⟵ 08 Scale (Problem Set) · Contents · 09 Microbiology ⟶
Scale: Answer Key
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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.
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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.
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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 rare event occurs, thermodynamic permission exists but kinetic action has not started.
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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.
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LSI measures only CaCO₃ scaling pressure. At 5 cycles, silica concentration reaches 80 × 5 = 400 mg/L - far above the ~150 mg/L practical solubility limit. Silica polymerization and deposition are likely, regardless of LSI. A negative LSI means the bulk water is not biased toward calcium carbonate precipitation. It does not mean the system is safe from all forms of scale.
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COC ≈ 3,400 / 850 = 4.0 cycles.
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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.
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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)
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RSI = 2 × 6.83 − 8.60 = 13.66 − 8.60 = 5.06. RSI < 6 indicates scale-forming tendency.
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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.