Chapter 2, Problem 2.1P

(a)

Interpretation Introduction

Interpretation:

The method by which the answers from examples 2-1 through 2-3 get changed if the flow rate $F_{\text{A0}}$ were cut in half and were get doubled is to be stated. The conversion that is achieved in a $4.5{\text{m}}^3$ PFR and in a $4.5{\text{m}}^3$ CSTR is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

If a fluidized CSTR and a PBR contains equal weights of catalyst for the given adiabatic reaction and very small amount of catalyst is required for the $80\%$ conversion then this can be done by joining first CSTR with PBR in series. The graph that is obtained after this connection is shown as,

Figure 1

In the above shown graph, the purple and rectangular area indicates the CSTR and the green area under the curve indicates the PBR.

(b)

Interpretation Introduction

Interpretation:

The weight of catalyst that is used to achieve $80\%$ conversion in a fluidized CSTR is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

Answer to Problem 2.1P

The weight of catalyst that is used to achieve $80\%$ conversion in a fluidized CSTR is $23.2\text{kg}$.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

The graph that indicates the $80\%$ area of conversion is shown as,

Figure 2

In the above shown graph, the purple and rectangular area indicates $80\%$ area of conversion. The weight of catalyst that is obtained from the graph is $29\text{kg}$. Thus, for $0.8$ conversion, the total weight of the catalyst is $0.8\times 29=23.2\text{kg}$.

(c)

Interpretation Introduction

Interpretation:

The weight of fluidized CSTR that is used to achieve $40\%$ conversion is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

Answer to Problem 2.1P

The weight of fluidized CSTR that is used to achieve $40\%$ conversion is $7.6\text{kg}$.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

The graph that indicates the $40\%$ area of conversion is shown as,

Figure 3

In the above shown graph, the purple and rectangular area indicates $40\%$ area of conversion. The weight of catalyst that is obtained from the graph is $19\text{kg}$. Thus, for $0.4$ conversion, the total weight of the catalyst is $0.4\times 19=7.6\text{kg}$.

(d)

Interpretation Introduction

Interpretation:

The weight of PBR that is used to achieve $80\%$ conversion is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

Answer to Problem 2.1P

The weight of PBR that is used to achieve $80\%$ conversion is $22.7\text{kg}$.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

The graph that indicates the $80\%$ area of conversion is shown as,

Figure 4

The scale of x-axis is $0.2$.

The scale of y-axis is $10$.

In the above shown graph, the green area under the shown curve is calculated as,

    $\text{Area}=\left(\begin{array}{l}\text{Nine}\text{complete}\text{boxes}\\ +\text{triangular}\text{box}\text{1}\\ +\text{triangular}\text{box}\text{2}\\ +\text{triangular}\text{box}\text{3}\end{array}\right)\times \left(\text{Scale}\text{of}\text{x}-\text{axis}\times \text{scale}\text{of}\text{y}-\text{axis}\right)$

Substitute the respective values in the above expression.

    $\begin{array}{c}\text{Area}=\left(\begin{array}{l}\text{9+}\frac{1}{2}\times 3\times 1+\frac{1}{2}\times 1\times 0.7+\frac{1}{2}\\ 1\times 1\end{array}\right)\times \left(\text{0}\text{.2}\times 10\right)\\ =11.32\times 2\\ =22.7\text{kg}\end{array}$

(e)

Interpretation Introduction

Interpretation:

The weight of PBR that is used to achieve $40\%$ conversion is to be stated.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

Answer to Problem 2.1P

The weight of PBR that is used to achieve $40\%$ conversion is $16\text{kg}$.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

The graph that indicates the $40\%$ area of conversion is shown as,

Figure 5

In the above shown graph, the green area under the shown curve is calculated as,

    $\text{Area}=\left(\text{Area}\text{of}\text{shaded}\text{rectangle}\right)\times \left(\text{Area}\text{of}\text{shaded}\text{triangle}\right)$

Substitute the respective values in the above expression.

    $\begin{array}{c}\text{Area}=\left(\begin{array}{l}\text{20}\times 0.4+\frac{1}{2}\times 0.4\left(60-20\right)\\ 1\times 1\end{array}\right)\\ =16\text{kg}\end{array}$

(f)

Interpretation Introduction

Interpretation:

The plot for the rate of reaction and the conversion as function of PBR catalyst weight, W is to be drawn.

Concept introduction:

The full form of CSTR is Continuous-Stirred Tank Reactor. This reaction has its application in the industrial processes. This reactor actually used for liquid-phase reactions.

The full form of PFR is Plug-Flow Reactor which consists of a cylindrical pipe and it is used for the gas-phase reactions.

The conversion, X can be defined as the moles of any species A that are reacted per mole of A fed in the reactor.

Answer to Problem 2.1P

The plot for the rate of reaction and the conversion as function of PBR catalyst weight, W is shown in Figure 6.

Explanation of Solution

The given adiabatic reaction is,

    $\text{A}\to \text{B}+\text{C}$

The given weight of the PBR catalyst is W. The expression for the weight of PBR catalyst is,

    $\begin{array}{c}{W}_{\text{PBR}}=F_{A0}{\displaystyle \underset{0}{\overset{x}{\int }}\frac{dX}{\left(-r_{\text{A}}\right)}}\\ =\frac{F_{A0}X}{\left(-r_{\text{A}}\right)}\\ -r_{\text{A}}=\frac{F_{A0}X}{W_{\text{PBR}}}\end{array}$

The given value of $F_{A0}$ is $2\text{mol/s}$.

After the calculation of rate of reaction and conversion against the weight, the plot for the rate of reaction and the conversion as function of PBR catalyst weight, W is shown as,

Figure 6

Conclusion

1. a. The arrangement of a fluidized CSTR and a PBR containing equal weights of catalyst for the given adiabatic reaction should be in series.
2. b. The weight of catalyst that is used to achieve $80\%$ conversion in a fluidized CSTR is $23.2\text{kg}$.
3. c. The weight of fluidized CSTR that is used to achieve $40\%$ conversion is $7.6\text{kg}$.
4. d. The weight of PBR that is used to achieve $80\%$ conversion is $22.7\text{kg}$.
5. e. The weight of PBR that is used to achieve $40\%$ conversion is $16\text{kg}$.
6. f. The plot for the rate of reaction and the conversion as function of PBR catalyst weight, W is shown in Figure 6.