Reactors in series

A CSTR is big because it drops straight to the final concentration. Split the job into several smaller tanks in a row and only the last one runs that low; the first ones work at higher concentration, faster. The total volume shrinks.

For first-order reactions in N equal CSTRs, each multiplies the remaining A by 1 ÷ (1 + kτ_each), so 1 − X = 1 ÷ (1 + kτ_each)ᴺ. To reach 90% with two tanks: (1 + kτ)² = 10, so kτ = √10 − 1 = 2.16, and with k = 0.1 per minute each tank needs τ = 21.6 minutes, 43.2 in total. One CSTR needed 90 minutes and a PFR 23.

As N grows, a chain of tanks behaves more and more like a plug flow reactor: with infinitely many, it is one. Even three or four tanks get most of the benefit. That's why big continuous fermenters and polymerization lines often use a short train of stirred tanks.

Order matters when reactors differ. For the usual positive-order reactions you want high concentration where the reaction is happening, so you'd put a PFR before a CSTR rather than after, if you had to have both. For conversion targets near 100%, a CSTR followed by a small PFR "polishing" step is common.

Choosing a reactor comes down to the reaction and the job: phases involved, how much heat it gives, the conversion and selectivity wanted, scale, cost and safety. The rest of the course covers heat and selectivity.