Effect of Mechanical Design – Mixing

Mixing changes the game. Mixing has a broad impact on disturbances, interactions, and noise. Mixing breaks paradigms on tuning, control, and performance. Mixing is at play in key unit operations offering incredible tightness of control and forgiveness of mistakes enabling exceptional product quality.

I became sensitized to the role of mixing early in my career as a specialist in pH control. For neutralizations with strong acids and/or bases, mixing would make or break the control system. What would be considered insignificant fluctuations in acid or base concentration and uniformity were amplified by a steep titration curve and the consequential extraordinarily high process gain. While most of us are fortunate enough to not have to deal with such systems, the essence of the problem is the same and the implications are pervasive.

Large volumes with high degrees of mixing will smooth out the oscillations from disturbances, interactions, stick-slip, backlash, and aggressive controller tuning. These volumes offer low noise and incredibly small process dead time to time constant ratios and hence exceptionally high PID gains and extremely low ultimate limits to integrated error, peak error, and rise time. If the user takes advantage of the high PID gain, the practical limit approaches the ultimate limit to loop performance. The best example of this opportunity is reactor control. Temperature loops on well mixed reactors can use PID gains of 50 or more provided there is no source of noise extraneous to the process such as sensor thermal noise or electromagnetic interference. Many are not accustomed or comfortable with such high controller gains.

In the final processing for paper, web, and fiber manufacturing where key unit operations are in-line and the product ends up as a solid, there is a low degree of mixing. Inline systems and extruders have some radial and negligible axial or back mixing. Sheet lines and spin lines have no mixing. Fluctuations are not smoothed out and are captured in the moment as changes in quality parameters. The emphasis is the minimization of all sources of oscillations. Control algorithms and tuning methods were developed to provide more gradual actions and smooth control. The coordination of the timing of loops particularly in blending became essential to minimize fluctuations from loops leading or lagging the action of others. The lack of mixing translates to high process deadtime to time constant ratios. The best a controller can do is be the inverse of the process, which on a deadtime dominant process translates to a PID controller gain that is the inverse of the open loop gain (the product of the final control element, process, and measurement gains). Internal Model Control and the Dahlin algorithm and many advanced control algorithms were developed with the goal of being the inverse of the process. For the Lambda tuning the goal was a Lambda factor of 1.0 so that Lambda (closed loop time constant) was equal to the process time constant. In practice, Lambda factors greater than 3.0 were necessary to provide smooth control. The enhanced PID developed for wireless offers the possibility of achieving a controller gain that is the inverse of the open loop gain for large wireless update times or analyzer cycle times where the total loop deadtime is much greater than the process time constant.

For a well mixed reactor the Lambda factor may be 0.02 or smaller, providing a 50 times faster approach to setpoint than a controller whose gain is the inverse of the open loop gain (assuming no constraint on final control element action from hitting an output limit). Mixing enables a loop to reach or return to setpoint in minutes rather than hours.

Large well mixed volumes downstream can attenuate the oscillations from less than ideal automation system performance. In one extreme case, there were no opportunities for more advanced control because the final control elements were wide open and the resulting variability was blended out by huge storage tanks. The quest for minimizing inventory makes these scenarios archaic, placing more importance on better mixing.

Mixing increases the heat transfer and mass transfer coefficients decreasing the response time of temperature and pH sensors, respectively. Mixing helps insure the process in contact with the sensor is representative of the process as a whole. The worst case without mixing is stagnation and an erroneous measurement.

So how do you increase the degree of mixing? The simple answer is increase turbulence from agitation, sparging, boiling, and stream entry. The mixing delay is theoretically half of the turnover time. For vessel with good geometry and baffles, the turnover time is the vessel volume divided by the sum of the agitation, feed, sparge, and recirculation volumetric flow rates. Eductors provide a multiplier of the recirculation flow rate (e.g. 3:1) in terms of turbulence created. The ideal geometry is a volume height about equal to the volume diameter. Baffles are used to prevent swirling. For large volumes without layering due to density differences there is also mixing by mass transfer from areas of higher to lower concentration and heat transfer from areas of higher to lower temperatures. Thus, large storage tanks without agitators still provide a significant smoothing and blending effect of concentration and temperature.

For more information on mixing checkout the blog “Stirring it Up