Chapter 2, Problem 2.8P

Interpretation Introduction

Interpretation:

The reactor volume of the two CSTRs and the PFR has to be estimated.

Concept introduction:

Plug–flow reactor: It is type of continuous flow reactor which is operator under steady state. It is the system where flow field modeled by that of plug–flow profile which will have no radial variation in reaction rate.

The ideal plug flow reactor depends only on total volume but not on its shape.

The mole balance for plug flow reactor in integral form is represented as follows,

    $V=F_{A0}{\displaystyle \underset{X_{in}}{\overset{X_{out}}{\int }}\frac{dX}{-r_A}}$

Continuous–stirred tank reactors (CSTR): It is type of continuous flow reactor which is commonly used in industrial processes. It is also known as back mix reactor which used for reactions in liquid phase.

The design equations for CSTR in algebraic form is $V=\frac{F_{A0}X}{-r_A}$

In terms of conversion, the differential and integral forms of the reactor design equations become,

$\begin{array}{cccc}& \text{Differential}\text{Form}& \text{Algebric}\text{Form}& \text{Integral}\text{form}\\ \text{CSTR}& & \text{V=}\frac{{\text{F}}_{\text{A0}}\left({\text{X}}_{\text{out}}{\text{-X}}_{\text{in}}\right)}{{\left({\text{-r}}_{\text{A}}\right)}_{\text{out}}}& \\ \text{PFR}& {\text{F}}_{\text{A0}}\frac{\text{dX}}{\left(\text{dV}\right)}\text{=}{\text{-r}}_{\text{A}}& & {\text{V=F}}_{\text{A0}}{\displaystyle \underset{{\text{X}}_{\text{in}}}{\overset{{\text{X}}_{\text{out}}}{\int }}\frac{\text{dX}}{\left({\text{-r}}_{\text{A}}\right)}}\end{array}$