What Have I Learned? – Cost and Source of Oscillations (Part 1)

All plants have oscillations. Process control improvement can reduce or eliminate these oscillations. In these days of tight budgets and resources, how do you justify cost and effort to fix the problem?

The “before” and “after” distribution and location of process variability depicted in slide 1 in ProcessControlBenefits.pdf is the classic presentation on how tighter control can result in benefits. If you can reduce the standard deviation (sigma), you can move the set point closer to the constraint without increasing the number of violations of the constraint. What I have added to the slide is the practical situation where operations give themselves a cushion or margin, particularly if there is no online monitoring system with data analytics that can provide the process knowledge and confidence needed to operate at edge of the product range to gain a competitive edge. In my experience the margin almost always exists, it is just a matter of how much. The margin is perhaps easiest to visualize in plastic sheet manufacturing. The greatest variability in sheet thickness and optical clarity occurs near the edge. An extra margin of sheet is trimmed off to make sure there are no off-spec sheets. Without doing anything to provide tighter thickness control, the trim width could be change if there was enough process knowledge and confidence. The benefit from less scrap can be taken as a decrease in raw material and utility cost to obtain the existing capacity or as an increase in capacity for the existing raw material and utility use as noted in the categorization of possible benefits on slide 2.

The key idea here is that most benefits are not achieved until we change a set point. We can find the existing margin by the intelligent use of an online data analytics system and we can create a new margin by tighter process control. Once we know the margin, we need to move the set point to eliminate the margin. A “good” process control engineer can draw straight lines. A “great” process control engineer can move the straight lines.

Often we are not so lucky to have an online measurement and closed loop control of the product quality or concentration that is the ultimate process output as implied by slide 1. What we have is lot of intermediate unit operations in a plant each with a multitude of process inputs and process outputs that can be oscillating. As a minimum many chemical and biochemical plants have a reaction unit operation followed by separation, purification, and formulation unit operations. For solid products, there is often additional equipment for crystallization, centrifuging, drying, and blending. Each of these unit operations has process inputs and outputs with a degree of variability.

So we have short term or long term oscillations at various points in the process and can reduce or eliminate these oscillations. How do we justify the cost and quantify the benefits of better process control?

In order to estimate what we can gain from process control improvement, we need to know process gains. A process gain is the change in a process output divided by the change in a process input. There is a steady state process gain which is the final change after all transients have dies out and the process has reached a new steady state. Steady state simulations can provide these process gains and through virtual experimentation quantify the changes in the product composition or quality for changes in an upstream process variable. For oscillations there is also a dynamic effect where the oscillations of a process variable are attenuated by downstream volumes. The attenuation is proportional to the period and inversely proportional to the residence time of volumes with back mixing from turbulence, recirculation, and agitation. The follow equation can be used to estimate the amplitude of oscillations in a process output (Ao) for oscillations in a process input (Ai), a steady state process gain (Kp) between the process output and input, a period of oscillation (Po), and for a residence time of a back mixed volume (Tm). The residence time is the volume divided by the total flow rate through the volume.

Ao = Ai * Kp * [Po / (6.28*Tm)]

We can compute the steady process gain from first principle equations as shown in Advanced Application Note 4 posted on March 25 or get it from a steady state simulation as long as we avoid a valve position as the process input. The installed characteristic of teh valve and hence the slope of this curve’s contribution to the process gain is typically not simulated correctly. Dynamic simulations that have a flow-pressure solver should be able to predict the oscillation amplitude but in practice the results are poor because these simulations do not sufficiently model process and automation system dead times, valve backlash and sticktion, and control loop tuning that determines the period of the oscillations.

The best way to estimate the relationship is the find the process variable furthest upstream with the same dominant period of oscillations that are in the product. The ratio of the amplitudes (Ao/Ai) is the dynamic process gain. For a given reduction in the amplitude Ai, you can estimate the corresponding reduction in amplitude Ao. A power spectrum analysis of the process variables can be used to find the variables with the corresponding dominant frequencies. We then need to follow through and see how much of a margin we can create by a reduction in the product oscillation amplitude.

Once we have the margin, we need to work backwards (upstream) to get at what is the corresponding reduction in utility flow or feed flow. How do we do this? Again we need to use process gains. We divide the product margin by the process gain to get the change to be made in a key upstream loop set point once we have reduced the oscillations in the product. Consider the case where the key loop is a reaction or distillation temperature loop. We then divide the change in reactor or column temperature set point by the steady state process gain for the required change in coolant temperature and reflux flow, respectively. Next we divide this change in coolant temperature or reflux flow by the steady state process gain for the required change in coolant flow and steam flow, respectively. Finally, we multiply the required changes in utility flow by their cost per unit flow to get at the cost savings. Knowledge of the process and the gains are in the process gains and the periods of oscillation. Online data analytics can find the margins, power spectrum analyzers can find periods, and online controller tuning can find the process gains.

The leading cause of oscillations is a level loop with overly aggressive tuning and in some cases excessively sluggish tuning. Several very sophisticated process studies have come to down to this simple fix. Next week we will look in more detail at this culprit and explore the other causes of oscillations.