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Drinking-Water Coagulation, Jar-Test Stoichiometry & Residuals

Alum Coagulation Alkalinity Consumed & Sludge Yield Formula

Calculate Filter Alum Alkalinity Consumed (mg/L CaCO3), Unadjusted Remaining Alkalinity (mg/L), Supplemental Alkalinity Dose Required (mg/L CaCO3), and Daily Dry Alum Sludge (kg/d).

Every 1 mg/L of commercial alum destroys ~0.45 mg/L CaCO3 alkalinity—crashing pH if unbuffered!

When commercial hydrated aluminum sulfate Al2(SO4)3·18H2O (MW = 666.4 g/mol) is dosed into raw surface water to sweep turbidity and color, each mole consumes 3 moles of natural calcium bicarbonate alkalinity (300 g/mol as CaCO3) to precipitate 2 moles of amorphous Al(OH)3 floc (156 g/mol)! Stoichiometrically, 1.0 mg/L of commercial alum destroys 300 / 666.4 = 0.45 mg/L of Alkalinity as CaCO3 and generates ~0.26 mg/L of dry Al(OH)3 chemical precipitate (on top of Removed_TSS_mg_L)! If Remaining_Alkalinity = Raw_Alk - 0.45 * Alum_Dose drops below a safe ~20 mg/L CaCO3 buffer, water pH crashes below 5.5 and dissolved aluminum passes straight through the sand filters unless supplemental lime or soda ash is fed!

Verify on a 50.0 MLD (50,000 m³/d) Surface-Water Plant—Plant_Flow = 50.0 MLD (B2), Jar_Test_Alum_Dose = 60.0 mg/L (B3 -> Alkalinity Consumed = 60 * 0.45 = 27.00 mg/L in E2), Raw_Water_Alkalinity = 35.0 mg/L CaCO3 (B4 -> Unadjusted Remaining = 8.00 mg/L in E3), Target_Residual_Alkalinity = 20.0 mg/L CaCO3 (B5 -> Supplemental Alkalinity Deficit = MAX(0, 20 - 8) = 12.00 mg/L CaCO3 in E4), and Raw_TSS_Removed = 40.0 mg/L (B6): Daily Dry Coagulation Sludge equals 50 * (40.0 + 0.26 * 60.0) = 2,780.00 kg/d (E5)!

Alum Jar-Test Stoichiometry KPI (50 MLD, 60 mg/L Alum, 35 Alk, 40 TSS)FormulaVerified Output
Alkalinity Consumed (mg/L CaCO3)0.45 * Alum_Dose_mg_L27.00 mg/L
Unadjusted Residual Alk (mg/L)Raw_Alkalinity - 0.45 * Alum_Dose8.00 mg/L (33.00 @ 60 Raw Alk)
Supplemental Alk Needed (mg/L)MAX(0, Target_Res_Alk - Unadj_Res_Alk)12.00 mg/L (0.00 @ 60 Raw Alk)
Total Dry Alum Sludge (kg/d)Flow_MLD * (TSS_Removed + 0.26 * Alum)2,780.00 kg/d

Alum Alkalinity Deficit & Dry Coagulation Sludge Formula

Validate Flow_MLD > 0, Alum_Dose > 0, Raw_Alkalinity >= 0, Target_Residual >= 5, and TSS_Removed >= 0!

=LET(qm_l, B2, al_d, B3, rw_a, B4, tg_a, B5, ts_r, B6, IF(OR(qm_l <= 0, al_d <= 0, rw_a < 0, tg_a < 5, ts_r < 0), "Invalid Alum Dose Input", LET(cn_a, 0.45 * al_d, rm_a, rw_a - cn_a, ROUND(MAX(0, tg_a - rm_a), 2))))

Well-Buffered Hard River Water Zero-Lime Check (Set Raw Alkalinity = 60 mg/L)

Raise Raw_Water_Alkalinity B4 from 35.0 mg/L to 60.0 mg/L: Unadjusted Residual Alkalinity E3 stays safely at 60 - 27 = 33.00 mg/L (> 20.0 mg/L floor), dropping Supplemental Lime/Soda Alkalinity Needed E4 to 0.00 mg/L!

=IF(ISTEXT(E4), E4, ROUND(B2 * (B6 + 0.26 * B3), 2))

Try the example

Use the original values or change them to test your understanding.

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