Example $2-5$ Comparing Volumes for CSTRs in Series

For the two CSTRs in series, $40\%$ conversion is achieved in the first reactor. What is the volume of each of the two reactors necessary to achieve $80\%$ overall conversion of the entering species A$?$

TABle $2-3$ PRocessed Data $-2$

$\backslash$table$[[x,0\mathrm{.}0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8],[[\frac{F_{A0}}{-}{r}_A](m^3),0\mathrm{.}89,1\mathrm{.}09,1\mathrm{.}33,2\mathrm{.}05,3\mathrm{.}54,5\mathrm{.}06,8\mathrm{.}0]]$

Example $2-6$ Sizing Plug$-$Flow Reactors in Series

Using either the data in Table $2-3$ or Figure $2-2,$ calculate the reactor volumes $V_1$ and $V_2$ for the plug$-$flow sequence shown in Figure $2-7$ when the intermediate conversion is $40\%$ and the final conversion is $80\%.$ The entering molar flow rate is the same as in the previous examples, $0\mathrm{.}4mo\frac{l}{s}.$

Solution

Table $2-3$ Processed Data $-2$

$\backslash$table$[[x,0\mathrm{.}0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8],[[\frac{F_{A0}}{-}{r}_A](m^3),0\mathrm{.}89,1\mathrm{.}08,1\mathrm{.}33,2\mathrm{.}05,3\mathrm{.}54,5\mathrm{.}06,8\mathrm{.}0]]$

In addition to graphical integration, we could have used numerical methods to size the plug$-$flow reactors. In this example, we shall use Simpson's rule $($see Appendix A$\mathrm{.}4)$ to evaluate the integrals.

$($f$)$ Revisit Example $2-5.(1)$ What is the worst possible way to arrange the two CSTRs and one PFR$?(2)$ What would be the reactor volumes if the two intermediate conversion were changed to $25\%$ and $55\%,$ respectively? $(3)$ What would be the conversions, $x_1,x_2,$ and $x_3,$ if all the reactors had the same volume of $80d{m}^3$ and were placed in the same order?

$($g$)$ Revisit Example $2-6.$ If the term $C_{A0}{\displaystyle \underset{0}{\overset{x}{}}}\frac{dx}{-r_A}$ is $2$ seconds for $80\%$ conversion, how much fluid $(\frac{m^3}{m}in)$ can you process in a $5m^3$ reactor?