The plug flow reactor

A plug flow reactor (PFR) is a long tube, or a bundle of tubes, that the reacting fluid flows along. Ideally each slice (plug) of fluid moves along without mixing with the slices before or after it, so it reacts like a tiny batch reactor travelling down the tube.

The concentration falls gradually along the length. Following one plug, the time it's spent in the tube plays the part of batch time, so for a first-order liquid reaction the residence time is τ = ln(1/(1 − X)) ÷ k, exactly the batch result. With k = 0.1 per minute and 90% conversion, τ = 23.0 minutes.

Compare the CSTR's 90 minutes for the same job: the PFR is nearly four times smaller. That's the general rule for ordinary reactions (positive order): plug flow needs less volume than a stirred tank, because most of it runs at higher concentration and so faster. The gap grows as you aim for higher conversion.

PFRs are the workhorse for big gas-phase processes, such as steam cracking furnaces, ammonia converters and packed tubes of catalyst. Their drawbacks: temperature varies along the tube, hot spots can form near the inlet where the reaction is fastest, and they're harder to clean.

Real reactors sit between the two ideals. Some mixing happens along a tube, and some dead corners occur in a tank. Engineers measure the spread of times fluid spends inside (by injecting a pulse of tracer and watching it come out) to see how close to ideal a real reactor is.