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Abstract.
This paper looks at control of a plant that consists of a reactor, separator and recycle of unreacted reactant. This configuration is very common in industry, and includes both liquid phase and gas phase systems. Some examples of gas phase systems are ammonia and methanol plants.

For example, consider a CSTR reactor where component A is converted to a product and the amount converted is given by k(T)Mz [moleA/s]. To increase the conversion one then has three options:

1. Increase the temperature which increases the reaction constant k
2. Increase the fraction of A in the reactor, z. This can be done indirectly by increasing the amount of recycle of A.
3. Increase the reactor holdup M.

Since at steady-state with given product specifications the conversion of A in the reactor is given by the feed rate, it follows that only one of the two remaining variables mentioned above can be controlled independently (or more generally, one variables that influences these variables), and we must let the second variable float and adjusts itself.

Two common control strategies are then (A) to keep the reactor holdup constant (and let the recycle flow float) or (B) to keep the recycle flow constant (and let the reactor holdup float). In case (A) one may encounter the so-called snowball effect where the recycle goes to infinity. This occurs because at infinite recycle flow we have z = 1 which gives the highest possible production. In effect, the snowball effect occurs because the reactor is too small to handle the given feed rate, so it is really a steady-state design problem.

Luyben has studied liquid phase systems in a number of papers, and has concluded that a variant of control strategy (B) (where the reactor level is used as through-put manipulator) should be used to avoid the snowball effect. However, from an economic point of view one should usually for liquid phase systems keep the reactor level at its maximum value (to maximize the conversion per pass), so Luyben's recommendation has an economic penalty which it seems that most researchers so far have neglected.

However, for the gas phase system the situation is different, there are a cost associated with reactor hold-up (pressure). The optimum are unconstrained in this variable. Fixing recycle rate, purge fraction, or reactor pressure had all good self-optimizing properties. This is linked to the behavior of these variables as conversion increases. As expected purge flow is a bad alternative as a controlled variable. More unexpectedly, inert composition in the recycle turned out to bad self-optimizing properties. This is also explainable by the behavior of this variable when conversion is increased. The results for the gas phase reactor carries well over to the methanol case study.

We support our conclusions by the use of simple models.