I have about 30 minutes here before I head out for the Memorial Day weekend and you probably have less than 5 minutes to read this so it will be short and hopefully sweet.
By now I may have conveyed the sources of transportation delay. For conveyors and paper machines, the delay is the equipment length divided by its speed. For sample and process piping, the delay is the total length of piping including fittings divided by the fluid velocity. For extruders, heat exchangers, and static mixers, the delay is the equipment volume divided by the total volumetric flow. For agitated vessels, the mixing delay is the turnover time (liquid volume divided by the summation of the volumetric feed, recirculation flow, and agitator pumping rate). For dip tubes, the transportation delay is the dip tube volume divided by the volumetric dip tube drain flow. It gets worse. When the control valve closes to the dip tube, the stuff inside the dip tube slowly migrates into the vessel. For sensitive systems such as pH, there can be a noticeable drift for several hours.
Is this the whole story for process dead time?
Based on transportation delay and conventional wisdom, it would be best to locate an electrode or thermowell in the vessel rather than a recirculation line. Is this always the case? The electrode and thermowell time constant can be larger by 20 or more seconds in a vessel because the local fluid velocity is typically less than 0.5 fps compared to the 5 fps in a recirculation line. If the measurement location in the recirculation line is within 20 feet of the vessel, you are only talking about 4 seconds of delay. If you consider the electrode or thermowell tip may be too close to the wall and is much more likely to foul and develop a coating at low velocities, you have the scenario for sensor time constants greater than 60 seconds besides the need for more frequent cleaning. If there are not any safety issues, I prefer the faster and cleaner sensor you get in a recirculation line (e.g. elbow about 20 pipe diameters downstream of pump with sensor tip near the center of the line). For exothermic reactors, temperature sensors inside the reactor are normally required.
It is important to remember the loop dead time is not just process transportation and mixing delays. You need to add sensor time constants, final element dynamics (delays, lags, deadband, and resolution), signal filter time constants, and digital scan and execution times. Now without further delay, have a great holiday.