Principles of Coagulation Chemistry Using Aluminum Sulfate
Coagulation and flocculation represent the primary physicochemical barrier in surface water and wastewater clarification facilities. Natural raw waters contain suspended colloidal solids, clay minerals, microorganisms, and natural organic matter (NOM) that carry negative surface electrostatic charges (ζ-potential typically between −15 mV and −30 mV). Mutual electrical repulsion prevents these microscopic particles from aggregating, maintaining a permanent colloidal suspension.
Aluminum sulfate, commonly referred to in municipal water engineering as alum with empirical formula $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O}$ (molecular weight approximately $594.4\text{ g/mol}$), acts as a multi-functional trivalent coagulant. When introduced into raw water, aluminum ions undergo instantaneous hydration and hydrolysis, generating a dynamic distribution of monomeric, polymeric, and amorphous precipitate species governed by pH, temperature, and mixing energy.
Two Primary Coagulation Mechanisms: Charge Neutralization vs. Sweep Floc
Depending on the coagulant dosage and aqueous pH regime, alum functions through two fundamental pathways:
- Charge Neutralization / Adsorption (Lower Dose, pH 4.5: 5.5): At acidic pH, positively charged hydrolyzed aluminum monomers and polymers (such as $\text{AlOH}^{2+}$, $\text{Al}_2(\text{OH})_2^{4+}$, and the tridecameric Keggin ion $\text{Al}_{13}\text{O}_4(\text{OH})_{24}^{7+}$) adsorb onto negatively charged colloidal surfaces, compressing the electrical double layer and collapsing the zeta potential toward zero. Under-dosing leaves particles negatively charged; over-dosing causes charge reversal and restabilization.
- Sweep Floc Coagulation (Higher Dose, pH 5.8: 7.2): At municipal operating pH and typical dosages (>15 mg/L), alum rapidly supersaturates with respect to amorphous aluminum hydroxide precipitate: $$\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O} + 6\text{HCO}_3^- \longrightarrow 2\text{Al(OH)}_3\downarrow + 3\text{SO}_4^{2-} + 6\text{CO}_2 + 14\text{H}_2\text{O}$$ The resulting sticky, volumetric $\text{Al(OH)}_3$ gel sweeps through the water column, physically entrapping suspended silts, algae, and colloidal color compounds as it settles.
Governing Mathematical Formulas for Alum Feed Systems
The calculation framework translates raw water volumetric flow rates ($Q$) and jar-tested target chemical dosages ($C_{\text{dose}}$) into physical pump feed rates and storage consumption.
The daily dry chemical demand in US standard waterworks units is:
In metric SI engineering units:
Because commercial water utilities almost universally handle liquid alum delivered in bulk tankers, the liquid volumetric feed rate ($Q_{\text{liquid}}$) must account for solution specific gravity ($SG$) and dry chemical weight fraction ($w$):
For standard AWWA B403 commercial liquid alum ($SG = 1.33, w = 0.485$):
The liquid volumetric feed rate delivered by the metering pumps is therefore:
For chemical pump stroke calibration using a graduated draw-down calibration cylinder (graduated in milliliters), the instantaneous volumetric rate is:
Stoichiometric Alkalinity Consumption and pH Control
Every mole of aluminum sulfate reacts stoichiometrically with six moles of bicarbonate alkalinity ($\text{HCO}_3^-$). Evaluating the molar ratio reveals the exact chemical consumption:
Thus, each $1.0\text{ mg/L}$ of dry alum dosed removes $0.505\text{ mg/L}$ of alkalinity. If raw water alkalinity is insufficient, the pH drops precipitously, destabilizing floc and causing elevated dissolved aluminum residuals (>0.20 mg/L) that violate the EPA Secondary Maximum Contaminant Level (SMCL). In such conditions, supplemental alkalinity must be fed:
- Hydrated Lime ($\text{Ca(OH)}_2$, 74.09 g/mol): $1.0\text{ mg/L}$ dry alum requires $0.374\text{ mg/L}$ pure $\text{Ca(OH)}_2$ for neutral balance.
- Caustic Soda ($\text{NaOH}$, 40.00 g/mol): $1.0\text{ mg/L}$ dry alum requires $0.404\text{ mg/L}$ $100\%\text{ NaOH}$ ($0.808\text{ mg/L}$ of $50\%\text{ NaOH}$).
- Soda Ash ($\text{Na}_2\text{CO}_3$, 105.99 g/mol): $1.0\text{ mg/L}$ dry alum requires $0.535\text{ mg/L}$ soda ash.
Coagulant Sludge Production Modeling
Alum sludge generated in sedimentation basins and backwash holding lagoons consists of both precipitated aluminum hydroxide flocs and removed raw water suspended solids:
Where $0.263$ represents the stoichiometric ratio of dry $\text{Al(OH)}_3$ solids generated per unit mass of commercial alum $(\frac{2 \times 78.0}{594.4} \approx 0.263)$.
Alum Dosing Benchmark Table Across Raw Water Quality Regimes
| Water Quality Regime | Raw Turbidity (NTU) | TOC / True Color (mg/L / Pt-Co) | Typical Alum Dose (mg/L) | Alkalinity Consumed (mg/L CaCO₃) | Recommended Coagulation pH |
|---|---|---|---|---|---|
| Low Turbidity, Low Color (Protected Aquifer/Lake) | 0.5: 3.0 | < 2.0 / < 5 | 8: 15 | 4.0: 7.6 | 6.8: 7.2 |
| Moderate Surface Water (Typical Reservoir) | 5.0: 25 | 2.5: 6.0 / 10: 25 | 18: 35 | 9.1: 17.7 | 6.4: 6.9 |
| Storm Runoff / River Flash Flood | 50: 250 | 6.0: 15 / 30: 80 | 40: 75 | 20.2: 37.9 | 6.0: 6.5 |
| High Organic Carbon / Humic Swamp Water | 2.0: 10 | 8.0: 25 / 50: 150 | 35: 65 (Enhanced Coagulation) | 17.7: 32.8 | 5.5: 6.2 |
| Cold Winter Water (< 4°C / 39°F) | 2.0: 15 | 3.0: 8.0 / 15: 30 | 25: 45 (+ Polymer Aid) | 12.6: 22.7 | 6.5: 7.0 |
Practical Worked Case Study: 10 MGD Municipal Clarification Facility
Engineering Design Example: River Intake Flash Runoff Event
Treatment Plant Context: A conventional surface water treatment facility treats an intake flow of $10.0\text{ MGD}$. A sudden upstream rain event increases river turbidity to $45\text{ NTU}$ and total organic carbon to $5.5\text{ mg/L}$. Raw water total alkalinity is measured at $50.0\text{ mg/L as CaCO}_3$. Jar tests establish an optimum dry alum dosage of $32.0\text{ mg/L}$. The plant utilizes commercial liquid alum with specific gravity $1.33$ and $48.5\%$ concentration ($5.38\text{ lb dry alum/gal}$). Two chemical metering pumps operate in parallel duty.
Step 1: Calculate Daily Dry Chemical Mass:
$$\text{Mass Rate}_{\text{dry}} = 10.0\text{ MGD} \times 32.0\text{ mg/L} \times 8.34 = 2,668.8\text{ lb/day dry alum (1,210.5 kg/day)}$$Step 2: Determine Commercial Liquid Volumetric Delivery:
$$Q_{\text{liquid}} = \frac{2,668.8\text{ lb/day}}{5.38\text{ lb/gal}} = 496.06\text{ gal/day}$$ $$\text{Hourly Feed Rate} = \frac{496.06\text{ GPD}}{24\text{ hours}} = 20.67\text{ GPH}$$Step 3: Diaphragm Metering Pump Calibration Rate:
For two duty metering pumps splitting the load evenly:
$$\text{Flow per Pump} = \frac{496.06\text{ GPD}}{2} = 248.03\text{ GPD (10.33 GPH)}$$ $$\text{Calibration Drawdown per Pump} = 248.03 \times 2.6288 = 652.0\text{ mL/min}$$Step 4: Stoichiometric Alkalinity Destruction & Residual Verification:
$$\text{Alkalinity Consumed} = 32.0\text{ mg/L} \times 0.505 = 16.16\text{ mg/L as CaCO}_3$$ $$\text{Residual Alkalinity} = 50.0 - 16.16 = 33.84\text{ mg/L as CaCO}_3$$Because residual alkalinity remains above the critical $30\text{ mg/L}$ floor, finished water pH remains stable without mandatory supplemental lime feed, though pre-lime readiness is advised if river alkalinity drops further.
Step 5: Coagulation Sludge Solids Generation:
Assuming 95% turbidity/TSS removal ($45 \times 0.95 = 42.75\text{ mg/L}$):
$$W_{\text{sludge}} = 10.0 \times \left(0.263 \times 32.0 + 42.75 \right) \times 8.34 = 10.0 \times (8.416 + 42.75) \times 8.34 = 4,267.2\text{ lb/day dry solids}$$Operational Guidelines and Storage Specifications
Handling and applying liquid aluminum sulfate requires careful engineering design:
- Crystallization Temperature: Commercial liquid alum has a freezing point of roughly −13°C (8°F) to −15°C (5°F). In northern climates, outdoor chemical bulk storage tanks require heat tracing and insulation to prevent viscous crystallization in pipe headers.
- Corrosion Resistance Materials: Alum solutions have an acidic pH between 2.1 and 2.7. All wetted piping, metering heads, valves, and tank linings must be constructed from non-metallic materials (HDPE, cross-linked polyethylene XLPE, PVDF, PTFE, or FRP) or high-grade alloys (Hastelloy C, Carpenter 20). Standard 304 or 316 stainless steels suffer rapid pitting and chloride-induced stress corrosion.
- Rapid Flash Mixing: Coagulant hydrolysis occurs within microseconds (10 to 100 milliseconds). Rapid mixing units (in-line static mixers or high-speed mechanical flash mixers with velocity gradients $G > 700\text{ s}^{-1}$) are mandatory at the point of chemical injection to ensure uniform micro-floc formation prior to slow flocculation ($G = 20\text{ to }70\text{ s}^{-1}$).
Frequently Asked Questions
How is dry alum feed rate calculated from raw water flow and dosage?
The dry chemical feed rate in pounds per day is determined by the standard waterworks formula: Feed Rate (lb/day) = Flow (MGD) * Target Dose (mg/L) * 8.34 lb/gal. In metric units, Mass Rate (kg/day) = Flow (m3/day) * Target Dose (g/m3) / 1,000.
How do you convert dry alum dosage to commercial liquid alum pump feed rate?
Commercial liquid alum typically has a specific gravity of 1.33 and contains approximately 48.5% dry aluminum sulfate by weight, yielding about 5.4 lbs of dry alum per gallon of solution. The liquid feed rate in gallons per day is: GPD = (Pounds Dry Alum per Day) / (5.4 lbs dry alum/gal). To calibrate a diaphragm metering pump, convert GPD to mL/min by multiplying by 2.6288.
How much natural alkalinity does alum coagulation consume?
Stoichiometrically, each 1.0 mg/L of commercial dry alum (Al2(SO4)3 * 14H2O) added consumes approximately 0.505 mg/L of natural alkalinity as calcium carbonate (CaCO3). If raw water alkalinity falls below 30-45 mg/L as CaCO3, the pH will plunge below the optimum sweep floc range (pH 5.8-7.2), requiring supplemental dosing of hydrated lime or caustic soda.
What is the optimal pH window for aluminum sulfate coagulation?
The optimum pH range for sweep floc coagulation with alum is 5.8 to 7.2. Below pH 5.5, aluminum remains partially dissolved as trivalent Al3+ and hydrated cations, leading to elevated residual aluminum in finished water. Above pH 7.8, the amphoteric aluminate ion Al(OH)4- forms, which increases solubility and causes turbidity carryover.