The continuous stirred tank

A continuous stirred tank reactor (CSTR) has feed flowing in and product flowing out all the time, and a stirrer so strong the contents are the same everywhere. That means the outlet is exactly the same as the inside of the tank: the whole tank reacts at the low, final concentration.

Its key size is the residence time, τ (tau) = V ÷ v₀: tank volume divided by volume flow. A 180 L tank fed 2 L/min has τ = 90 minutes, the average time a bit of fluid spends inside.

At steady state the balance on A is: in − out − consumed = 0, so F_A0 − F_A − (−r_A)V = 0, where F is a molar flow. For a first-order liquid reaction this becomes τ = X ÷ (k(1 − X)), or turned around, X = kτ ÷ (1 + kτ).

With k = 0.1 per minute and X = 0.9: τ = 0.9 ÷ (0.1 × 0.1) = 90 minutes. A batch reactor needed only 23 minutes of reaction for the same conversion. The CSTR is bigger because it runs entirely at the outlet concentration, where the reaction is slowest.

So why use one? A CSTR is simple, easy to control and keeps the whole tank at one temperature, which helps with very exothermic reactions. It's good for liquid reactions, for reactions in slurries, and for fermentation, and its disadvantage shrinks if you put several in series (lesson after next).