The heat of reaction can raise the temperature and hence the reaction rate of exothermic reactions so fast the temperature accelerates upscale. There is a point of no return reached where the cooling rate is not enough to keep the temperature from rising. If the relief valves and flare stack are sized properly, the day is saved. Polymerization reactions are the most notorious runaways (particularly batch reactors where there is no self-regulation from a discharge stream).

The temperature controllers on runaways need rate action to react to acceleration and compensate for thermal lags in the heat transfer surface and the temperature sensor. Reset action is dangerous because it has no sense of direction. For this reason, some batch polymerization reactors have proportional plus rate controllers (no integral action).

These controllers cannot be put in manual for the type of step testing normally done for loops. The relay auto tuner oscillation may work if the step size is large enough to force the temperature back when it starts to accelerate. The tuning method that generally works best is where the controller is kept in auto, the reset time is increased by a factor of 100, the controller gain is increased and small set point changes are made until the control is fast enough or there is the start of a small oscillation. The controller gain is then halved and the rate time is set equal to the total delay time between a set point change and the start of the change in temperature. If any reset time is used, it is set at least 10 times larger than the rate time. This procedure, which involves approaching but not getting too close to the ultimate gain, is just a general guide and exceptions are to be expected. Tests and new tuning settings must be closely monitored.

It is critical to realize that there is a window of allowable gains where too low besides too high of a controller gain causes instability and loss of control. If the total loop dead time or the thermal lags exceed the positive feedback time constant of the runaway, the window of allowable controller bands is closed and there are no tuning settings that will stabilize the reactor. Slide 14 in the attached lecture I used at Washington University, provides an equation for the ultimate period that details the problem. The lecture introduces frequency response and how this leads to the equations for the ultimate gain and period for self-regulating, integrating, and runaway processes.
WU ChE462 Lecture on Ultimate Gains and Periods