- For an equal-percentage valve, the minimum and maximum limits correspond to valve positions of about 30% and 50% (again rounding to the nearest 5%), respectively. So, we’re using the valve only over 20% of its full range. This is the customary consequence of oversizing an equal-percentage valve. Fortunately, we’re often able to get by with this.
- For a linear valve, the minimum and maximum limits correspond to valve positions of about 5% and 15%, respectively. These are small valve openings coupled with a narrow operating range. As is normally the case for an oversized valve, a linear valve isn’t a good choice.
Departure from linearity. Over the region of 30% to 50% for the equal-percentage valve, the departure from linearity is modest and shouldn’t necessitate any form of scheduled tuning or the like.
Regions where the operating line is flat. For the equal-percentage valve, such a region exists for valve openings above 50%. Even if the controller gain is increased dramatically, the liquid outlet temperature won’t be controlled very effectively in this region.
Regions where the operating line is vertical. The operating lines in Figure 6 don’t exhibit this characteristic.
Effect of process operating variables. Throughput has the most significant influence on the operating lines. (We’ll examine this in the next section.) Other variables such as steam supply pressure and liquid inlet temperature for the exchanger also influence the operating lines. Usually the effect of such variables is less than the effect of throughput — but this is a generalization for which exceptions definitely exist. So, for any process in which you expect a significant change in some operating variable, evaluate its impact on the process operating lines.
Effect of throughput
Figure 7 presents the process operating lines (equal-percentage valve only) for liquid flows of 1,000, 2,000 and 4,000 lb/min for our exchanger. The heat transfer generally increases as the flow increases but not in a linear fashion. The shape of the operating lines is basically the same for all, the major difference being that the increase in temperature from liquid inlet to liquid outlet decreases as the liquid flow increases.
Figure 7 also illustrates the effect of throughput on the valve positions corresponding to the minimum and maximum heat transfer rates. The effect of increasing throughput is to increase these valve positions; however, the difference between the valve positions for maximum and minimum heat transfer remains at about 20%. Over this range, all of the operating lines exhibit only a modest departure from linearity.
While some processes, e.g., in refining, operate at essentially constant throughput, others, such as most utility processes, are expected to handle significant changes in throughput. For example, most industrial boilers are designed for a turndown ratio of at least 4:1.
Batch processes also can exhibit extreme variations in throughput. Consider a batch reactor with a jacket for removing heat. The contents of the reactor, that is, the reacting media, determine the dynamics of a production-scale reactor. The dynamics associated with the jacket are far shorter, which means that the jacket is essentially at an equilibrium state that reflects the conditions within the reactor. As the conditions within the reactor change, the jacket basically tracks those conditions.
For batch reactors, the turndown ratio pertains to the heat transfer rate between the reactor and the jacket. For many batch applications, this heat transfer rate varies substantially during the batch. Typically the heat transfer rate is highest in the early stages and usually drops off considerably during the later stages. Turndown ratios of 50:1 are experienced in practice — this has major repercussions on all aspects of the process (jacket design, valve sizing, cooling/heating media flow measurement, controller tuning, etc.).
For operating lines such as those in Figure 7, the temperature controller usually must be tuned to give acceptable performance for the throughput for which the slope of the operating line is the steepest. This is where the process will have its highest sensitivity, which in turn requires the smallest value for the controller gain. The steepest slope decreases in magnitude as the throughput increases. Consequently, the higher the throughput, the lower the process sensitivity and the higher the controller gain required to achieve consistent loop performance.
This is another potential application for scheduled tuning. A measurement is required for the liquid flow through the exchanger. For low liquid flows, the process gain is high, so a low controller gain is appropriate. As the liquid flow increases, the controller gain should be raised (approximately proportional to the increase in liquid flow). These applications of scheduled tuning usually are successful. But when other operating variables are added to the mix, the logic becomes more complex and success less assured.