to main test pageWhen you regard the starting point 'kinetic
equation':
r = - dcA/dt = k*
CA*CB
you realize that with CB,0 = 0
the reaction will never start. This means that in this case the reaction rate
is and remains equal to zero, no production will take place. When you admit
small amounts of B at the beginning, the reaction rate will mount till it
reaches a maximum. You can show that by substituting CB with
(CA,0 - CA) : when you plot the graph r versus
CA, you get a parabolic curve (see graph). You can see that the maximum
rate is found at CA = CA,0/2 (finding maximum by
differentiating) : at 50% conversion you have a maximum production (reaction)
rate. On the other side, when you regard the function 1/r(U) you see that at
zero conversion with zero reaction rate the function 1/r gets infinite and will
drop down from infinite to a minimum at 50% conversion !! As you know, the area
under the function is a measure for the space time in the not-back-mixed
reactor types STR and TFR. When starting with CB,0 = 0 the space
time gets infinite. With mounting concentrations of CB,0 you start
the integration a bit later and get a minor area (space time). This can be
shown in two simulation snapshots where CB,0 is 0.01 and 0.1 mol/l .
The reaction time till you reach a remarkable conversion gets shorter for
higher initial concentrations. Once again: we see that STR and TFR are not good
for the 'initial reaction phase', compound B has to be 'added'. What about the
totally back-mixed CSTR ? Let us take an extreme situation at once: take 50%
conversion: here we have a stationary concentration of 50% B in the whole
vessel - and a maximum reaction rate (the space-time rightangle area lies
beneath the area 'under the function 1/r (see graph)'!!)
At conversions over 50%
the 1/r - function mounts steadily as usual, - therefore the CSTR gets more and
more 'worse' here and you will be well advised to take a serial combination
with a following (after 50% conversion) TFR or at least Cascade. A further
possibility is to take a loop reactor with an adapted recirculation
factor.
Let us 'derive' the logistic equation now !
r = -
dcA/dt = k* CA*CB
CB =
CB,0 +(CA,0 - CA)
- dcA/dt =
k *CA (CA,0 - CA +
CB,0)
dCA = CA*CA,0*k*dt -
CA2*k*dt +
CA*CB,0*k*dt
CA,j+1 = CA,j -
CA,j*CA,0*k*dt + CA,j2*k*dt -
----------------------------------------CA,j*CB,0*k*dt
CA,j+1
= CA,j(1 - CA,0*k*dt + CA,j*k*dt -
CB,0*k*dt)
You can write this in unisim as:
X =
Xv(1-n*X0*dt + n*Xv*dt - n*m*dt)
where n = k = reaction rate, m =
CB,0 and X0 = CA,0
now the simulation for the
batch should run !!
and now: reaction running in a CSTR
or do you want to try the direct link to the loop reactor ?
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