A liquid$-$phase isomerisation reaction is to be conducted such that $1000$ tonnes of the

desired product are produced per year of operation. Accounting for start$-$up$,$ shutdown

and maintenance periods this can be taken as $8000h$ of reactor operation, regardless

of reactor type. The reaction is operated isothermally at $150C.$ Over the course of

reaction $95\%$ of all of the initial reactant is converted into the desired product. The

following additional parameters are known:

Rate constant: $0\mathrm{.}2h^{-1}$

Density of reactant: $0\mathrm{.}75gc{m}^{-3}$

Density of product: $0\mathrm{.}75gc{m}^{-3}$

Enthalpy of reaction: $-300k\frac{J}{k}g$

Heat capacity of reactant: $2kJk{g}^{-1}{K}^{-1}$

Heat capacity of product: $2kJk{g}^{-1}{K}^{-1}$

$($a$)$ If a single CSTR is used for the reaction, then what rate of heat removal will be

required to ensure isothermal operation? The reactant is initially fed to the reactor

at $20C.$

$($b$)$ If two identical CSTRs connected in series are used for this reaction then what

rate of heat removal will be required to ensure isothermal operation in each reactor?

The reactant is initially fed to the first reactor at $20C$ and the transfer of material

between the reactors can be considered adiabatic.

$($c$)$ Comment on the relative values obtained for the first and second reactors in part

$($b$)$ and suggest how this would influence your process design.

$($d$)$ Often reactors in series are operated with inter$-$stage cooling. With reference

to conversion$-$temperature diagrams, explain how this can enhance the rate of

production of a given product in a reversible exothermic reaction.