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The elementary irreversible gas phase reaction A --> B + C is carried out in a PFR packed with catalyst. Pure A enters the reactor at a volumetric flowrate of 20 dm3 /s at a pressure of 10 atm and 450K. Consider that the heat is removed by a heat exchanger jacketing the reactor. The flowrate of coolant through the jacket is sufficiently high so that the ambient exchanger temperature is constant at 50oC.
CpA=40 J/mol.K HfA=-70 kJ/mol
CpB=25 J/mol.K HfB=-50 kJ/mol (TR=273 K)
CpC=15 J/mol.K HfC=-40 kJ/mol
k = 0.133 exp (E/R [ 1/450 ? 1/T ]) dm3 kg cat. s with E = 31.4 kJ/mol
U= 100 W/m2 .K
Dt=10 cm
pb=5 g/cm3
a) Plot the conversion and temperature down the plug flow reactor until 80% conversion is achieved. Discuss the effect of feed temperature on the temperature profile and conversion.
b) Calculate the amount of catalyst required to achieve 80% conversion
Please do not copy the previous solutions. This question is different
The given gas phase reaction
A --> B + C
volumetric flowrate v = 20 dm3 /s
pressure P0 = 10 atm
Temperature T0 = 450K
Design equation for catalytic PFR
dX/dW = - rA'/FA0
Rate constant
k = 0.133 exp ( E/R*[ 1/450 ? 1/T ] )
E = 31.4 kJ/mol x 1000J/kJ = 31400 J/mol
Heat of reaction = sum of heat of formation of products - sum of heat of formation of reactants
H rxn = HfC + HfB - HfA
= - 40 - 50 + 70
= - 20 kJ/mol
= - 20000 J/mol
Cp = CpC + CpB - CpA
= 15 + 25 - 40
= 0
Energy balance equation
From the polymath
For the differential and explicit equations
conversion (X) along with the plug flow reactor until 80%
Temperature (T) along with the plug flow reactor until 80%
Part b
T (at X = 0.8) = 450 + 500*0.8
T = 850 K
k = 0.133 exp ( 31400/8.314*[ 1/450 ? 1/850] )
k = 6.9 dm3 kg cat. s
amount of catalyst
W = FA0*X/(-rA')
= CA0*v*X/(kCA)
CA0 = P0/RT0 = 10 atm / 0.0821 dm3-atm/mol-K x 450 K
= 0.2707 mol/dm3
CA = CA0 ( 1 - X)T /(1+X)T0
= 0.2707 (1-0.8)*850/(1+0.8)*450
= 0.0568 mol/dm3
W = 0.2707*20*0.8/(6.9*0.0568)
= 39.42 Kg