Chapter 4, Problem 4.1Q

1. (a) List the important concepts that you learned from this chapter. Make a list of concepts that you are not clear about and ask your instructor or colleague about them.
2. (b) Explain the strategy to evaluate reactor design equations and how this chapter expands on Chapters 2 and 3.

Interpretation Introduction

Interpretation:

The important concepts that are learned by the mentioned chapter are to be stated. The concepts that are not clear to an individual are to be stated.

Concept Introduction:

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

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

The full form of PBR is Packed-Bed Reactor which is used for the fluid-solid heterogeneous reactions. These fluid-solid heterogeneous reactions take place at the surface of the catalyst.

Explanation of Solution

The first concept that is learned by the mentioned chapter is that the equation corresponding to the stoichiometric table for the reaction which takes place in the flow system is given as follows.

    $\text{A}+\frac{b}{a}\text{B}\to \frac{c}{a}\text{C+}\frac{d}{a}\text{D}$

The expression that is used to calculate the concentration of reactants A and B corresponding to the incompressible liquids is given below.

    $C_{\text{A}}=\frac{F_{\text{A}}}{\upsilon }$

Where,

$C_{\text{A}}$ is the concentration of A.

$F_{\text{A}}$ is the molar flow rate.

  $\upsilon$ is the volumetric flow rate of A.

The value $F_{\text{A}}=F_{\text{A0}}\left(1-X\right)\left(\text{initial}\text{molar}\text{flow}\text{rate}\right)$ and $\upsilon ={\upsilon }_0\left(\text{initial}\text{volumetric}\text{flow}\text{rate}\right)$.

    $C_{\text{A}}=\frac{F_{\text{A0}}}{{\upsilon }_0}\left(1-X\right)$

Where,

$X$ is the conversion.

The value of $\frac{F_{\text{A0}}}{{\upsilon }_0}=C_{\text{A0}}\left({\Theta }_{\text{C}}+\frac{c}{a}X\right)$.

Thus, the above equation becomes as follows.

    $C_{\text{A}}=C_{\text{A0}}\left({\Theta }_{\text{C}}+\frac{c}{a}X\right)$

This reaction takes place in a batch system at constant volume.

The second concept that is learned by the mentioned chapter is the definition corresponding to the concentration for $C_{\text{A}}=\frac{F_{\text{A}}}{\upsilon }$ for the reaction of gas-phase reactions. So, the concentration of A and C in term of pressure and temperature is given as follows.

    $C_{\text{A}}=C_{\text{A0}}\left(\frac{{\Theta }_{\text{C}}+\frac{c}{a}X}{1+\epsilon X}\right)\frac{P}{P_0}\left(\frac{T_0}{T}\right)$

The concentration of C is $C_{\text{C}}=C_{\text{A0}}\left(\frac{{\Theta }_{\text{C}}+\frac{c}{a}X}{1+\epsilon X}\right)\frac{P}{P_0}\left(\frac{T_0}{T}\right)$.

Where,

${\Theta }_{\text{C}}$ is equal to $F_{\text{C0}}/F_{\text{A0}}$ and $C_{\text{C0}}/C_{\text{A0}}$.

The third concept that is learned by the mentioned chapter is about the concentration of different species till the $i^{th}$ terms for the molar flow rates of the gas phase is given as follows.

    $C_{\text{i}}=C_{\text{T0}}\frac{F_i}{F_T}\frac{P}{P_0}\left(\frac{T_0}{T}\right)$

The concepts which are not clear are that how to express the reaction rate as the function of time and secondly the determination of the equilibrium conversion for batch reactor as well for flow reactors.

Interpretation Introduction

Interpretation:

The strategy to evaluate the design equations of the reactor is to be explained.

Concept introduction:

The sufficient energy that can be possessed by an effective collision is known as activation energy.

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

Explanation of Solution

The strategy to evaluate the design equations of the reactor is the accumulation which expresses the in-out and generation consumption sum. The expression for the mass balance for this type of system is given below.

    $\frac{d{N}_{\text{A}}}{dt}=F_{\text{A0}}-F_{\text{A}}+G_{\text{A}}$        (1)

Where,

$N_{\text{A}}$ is the mass of A in the system.

$F_{\text{A}}$ is the molar flow rate.

$F_{\text{A0}}$ is the initial molar flow rate

$G_{\text{A}}$ is the regeneration rate or consumption rate.

The value of $G_{\text{A}}$ is expressed as follows.

    $G_{\text{A}}=r_{\text{A}}V$

Where,

$r_{\text{A}}$ is the rate of the reaction.

$V$ is the volume of the reactor.

The value of $G_{\text{A}}$ varies according to the volume and position of the system. Thus, the expression to calculate is given as follows.

    $\Delta G_{\text{A1}}=r_{\text{A1}}\Delta V_1$

The expression for sum of the different terms is given below.

    $\begin{array}{c}{G}_{\text{A}}={\displaystyle \sum _{i=1}^k\Delta G_{\text{A}}}\\ ={\displaystyle \sum _{i=1}^k{r}_{\text{A1}}\Delta V_1}\end{array}$

If $\Delta V$ limits to $0$ then the above equation can be written as follows.

    $G_{\text{A}}={\displaystyle \underset{V}{\int }{r}_{\text{A}}dV}$

Substitute the value of $G_{\text{A}}$ as ${\displaystyle \underset{V}{\int }{r}_{\text{A}}dV}$ in equation (1).

    $\frac{d{N}_{\text{A}}}{dt}=F_{\text{A0}}-F_{\text{A}}+{\displaystyle \underset{V}{\int }{r}_{\text{A}}dV}$

Thus, the above equation is the reactor design equation.