Residing on Residence Time

The post, Residing on Residence Time, first appeared on's Control Talk blog.

The time spent residing on this column is time well spent if you want to become famous for improving process performance with the side benefit of becoming best buds with the process engineer.  The implications are enormous in terms of process efficiency and capacity from the straightforward concept of how much time a fluid resides in process equipment.

The residence time is simply the equipment volume divided by the fluid volumetric flow rate. The fluid can be back mixed (swirling in opposite direction of flow) in the volume due to agitation, recirculation or boiling. A lot of back mixing makes nearly all of the residence time a process time constant. If there is hardly any back mixing, we have plug flow and nearly all of the residence time becomes deadtime (transportation delay).

Deadtime is always bad. The ultimate limit to the peak and integrate errors for a load disturbance is proportional to the deadtime and deadtime squared, respectively.

A particular process time constant can be good or bad. If the process time constant in question is the largest time constant in the loop, it slows down disturbances on the process input and enables a larger PID gain. The process variability can be dramatically reduced for a process time constant much larger than the total loop deadtime. The slower time to reach setpoint can be speeded up by the higher PID gain provided there is proportional action on error and not just on PV in the PID structure. 

If the process time constant in question is smaller than another process time constant possibly due volumes in series or heat transfer lags, a portion of the smaller time constants become effectively deadtime in a first order approximation.  Thus, heat transfer lags and volumes between the manipulated variable and controlled variable create detrimental time constants. A time constant due to transmitter damping or signal filtering will add effective deadtime and should be just large enough to keep fluctuations in the PID output due to noise from exceeding the valve or variable speed driver deadband and resolution, whichever is largest.

At low production rates, the residence time gets larger, which is helpful if the volume is back mixed, but the process gain increases dramatically for temperature and composition control. If the volume is plug flow, we are in dire straits because the larger residence time creates a larger transportation delay resulting in a double whammy of high process gain and high deadtime causing oscillations as explained in the Control Talk Blog “Hidden factor in Our Most Important Loops”.  For gas volumes (e.g., catalytic reactors), the residence time is usually very small (e.g., few seconds) and the effect is mitigated.

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