Runaway processes are unstable in the open loop. That is, if the controller is left on manual, the measurement will continue to climb or fall until some physical (possibly disastrous) limit is reached. An example is an exothermic reactor. As the temperature rises, the reaction rate increases, causing a greater rate of heat evolution, and consequently a more rapid rise in temperature. Such processes are often controlled by modulating the flow of cooling water to the jacket of the reactor.

An interesting phenomenon occurs with runaway processes. As with most processes, an excessive controller gain will cause the loop to oscillate. But, in contrast with most processes, a gain that is too low will also cause loss of process control by allowing the measurement to continue to climb or fall. Thus, there is both an upper limit and a lower limit for the controller gain. The difference between these limits is the permissible window for the gain. If there is a wide window, then the process should be relatively easy to control. On the other hand, much trouble may ensue if the window is narrow.

Exothermic chemical reactors are often developed by first constructing a laboratory or pilotsized unit. Suppose such a reactor has been built and, because of the wide window of permissible controller gain, is relatively easy to control. Then, the reactor is scaled up to a productionsized unit. As the size is increased, the volume, which determines the rate of heat evolution,...