Problem 12.3: Which constraint governs and at that cycle

From Chapter 12 Problem Set. Level 3: Optimization.

Question

Which constraint governs, and at that cycle count, what are the tower concentrations of calcium, alkalinity, and chloride?

Answer

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Conductivity tracks total dissolved solids but does not distinguish between species. If calcium carbonate is precipitating as scale, its contribution to conductivity disappears – but the controller does not know this. Makeup continues entering, the conductivity setpoint holds, and the true concentration of scaling species drifts from what conductivity reports. The diagnostic is to compare cycles of concentration calculated from a soluble tracer ion (chloride) against cycles calculated from a scaling-risk ion (calcium). If chloride-based COC is significantly higher than calcium-based COC, calcium is leaving the water as scale. The divergence quantifies how much.