If you ever wondered if you are agitated enough, then this blog may help stir up some thoughts. Specifically, how does the relative type and degree of mixing in the plant design affect your job as an automation professional? If the process engineer tells you the project is installing a radial instead of an axial agitator, do you shudder with profound disappointment or just utter a sigh? What if the agitated vessel is replaced with a static mixer? Do you turn the project over to the intern and take early retirement?
I will first continue my role in life as a pH stalker but then move on to other processes and more general considerations.
I became sensitized to mixing because of the extreme sensitivity of pH loops to plant design. I have talked before about how pH processes are the best known indicators of valve stick-slip, particularly near the neutral point, A control valve resolution of 0.1% (exceptional by any standards) can cause a pH swing that is more than noticeable.
Similarly, pH processes are the best known indicators of the uniformity of mixing. Concentration fluctuations in hydrogen ion concentration as small as 0.0000001 normality can cause noise with a 1 pH amplitude at the neutral point. The only study I have seen on the mixing required for pH was a cop out because it was done at 4 pH where the sensitivity (slope of the titration curve) was 1000 times less.
Additionally, the consequences of mixing delays are most severely felt in pH processes. An increase in loop dead time increases the excursion in pH for a given load upset, which increases the nonlinearity seen by the control loop. The operating point nonlinearity for pH can be extreme. The process gain is proportional to the slope of the titration curve and inversely proportional to the total flow and can change by a factor of ten for each pH unit deviation from the neutral point in a strong acid and base system.
The game in a pH loop more than any other loop is to minimize noise and dead time.
For other processes, the required degree of mixing is a lot less, but whether you are talking about temperature or concentration control, poor mixing still shows up as more noise and more dead time. The percent nonuniformity from mixing multiplied by the conversion factors to get to percent of the measurement scale gives you the noise amplitude seen by the controller algorithm. The dead time from mixing in a well designed agitated vessel is roughly the turnover time, which in turn can be approximated as the liquid volume divided by the sum of the feed flow, recirculation flow, and agitator pumping rate. The average dead time is ideally more like ½ of the turnover time whereas the maximum dead time is the turnover time. This helps explain why you see ½ to 1 times the turnover time in the literature as the mixing delay. Since we are generally short on our dead time estimates because there are so many sources of process dead time, I don’t like to skimp on the mixing delay. See my Nov 20 2006 blog “Without Dead Time and Disturbances I Would Be Out of a Job” in the Plant Design category for a list of sources.
Unfortunately, the above assumes the liquid height is about the same as the vessel diameter (unless there a multiple levels of impellers), baffles every 90 degrees to prevent swirling, and an axial agitator to pull down liquid (not air) from the surface. If a camera shows the surface not being broken or swirling, or there is foaming, you can say “Houston we have a problem”, particularly if the vessel vendor or design firm is in Houston. In processes that cannot withstand high agitation because crystals or cells may be broken by the blades, there may be an opportunity to increase the recirculation flow and use a jet or eductor to amplify the effect of the flow (e.g. jet fermentors).
Bob Heider, adjunct Washington University professor, wisely pointed out that baffles cannot be used for biomass, crystals and particles when the baffles cause the solids to dam up or break up. Bob also provided the following memory dump on agitation.
A bigger potential source of dead time is the injection delay from dip tubes for small manipulated flow (e.g. nutrient, reagent, reactant, or additive). The normal design practice is to have a robust sized dip tube go about halfway down the liquid to the impeller. Unfortunately, this creates a dead time when the manipulated flow is shutoff for a prolonged period of time that is the submerged dip tube volume divided by the flow. For example, just a gallon volume will cause a dead time of 1 hour for a 1 gph flow when the control valve reopens. There can be an even larger dead time because to see the final effect of stopping the flow, you have to wait till the concentration inside the dip tube drains and migrates into the mixture in the vessel. Various method of reducing injection and mixing delays are discussed in the ISA book Advanced pH Measurement and Control, 3rd edition, 2005.
This brings us to one grand generalization. For concentration changes, the residence time (volume divided by flow) becomes a process dead time for a pipe but becomes a process time constant for a well mixed vessel. Check out next week’s blog for the effect on tuning and loop performance. In the mean time, stay agitated.