Problem 12.9: Your makeup water contains 320 mgL calcium
From Chapter 12 Problem Set. Level 3: Optimization.
Question
Your makeup water contains 320 mg/L calcium hardness as CaCO₃, 210 mg/L alkalinity as CaCO₃, and 150 mg/L chloride. Your scale inhibitor is rated for a maximum of 1,400 mg/L calcium hardness and 1,000 mg/L alkalinity in the tower water.
- What is the maximum number of cycles allowed by the calcium hardness limit?
- What is the maximum number of cycles allowed by the alkalinity limit?
- Which constraint governs, and at that cycle count, what are the tower concentrations of calcium, alkalinity, and chloride?
- Explain why the actual maximum safe cycle count may be lower than the value you calculated, considering pH, temperature, and the interactions between scaling parameters.
Answer
Show answer
Calcium limit: 1,400 ÷ 320 = 4.38 cycles. Alkalinity limit: 1,000 ÷ 210 = 4.76 cycles. Calcium governs – round down to 4 cycles for safety margin. At 4 cycles: calcium = 320 × 4 = 1,280 mg/L as CaCO₃; alkalinity = 210 × 4 = 840 mg/L as CaCO₃; chloride = 150 × 4 = 600 mg/L. The actual safe maximum may be lower because CO₂ stripping in the tower drives pH upward. At 840 mg/L alkalinity, pH will likely exceed 8.3, shifting the carbonate equilibrium strongly toward CO₃²⁻ and increasing CaCO₃ supersaturation beyond what calcium hardness alone would suggest. The LSI will be significantly positive. Additionally, condenser tube surface temperatures are higher than bulk water temperature, and inverse solubility means calcium carbonate is least soluble exactly where heat transfer matters most. The true operating limit is determined by the interaction of hardness, alkalinity, pH, and temperature – not by any single parameter.