2.1 Physical & Chemical Water Treatment

Physical & Chemical Water Treatment

Physical and chemical water treatment processes form the backbone of conventional surface water treatment plants. These processes are designed to remove suspended solids, colloidal particles, and dissolved organics that cause turbidity, color, and harbor pathogens.

Coagulation and Flocculation Chemistry

Most natural particles in surface water are negatively charged and repel each other, keeping them in stable suspension. Coagulation is the rapid chemical process of neutralizing these charges. When a coagulant like aluminum sulfate (alum) or ferric chloride is added to water, it hydrolyzes to form highly charged, polynuclear metal species that compress the electrical double layer around particles.

Alum Coagulation Stoichiometry

The reaction of alum (often $Al_2(SO_4)_3 \cdot 14H_2O$) with natural alkalinity (represented by calcium bicarbonate) is:

$Al_2(SO_4)_3 \cdot 14H_2O + 3Ca(HCO_3)_2 \rightarrow 2Al(OH)_3(s) + 3CaSO_4 + 6CO_2 + 14H_2O$

Notice that this reaction:

1. Consumes alkalinity ($3$ moles of alkalinity per mole of alum)
2. Produces carbon dioxide, which can lower the pH
3. Forms an insoluble precipitate of aluminum hydroxide ($Al(OH)_3$), known as sweep floc

If natural alkalinity is insufficient, supplemental alkalinity must be added, usually in the form of lime ($Ca(OH)_2$) or soda ash ($Na_2CO_3$). Polymers (cationic, anionic, or non-ionic) are often added as coagulant aids to bridge particles and form larger, denser flocs that settle faster.

Rapid Mix and Flocculation Design

The hydrodynamics of mixing are described by the velocity gradient ($G$), which represents the intensity of mixing. $G$ (with units of $s^{-1}$) is defined as:

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

Where:

• $P$ = Power input (Watts)
• $\mu$ = Dynamic viscosity of water ($Pa \cdot s$)
• $V$ = Volume of the mixing basin ($m^3$)

The product of $G$ and the hydraulic detention time ($t$) gives the dimensionless $GT$ value, which is a measure of the total work done on the water. For rapid mix, typical $G$ values are $700$ to $1,000 \ s^{-1}$ with $t$ around $30$ to $60$ seconds, yielding $GT$ values around $20,000$ to $60,000$. Flocculation requires gentler mixing to promote particle collisions without shearing the fragile flocs, with $G$ values typically tapering from $70$ to $10 \ s^{-1}$ over a $20$ to $45$ minute detention time.

Sedimentation Basin Hydraulics

After flocculation, water enters a sedimentation basin where flocs settle by gravity. The most critical design parameter is the Surface Overflow Rate ($V_0$):

$V_0 = \frac{Q}{A}$

Where $Q$ is the flow rate and $A$ is the surface area of the basin. Particles with a settling velocity ($v_s$) greater than $V_0$ will be completely removed. Particles with $v_s < V_0$ will be removed at a fractional rate of $v_s / V_0$.

Other key hydraulic parameters include:

• Detention Time ($t$): $t = V / Q$
• Weir Loading Rate (WLR): The flow over the effluent weir per unit length. WLR = $Q / L$, where $L$ is the weir length. Typical values are $100$ to $250 \ m^3/day/m$.

Settling Types

There are four distinct types of settling in water and wastewater treatment:

• Type I (Discrete Particle Settling): Unhindered settling of individual particles (e.g., grit removal). Described by Stokes' Law.
• Type II (Flocculant Settling): Particles agglomerate as they settle, increasing their mass and settling velocity (e.g., primary sedimentation).
• Type III (Hindered/Zone Settling): High particle concentration causes particles to settle as a blanket (e.g., secondary clarifiers).
• Type IV (Compression Settling): Particles physically rest on each other and compress under the weight of overlying layers (e.g., bottom of deep clarifiers or sludge thickeners).

Filtration Kinetics and Head Loss

Filtration removes remaining suspended particles. Rapid sand filters use a single layer of sand, but dual-media filters (anthracite coal over sand) are more common today. Dual-media allows for deeper penetration of particles, increasing the filter run time before backwashing is necessary.

Head loss through a clean filter bed can be modeled using the Carmen-Kozeny equation or the Ergun equation. The basic form of the Carmen-Kozeny equation for laminar flow is:

$h_L = f \cdot \frac{L}{d} \cdot \frac{v^2}{2g}$

Where the friction factor $f$ depends on the porosity ($\epsilon$), sphericity ($\phi$), and Reynolds number. Head loss increases over time as particles accumulate in the pores. When head loss reaches a critical threshold or effluent turbidity spikes (particle breakthrough), the filter must be backwashed.

Worked Example: Surface Overflow Rate

A water treatment plant processes $10,000 \ m^3/day$ through a rectangular clarifier measuring $20$m long and $10$m wide. What is the surface overflow rate, and will a particle with a settling velocity of $60 \ m/day$ be fully removed?

$A = 20 \times 10 = 200 \ m^2$ $V_0 = \frac{Q}{A} = \frac{10,000}{200} = 50 \ m/day$

Since $v_s$ ($60 \ m/day$) is greater than $V_0$ ($50 \ m/day$), the particle will be 100% removed.