## Self Assessment Quiz

**Q8.1. **A sample of tracer was injected as pulse to a reactor and the effluent concentration measured as a function of time. The results are

T (min) |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
14 |

C (g/cum) |
0 |
1 |
5 |
8 |
10 |
8 |
6 |
4 |
3 |
2.2 |
1.5 |
0.6 |
0 |

a. Construct C and E curves

b. Calculate the mean and variance of the distribution

**Q8.2**. Determine the RTD function for a sequence of stirred tanks.

**Q8.3**. Derive the RTD function for a laminar flow reactor.

**Q8.4**. A first order reaction is carried out in a CSTR/PFR sequence. What is conversion attainable for different arrangements ?

Rate constant k = 1.0/min C_{AO} = 1 kmol/cum and residence time = 5.0 min.

**Q8.5**. A second order reaction with rate constant K, C_{Ao} = 1.0/min is carried out in a CSTR – PFR sequence . If the residence time is 5 min what conversion is attainable for difference arrangements ? Feed concentration 1.0 kmol/cum.

**Q8.6**. Consider the real vessel of problem 8.1. The mean and the variance of the distribution are 5.15 min and 6.1 min^{2}. A first order chemical reaction (k = 0.1/min) is carried out in the vessel. Determine conversion expected.

(a) Using tanks in series model

(b) Using maximum mixedness model.

**Q8.7.** A pulse test on a piece of reaction equipment gave the following the results. The output concentration rose linearly from 0 to 0.5 mol/lit in 5 min and then fell linearly to zero in 10 min.

(a) Calculate the E and F functions .

(b) What is the mean residence time, if volume flow is 680 lit/min?

(c) What is the reactor volume ?

**Q 8.8 **A second order reaction of rate constant kC_{A0} = 1.2/min is carried out in the above vessel of problem 7.

(a) Estimate to conversion if plug flow had prevailed
(X = 0.889)

(b) Estimate conversion if the vessel can be described as a CSTR
(X = 0.70)

(c) What is conversion if the flow is completely segregated
(X = 0.86) ?

(d) How many CSTRs are needed to model the reactor by tanks in series model and what is the conversion expected ?

**Q8.9.** A batch reactor has been found to perform unsatisfactorily. It was then suggested that the reactor has two well mixed regions with fluid circulating between them. The volume of these two regions were estimated as 900 lit and 300 lit when a tracer (50g) is introduced into region I. What would be the tracer concentration in tank 1 after 100s ?

**Q8.10. Residence Time Distribution:**

The pulse response of an arbitrary vessel increases linearly from 0 to 20 mg/L in 5 mins and drops to zero linearly in 5 mins.

**Q8.10.1.** Determine the E, F and I functions.

Q8.10.2. What is the mean and variance of the E curve ?

8.10.3. It is a first order reaction A→B with K = 0.5/min takes place in the vessel, what is conversion expected on the basis of completely segregated model ?

Q8.10.4. If a first order reaction A→B with K = 0.5/min takes place in the vessel, what is conversion expected on the basis of tanks in series model ?

Q8.10.5. If a first order reaction A→B with K = 0.5/min takes place in the vessel, what is conversion expected on the basis of dispersion model ?

Q8.10.6. Explain the meaning of complete micro-mixing and complete segregation.

Give an example from real life (not from reaction engineering) to illustrate and explain the meaning.

**Q8.11**. Understanding Non-ideal vessels

The response of a biofilter to a tracer test is given as.

T (min) |
1 |
2 |
4 |
6 |
8 |
9 |
10 |

C (mg/L) |
19 |
16 |
13 |
9 |
5 |
1 |
0 |

**Q8.11.1.** Find the E function and hence determine the mean and variance of the distribution.

Q8.11.2. Estimate the conversion expected on the basis of complete segregation model, if a first order reaction with k = 0.2/min is carried out in this vessel.

Q8.11.3. Estimate the conversion expected on the basis of tanks in series model, if a first order reaction with K = 0.2/min is carried out in this vessel.

Q8.11.4. Estimate the conversion expected on the basis of dispersion model, if a first order reaction with k = 0.2/min is carried out in the vessel.

Q8.11.5. In scale-up, trouble shooting, and/or operation of process equipments do you see sope where such models apply.

**Q8.12**. Pure water is flowing through sequence of CSTR followed by PFR (scheme A). The feed is suddenly changed to another tank containing a coloured dye solution of known concentration call it scheme (B). Using results in scheme A, write down the results for scheme B. Determine the E function for case A and case B.

**Q8.13.** It is observed from the experiments in an arbitrary vessel that conversion obtained is 0.88 for a residence of τ = 10 min for a first order reaction A→B with rate constant 0.3/min.

It is proposed to model this vessel using recycle reactor model with R as parameter, tanks in series model with N the number of tanks as parameter and dispersion model with Peclet number as parameter.

Q8.13.1. (A) Determine the value of R, N, Pe for the data given and

(B) comment on the usefulness of these models for design and operation of commercial reacting equipment.

**Q8.14.** (*) Give two example from real life or industry to illustrate and explain the meaning of

(A) complete micro mixing

(B) complete segregation and

(C) the implications of these terms for process and process operation.

**Q8.15. RTD Models**

Consider a system of two CSTR of equal volume exchanging fluid. A pulse of tracer is introduced into tank 1.

Q8.15.1. Set up the balance equations. What is the way of determining the E functions for each of the two tank system.

Q8.15.2. What is the way of determining the internal age distribution functions for the two tanks.