13.1 Coagulation, Flocculation, and Sedimentation

From Raw Water Particle to Settled Water

The April 2024 PE Civil Water Resources and Environmental (WRE) specification lists drinking-water treatment, sedimentation, and coagulation/flocculation as explicit knowledge areas. The exam is an 80-question, 9-hour computer-based test; the supplied references are the NCEES PE Civil Reference Handbook and Recommended Standards for Water Works (Ten States Standards). Many surface-water-treatment items are design checks or troubleshooting scenarios tied to a conventional treatment train. Keep the sequence straight: destabilize, grow floc, settle, then filter.

Coagulation adds a chemical such as alum, ferric chloride, or a cationic polymer to neutralize the negative surface charge on colloids (charge neutralization) or to form a hydroxide precipitate that enmeshes particles (sweep floc). Raw-water colloids are too small for gravity removal in a practical basin, so coagulation enables every downstream physical step. It is sensitive to dose, alkalinity, pH, temperature, and natural organic matter (NOM).

Flocculation is gentle mixing after rapid mix: enough collisions to grow floc, not so much shear that floc shatters and carries through to the filters. Sedimentation then removes floc by gravity - in ideal (Type I) settling, any particle whose settling velocity exceeds the surface overflow rate (SOR) is captured regardless of basin depth.

Mixing Energy and Core Design Checks

Mixing intensity is the velocity gradient G = sqrt(P / (mu * V)), where P is power input (W), mu is dynamic viscosity (N-s/m^2), and V is basin volume (m^3). Typical targets: rapid mix G = 500-1,000 s^-1 with detention of 10-60 s; flocculation G = 20-80 s^-1 with detention of 20-30 min. The product Gt (often 10^4 to 10^5) characterizes total floc-contact opportunity. Tapered flocculation steps G down from one stage to the next so newly formed floc is not torn apart.

Area A is plan area, never sidewall area. With multiple basins in service, use total active plan area; if a basin is offline, recompute at firm capacity. Apply the same rule to weir length - count only launders actually receiving settled water.

Alkalinity, pH, and the Jar Test

Alum and ferric salts consume alkalinity and depress pH. Roughly, each mg/L of alum consumes about 0.5 mg/L of alkalinity (as CaCO3). Coagulation has an effective pH window (alum near pH 5.5-7.5; ferric works over a broader, generally lower range). A low-alkalinity raw water can run out of buffering, the pH crashes, and the intended hydroxide floc never forms. The fix is to add lime, caustic soda, or soda ash so the coagulant can react - not simply more alum.

If a troubleshooting item says turbidity removal worsened after a higher alum dose while pH fell, the supported answer is pH/alkalinity correction confirmed by jar testing - not more coagulant. Jar testing screens dose, pH adjustment, polymer aid, floc formation, settling, and sludge production before changing plant feed. PE items may hand you jar-test data and ask for the least chemical dose meeting settled-water turbidity and pH.

Sedimentation Calculation Workflow

1. Convert flow to the unit the criterion uses (gpd, MGD, cfs, gpm).
2. Identify active basin count, active plan area, basin volume, and effective weir length.
3. SOR = Q / A.
4. Detention time t = V / Q (consistent units).
5. Weir overflow rate = Q / L.
6. Compare each to the supplied criterion and name the controlling failure.
7. For removal questions use a mass balance if flow or solids change through the unit.

What the Exam Is Really Testing

A long-detention basin can still fail if SOR is too high, inlet baffles short-circuit flow, or sludge resuspends. A shallow basin can succeed if plan area and hydraulic distribution are adequate. This is the heart of ideal (Type I) settling theory: the critical settling velocity v_c equals Q/A, the overflow rate, and depth only sets the detention time, not whether a given particle is caught.

Before picking an option, sanity-check units: SOR in gpd/ft^2, detention in hours, weir loading in gpd/ft. If your answer comes out as ft^3/day or mg/L, you solved a different problem. Watch unit mixing too - a basin volume in million gallons divided by flow in MGD gives detention in days, so convert to hours (x24) before comparing to a 2-4 hour criterion.

Settling Velocity and Coagulant Quick Reference

For discrete spherical particles in the laminar regime, Stokes' law gives settling velocity v = g(rho_p - rho_w)d^2 / (18*mu): velocity scales with the square of particle diameter, which is exactly why coagulation/flocculation must grow floc before sedimentation can work. A 10-fold larger floc settles roughly 100 times faster.

• Alum, Al2(SO4)3.14H2O: dose typically 10-50 mg/L; consumes alkalinity; best near pH 5.5-7.5.
• Ferric chloride, FeCl3: effective over a broader, generally lower pH; good in cold or high-color water.
• Cationic polymer: low dose (0.1-1 mg/L) as primary coagulant or filter aid; does not consume alkalinity.
• Lime/soda ash: added to restore alkalinity and hold pH in the coagulation window.

Knowing these ranges lets you reject implausible dose answers without a full jar-test table.