A key step in the batch production process for the synthetic pharmaceutical API

intermediate P is the liquid phase condensation of chloroquinaldine $($Q$)$ and

hydroquinone $($H$)$ in a $1200$ L stirred batch reactor in a water$-$methanol mixture as

solvent. Prior to reaction, hydroquinone is neutralized with NaOH yielding the salt

hydroquinone.Na $($H$.$Na$)$ with limited solubility in the water$-$methanol mixture.

Chloroquinaldine is fed to the $($fed$)$ batch reactor where it reacts with dissolved

hydroquinone.Na to yield the desired product P$,$ that can crystallise. A small amount

of chloroquinaldine forms with the main product an undesirable by$-$product $($Impurity$)$

that needs to be removed later. The stoichiometry and rate of the reactions:

Chloroquinaldine $+$ Hydroquinone.Na $$ Product $($dissolved$)+$ NaCl r$1=$ k$1$ cQ cH

SAT

Chloroquinaldine $+$ Product $+2$NaOH $$ Impurity $+2$NaCl $+2$H$2$O r$2=$ k$2$ cQ cP

Product $($dissolved$)$ Product $($crystal$)$

We focus on the production of P crystals. The $($seeded$)$ crystallisation of P is slow

relative to the chemical reaction$($s$)$ and ideally performed at constant crystal growth

rate G to obtain pure cubic crystals. The H$.$Na$-$salt has a limited solubility but

dissolves fast $($relative to P crystallisation$)$ so it is assumed that H$.$Na is at its

solubility as long as there are H$.$Na crystals.

a$.$ Formulate a $($fed$)$ batch strategy of Q to control crystallisation of P at constant

growth rate G$,$ assuming H$.$Na is not fully dissolved yet. Ignore the effect of

volume change on the reacting liquid mixture.

b$.$ Write down the liquid phase mass balances of Q$,$ P$,$ and H$.$Na$.$ What is the

implication of a constant crystal growth rate on $($change in$)$ both liquid phase

concentrations of P and Q $?$

c$.$ Derive the mass balance for the growing crystal mass of P$,$ assuming

constant crystal growth G of the seeds Ns$.$ with initial crystal length Ls$.$

d$.$ How should the feed rate of Q $($FQ$)$ develop in time $?$ Draw FQ versus time.

e$.$ How do you propose to incorporate $($i$)$ the effect of limited H$.$Na $($depletion of

the solid reagent$),$ and $($ii$)$ when the volume change due to the feed of Q

cannot be ignored. How will that change the mass balance based model $?$