(654g) Multi-Component Batch Distillation Control

Due to its flexibility, batch distillation is attractive for many low volume separations, such as for pharmaceutical, fine chemical and seasonal chemical products. Product composition control for these systems is challenging because the process gain changes significantly during the processing of the batch. For example, the process gain (e.g., for a batch rectifier, the change in the composition of the overhead product for a change in the reflux flow rate) is relatively high at the beginning of the batch separation and relatively low near the end of the batch. As a result, a linear controller, such as a PID controller or a linear MPC controller, will be unable to effectively control these systems. On the other hand, even though these problems are usually SISO systems, various nonlinear model-based controllers have been applied to this problem. The work described here uses a gain-scheduled PI controller to control a multi-component batch rectifier distillation process. The controller gain scheduling is based on the fraction of the light component originally present at the beginning of the batch that has been removed in the overhead product. A tray-to-tray dynamic model of a depropanizer (i.e., a multi-component column with six components in the feed: 1.9% ethane, 31.5% propane, 8.4% iso-butane, 21.0% n-butane, 16.0% pentane and 21.2% hexane) was used for this study. The SRK EOS was used to describe the vapor/liquid equilibrium for this system. Propane was taken as the first product while iso-butane was considered as the second product. The column has 50 trays and each tray was assumed to have a hydraulic time constant of 6 seconds. A gain-scheduled PI controller was implemented using an overhead composition analyzer with a cycle time equal to 6 min. The composition controller was cascaded to a tray temperature controller, which in turn adjusted the reflux flow rate. The temperature of the 34th tray from the bottom was selected as the control point for the tray temperature controller. The tray temperature controller was implemented first. Using a fixed setpoint for the tray temperature controller resulted in producing an over-purified product at the beginning of the batch and later in the batch an under-purified product resulted. Therefore, it was necessary to add a composition controller on top of the tray temperature controller to maintain a fixed overhead product composition during a batch. The process gain for the composition controller (i.e., changes in the overhead composition for changes in the setpoint for the tray temperature controller) was studied over the duration of the batch by performing step input changes at various times during the batch. It was found that the process gain decreased by a factor of 10 from the beginning to the end of the batch. When the process gain was plotted versus the duration of the batch, the process gain decreased in a high nonlinear fashion, approximating an exponential decay. On the other hand, when the process gain was plotted versus the fraction of propane removed in the overhead product, a relatively linear plot resulted. For the tray temperature controller, fixed PI controller settings were observed to perform satisfactory. The composition controller was tuned for the initial operation of the batch to produce an overhead product that contained 92.5% propane and the controller gain was modified twice during the batch. At a time corresponding to one-third and two-thirds of the batch processing time, the controller gain for the PI composition controller was adjusted. At each of these times, the fraction of the propane removed in the overhead product was estimated using the product flow rate and composition information. Then the correlation between the process gain and the fraction of propane removed was used to determine the process gain and this value was used to scale the original controller gain. When the controller gain was changed in stepwise fashion, a significant upset in the overhead product resulted. Instead, each time the controller gain was adjusted, the integral of the error was scaled so that the output of the composition controller before the controller gain was changed and after it was changed were equal. In this manner, bumpless transfer from one controller gain to another resulted. This gain-scheduled composition controller exhibited tight composition control without sluggish behavior and without poorly damped oscillations. As the batch separation proceeds, eventually the flow rate of the overhead product will become too small to warrant further operation and the batch can be shutdown or the operation can be switched to produce the next lightest component. For this case, we chose to produce a 92.5% iso-butane product. The scheduling for the iso-butane composition controller was implemented in a fashion similar to the procedure used for the propane composition controller. In this manner, the complete production of the propane product and the transition to the iso-butane product were both simulated. The composition control for the propane product was excellent and the transition to the iso-butane product was smooth with accurate composition control for the iso-butane product.