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PROCESS DESIGN - EXAMPLE 21.1 : According to rules of thumb in chemical process design, consider the use of an expander for reducing the pressure of a gas when more than 20 horsepowers can be recovered. The theoretical adiabatic horsepower (THp) for expanding a gas could be estimated from the equation : THp = Q [ Ti / (8130a) ] [ 1 - (Po / Pi) ^ a ] where 3 ^ 3 is 3 power 3 or 27, Q is volumetric flowrate in standard cubic feet per minute, Ti is inlet temperature in degree Rankine, a = (k - 1) / k where k = Cp / Cv, Po and Pi are reference and systemic pressures respectively. (a) Assume Cp / Cv = 1.4, Po = 14.7 psia, (temperature in degree Rankine) = [ (temperature in degree Celsius) + 273.15 ] (9 / 5), nitrogen gas at Pi = 90 psia and 25 degree Celsius flowing at Q = 230 standard cubic feet per minute is to be vented to the atmosphere. According to rules of thumb, should an expander or a valve be used? (b) Find the outlet temperature To by using the equation To = Ti (Po / Pi) ^ a.
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Answer Posted / kangchuentat
PROCESS DESIGN - ANSWER 21.1 : (a) a = (k - 1) / k = (1.4 - 1) / 1.4 = 0.286. Ti = 25 degree Celsius to degree Rankine = (25 + 273.15) (9 / 5) = 536.67 degree Rankine. THp = Q [ Ti / (8130a) ] [ 1 - (Po / Pi) ^ a ] = 230 [ 536.67 / (8130 x 0.286) ] [ 1 - (14.7 / 90) ^ 0.286 ] = 21.469 horsepowers which is more than 20 horsepowers for expander to be used. (b) To = 536.67 (14.7 / 90) ^ 0.286 = 319.629 degree Rankine. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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