P$2-2$ A $($a$)$ Revisit the data in Table $2-1$ Raw Data and calculate the batch reactor $($BR$)$ times to achieve $5\%,45\%,$ and $75\%$ conversion when $100$ moles of A are charged to a $400d{m}^3$ reactor.

$($b$)$ Revisit Example $2-1$ through $2-3.$ How would your answers change if the flow rate, $F_{A0},$ were reduced to one quarter? If it were tripled? What conversion can be achieved in a $5\mathrm{.}5m^{3}PFR$ and in a $5\mathrm{.}5m^3$ CSTR$?$

$($c$)$ Revisit Example $2-2.$ Being a company about to go bankrupt, you can only afford a $2\mathrm{.}0m^3$ CSTR$.$ What conversion can you achieve?

$($d$)$ Revisit Example $2-3.$ What conversion could you achieve if you could convince your boss, Dr$.$ Pennypincher, to spend more money to buy a $1\mathrm{.}2m^3$ PFR to attach to a $2\mathrm{.}40m^3$ CSTR$?$

$($e$)$ Revisit Example $2-4.$ How would your answers change if the two CSTRs $($one $0\mathrm{.}82m^3$ and the other $3\mathrm{.}2m^3)$ were placed in parallel with the flow, $F_{A0},$ divided equally between the reactors?

$($e$)$ 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?

P$2-3$ B ${?}_B$ You have two CSTRs and two PFRs$,$ each with a volume of $1\mathrm{.}2m^3.$ Use Figure $2-2($b$)$ on page $79$ to calculate the conversion for each of the reactors in the following arrangements.

$($a$)$ Two CSTRs in series. $($Ans: $x_1=0\mathrm{.}475,x_2=0\mathrm{.}718)$

$($b$)$ Two PFRs in series.

$($c$)$ Two CSTRs in parallel with the feed, $F_{A0},$ divided equally between the two reactors.

$($d$)$ Two PFRs in parallel with the feed divided equally between the two reactors.

$($e$)$ A PFR followed by a CSTR$.$

$78$

If we know $-r_A$ as a function of $x,$ we can size any isothermal reaction system.

We shall use the data in this table for the next five Example Problems.

'Proprietary coded data courtesy of Jofostan Central Research Laboratory, $$low$,$ Jofostan, and published in Jofostan Journal of Chemical Engineering Research, Volume $21,$ page $73(2023).$

Recalling the CSTR and PFR design equations, $(2-13)$ and $(2-16),$ we see that the reactor volume varies directly with the molar flow rate $F_{A0}$ and with the reciprocal of $-r_A,(\frac{1}{-r_A}),$ for example, $V=(\frac{F_{A0}}{-r_A})x.$ Consequently, to size reactors, we first convert the raw data in Table $2-1,$ which gives $-r_A$ as a function of $x$ first to $(\frac{1}{-r_A})$ as a function of $x.$ Next, we multiply by the entering molar flow rate, $F_{A0},$ to obtain $(\frac{F_{A0}}{-r_A})$ as a function of $x$ as shown in Table $2-2$ of the processed data for $F_{A0}=0\mathrm{.}4mo\frac{l}{s}.$

TABLE $2-2$ PRocessed Data

$\backslash$table$[[x,0\mathrm{.}0,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}7,0\mathrm{.}8],[-r_A(\frac{\text{m}\text{o}\text{l}}{m^3*s}),0\mathrm{.}45,0\mathrm{.}37,0\mathrm{.}30,0\mathrm{.}195,0\mathrm{.}113,0\mathrm{.}079,0\mathrm{.}05],[(\frac{1}{-}{r}_A)(\frac{m^3*s}{\text{m}\text{o}\text{l}}),2\mathrm{.}22,2\mathrm{.}70,3\mathrm{.}33,5\mathrm{.}13,8\mathrm{.}85,12\mathrm{.}7,20],[(\frac{F_{AO}}{-}{r}_A)(m^3),0\mathrm{.}89,1\mathrm{.}08,1\mathrm{.}33,2\mathrm{.}05,3\mathrm{.}54,5\mathrm{.}06,8\mathrm{.}0]]$

To size reactors for different entering molar flow rates, $F_{A0},$ we would use rows $1$ and $4,$ as shown by the arrows in Table $2-2$ to construct the following figure: