pH is a logarithmic measure, so each unit represents a tenfold change in hydrogen ion activity. For a strong acid neutralised with a strong base the titration curve is nearly vertical around neutrality: a minute excess of reagent moves the pH by several units. To bring a strongly acidic stream into a narrow band the reagent must be metered with a precision, relative to its full flow, that is orders of magnitude beyond what a single control valve can deliver. Shinskey (1973) set out this rangeability problem and the classical answers to it: neutralise in stages, with coarse adjustment first and fine adjustment later, and use valves or pumps of different sizes in sequence.

Real effluents are seldom pure strong acids. Weak acids and bases, carbonates, phosphates and amines buffer the solution and flatten the curve, which makes control easier but raises reagent demand. Models of pH dynamics built from chemical equilibria and from reaction invariants capture this behaviour (McAvoy et al., 1972; Gustafsson and Waller, 1983), and the strong acid equivalent of Wright and Kravaris (1991) offers a way of linearising it. At a multiproduct site the difficulty is that the buffering changes with the campaign, so that controller settings which suit one effluent oscillate or respond sluggishly with another.

A pH loop can only correct what it has seen. The delay between adding reagent and observing its effect at the electrode includes the time to disperse the reagent through the vessel, transport delay to the electrode, and the response of the electrode itself. McMillan (1994) treats the ratio of this dead time to the vessel residence time as the central design quantity: a large, poorly agitated tank has plenty of volume and still controls badly. Short-circuiting from inlet to outlet and stagnant zones make matters worse and can be diagnosed by the tracer methods of residence time distribution analysis (Levenspiel, 1999). Agitator selection and the point of reagent addition govern blend time (Paul et al., 2004). Coated or aged electrodes add a slow, drifting lag that is easily mistaken for a process problem.

Reagents differ in speed as well as in price. Sodium hydroxide and mineral acids react almost instantly. Lime slurry is cheaper per unit of alkalinity but must dissolve before it reacts, needs longer residence time, and with sulfate-bearing effluent forms calcium sulfate scale and sludge (Eckenfelder, 2000). A unit can therefore be limited not by its vessels but by reagent preparation, by the size of a dosing pump, or by solids handling downstream.

The first phase defines what the unit is being asked to do. Flow records are examined for peaks and their duration, not only for averages. Samples of the influent are taken across the campaigns that matter and titrated in the laboratory with the plant reagent, giving a family of titration curves. From these follow the range of reagent demand, the steepness of the curve at the target pH, and so the precision of reagent delivery that control within the permit band requires. The permit conditions themselves, including any averaging period, are read carefully, because a limit on an instantaneous value and a limit on a composite sample call for different designs.

The second phase asks which element fails first as load rises. Table 1 lists the candidate constraints, the way each shows itself in operation, a diagnostic check, and the remedies that should be considered before new vessels. The checks are deliberately simple. A step test with the controller in manual gives the dead time and the process gain at the current operating point. Valve position and pump stroke records show whether reagent delivery saturates. A tracer test shows whether the working volume is the nominal volume. Comparing the on-line electrode with a freshly calibrated portable instrument separates measurement faults from process faults.

Once the constraint is known, the third phase seeks capacity that needs no capital. Controller tuning is revisited with a method suited to processes dominated by dead time (Skogestad, 2003), and the gain is scheduled against pH or against campaign where the titration curve changes (Åström and Hägglund, 2006). Feedforward from influent flow removes the largest measurable disturbance (Seborg et al., 2016). Electrode cleaning and calibration intervals are set from observed drift. Production scheduling can be asked to avoid the simultaneous discharge of the two most demanding streams, which is subordination in Goldratt's sense: the rest of the plant adapts to the constraint while it remains one.

If exploitation is not enough, the constraint is elevated by modification. The options, roughly in order of cost, are moving the reagent injection point or the electrode, adding a small trim valve or dosing pump, improving agitation, adding an in-line mixer with a fast loop ahead of the tank, installing upstream equalisation, and adding a further stage. More elaborate nonlinear or adaptive controllers have been demonstrated on laboratory neutralisation rigs (Henson and Seborg, 1994) and may suit a site with the skills to maintain them. Every modification, including a change of reagent, passes through the site's management of change system (CCPS, 2008) with a hazard study where warranted (IEC, 2016), since neutralisation involves corrosive reagents, heat of reaction and, with some effluents, the possibility of gas evolution.

The final phase repeats the diagnostic checks of the second under the new arrangement and at the highest load that can be arranged safely. The purpose is twofold: to confirm that the constraint addressed has moved, and to learn which element now limits the unit. A debottlenecking exercise ends when the required capacity is met with a stated margin, or when the next constraint can only be relieved by an investment that has to be justified on its own terms by the usual methods of project evaluation.