a) A first order irreversible reaction A rightarrow B is carried out in a series
ID: 530154 • Letter: A
Question
a) A first order irreversible reaction A rightarrow B is carried out in a series of a number (N) of equal volume Continuous Stirred Tank Reactors (CSTRs) whose total volume is V_R. By writing the material balances across each CSTR in the series, develop an equation for the overall conversion as a function of N. Use symbols for volumetric flow rate (V dot) and kinetic constant (k_l) rather than replacing them with numbers. b) Apply this equation to calculate the overall conversion for N = 1, N = 2, N = 5, N = 20, and N = 100 when total volume, the volumetric flow rate and the kinetic constant are: V_R = 3.31 m^3 V dot = 4 m^3 h^-1 and k_l = 6.85 h^-1, respectively. c) Plot the above conversion results against N. Comment on your results.Explanation / Answer
For a 1st order reaction carried out in a CFSTR, under steady state
Rate of mass in =Rate of mass out + Rate of loss due to chemical reaction
FAO= FAO*(1-XA)+ KCAV, V= Volume of reactor, K= rate constant and FAO= molar flow rate of A.
FAOXA= KCAV, CA=CAO*(1-XA)
FAOXA= KCAO*(1-XA)*V
VCAO/FAo= T =V/VO, V= volume of reactor and Vo= volumetric flow rate
XA= KT*(1-XA)
KT= XA/(1-XA), K* V1/VO= XA/(1-XA)
For 1st reactor of volume V
KV1/VO= (CO-C1)/C1, C1= concentration at the end of 1st reactor
KV1/VO= CO/C1-1
C1= CO/ (1+KV1/VO)
Since all the reactors are of equal volume, for the 2nd reactor
C2= C1/(1+KT) = CO/ (1+KT)2,
For N reactors in series, CN= CO/(1+KT)n,
The space time for N reactors become TN= N*T=(N/K)*(CO/CN)1/N-1)
TN= VR/Vo, VR= volume of all reactors put together
CN= CO*(1-X)
Or CO/CN= 1/(1-X) where X= conversion
TN= VR/Vo= (N/K){ 1/(1-X) 1/N-1}
(VR/VO)*(K/N)+1= 1/(1-X)1/N ,
(1-X)1/N= 1/ (1+( VR/VO)*(K/N)
(1-X ) = {1/(1+(VR/VO)*K/N)}N
The calculations for N=1, N=2 and N=5, N=20 and N=100 are done in excel and shown in the following table.
As the no of reactors increases, the conversion reaches a constant value and as n becomes infinity, N CSTRs in series will be equal to one plug flow reactor.
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