Workshop 06: Multiple reactions

Lecture notes for chemical reaction engineering

Solutions

Solutions to these problems are uploaded at Workshop 6 solutions

Try following problems from Fogler 5e (Fogler 2016). P 8-3, P 8-4, P 8-7, P 8-9

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

P 8-3

The following reactions

$$\ce{A <=>[ k1 ] D} \qquad -r_{1A} = k_1 \left[ C_A - C_D/K_{1A}\right]$$

$$\ce{A <=>[ k2 ] U} \qquad -r_{2A} = k_2 \left[ C_A - C_U/K_{2A}\right]$$

take place in a batch reactor.

Additional information:

$k_1$ = 1.0 min^–1; $K_{1A}$= 10

$k_2$ = 100 min^–1; $K_{2A}$ = 1.5

$C_{A0}$ = 1 mol/dm³

1. Plot and analyze conversion and the concentrations of A, D, and U as a function of time. When would you stop the reaction to maximize the concentration of D? Describe what you find.

2. When does the maximum concentration of U occur? (Ans.: t = 0.04 min)

3. What are the equilibrium concentrations of A, D, and U?

4. What would be the exit concentrations from a CSTR with a space time of 1.0 min? Of 10.0 min? Of 100 min?

P 8-4

Consider the following system of gas-phase reactions:

$$\begin{aligned} \ce{A -> X} & \quad r_X = k_1 C_A^{1/2} & \quad k_1 &= 0.004 \ \left(mol/dm^3\right)^{1/2} \cdot min^{-1} \\ \ce{A -> B} & \quad r_B = k_2 C_A & \quad k_2 &= 0.3 \ min^{-1} \\ \ce{A -> Y} & \quad r_Y = k_3 C_A^{2} & \quad k_3 &= 0.25 \ dm^3/mol \cdot min^{-1} \\ \end{aligned}$$

B is the desired product, and X and Y are foul pollutants that are expensive to get rid of. The specific reaction rates are at 27 $^{\circ}$C. The reaction system is to be operated at 27 $^{\circ}$C and 4 atm. Pure A enters the system at a volumetric flow rate of 10 dm³/min.

1. Sketch the instantaneous selectivities $(S_{B/X}, S_{B/Y}, \text{and} \, S_{B/XY} = r_B /(r_X + r_Y))$ as a function of the concentration of C_A.

2. Consider a series of reactors. What should be the volume of the first reactor?

3. What are the effluent concentrations of A, B, X, and Y from the first reactor?

4. What is the conversion of A in the first reactor?

5. If 99% conversion of A is desired, what reaction scheme and reactor sizes should you use to maximize $S_{B/XY}$?

6. Suppose that E₁ = 20,000 cal/mol, E₂=10,000 cal/mol, and E₃=30,000 cal/mol. What temperature would you recommend for a single CSTR with a space time of 10 min and an entering concentration of A of 0.1 mol/dm³ ?

P 8-9

The elementary liquid-phase series reaction

$$\ce{A ->[ k1 ] B ->[ k2 ] C}$$

is carried out in a 500-dm³ batch reactor. The initial concentration of A is 1.6 mol/dm³. The desired product is B, and separation of the undesired product C is very difficult and costly. Because the reaction is carried out at a relatively high temperature, the reaction is easily quenched.

1. Plot and analyze the concentrations of A, B, and C as a function of time. Assume that each reaction is irreversible, with $k_1 = 0.4 \, h^{-1}$ and $k_2 = 0.01 \, h^{-1}$.

2. Plot and analyze the concentrations of A, B, and C as a function of time when the first reaction is reversible, with $k_{-1} = 0.3 \, h^{-1}$.

3. Plot and analyze the concentrations of A, B, and C as a function of time for the case where both reactions are reversible, with $k_{-2} = 0.005 \, h^{-1}$.

4. Compare (a), (b), and (c) and describe what you find.

5. Vary $k_1, k_2, k_{-1}, \text{and} \, k_{-2}$. Explain the consequence of $k_1 > 100$ and $k_2 < 0.1$ and with $k_{-1} = k_{-2} = 0$ and with $k_{-2}= 1, k_{-1} = 0$, and $k_{-2} = 0.25$.

References

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