Life's a batch!

Efficient batch control can be both an art and science, writes CONTROL contributor Gregory K. McMillan, so act accordingly for best results, and always remember "it's survival of the fittest" out there.

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By Gregory K. McMillan

SOME SAY ANY PROCESS with a distinct beginning and end is a batch process. According to this definition, continuous processes are just long batches. It is true that sequence expertise developed for batch operation can be applied to automate the startup, transition in grade, and shutdown of continuous processes to provide a faster, safer, and more efficient change in operating states.

In a conventional cascade temperature control system, the primary reactor temperature controller output is the setpoint of a secondary temperature control loop. In Figure 1 (Click the Download Now button at the end of this article to view a PowerPoint document with the figure mentioned here) the secondary loop controlled variable (CV) is the jacket or coil outlet temperature to pick up on changes in the heat transfer coefficient. This reactor also has a byproduct vapor stream and uses a condenser to reflux reactants or products trying to escape overhead.

A second common scheme uses the jacket or coil inlet temperature as the secondary loop’s controlled variable to correct upsets to the inlet faster or enforce limits on the inlet temperature associated with heat transfer surfaces, particularly important for biological reactors. A third scheme uses the outlet temperature of a heat exchanger in the recirculation line of a reactor as the secondary loop’s controlled variable.

If the secondary loop uses the difference between the inlet and outlet coil or jacket temperature for heat transfer or enthalpy control, changes in inlet temperature should be synchronized with the consequential changes in the outlet temperature by a time delay of the inlet temperature used in the calculation of the heat transfer. A time delay of the inlet temperature that does not match the actual transportation delay through the coil or jacket will cause an irregular response that can confuse the controller.

In all the schemes, the flow of coolant, steam, tempered water, oil or special heat transfer fluid such as Therminol to the jacket, coil or exchanger is manipulated by the secondary loop via the throttling of single or split-ranged valves. The addition of a flow controller to make a triple cascade of primary temperature to secondary temperature to flow to digital valve controller can be beneficial in terms of the reduction in the effect of pressure upsets and a nonlinear installed characteristic of the valve. The benefit may be questionable when the flow controller is detuned or when an equal percentage trim compensates for the nonlinearity of the secondary loop’s process gain.

The addition of a fast secondary loop makes the primary loop linear and corrects for any coil, jacket or heat exchanger upsets before they affect the reactor temperature. However, the true value of cascade control is achieved only when certain criteria is adhered to during the design and tuning of the secondary loop. The importance of the suggestions increases as the tendency of the reactor temperature response to accelerate increases.

Too Small
Probably the biggest mistake is to have the secondary temperature controller throttle a liquid flow through the coil or jacket. For these systems the combination of high process gain and high process dead time for a small liquid flow at low loads will cause a limit cycle. The secondary controller should throttle a makeup flow and control the mixture of hot and cold fluids with the total flow through the jacket or coil constant. There should be a displacement of return flow out of the coil or jacket recirculation system equal to the makeup flow to increase the self-regulation and reduce ramping in the secondary loop.

A common mistake is to tune the primary and secondary temperature controllers with too small of a controller gain, reset time and rate time. We will see in the tuning discussion how being too small in these settings can intensify the oscillations from valve deadband and in some cases lead to a runaway condition.

The overall heat transfer coefficient for the coils can be too small. In general, heat transfer coefficients are proportional to the flow rate next to the surface to approximately the 0.6 power and are tremendously degraded by coatings, whose formation rate greatly increases at low coil or jacket flow and reactor agitation rates. The integrated error for reactor control is proportional to the square of the heat transfer lag and an exothermic reactor can become unstable, regardless of tuning, if it becomes larger than the positive feedback time constant of an accelerating response.

Too Big
Large control valves will increase the amplitude of the limit cycle from valve deadband (backlash) caused by loose shaft/stem connections and gaps in linkages and resolution (stick-slip) from packing and seating friction, since both are a percent of valve stroke and hence valve capacity 2. Sliding stem (globe) valves with digital positioners are a must for tight temperature control of batch reactors. 

Controllers tend to cycle around the split range point because the stick-slip is generally larger as a valve is trying to break free from its seat. A switch from steam to coolant introduces a dead zone, discontinuity and change in coil and jacket dynamics. For minimization of the severe upset associated with a transition between heating and cooling, trim valves should be used. To avoid additional split-ranged points, a valve position control strategy can be used where small changes are handled by the trim valve and only large changes are passed on to the large valve. There is also a significant opportunity for deadband and stick-slip compensators to be inserted into the output of the secondary loop controller, and a feedforward signal of the secondary set point to be added to the output of the secondary controller with the appropriate feedforward gain and action if the secondary controller gain is low.

A large gap between the tip of the sheath and the bottom of the thermowell can introduce a disastrously large lag in the sensor’s response. If the excessive lag is in the secondary temperature measurement, it can cause the secondary loop to be too slow and even violate the cascade rule that it be five times faster than the primary loop. If it is in the primary temperature measurement, the reactor can move to undesirable operating regions before the control system sees it and become unstable if it becomes larger than the positive feedback time constant of an accelerating response of an exothermic reaction.

Profiles in Courage
Often operators or process engineers will find times to manually step up the feed rate. Sometimes this sequence is automated as part of the batch operation. A more effective method that has been shown to reduce batch cycle times by 25% uses a model predictive control (MPC) system to maximize the feed without violating constraints. Figure 2 shows that an MPC can look at the positions of jacket, condenser, and vent system valves and maximize a feed rate that prevents these valves from exceeding their maximum throttle positions for good temperature and pressure control. (Click the Download Now button at the end of this article to view a PowerPoint document with the figure mentioned here)

If the reaction rate is proportional to the product of the mole fractions of reactants, the optimum ratio of reactants can be computed. If Coriolis flow meters are used on the feeds, the concentration of reactant in each feed stream can often be computed from the density of the feed. The inventory of each reactant can be totalized and the mole fraction in the batch computed. The actual exponential ratio of mole concentrations in the reactor can become a controlled variable in an MPC that then manipulates the ratio factor for the feed rates to achieve an optimum target.  If the exponents of the mole concentrations in the reaction kinetics are not exactly known, a first principal model can be run and adapted online by a separate MPC to identify these parameters1. These models can also be run much faster than real time to predict the batch cycle time and yield.

When there is hold time in a batch phase to wait for a reaction to go to completion, it is usually conservatively set to make sure there is never a customer complaint. Process simulations can provide the ammunition and an adapted online process model can predict the proper hold time and the product concentration, which can also eliminate operator attention requests and wait times for lab sample results.

Ultimate Gain
Figure 3 shows the reactor temperature response if the primary loop was in manual or the secondary controller was in the local automatic instead of the cascade mode. (Click the Download Now button at the end of this article to view a PowerPoint document with the figure mentioned here) This is called the open loop response for the primary controller. All the responses accelerate and then ramp but the self-regulating response decelerates to a steady state, the integrating response continues ramping, and the runaway response further accelerates. If you look at the energy and material balances, there are few true integrating or runaway responses, but in the operating region many fed-batch reactors look like an integrating response because the lack of a discharge flow reduces process self-regulation. Often if there is a steady state it is beyond the limits of time or conditions for a batch phase.

The oscillations from valve deadband show up in the primary loop with a larger amplitude and period than those associated with a resolution equivalent to the offset from deadband. Previously, it was thought that deadband only caused sustained oscillations in integrating and runaway processes because the investigations centered on a single loop2. However, recent tests show the oscillations from deadband will not die out in a self-regulating process with a cascade loop because of the interaction between the primary and secondary controller. The effect of deadband can be minimized by tuning the controllers with a gain setting closer to the ultimate gain.

The ultimate gain is the controller gain that causes sustained equal amplitude oscillations. Unfortunately, deadband and resolution can also cause such oscillations. However, the oscillations from being close to the ultimate gain will decay and grow in amplitude, as the controller gain is lower and higher, respectively, than the ultimate gain. A controller gain exactly equal to the ultimate gain is unlikely, so an equal amplitude oscillation is almost always associated with valve deadband or resolution.

Normally, controller gains are less than one-fourth the ultimate gain to ensure stability despite a change in dynamics. However, low controller gains lead to more oscillations from non-ideal valve performance and can cause slow, nearly sustained oscillations for an integrating process and instability for a runaway process. Thus, for reactors, there is a gain window, where too low of a gain beside too high of a gain is a problem. Since the large process lag (open loop time constant) of reactors makes the ultimate gain larger than users realize, the more common problem is for reactor loops to be too close to or even below the low gain limit, which for a runaway is the inverse of the process gain. Since conventional wisdom is that the oscillations are caused by too high of a controller gain, the gain setting is decreased and the problem gets worse.

Equations 1a, 2a, and 3a show that the ultimate period as a multiple of the dead time (d) increases as you increase the process time lag also known as the open loop time constant (o)3. For an integrating and a runaway process, the multiple is greater than four. If this time constant (o) is taken as additional dead time, the multiple is exactly four for an integrating process. The multiple approaches infinity when the either the dead time or this time constant (o) approaches the positive feedback time constant for a runaway. In other words, if the slowness in the correction of the response indicated by the dead time or process time lag approaches or exceeds the speed at which the process is accelerating, the controller is unstable regardless of tuning and the window of allowable gains is closed.

Equations 1b, 2b, and 3b show that the ultimate gain increases as the ultimate period and process gain decreases and as the largest process time constant increases. For properly designed reactors, the ultimate gain for the primary loop is normally greater than five unless an extremely narrow temperature measurement span is used, which increases the process gain seen by the controller. Primary temperature controller gains less than one are the sign of poor tuning, a slow secondary loop, or an unusual reactor design. The ultimate gain in benefits from a cascade control system depends upon the user recognizing the ultimate gain of the controller and tuning the controller to have a closed loop time constant less than the open loop time constant by initially overdriving the setpoint of the secondary controller beyond its resting value. However, for split-ranged valves, this requires that tuning be switched to match the valve and heat transfer media. If the overdrive causes an unnecessary transition from heating to cooling or vice versa, the dead zone and discontinuity from overdrive may cause hesitation or oscillation. In this case it may be necessary to limit the overdrive to be just short of the transition point.

Traditional manual open-loop tuning methods, where step changes are made and held in the manual output of the primary controller, are not practical for these reactors because the steady state is too long and reactor temperature may ramp or accelerate into an undesirable operating region that ends up testing interlock, relief, and flare systems and evacuation procedures. An adaptive controller that is set up for tight feedback and feedforward control of an integrating process that looks at the normal set point changes in the batch with the cascade control system in its normal mode provides the fastest tuning.

Survival of the Fittest
The process time constants and process gain are highly nonlinear in batch operation because the reaction rate is a moving target. If you throw a transition between heating and cooling into the mix, you are headed for less than the best quality and efficiency. The preemptive adaptation of the controller to changing batch conditions is as important as the preemptive adaptation of a company to changing business conditions. The primary controller tuning settings should be scheduled based on totalized feeds and the secondary controller tuning settings scheduled based on the position of the split ranged valves4. The adaptive controller should trim the settings as the reactor moves into the scheduled regions and provide a closed loop response faster than the open loop response.

Technical Terms Used Interchangeably in Process Control

Time Delay – Dead Time
Derivative Action – Rate Action
Derivative Time – Rate Time
Digital Valve Controller – Digital Valve Positioner
Integral Action – Reset Action
Integral Time – Reset Time
Time Lag – Time Constant*
Open Loop Gain – Process Gain
Proportional Action – Gain Action

* A closed loop time constant defines the exponential response for a step change in the controller set point with the controller in automatic. An open loop time constant defines the exponential response for a step change in the controller output with the controller in manual. An open loop time constant for a self-regulating process is a negative feedback time constant. The positive feedback time constant for a runaway process is not common but is useful for describing the acceleration. There is no steady state for a runaway except as forced by the gain action of a controller in automatic.

Click the Download Now button below for a PowerPoint document containing the figures and equations referred to in this article.

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