CHEMICAL REACTION ENGINEERING (CHEG-511) PROJECT
QUESTION:The following E(t) curve was obtained from a tracer
test on a tubular reactor in which dispersion is believed to
occur.
Part 1Part 2
with kCA0 = 2 min-IA second-order reaction is to be carried out
in this reactor. There is no dispersion occurring either upstream
or downstream of the reactor, but there is dispersion inside the
reactor. Find the quantities asked below.(a) What is the mean
residence time tm?(b) What is the variance?(c) What conversions do
you expect from an ideal PFR and an ideal CSTR in a real reactor
with tm?(d) What is the conversion predicted by (1) the segregation
model? (2) the maximum Mixedness model?(e) What conversion is
predicted by an ideal laminar flow reactor?
ANSWER:Part 1:a) Here we have E(t) vs t as below
We have
This implies that t1=5 min.Now the function E (t) can be
represented as below
Now to find tm, we have
Substituting E (t), we have
This implies,
b) To find the variance consider the function
Equation for variance could be written as
1
Plug E(t) in the above equation we get
Hence variance was found to be
c) We are given a second order reaction:
With
Case for Ideal CSTR:
The design equation for a CSTR is:
; []
On simplifying; ; []
Substituting mins and in the above equation we get
Case for Ideal PFR:The design equation for a PFR is:
[]
On integrating we get:
Substituting mins and in the above equation we get
c) For Segregation Model,
We have the equation
As we know the function X and E(t), we use Polymath to obtain
results.
And
The polymath solution is:
Calculated values of DEQ variables VariableInitial valueMinimal
valueMaximal valueFinal value
1 E 0 0 0.1997902 0
2 E1 0 0 0.4 0.4
3 E2 0.4 0 0.4 0
4 k1 0.2 0.2 0.2 0.2
5 t 0 0 10. 10.
6 t1 10. 10. 10. 10.
7 tav 5. 5. 5. 5.
8 X 0 0 0.6666667 0.6666667
9 xbar 0 0 0.4767522 0.4767522
Differential equations 1 d(xbar)/d(t) = X*E
Explicit equations 1 tav = 5
2 k1 = 0.2
3 t1 = 2*tav
4 X = k1*t/(1+k1*t)
5 E1 = t/tav^2
6 E2 = -(t-t1)/tav^2
7 E = if(t
