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Problem 1
A tower is running at LSI = +1.1 but has no visible scaling. Give two operational reasons this can be true.
Authored answer
Any two: effective scale inhibitor program extending induction time; good dispersion and low residence time; clean surfaces with few nucleation sites; high turbulence preventing particle adhesion; side-stream filtration removing seed crystals; effective control of hot-spot temperatures.
Read the connected sectionProblem 2
Explain why CaCO₃ often precipitates on heat-transfer surfaces even when the bulk water looks stable.
Authored answer
CaCO₃ exhibits inverse solubility: its solubility decreases as temperature rises. Heat-exchange surfaces are the hottest points in the system. Additionally, boundary layers at the surface concentrate ions, local pH can rise at cathodic sites, and the metal surface provides nucleation and anchoring points. Bulk water may be below saturation while the surface microenvironment is above it.
Read the connected sectionProblem 3
Define supersaturation in one sentence. Then explain why supersaturated water can remain clear for weeks.
Authored answer
Supersaturation means dissolved ions exceed their equilibrium solubility but no stable solid has yet formed. Water can remain clear because nucleation requires an activation barrier to be overcome: ions must collide with compatible orientation and persist long enough to reach a critical cluster size. Until that occurs, thermodynamic permission exists but kinetic action has not started.
Read the connected sectionProblem 4
Explain how a phosphate-based inhibitor can itself become a source of scale. Name the scaling salt involved.
Authored answer
Polyphosphates hydrolyze into orthophosphate at elevated temperatures. Phosphonates can also revert under thermal or oxidative stress. The resulting orthophosphate reacts with calcium at elevated pH to precipitate calcium phosphate, Ca₃(PO₄)₂. The inhibitor chemistry itself becomes the source of a scaling ion.
Read the connected sectionProblem 5
A water treater says, “Our LSI is negative, so we don’t have a scale problem.” The makeup water contains 80 mg/L silica and the tower is running at 5 cycles. Why might the treater be wrong?
Authored answer
LSI measures only CaCO₃ scaling pressure. At 5 cycles, silica concentration reaches 80 × 5 = 400 mg/L, far above the ~150 mg/L conservative operating limit for near-neutral water. Silica polymerization and deposition are likely, regardless of LSI. A negative LSI means the water is safe from calcium carbonate scale, not from all scale.
Read the connected sectionProblem 6
Makeup conductivity = 850 µS/cm; tower conductivity = 3,400 µS/cm. Estimate cycles of concentration.
Authored answer
COC ≈ 3,400 / 850 = 4.0 cycles.
Read the connected sectionProblem 7
A tower uses sulfuric acid for pH control. Makeup sulfate = 50 mg/L. At 6 cycles, tower sulfate is measured at 480 mg/L, significantly higher than 50 × 6 = 300 mg/L. Why is the measured value higher than predicted?
Authored answer
Sulfuric acid (H₂SO₄) adds sulfate to the system in addition to what enters with the makeup water. At each cycle, both the makeup sulfate and the acid-contributed sulfate concentrate. The measured value is higher because the acid feed is introducing sulfate ions not present in the makeup analysis. This is why CaSO₄ risk must be checked in any acid-fed system.
Problem 8
Compute pHₛ and LSI for: pH = 8.6, T = 40°C, TDS = 2,200 mg/L, Ca hardness = 320 mg/L as CaCO₃, M-alkalinity = 220 mg/L as CaCO₃. Round logs to 2 decimals.
Authored answer
A = (log₁₀(2,200) − 1) / 10 = (3.34 − 1.00) / 10 = 0.23. B = −13.12 × log₁₀(313) + 34.55 = −13.12 × 2.50 + 34.55 = 1.75. C = log₁₀(320) − 0.4 = 2.51 − 0.40 = 2.11. D = log₁₀(220) = 2.34. pHₛ = (9.30 + 0.23 + 1.75) − (2.11 + 2.34) = 11.28 − 4.45 = 6.83. LSI = 8.60 − 6.83 = +1.77. Strongly scale-forming. (values are rounding-sensitive; full-precision yields LSI ≈ 1.70, same interpretation)
Read the connected sectionProblem 9
Using pHₛ from Question 8, compute RSI and interpret.
Authored answer
RSI = 2 × 6.83 − 8.60 = 13.66 − 8.60 = 5.06. RSI < 6 indicates scale-forming tendency.
Read the connected sectionProblem 10
Using alkalinity from Question 8, compute pHeq and PSI. Interpret.
Authored answer
pHeq = 1.465 × log₁₀(220) + 4.54 = 1.465 × 2.34 + 4.54 = 3.43 + 4.54 = 7.97. PSI = 2 × 6.83 − 7.97 = 13.66 − 7.97 = 5.69. PSI < 6 indicates scale-forming tendency, consistent with both LSI and RSI. PSI's contribution here is nuance rather than contradiction. By substituting the equilibrium pH for the measured pH, it accounts for the buffering capacity of the alkalinity during precipitation. The result is still scale-forming, but the PSI value (5.69) sits closer to the borderline than RSI (5.06), reflecting that this water's alkalinity provides some resistance to runaway precipitation compared to a low-alkalinity water at the same LSI.