Workshop 02: Conversion and reactor sizing

Lecture notes for chemical reaction engineering

Try following problems from Fogler 5e(Fogler 2016).

P2-3, P2-4, P2-7, P2-10.

We will go through some of these problems in the workshop.

Specimen code

A collab notebook that contains specimen code can be obtained by clicking on link below.

Workshop 02 Levenspeil Plots and Reactor sizing - Help

Note

Solutions to these problems are uploaded at Workshop 2 solutions

1. P2-3: You have two CSTRs and two PFRs, each with a volume of $1.6 m^3$ . Use Figure 1 to calculate the conversion for each of the reactors in the following arrangements.

1. Two CSTRs in series.

2. Two PFRs in series.

3. Two CSTRs in parallel with the feed, $F_{A0}$, divided equally between the two reactors.

4. Two PFRs in parallel with the feed divided equally between the two reactors.

5. A CSTR and a PFR in parallel with the flow equally divided. Calculate the overall conversion, $X_{ov}$

   $$X_{ov} = \frac{F_{A0}-F_{A,CSTR} - F_{A,PFR}}{F_{A0}}$$

   with

   $$F_{A,CSTR} = \frac{F_{A0}}{2} - \frac{F_{A0}}{2} X_{CSTR}$$

   and

   $$F_{A,PFR} = \frac{F_{A0}}{2} (1 - X_{PFR})$$

6. A PFR followed by a CSTR.

7. A CSTR followed by a PFR.

8. A PFR followed by two CSTRs. Is this arrangement a good arrangement or is there a better one?

The data from Figure 1 is provided in file workshop-02-problem-1-data.csv

Figure 1: Figure-2-2b

2. P2-4: The exothermic reaction of stillbene (A) to form the economically important trospophene (B) and methane (C), i.e.,

   $$\ce{A -> B + C}$$

   was carried out adiabatically and the following data recorded:

Table 1: Problem 2.4 rate data

X	$r_A (mol/dm^3 min)$
0	1
0.2	1.67
0.4	5
0.45	5
0.5	5
0.6	5
0.8	1.25
0.9	0.91

The entering molar flow rate of A was $300 mol/min$.

1. What are the PFR and CSTR volumes necessary to achieve 40% conversion?
2. Over what range of conversions would the CSTR and PFR reactor volumes be identical?
3. What is the maximum conversion that can be achieved in a $105 dm^3$ CSTR?
4. What conversion can be achieved if a $72 dm^3$ PFR is followed in series by a $24 dm^3$ CSTR?
5. What conversion can be achieved if a $24 dm^3$ CSTR is followed in a series by a $72 dm^3$ PFR?
6. Plot the conversion and rate of reaction as a function of PFR reactor volume up to a volume of $100 dm^3$.

The data from Table 1 is provided in file workshop-02-problem-2.csv

3. P2-7: The adiabatic exothermic irreversible gas-phase reaction

   $$\ce{2A + B -> 2C}$$

   is to be carried out in a flow reactor for an equimolar feed of A and B. A Levenspiel plot for this reaction is shown in Figure 2 .

   1. What PFR volume is necessary to achieve 50% conversion?
   2. What CSTR volume is necessary to achieve 50% conversion?
   3. What is the volume of a second CSTR added in series to the first CSTR (Part b) necessary to achieve an overall conversion of 80%?
   4. What PFR volume must be added to the first CSTR (Part b) to raise the conversion to 80%?
   5. What conversion can be achieved in a $6 \times 10^4 m^3$ CSTR? In a $6 \times 10^4 m^3$ PFR?
   6. Think critically to critique the answers (numbers) to this problem.

Figure 2: fig-p2-7b

4. P2.10: The curve shown in Figure 3 is typical of a gas-solid catalytic exothermic reaction carried out adiabatically.

   1. Assuming that you have a fluidized CSTR and a PBR containing equal weights of catalyst, how should they be arranged for this adiabatic reaction? Use the smallest amount of catalyst weight to achieve 80% conversion of A.
   2. What is the catalyst weight necessary to achieve 80% conversion in a fluidized CSTR?
   3. What fluidized CSTR weight is necessary to achieve 40% conversion?
   4. What PBR weight is necessary to achieve 80% conversion?
   5. What PBR weight is necessary to achieve 40% conversion?
   6. Plot the rate of reaction and conversion as a function of PBR catalyst weight, W.

   Additional information: FA0 = 2 mol/s.

Figure 3: Figure P2-10b

The data from Figure 3 is provided in file workshop-02-problem-4.csv

References

Fogler, H. Scott. 2016. Elements of Chemical Reaction Engineering. Fifth edition. Boston: Prentice Hall.