2.3 Disinfection Kinetics & Chemistry

Disinfection Kinetics & Chemistry

Disinfection is the mandatory final barrier in municipal water treatment, engineered to deactivate or destroy pathogenic micro-organisms (bacteria, viruses, and protozoan parasites such as Giardia lamblia and Cryptosporidium parvum). Disinfection is a chemical kinetic process governed by disinfectant type, chemical concentration, exposure time, pH, temperature, and water matrix chemistry. Mastering Chick-Watson kinetics, the EPA $CT$ concept, chlorine speciation equilibrium, breakpoint chlorination pathways, and disinfection byproduct (DBP) regulations is essential for NCEES PE exam calculations.

Disinfection Kinetics: Chick's Law & The Chick-Watson Model

Disinfection decay kinetics evaluate microbial survival as a function of disinfectant exposure over time.

Mathematical Kinetic Derivations

1. Chick's Law (First-Order Microbial Inactivation): Assumes a constant disinfectant concentration and first-order decay of viable organisms: $\frac{dN}{dt} = -k N \implies \ln\left(\frac{N}{N_0}\right) = -k t$

2. Chick-Watson Law: Incorporates disinfectant concentration ($C$, in $mg/L$) raised to a coefficient of dilution ($n$): $\ln\left(\frac{N}{N_0}\right) = -k C^n t$

   Where:

   • $N_0$ = Initial concentration of viable micro-organisms
   • $N$ = Surviving micro-organism concentration at time $t$
   • $k$ = Specific lethality coefficient ($L/mg\cdot min$)
   • $C$ = Residual disinfectant concentration ($mg/L$)
   • $n$ = Coefficient of dilution (when $n=1$, disinfection efficiency is equally sensitive to concentration and contact time)
   • $t$ = Contact time ($min$)

3. Hom-Haseman Model: Accounts for initial lag phases (shoulder curves) or declining inactivation rates (retarding curves): $\ln\left(\frac{N}{N_0}\right) = -k C^n t^m$

Log Inactivation & Removal Efficiency

Microbial reduction is expressed as "log inactivation":

$\text{Log Inactivation} = \log_{10}\left(\frac{N_0}{N}\right) = -\log_{10}\left(\frac{100 - \% \text{ Inactivation}}{100}\right)$

• 2-log inactivation: $99%$ reduction ($N/N_0 = 0.01$)
• 3-log inactivation: $99.9%$ reduction ($N/N_0 = 0.001$)
• 4-log inactivation: $99.99%$ reduction ($N/N_0 = 0.0001$)

The EPA $CT$ Concept & Contact Basin Hydraulics

Under the EPA Safe Drinking Water Act Surface Water Treatment Rule (SWTR), disinfection compliance is demonstrated using the $CT$ parameter ($mg\cdot min/L$):

$CT_{calc} = C_{actual} \times T_{10}$

Where:

• $C_{actual}$ = Residual disinfectant concentration measured at the basin exit ($mg/L$)
• $T_{10}$ = Hydraulic contact time required for $90%$ of the water to pass through the contact basin ($min$)

Hydraulic Baffling Factors

Ideal plug flow is never achieved in real basins due to short-circuiting and dead zones. $T_{10}$ is calculated using the theoretical hydraulic detention time ($T = V/Q$) modified by a baffling factor ($BF = T_{10}/T$):

$T_{10} = T \times BF = \left(\frac{V}{Q}\right) \times BF$

• Unbaffled / Single-inlet basin: $BF \approx 0.10$
• Poor baffling: $BF \approx 0.30$
• Average baffling: $BF \approx 0.50$
• Superior serpentine baffling: $BF \approx 0.70$
• Perfect plug flow pipe reactor: $BF = 1.00$

Required $CT_{req}$ values for target log inactivations (e.g., 3-log Giardia, 4-log Virus) are published in EPA lookup tables. $CT_{req}$ increases substantially at lower temperatures and higher pH levels.

Aqueous Chlorine Chemistry & Equilibrium Speciation

Chlorine gas ($Cl_2$) or sodium hypochlorite ($NaOCl$) added to water hydrolyzes rapidly ($<1 \text{ second}$):

$Cl_2(g) + H_2O \rightarrow HOCl + H^+ + Cl^-$ $NaOCl + H_2O \rightarrow HOCl + Na^+ + OH^-$

Weak Acid Dissociation of Hypochlorous Acid

Hypochlorous acid ($HOCl$) is a weak acid that reversibly dissociates into hydrogen ion ($H^+$) and hypochlorite ion ($OCl^-$):

$HOCl \rightleftharpoons H^+ + OCl^- \quad (pK_a \approx 7.54 \text{ at } 25^\circ C)$

The concentration sum $[HOCl] + [OCl^-]$ represents Free Available Chlorine. The fraction of hypochlorous acid ($\alpha_{HOCl}$) is controlled strictly by pH:

$\alpha_{HOCl} = \frac{[HOCl]}{[HOCl] + [OCl^-]} = \frac{1}{1 + 10^{\text{pH} - pK_a}}$

• At pH 6.0: $\alpha_{HOCl} \approx 97%$ $HOCl$
• At pH 7.54: $\alpha_{HOCl} = 50%$ $HOCl$, $50%$ $OCl^-$
• At pH 9.0: $\alpha_{HOCl} \approx 3%$ $HOCl$

Disinfection Implication: $HOCl$ is $80 - 100$ times more effective at pathogen cell membrane penetration than the negatively charged $OCl^-$ ion. Consequently, free chlorine disinfection is far more potent at lower pH ($< 7.5$).

Breakpoint Chlorination Chemistry

When raw water contains ammonia ($NH_3$), free chlorine reacts step-wise to form chloramines (combined chlorine):

1. Monochloramine Formation: $HOCl + NH_3 \rightarrow NH_2Cl + H_2O$
2. Dichloramine Formation: $HOCl + NH_2Cl \rightarrow NHCl_2 + H_2O$
3. Trichloramine Formation: $HOCl + NHCl_2 \rightarrow NCl_3 + H_2O$

The Breakpoint Curve Phases

As the dosage of chlorine to ammonia ratio ($Cl_2 : NH_3-N$) increases:

• Zone 1 (Initial Chlorine Demand): Chlorine reacts with reducing agents ($Fe^{2+}, Mn^{2+}, H_2S$). No residual forms.
• Zone 2 (Combined Residual Formation): Chlorine reacts with ammonia to form monochloramine and dichloramine. Combined residual rises to a peak at a $Cl_2:N$ weight ratio of $\sim 5:1$.
• Zone 3 (Anoxic Oxidation / Breakpoint Dip): Additional chlorine oxidizes chloramines into nitrogen gas ($N_2$) and nitrous oxide ($N_2O$), destroying combined chlorine. The residual drops to a minimum (the Breakpoint) at a $Cl_2:N$ weight ratio of $\sim 8:1 - 10:1$.
• Zone 4 (Free Chlorine Residual Accumulation): Past the breakpoint, all ammonia is destroyed. Any additional chlorine added forms true Free Available Chlorine ($HOCl + OCl^-$).

Alternative Disinfectants & Disinfection Byproducts (DBPs)

Disinfection Byproduct Regulations (Stage 1 & Stage 2 DBPR)

Reaction of chlorine or ozone with Natural Organic Matter (NOM, measured as TOC) produces regulated DBPs:

• Total Trihalomethanes (TTHM): $80 \ \mu g/L$ limit (Chloroform, Bromoform, Bromodichloromethane, Dibromochloromethane).
• Haloacetic Acids (HAA5): $60 \ \mu g/L$ limit (Monochloroacetic, Dichloroacetic, Trichloroacetic, Monobromoacetic, Dibromoacetic acids).
• Bromate ($BrO_3^-$): $10 \ \mu g/L$ limit (Ozonation DBP).
• Chlorite ($ClO_2^-$): $1.0 \ mg/L$ limit ($ClO_2$ DBP).
• Compliance under Stage 2 DBPR is evaluated using a Locational Running Annual Average (LRAA) at individual monitoring sites across the distribution system.