Control operators would say to me, “Can you do something to slow down the pH changes?” For a setpoint on a steep titration curve, the pH would often zip right past the setpoint on its way from one tail of the curve to the other tail. Titration curve plots from the lab for strong acids and bases have nearly horizontal lines, affectionately called “tails,” below 2 pH and above 12 pH. Between 2 and 12 pH is a vertical line, with slightly rounded corners at the tails. When the pH enters the vertical portion (the neutral region), the pH change accelerates as the pH approaches the neutral point (i.e., 7 pH at 25°C). To the PID controller, the accelerating response looks like a runaway response. Stopping the pH at a setpoint in the neutral region is like trying to stop on a dime in an accelerating car exceeding the speed limit with your foot still on the gas.
The process time constant predicted from the material balance (Tip #79) is for the response of the acid and base concentrations. The entire nice process time constant from having a well-mixed vessel essentially disappears as the process goes from the titration curve X axis, which is the ratio of reagent to influent, to the Y axis, which is pH. For example, a strong acid and strong base can cause a 20-minute time constant for the concentration response to become a 0.04 minute time constant for the pH response.
Fortunately, systems identified as strong acid or strong base have a slight concentration of a weak acid, carbonic acid, by virtue of the absorption of carbon dioxide. A little bit of a weak acid or a weak base goes a long way. The slight absorption of carbon dioxide from simple exposure to air causes a moderation of the titration curve slope near 6 pH that reduces the change in process gain from seven to three orders of magnitude in the neutral region.
In linear reagent control, the process variable for the controller becomes the X axis instead of the Y axis of the titration curve. The controller sees a concentration response that is more linear and slower. The process time constant achieved by the considerable investment in having a well-mixed vessel is restored.
Concept: The use of the X axis of the titration curve can reduce the nonlinearity by orders of magnitude. The fit of the control system curve to the lab curve is best measured in terms of how well the slopes (process gains) match near the setpoint. Even if the fit is not perfect, the improvement can be dramatic.
Details: The greatest benefits of this approach are seen for setpoints on the steep portion of the titration curve. A steep slope on the titration curve causes an acceleration of the pH change and amplifies valve limit cycles. The pH acceleration and the oscillations from an imperfect valve upset the controller and the operators. To slow down this pH excursion and reduce the amplitude of oscillations, translate the process variable (PV) from pH (Y axis) to percent reagent demand (X axis).
Use a signal characterizer in a Distributed Control System (DCS). The input to the characterizer is pH and the output is the PID PV in percent reagent demand. Add cascaded signal characterizers to provide enough resolution near the setpoint. Ask the plant lab to provide the titration curve data points in an Excel file. Make sure there are at least 20 data points in the operating range. Get the temperature of the sample and the concentration and type of reagent used. If there are not enough data points, ask the lab to repeat the titration in the operating range with a smaller reagent dose to create more points. Change the X axis scale from a ratio of reagent to sample volume to percent reagent demand.
Plot the curve and the slope of the curve created in the lab and created by the signal characterizer. Zoom in on the steep slope regions to compare the nonlinearity. Adjust the signal characterizer for a better match of the slopes near the setpoint. Provide the ability for the operator to enter a setpoint in pH and to read a PV in pH. Display and trend the linear reagent demand setpoint and PV. To facilitate operator understanding, add XY plots to the displays with the ability to zoom in on the control region. Train operators using a virtual plant so they become confident in the use of a linear reagent demand controller. Use solution pH temperature compensation besides the standard electrode temperature compensation of pH measurements. The reference temperature is the sample temperature when titration was done.
The use of linear reagent demand control does not eliminate the need for the precise, high rangeability control valves justified and obtained per Tips #65 and #80, #81, #82, #83, and #84. The need for linear reagent demand control is often greatest on the first stage of neutralization because this stage must cover the most ground and must deal with the majority of the disturbances. The last stage should be designed with a greater volume, better mixing, and more precise valves to keep the pH close enough to setpoint to reduce the nonlinearity seen by the controller. Use an adaptive tuner to compensate for changes in the titration curve.
Watch-outs: Temperature changes will change the water, acid, and base dissociation constants and consequently the solution pH and the titration curve slope. Chemists will sometimes use a weaker reagent to make the titration easier. For processes not exposed to air, the exposure of the sample to air and to humans exhaling carbon dioxide may cause enough carbon dioxide absorption to change the curve. The absorption of carbon dioxide and ions from the beaker and reference electrode becomes more problematic as water purity increases (e.g., boiler feed water, condensate, and deionized water).
Exceptions: For systems going from a steep part to a flat part of a titration curve or for titration curves that dramatically change in terms of slope, signal characterization is not beneficial.
Insight: Linear reagent demand control reduces pH nonlinearity and the amplification of limit cycles.
Rule of Thumb: Use linear reagent demand control when going from a flatter part to a steeper part of a titration curve for tighter control and less wear and tear on the valves and the operators.