-1- ENVR 754 – AIR POLLUTION CONTROL HOMEWORK PROBLEMS SPRING, 2009 Introduction to the Course 1. Horsepower and Cost – Calculate the horsepower requirements, kw requirements, and annual cost for each of the following control devices: a. A cyclone that operates 8 hr/day, weekdays only, to collect wood dust from a furniture making operation. Gas flow is 1000 cfm; pressure drop is 4.5 inches w.g. b. A venturi scrubber that collects fume from a basic oxygen furnace that operates for 30 minutes out of each six hour batch, 330 days per year. Gas flow is 8000 cfm; pressure drop is 80 inches w.g. c. A furnace filter in your house that collects dust from the return air duct. Flow is 500 cfm; pressure drop is 0.3 inches w.g. The fan operates 20% of the time, on an yearly basis. d. A fabric filter at a power plant that collects fly ash. Flow is 9,500,000 cfm; pressure drop is 8 inches w.g. The plant operates 24 hours a day, 345 days per year. Note: This flow comes from the Roxboro Steam Electric Plant, near Roxboro NC, about 50 miles from Chapel Hill, operated by Progress Energy. e. Suppose that after taking this course, you devise a way to reduce pressure drop through each of the above devices by 20%. After graduation, you decide to become a consultant to advise on these matters. You promise your clients that they will be able to recover the cost of your fee within six months after taking the advice you give them. Assume for the moment that taking this advice requires no new equipment; that is, your advice can be implemented for free. For each of the four cases above, how much should you charge for your fee?-2- 2. Size Distributions – The following results were obtained from a Bahco analysis of fly ash, specific gravity 2.63. This device produces a cumulative size distribution by mass. Aerodynamic Diameter, Weight % Finer Than Micrometers 99.54 250 96.72 149 78.66 61 66.55 25.4 66.44 23.7 66.10 19.7 62.56 11.1 54.31 7.7 33.94 4.4 8.94 2.1 2.84 1.3 a. Plot the cumulative size distribution by mass for these data on log-probability paper. b. In 750 kg of fly ash, how much will lie between 10 and 50 µm in aerodynamic diameter? How much will be less than 10 µm in aerodynamic diameter? c. What is the mass median size? d. Plot a frequency distribution by mass for these data. e. Does this distribution fit any regular pattern? 3. Probe Design – On your first job after graduation, you are asked to determine the size distribution and concentration of particles in a horizontal duct with an inside diameter of 10 inches. This information will be used to specify a piece of gas cleaning equipment. Before taking the sample, you find out from the plant engineer that the average gas velocity in the duct should be 3200 feet per minute. You decide to sample isokinetically at the centerline of the duct into an Andersen cascade impactor that is designed to operate at 28.3 Lpm (1 cfm). Your probe must have a 90 degree bend as shown in the figure below. You orient the probe to be as vertical as possible to minimize collection by gravity in the probe and to lead directly into the top of the impactor. The particle-generating process is far enough upstream that you are confident that a sample taken at the centerline will be representative of the aerosol in the whole duct. Before going into the field to take the sample, you need to design a sampling probe to sample isokinetically from the duct center line.Part a: Review the article by Pui et al. and note the method to determine particle collection in a bend; alternatively, review the article by McFarland et al. Note that Peters reports an error in the coefficients of McFarland’s equation. All these articles are available on-line through the UNC library. Then specify the dimensions of your sampling probe, including inside diameter, straight length before the bend, radius of the bend, and straight length after the bend. As you do this, consider the problem of particle loss due to the bend of your sampling probe. Is it is possible to minimize collection in the bend of the probe by controlling the radius of curvature of the bend? Gas passing through a sharp bend with small radius of curvature would have a small residence time in the bend, which is good, but would also cause high radial acceleration which is bad. Use the equation you choose to determine whether the probe should have a sharp bend or a gradual, sweeping bend. Part b: For the probe you design, use your equation to plot the relationship between particle removal efficiency due to the bend in the probe against aerodynamic particle diameter. Sampling Set-up Sampling Probe Pui, D. Y. H., F. Romay-Novas, et al. (1987). "Experimental study of particle deposition in bends of circular cross section." Aerosol Sci. and Technol. 7: 301-315. McFarland, A. R., H. Gong, et al. (1997). "Aerosol deposition in bends with turbulent flow." Environ. Sci. Technol. 31: 3371-3377. Peters, Thomas and David Leith (2004). “Modeling large particle deposition in bends of exhaust ventilation systems”, Aerosol Sci. and Technol. 38: 1171-1177. -3--4- 4. Isokinetic Sampling – When you get to the plant to sample, you measure the actual gas velocity at the duct centerline and find that it is only 2830 fpm instead of the 3200 fpm expected. Instead of adjusting the sample flow, which you realize would change all the cut points for the impactor, you elect to sample at 28.3 Lpm as originally planned in the hope that the aerosol particles will all be small so that the non-isokinetic sampling that results will not cause undue bias in the sample. When you return to the lab, you obtain the following data from the impactor. Sample flow: 28.3 Lpm Probe inlet velocity: 3200 fpm Sample time: 50 minutes Duct velocity: 2830 fpm Data from Andersen Impactor Measurements Impactor Stage Aerodynamic Size Range, µm milligrams collected Pre-selector > 10 445.2 0 9.0 to 10.0 202.4 1 5.8 to 9.0 282.1 2 4.7 to 5.8 165.8 3 3.3 to 4.7 85.2 4 2.1 to 3.3 80.9 5 1.1 to 2.1 75.2 6 0.65 to 1.1 45.5 7 0.43 to 0.65 15.1 Filter < 0.43 10.0 Your co-worker, whose graduate work did not include a course like this one, tells you that correcting for the non-ideality in sampling is probably a waste of your time because nobody ever does it. Correct your data for non-isokinetic sampling and for the bend in