Ans. θ from data = 2,130 sec. b) Plot a graph of the observed concentration vs. time for fluid in the stream. On the same graph, plot the concentration vs. time distributions that you would expect for an ideal completely-mixed flow reactor and for an ideal plug flow reactor, each having the same theoretical residence time as the real reactor tested (the ideal PFR response can be represented as a spike that goes off scale at the appropriate time). Note that your CSTR 1

2 model calculations should be based on a C o calculated with the assumption that the dye mass added was distributed over the entire river volume not just the first 300 m 3. c) Use the data for dye concentration vs. time to estimate the dispersion coefficient for the river. Use your value of the dispersion coefficient and the AFR model we developed in class to create a plot of what the model prediction of the dye concentration vs. time would be, and plot the real data on this same graph so that you can compare the model simulation to the actual behavior. Partial answer E = 262 m 2 /sec. Problem 2 [Adapted from Wastewater Engineering by Metcalf and Eddy] Bacterial removal in disinfection tanks can be modeled as a first order reaction where dx = kx, dt X = cell concentration, and k is a rate constant. Determine the number of completely mixed chlorine contact chambers each having an average hydraulic retention time of 30 min. that would be required in a series arrangement to reduce the bacterial count of a polluted water sample from 10 6 organisms/ml to 14.5 organisms/ml if the first-order rate constant for bacterial removal by the chlorine disinfectant is equal to 6.1/hour and each CSTR is operating at steady state. If a plug-flow chlorine contact chamber were used with the same detention time as the sum of the average detention times of the series of completely mixed chambers, what would the bacterial count be after treatment? Explain the difference in your answers. Partial ans.: you need 8 CSTRs in series. Problem 3. Consider the following body of water that is receiving a continuous input of BOD L. C p= 100 mg/l BODL p =.3 m 3 X /s L = 10 km r = 3.0 m 3 /s C r = 0 A = 100 m 2 upstream downstream It is desired to determine the concentration of BOD L at point X assuming steady-state conditions of flow and waste concentration. Assume that the BOD reaction rate constant (k 1 ) equals 0.23 day -1. Compute and compare the BOD L concentration at point X for each of the following cases: 2

3 a) Assume complete mixing in the body of water. Ans. L = 5.03 mg/l b) Assume plug flow (no longitudinal mixing). Ans. L = 4.06 mg/l c) Assume partial longitudinal mixing, with E = 200 m 2 /sec (estuarine-type mixing often results in such high dispersion coefficients). Ans. L = 2.92 mg/l d) For the last case above, what would be the pollutant concentration at a distance upstream equal to 100 m from the point of discharge? Assume the flow velocity of the stream is the same upstream from the discharge points as it is downstream. Ans. L = 5.17 mg/l Problem 4 (Adapted from Water uality by Tchobanoglous and Schroeder.) A series of salinity measurements has been made on a 5-km section of an estuary. The section can be considered a uniform cross section, and during the period of interest, the freshwater flow rate was 13 m 3 /s and the freshwater velocity was 0.13 m/s. Estimate the tidal dispersion coefficient from the data given below. Chloride concentration at the ocean end of the estuary is 18.2 kg/m 3. Samples were all taken at high water slack tide. Distance from mouth of estuary, km chloride conc., kg/m Ans. E = 252 m 2 /sec. Problem 5. (Adapted from Water uality by Tchobanoglous and Schroeder.) The river and tributary shown on the next page have flow rates of 4.0 m 3 /s and 0.5 m 3 /s respectively. Under the conditions given, the flow split at point A is 0.7 to AB and 0.3 to AC. Tracer studies have peen performed and the flow from A to B to C can be characterized as a PFR between A and B - followed by a CSTR at point B - followed by a PFR from B to C. The flow from A to C behaves as a single PFR. Volumes of these reactors are given below: Reactor Volume (m 3 ) PFR AB 15,000 BC 10,000 AC 30,000 CSTR 135,000 3

4 T (tributary) B R (river) A island Island C R + T Determine the concentration of reactant A at point C for the following conditions: steady state, first order decay rate for A =.5/day; C A of the tributary input = 50 g/m 3 and C A of the river at point A = 100 g/m 3. Ans g/m 3 Problem 6. A small, completely-mixed pond (volume = V) is fed by a single, clean stream (flow = ). Once every three days an industry discharges a slug of BOD L directly into this pond. If this frequency of BOD L inputs continues indefinitely, and the concentration of BOD L in the pond before each discharge (L 1 ) is routinely found to be 20 mg/l, what amount (in kg) of BOD L must be discharged? w Ans. W = 4.47 x 10 4 kg Assume k 1 = 0.25 day -1 = 8 x 10 7 L/d V = 10 8 liters slug amount =??? The expected form of the response for a CSTR with this type of loading is illustrated on the following page. 4

5 L This line indicates the trend in 2 the data, not the actual concentrations L 2 L 2 reactor effluent concentration L1 L1 L1 L1 Eventually, a pseudo "steady-state" is attained with 37 day-interval fluctuations between BOD concentration levels L 2 and L 1. Problem 7. Do STELLA Exercise #4. Please remember to turn it in separately (with a separate transmittal letter). time 5