2.2 Coagulation Chemistry, Rapid Mixing & Chemical Dosing (Alum, Ferric, Polymers)

Coagulation Chemistry, Rapid Mixing & Chemical Dosing

Coagulation is the foundational chemical unit process in conventional and direct surface water treatment. Natural raw water contains colloidal suspensions that cannot settle by gravity within reasonable operational timeframes. A certified water treatment operator must master the electrokinetic forces governing colloidal stability, the chemical behavior of primary coagulants and polymer aids, and the precise mechanical and hydraulic parameters required for rapid mixing.

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1. Colloidal Suspensions and Electrokinetic Theory

Turbidity, natural organic matter (NOM), humic acids, and microscopic clays exist in natural water as colloidal particles ranging in diameter from 0.001 to 1.0 micrometers (μm).

Because of their minute mass and massive surface-area-to-mass ratio, gravitational forces are negligible compared to surface electrokinetic forces. A 0.1 μm clay colloid would require hundreds of years to settle just one foot through quiescent water.

The Electrical Double Layer and Zeta Potential

Colloids in natural surface waters carry a net negative surface electrical charge. This negative surface charge develops from isomorphic substitution in mineral lattices, ionization of surface carboxyl and hydroxyl functional groups on organic matter, and preferential adsorption of natural anions.

   +-------------------------------------------------------------+
   |                    THE ELECTRICAL DOUBLE LAYER              |
   |                                                             |
   |   [ Colloid Surface (-) ]                                   |
   |      |  STERN LAYER (Bound Cations + + + + +)               |
   |      |---- SLIPPING PLANE / SHEAR PLANE  <-- Zeta Potential |
   |      |  DIFFUSE LAYER (+ - + - + + - + -)                   |
   |      v                                                      |
   |   BULK SOLUTION (Electroneutral Bulk Water)                 |
   +-------------------------------------------------------------+

1. Stern Layer: A rigidly held, compact layer of positively charged counter-ions (cations) attracted to the negative particle surface.
2. Diffuse Layer: A surrounding outer zone where positive cations outnumber anions, but ion concentration gradually transitions to match the bulk solution.
3. Slipping Plane (Plane of Shear): The boundary where the liquid moves with the particle relative to the bulk water.
4. Zeta Potential (ZP): The measurable electrical potential (voltage) at the slipping plane, expressed in millivolts (mV). In stable natural waters, zeta potential ranges between -15 mV and -30 mV. This negative electrical potential generates electrostatic repulsive forces that exceed the attractive van der Waals forces, preventing particles from colliding and agglomerating.

Primary Coagulation Mechanisms

Coagulation achieves destabilization through four primary physical-chemical mechanisms:

1. Charge Neutralization: Highly charged trivalent cations ($\text{Al}^{3+}$, $\text{Fe}^{3+}$) adsorb specifically onto the negative colloid surface, compressing the electrical double layer and reducing the zeta potential toward neutral (-5 to 0 mV). Van der Waals attraction then dominates upon contact.
2. Enmeshment in a Precipitate (Sweep Flocculation): When metal coagulants are added in concentrations exceeding the solubility limit of the metal hydroxide at pH 6.5–8.0, amorphous precipitates $[\text{Al(OH)}_3\text{(s)}$ or $\text{Fe(OH)}_3\text{(s)}]$ rapidly form. Colloidal particles are physically trapped ("swept") within the settling sticky mass.
3. Interparticle Polymer Bridging: Long-chain synthetic polymer molecules attach simultaneously to multiple colloidal particles, forming physical molecular bridges.
4. Double-Layer Compression: High concentrations of inert electrolytes in the bulk solution reduce the physical thickness of the diffuse layer without specific adsorption.

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2. Primary Coagulants and Reaction Chemistry

The most widely utilized primary coagulants in drinking water treatment are aluminum- and iron-based metallic salts.

Aluminum Sulfate (Alum)

Commercial dry alum has the chemical formula $\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O}$ (molecular weight $\approx 594\text{ g/mol}$). Liquid alum is delivered as an approximate 48.5% solution (containing approximately 5.4 lbs of dry alum per gallon of solution, or 8.3% active $\text{Al}_2\text{O}_3$).

When added to water containing natural calcium bicarbonate alkalinity, alum reacts according to the following stoichiometric relationship:

$\text{Al}_2(\text{SO}_4)_3 \cdot 14\text{H}_2\text{O} + 3\text{Ca}(\text{HCO}_3)_2 \longrightarrow 2\text{Al}(\text{OH})_3\downarrow + 3\text{CaSO}_4 + 6\text{CO}_2\uparrow + 14\text{H}_2\text{O}$

• Optimal Coagulation pH Range: 5.8 to 7.5
• Alkalinity Consumption: Every 1.0 mg/L of commercial alum fed consumes approximately 0.45 to 0.50 mg/L of natural alkalinity (expressed as $\text{CaCO}_3$).
• Carbon Dioxide Generation: The reaction releases dissolved free carbon dioxide ($\text{CO}_2$), which further lowers water pH.

Ferric Chloride and Ferric Sulfate

• Ferric Chloride ($\text{FeCl}_3$): Delivered as a dark brown, highly acidic liquid (35–45% strength, pH < 1.0).
• Ferric Sulfate [$\text{Fe}_2(\text{SO}_4)_3$]: Commercial liquid or granular iron coagulant.

\text{FeCl}_3 + 3\text{H}_2\text{O} \longrightarrow \text{Fe}(\text{OH})_3\downarrow + 3\text{H}^+ + 3\text{Cl}^-$$$$3\text{H}^+ + 3\text{HCO}_3^- \longrightarrow 3\text{CO}_2 + 3\text{H}_2\text{O}

• Optimal Coagulation pH Range: 4.0 to 11.0 (exceptionally broad operating window compared to alum).
• Alkalinity Consumption: Every 1.0 mg/L of ferric chloride consumes approximately 0.92 mg/L of alkalinity as $\text{CaCO}_3$.
• Operating Advantages: Forms heavier, denser ferric hydroxide floc that settles faster than alum floc in cold high-altitude water. Does not leave residual dissolved aluminum in finished water.
• Disadvantages: Extremely corrosive to feed lines, pump heads, and concrete; produces yellow/brown stains if overdosed or poorly mixed.

Polyaluminum Chloride (PACl) and Aluminum Chlorohydrate (ACH)

PACl coagulants are pre-hydrolyzed inorganic aluminum polymers with the general formula $\text{Al}n\text{Cl}{(3n-m)}(\text{OH})_m$.

• Pre-Neutralized: PACl contains engineered polymeric aluminum species (such as the $\text{Al}{13}$ tridecamer cation $\text{AlO}4\text{Al}{12}(\text{OH}){24}(\text{H}2\text{O}){12}^{7+}$) with high cationic charge density.
• Minimal Alkalinity Destruction: Consumes 50% to 80% less natural alkalinity than standard alum.
• Superior Cold-Water Performance: Because hydrolysis has already taken place during manufacturing, PACl forms robust, rapidly settling floc in cold mountain runoff ($<4^\circ\text{C}$) without requiring supplemental base dosing.

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3. Coagulant Aids and Polymers

Coagulant aids (polyelectrolytes) are high-molecular-weight synthetic organic compounds composed of repeating acrylamide or amine monomer units.

CRITICAL OPERATING WARNING: Polymer Overdosing Overdosing polymers is a severe operational error. Excessive cationic polymer reverses colloidal charge (making particles positive), causing charge restabilization. Overdosing long-chain flocculant aids causes steric hindrance (polymer coats particle surfaces, leaving no open attachment sites) and creates sticky, viscous residues that rapidly bind and permanently blind granular filter media, causing rapid headloss accumulation.

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4. Chemical Dosing Calculations and Alkalinity Balancing

Maintaining adequate buffering capacity post-coagulation is mandatory to prevent acidic, highly corrosive finished water. Plants must maintain a minimum finished water alkalinity of 20 to 30 mg/L as $\text{CaCO}_3$.

Standard Chemical Feed Formula (The Pounds Formula)

$\text{Chemical Feed (lb/day)} = \text{Flow (MGD)} \times \text{Dosage (mg/L)} \times 8.34\text{ lb/gal}$

$\text{Commercial Product (lb/day)} = \frac{\text{Pure Chemical Feed (lb/day)}}{\text{Active Strength (Decimal Fraction)}}$

Worked Example: Alum Dosing and Alkalinity Supplementation

A Colorado conventional water treatment plant treats a spring snowmelt flow of 4.0 MGD. The raw water has a natural alkalinity of 18.0 mg/L as $\text{CaCO}_3$. Jar testing indicates an optimal alum dose of 28.0 mg/L. The plant standard requires maintaining at least 25.0 mg/L residual alkalinity entering the sedimentation basins. Hydrated lime [$\text{Ca(OH)}_2$, 100% active, where 1.0 mg/L lime yields 1.35 mg/L alkalinity as $\text{CaCO}_3$] is used for supplemental buffering.

Step 1: Calculate pure daily alum feed: $\text{Alum (lb/day)} = 4.0\text{ MGD} \times 28.0\text{ mg/L} \times 8.34 = 934.08\text{ lb/day}$

Step 2: Calculate alkalinity consumed by alum: $\text{Alkalinity Consumed} = 28.0\text{ mg/L alum} \times 0.45\text{ mg/L Alk / mg/L Alum} = 12.6\text{ mg/L as }\text{CaCO}_3$

Step 3: Determine remaining natural alkalinity: $\text{Remaining Alkalinity} = 18.0\text{ mg/L} - 12.6\text{ mg/L} = 5.4\text{ mg/L as }\text{CaCO}_3$

Step 4: Calculate required supplemental alkalinity: $\text{Deficit} = 25.0\text{ mg/L target} - 5.4\text{ mg/L remaining} = 19.6\text{ mg/L as }\text{CaCO}_3$

Step 5: Calculate required hydrated lime dosage: $\text{Lime Dose} = \frac{19.6\text{ mg/L Alk}}{1.35\text{ mg/L Alk / mg/L Lime}} = 14.52\text{ mg/L }\text{Ca(OH)}_2$

Step 6: Calculate daily lime mass feed rate: $\text{Lime Feed (lb/day)} = 4.0\text{ MGD} \times 14.52\text{ mg/L} \times 8.34 = 484.39\text{ lb/day}$

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5. Rapid Mixing Hydraulics and Equipment

Rapid mixing (flash mixing) serves one singular, critical objective: to instantly and uniformly disperse the concentrated chemical coagulant throughout the entire raw water stream before primary hydrolysis and charge-neutralization reactions occur (which complete in less than 0.1 to 1.0 second).

+-------------------------------------------------------------+
|                  RAPID MIX DESIGN PARAMETERS                |
|                                                             |
|  Hydraulic Retention Time (HRT):  <1 to 30 seconds          |
|  Velocity Gradient (G Value):     700 to 1,000+ s^-1        |
|  Camp Parameter (G x t):          10,000 to 30,000          |
+-------------------------------------------------------------+

The Velocity Gradient ($G$)

The intensity of mixing is mathematically quantified by the velocity gradient ($G$), introduced by Camp and Stein:

$G = \sqrt{\frac{P}{\mu V}}$

Where $P$ is power dissipated into the water (ft-lb/s or Watts), $\mu$ is dynamic viscosity (lb-s/ft² or $\text{Pa}\cdot\text{s}$), and $V$ is basin liquid volume (ft³ or m³). In rapid mixing, target $G$ values range from $700\text{ s}^{-1}$ to over $1,000\text{ s}^{-1}$.

Rapid Mix Technologies

1. Mechanical Flash Mixers: High-speed impellers (radial turbine or axial marine propellers rotating at 100–350 RPM) housed in small compartmentalized chambers with detention times of 10 to 30 seconds. If detention time exceeds 30 seconds, energy is wasted and early micro-flocs begin to shear.
2. Inline Static Mixers: Unpowered stationary geometric elements installed directly inside the raw water pipeline. As water flows through the helical vanes at high velocity ($>4–6\text{ ft/s}$), intense turbulent eddies and fluid shear instantly disperse chemicals with detention times $<2\text{ seconds}$ and no mechanical drive maintenance.
3. Hydraulic Jumps: Coagulant is injected directly at the supercritical toe of a hydraulic jump formed across a Parshall flume or weir drop. High hydraulic energy dissipation achieves instantaneous, violent mixing without external electrical power.