Continuous manufacturing replaces a single large batch vessel with
a cascade of smaller, continuously-fed stirred tanks (CSTRs). Each
tank runs at steady state; the PAT sensors (glowing rings) stand in
for the inline spectroscopy real plants use to verify quality without
stopping the line. Adding more tanks in series, for the same total
volume, pushes the cascade's behaviour toward an ideal plug-flow
reactor and raises conversion for a first-order reaction.
tau = V / Q (residence time per tank)
k(T) = k0 * exp[-(Ea/R)(1/T - 1/Tref)]
X_N = 1 - 1 / (1 + k*tau)^N (cascade conversion)
- Feed flow rate — volumetric throughput Q; higher flow means less time per tank and lower conversion, but higher production rate.
- Tank volume — volume V of each individual reactor in the cascade.
- Temperature — sets the rate constant k through an Arrhenius relationship; hotter runs faster.
- Reactors in series (N) — splitting the same total volume into more, smaller tanks approaches plug-flow performance.
This is the same reasoning pharmaceutical and fine-chemical
plants use when choosing between a single large batch reactor and
a continuous train: more, smaller stages with real-time analytics
give tighter quality control and higher conversion per unit volume.