Chapter 13

Self Test 13.6: Batch, PFR, CSTR, and Segregation Models

The second order reaction

occurs in the liquid phase. The RTD function for the reactor in which it is to be carried out is given by

E(t) for 0 < t < 10

E(t) = 0.01 (t–10) for 10 < t < 20

E(t) = 0.01 (30–t) for 20 < t < 30

E(t) = 0 for t > 30

This RTD function is the same one we previously studied in these lectures. The entering concentration is 2 molar and the specific reaction rate is 0.06 dm3/mol•s.

(a) What is the conversion after 30 seconds in a batch reactor?

Solution

(b) What conversion would be achieved in a PFR with the same mean residence time?

Solution

(c) What conversion would be achieved in a CSTR with the same mean residence time?

Solution

(d) What is the conversion predicted by the segregation model?

Solution






















































(a) What is the conversion after 30 seconds in a batch reactor?

Batch reactor

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(b) What conversion would be achieved in a PFR with the same mean residence time? PFR:

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(c) What conversion would be achieved in a CSTR with the same mean residence time?

CSTR

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(d) What is the conversion predicted by the segregation model?

Segregation model

T

0

10

15

17.5

20

22.5

25

30

E(t)

0

0

.05

.075

.1

.075

.05

0

X(t)

0

.55

.643

.67

.706

.73

.75

.78

XE(t)

0

0

.032

.051

.071

.055

.038

0

Plotting the above data of XE(t) vs. t.

Summary

t = 30s XBatch = 0.78

t = 20s XPFR = 0.71

t = 20s XCSTR = 0.53

t = 20s XSeg = 0.7

Segregation Model Software Package Solution

Fit the RTD to one or more polynomials

E (t) = a0 + a1t + a2t2 + …

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