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Solutions%20to%20Homework#2

Solutions%20to%20Homework#2 - Assignment Solution 2...

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Assignment Solution 2 Chemical Engineering 2800 (Summer 2008) Fundamentals of Process Engineering University of Utah Dr.Mataz Alcoutlabi Problem 1 8.8, p.220 A gas containing 80% CH4 and 20% He is sent through a quartz diffusion tube (see Figure P8.8) to recover the helium. Twenty percent by weight of the original gas is recovered, and its composition is 50% He. Calculate the composition of the waste gas if 100 kg moles of gas are processed per minute. Solution Recovery of He from natural gas. F W P yCH 4 = 0.80 yHe = 0.20 F = 100 kgmol/min yCH4 = ? yHe = ? yHe = 0.50 Product gas is 20% by weight of feed gas Basis: 1 min Calculate and feed rate in kg ( 29 ( 29 kgmol kg MW y MW y MW CH CH He He 63 . 13 044 . 16 8 . 0 00 . 4 2 . 0 4 4 = + = + = ( 29 ( 29 ( 29 kg kgmol kg kgmol MW kgmol F kg F F 1363 63 . 13 100 = = = Calculate product rate in kgmol ( 29 ( 29 kg kg kg P 7 . 272 1363 2 . 0 = = ( 29 ( 29 kgmol kg MW y MW y MW CH CH He He 02 . 10 044 . 16 5 . 0 00 . 4 5 . 0 4 4 = + = + = ( 29 ( 29 kgmol kgmol kg kg MW kg P kgmol P P 21 . 27 / 02 . 10 7 . 272 = = =

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Overall mole balance F-P-W =0 or W = F-P Balance on He (moles) 0 F P W He He He Fy Py Wy - - = Solving for gives ( 29 ( 29 100 0.2 27.21 0.5 100 27.21 F P W He He He Fy Py y F P - - = = - - 4 0.08786 1 0.9121 W He W W CH He y y y = = - = Problem 2 8.11, p.221 Your boss asks you to calculate the flow through a natural-gas pipeline. Since it is 26 in. in diameter. It is impossible to run the gas through any kind of meter or measuring device. You decide to add 100 lb of CO2 per minute to the gas through a small 1/2 –in. piece of pipe, collect samples of the gas samples of the gas down stream, and analyze them for CO2. Several consecutive samples after 1 hr are time %CO2 1 hr, 0 min 2.0 10 min 2.2 20 min 1.9 30 min 2.1 40 min 2.0 Upstream Downstream U=? D C CO 2 injection, 100 lb/ min a) Calculate the flow of gas in pounds per minute at the point of injection. (the natural gas is all methane, CH 4 ) Solution Assume 2 0 U CO y = with 4 1.00 U CH y = Basis: 1 min
Calculate C in kgmol/min 2 100 1 100 1.031 min 2.2046 min 44 min kg kgmol kgmolCO lb C kg = = = g Calculate average 2 0.0204 D CO y = Balance on CO2 to give D 2 0 D CO C Dy - = or 2 1.031 50.53 0.0204 min D CO C kgmol D y = = = Overall balance to get U U C D + = or 50.53 1.03 49.50 min kgmol U D C = - = - = or 2.2046 49.50 16.04 1751 min 1 min kgmol kg lb lb U kgmol kg = = b) Unfortunately for you, the gas upstream of the point of injection of CO2 already contained 1.0 percent CO2. How much was your original flow estimate in error (in percent)?

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Solutions%20to%20Homework#2 - Assignment Solution 2...

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