Size the afterburner chamber and specify the flow rate for propane fuel (C_3H_8)

Question

Size the afterburner chamber and specify the flow rate for propane fuel (C_3H_8) required to control 5000 cfm of waste gases from a paint drying operation. The waste gases have an initial temperature of 300 degree F. Assume a design temperature of 1500 degree F and residence time of 0.5 sec for the combustion chamber. The air-to-fuel ratio (A/F) is 13:1 (mass ratio). Assume that none of the organic compounds in the waste stream contribute to the heat released in the combustion process. State all other assumptions. Data: MW_propane = 44.1 lb/lb middot mol R_air = 0.7302 atm middot ft^3/lb middot mol middot R P_PA = 1.0 atm Use New Hampshire OEP for propane data:

Explanation / Answer

Input to chamber = Propane fuel + Air

Output to chamber = Waste gases

Assuming waste gases follow ideal gas equation and they are released at atmospheric pressure

P = 1 atm, V= 5000 cfm x 0.5/60 min = 41.67 ft3 (Volume = Volumteric flow rate x time), T = 300oF

R = 0.7302/R = 0.7302/ 8.314 = 0.087

PV = nRT

1*41.67 = n* 0.7302*300/8.314

n=1.58 = no of moles of exhaust gases

Assuming No of moles of air = No of moles of exhaust gases released = 1.58

Total wieght of air = 1.58*29 = 45.82 lbs

Mass of propane fuel = 45.82/13 = 3.52 lbs (Mass ratio air : fuel = 13:1)

Moles of propane fuel = 0.08

Apply PV =nRT for propane fuel

T = 1500oF V = Volumetric flow rate*0.5/60 P= 1 atm (assumption)

1XVx0.5/60 = 0.08*0.7302/8.314*1500

Flow rate of propane fuel = 1264.7 cfm

Apply PV = nRT for air

n = 1.58, P = 1 atm, T = 1500

1*V*0.5/60 = 1.58*0.7302/8.314*1500

Flow rate of air = 24,978 cfm

Total flow rate = flow rate of air + flow rate of propane = 26242.9 cfm

Capacity of chamber = 26242.9*0.5/60 = 218.7 ft3

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