💡 Exam tip: OUR reflects biological activity. High OUR = active biomass. Low OUR = endogenous decay or process upset. Used to diagnose bulking, toxicity, and nitrification.

Specific Oxygen Uptake Rate (SOUR)

SOUR = (OUR × 1000) ÷ MLVSS

Units: mg O₂/g VSS·h

Variables

OUROxygen uptake rate (mg/L·min)

MLVSSMixed liquor volatile suspended solids (mg/L)

Worked Example

OUR = 0.20 mg/L·min, MLVSS = 2,400 mg/L. What is SOUR?

SOUR = (0.20 × 60 × 1000) ÷ 2,400 = 12,000 ÷ 2,400 = 5.0 mg O₂/g VSS·h

Answer: 5.0 mg O₂/g VSS·h

💡 Exam tip: SOUR 8–20 mg O₂/g VSS·h = healthy aerobic conditions. SOUR < 5 = low activity (old sludge, toxicity). SOUR > 25 = overloaded system.

Volumetric Oxygen Transfer Rate (OTR)

OTR = α × SOTR × (β × C_s − C_L) ÷ C_s20

Units: kg O₂/h

Variables

αProcess water correction factor (typically 0.5–0.8)

SOTRStandard oxygen transfer rate (kg O₂/h)

βSalinity/surface tension correction (typically 0.95–1.0)

C_sSaturation DO at process temperature (mg/L)

C_LActual process DO (mg/L)

C_s20DO saturation at 20°C (9.09 mg/L)

💡 Exam tip: α accounts for surfactants and contaminants reducing oxygen transfer. β accounts for salinity. Always derate aeration equipment using α·β factors in design.

Nitrification Rate (NR)

NR = (TKN_in − TKN_out) × Q ÷ (V × MLVSS × 1000)

Units: g NH₄-N/g VSS·d

Variables

TKN_inInfluent TKN (mg/L)

TKN_outEffluent TKN (mg/L)

QFlow rate (m³/d)

VAeration basin volume (m³)

MLVSSMixed liquor volatile suspended solids (mg/L)

💡 Exam tip: Nitrification requires SRT > 10 days at 20°C. Temperature correction: SRT doubles for every 7°C drop below 20°C. Nitrifiers are slow-growing and sensitive to pH < 6.5 and toxics.

Denitrification Rate (DNR)

DNR = (NO₃_in − NO₃_out) × Q ÷ (V_anoxic × MLVSS × 1000)

Units: g NO₃-N/g VSS·d

Variables

NO₃_inNitrate entering anoxic zone (mg/L)

NO₃_outNitrate leaving anoxic zone (mg/L)

QFlow rate (m³/d)

V_anoxicAnoxic zone volume (m³)

MLVSSMixed liquor volatile suspended solids (mg/L)

💡 Exam tip: Denitrification requires anoxic conditions (DO < 0.5 mg/L) and a carbon source. Internal recycle ratio (IR) controls nitrate removal efficiency. IR = 3–5× Q is typical for MLE process.

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Biological Nutrient Removal (BNR)

Total Nitrogen Removal Efficiency

TN_removal (%) = (TN_in − TN_eff) ÷ TN_in × 100

Units: %

Variables

TN_inInfluent total nitrogen (mg/L)

TN_effEffluent total nitrogen (mg/L)

Worked Example

Influent TN = 38 mg/L, effluent TN = 8 mg/L. What is the removal efficiency?

TN_removal = (38 − 8) ÷ 38 × 100 = 30 ÷ 38 × 100 = 78.9%

Answer: 78.9%

💡 Exam tip: Ontario Class 3 facilities often have TN effluent limits of 10–15 mg/L. BNR processes (MLE, A²O, Bardenpho) are required to meet these limits.

Phosphorus Removal — Enhanced Biological (EBPR)

P_removed (kg/d) = (TP_in − TP_eff) × Q × 10⁻³

Units: kg/d

Variables

TP_inInfluent total phosphorus (mg/L)

TP_effEffluent total phosphorus (mg/L)

QFlow rate (m³/d)

Worked Example

TP_in = 6.5 mg/L, TP_eff = 0.8 mg/L, Q = 15,000 m³/d. How much P is removed per day?

P_removed = (6.5 − 0.8) × 15,000 × 10⁻³ = 5.7 × 15 = 85.5 kg/d

Answer: 85.5 kg/d

💡 Exam tip: EBPR requires an anaerobic zone before the aerobic zone. PAOs (phosphorus-accumulating organisms) release P in anaerobic zone and uptake P in aerobic zone. VFA availability is critical.

Chemical Phosphorus Removal (Alum Dose)

Alum dose (mg/L) = Al:P molar ratio × (P_to_remove × 26.98 ÷ 30.97)

Units: mg Al/L

Variables

Al:PMolar ratio (typically 1.5–2.5 mol Al per mol P)

P_to_removePhosphorus to remove (mg/L)

26.98Atomic mass of Al

30.97Atomic mass of P

💡 Exam tip: Alum (Al₂(SO₄)₃·18H₂O) precipitates P as AlPO₄. Ferric chloride (FeCl₃) also used. Chemical P removal increases sludge production. pH should be 6.0–7.0 for optimal precipitation.

Internal Recycle Ratio (IR)

IR = Q_recycle ÷ Q_influent

Units: dimensionless

Variables

Q_recycleInternal recycle flow from aerobic to anoxic zone (m³/d)

Q_influentPlant influent flow (m³/d)

Worked Example

Q_influent = 20,000 m³/d, Q_recycle = 80,000 m³/d. What is the IR?

IR = 80,000 ÷ 20,000 = 4

Answer: IR = 4 (400%)

💡 Exam tip: Higher IR = more nitrate returned to anoxic zone = better denitrification. But energy cost increases. Typical IR = 2–5. Maximum TN removal limited by IR: TN_removal_max = IR ÷ (IR + 1).

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Anaerobic Digestion

Digester Hydraulic Retention Time (HRT)

HRT = V_digester ÷ Q_sludge

Units: days

Variables

V_digesterDigester volume (m³)

Q_sludgeSludge feed rate (m³/d)

Worked Example

Digester volume = 3,500 m³, sludge feed = 175 m³/d. What is the HRT?

HRT = 3,500 ÷ 175 = 20 days

Answer: 20 days

💡 Exam tip: Minimum HRT for mesophilic digestion (35°C) = 15–20 days. Thermophilic (55°C) = 10–12 days. HRT < 10 days risks washout of methanogens. Ontario typically requires HRT ≥ 15 days.

Volatile Solids Reduction (VSR)

VSR (%) = (VS_in − VS_out) ÷ VS_in × 100

Units: %

Variables

VS_inVolatile solids entering digester (kg/d or mg/L)

VS_outVolatile solids leaving digester (kg/d or mg/L)

Worked Example

VS_in = 4,200 kg/d, VS_out = 2,100 kg/d. What is VSR?

VSR = (4,200 − 2,100) ÷ 4,200 × 100 = 50%

Answer: 50%

💡 Exam tip: Target VSR for mesophilic digestion: 50–60%. VSR < 40% indicates under-digestion (overloading, temperature issues, or toxicity). VSR > 65% is excellent performance.

Biogas Production Rate

Biogas (m³/d) = VS_destroyed × 0.85 × 1000 ÷ 1000

Units: m³ biogas/d

Variables

VS_destroyedVolatile solids destroyed (kg/d)

0.85Biogas yield factor (m³ biogas per kg VS destroyed, typical)

Worked Example

VS_destroyed = 2,100 kg/d. How much biogas is produced?

Biogas = 2,100 × 0.85 = 1,785 m³/d

Answer: 1,785 m³/d

💡 Exam tip: Biogas is ~65–70% methane (CH₄) and ~30–35% CO₂. Methane has energy content of ~37.3 MJ/m³. Biogas can fuel boilers, engines, or CHP (combined heat and power) units.

Digester Organic Loading Rate (OLR)

OLR = VS_in ÷ V_digester

Units: kg VS/m³·d

Variables

VS_inVolatile solids fed to digester (kg/d)

V_digesterDigester volume (m³)

Worked Example

VS_in = 4,200 kg/d, V_digester = 3,500 m³. What is the OLR?

OLR = 4,200 ÷ 3,500 = 1.2 kg VS/m³·d

Answer: 1.2 kg VS/m³·d

💡 Exam tip: Acceptable OLR for mesophilic digestion: 1.6–4.8 kg VS/m³·d. OLR > 4.8 risks VFA accumulation and pH drop. OLR < 1.0 = under-utilization of digester capacity.

Alkalinity-to-VFA Ratio

Alk:VFA ratio = Total alkalinity (mg/L as CaCO₃) ÷ VFA (mg/L as acetic acid)

Units: dimensionless

💡 Exam tip: Healthy digester: Alk:VFA > 10. Ratio 6–10 = caution, reduce loading. Ratio < 6 = imminent souring risk. Alkalinity should be > 2,000 mg/L as CaCO₃ for stable digestion. Add lime or bicarbonate to correct.

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Biosolids & Dewatering

Solids Capture Efficiency (Centrifuge/Belt Press)

Capture (%) = (TS_cake × Q_cake) ÷ (TS_feed × Q_feed) × 100

Units: %

Variables

TS_cakeTotal solids in dewatered cake (%)

Q_cakeCake production rate (kg/d or m³/d)

TS_feedTotal solids in feed sludge (%)

Q_feedFeed sludge flow rate (kg/d or m³/d)

💡 Exam tip: Target solids capture: centrifuge ≥ 95%, belt press ≥ 90%. Low capture = high solids in centrate/filtrate, which recycles back to the plant head and increases loading.

Cake Solids Content

Cake TS (%) = (Dry solids mass ÷ Wet cake mass) × 100

Units: %

Worked Example

Wet cake = 5,000 kg/d, dry solids = 1,250 kg/d. What is the cake TS?

Cake TS = (1,250 ÷ 5,000) × 100 = 25%

Answer: 25%

💡 Exam tip: Centrifuge cake: 20–28% TS. Belt press cake: 18–25% TS. Higher TS = lower hauling costs. Polymer dose affects cake TS — optimize polymer type and dose for best performance.

Biosolids Land Application Rate

Application rate (t/ha) = Agronomic N rate ÷ (Biosolids TKN × Availability factor)

Units: t dry solids/ha

Variables

Agronomic N rateCrop nitrogen requirement (kg N/ha)

Biosolids TKNTotal Kjeldahl nitrogen in biosolids (kg N/t dry)

Availability factorFraction of N available to crop (0.5–0.7 for Class B)

💡 Exam tip: Ontario O. Reg. 267/03 governs biosolids land application. Class A biosolids have fewer restrictions than Class B. Application rates are limited by agronomic N need, P loading, and setback distances.

Polymer Dose

Polymer dose (kg/t DS) = Polymer flow (L/h) × Concentration (g/L) ÷ (Sludge flow (m³/h) × TS (g/L))

Units: kg polymer/t dry solids

💡 Exam tip: Typical polymer dose: belt press 3–8 kg/t DS, centrifuge 2–6 kg/t DS. Jar tests determine optimal polymer type and dose. Over-dosing wastes polymer and can reduce cake TS.

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Tertiary Treatment & Effluent Filtration

Filter Loading Rate (Effluent Filtration)

Loading rate = Q ÷ A_filter

Units: m³/m²·h (m/h)

Variables

QFlow rate (m³/h)

A_filterTotal filter surface area (m²)

Worked Example

Q = 800 m³/h, filter area = 50 m². What is the loading rate?

Loading rate = 800 ÷ 50 = 16 m/h

Answer: 16 m/h

💡 Exam tip: Typical effluent filter loading rates: 5–15 m/h for sand/anthracite dual media. Exceeding design rate causes breakthrough and poor effluent quality. Backwash when head loss reaches 2–3 m.

UV Dose (Disinfection)

UV dose (mJ/cm²) = UV intensity (mW/cm²) × Exposure time (s)

Units: mJ/cm²

Variables

UV intensityIrradiance at the target point (mW/cm²)

Exposure timeHydraulic retention time in UV reactor (s)

Worked Example

UV intensity = 12 mW/cm², HRT in reactor = 8 seconds. What is the UV dose?

UV dose = 12 × 8 = 96 mJ/cm²

Answer: 96 mJ/cm²

💡 Exam tip: Ontario O. Reg. 170/03 requires UV dose ≥ 40 mJ/cm² for drinking water. For wastewater reuse, higher doses (80–120 mJ/cm²) are typical. Transmittance (UVT) must be monitored — low UVT reduces effective dose.

Membrane Flux (MBR)

Flux = Q_permeate ÷ A_membrane

Units: L/m²·h (LMH)

Variables

Q_permeatePermeate flow rate (L/h)

A_membraneTotal membrane area (m²)

💡 Exam tip: Sustainable flux for MBR: 15–25 LMH. Operating above sustainable flux causes fouling and TMP increase. Backpulsing and chemical cleaning (CIP) restore flux. TMP should be < 30 kPa for healthy operation.

Transmembrane Pressure (TMP)

TMP = (P_feed + P_retentate) ÷ 2 − P_permeate

Units: kPa or bar

Variables

P_feedFeed side pressure (kPa)

P_retentateRetentate/concentrate pressure (kPa)

P_permeatePermeate side pressure (kPa)

💡 Exam tip: Rising TMP at constant flux = fouling. Sudden TMP drop = membrane breach. TMP > 50 kPa triggers chemical cleaning. Maintenance cleaning (hypochlorite) weekly; recovery cleaning (citric acid + NaOCl) monthly.

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Laboratory Analysis (Class 3 Level)

Ammonia Nitrogen (NH₃-N) Removal

NH₃-N removal (%) = (NH₃_in − NH₃_eff) ÷ NH₃_in × 100

Units: %

Worked Example

Influent NH₃-N = 28 mg/L, effluent NH₃-N = 1.5 mg/L. What is the removal?

Removal = (28 − 1.5) ÷ 28 × 100 = 94.6%

Answer: 94.6%

💡 Exam tip: Class 3 effluent limits often include NH₃-N < 3 mg/L (summer) and < 10 mg/L (winter). Nitrification is temperature-sensitive — expect reduced performance below 12°C.

Specific Conductance (Temperature Correction)

SC₂₅ = SC_T ÷ [1 + 0.02 × (T − 25)]

Units: μS/cm at 25°C

Variables

SC_TMeasured conductance at temperature T (μS/cm)

TSample temperature (°C)

0.02Temperature coefficient (2% per °C)

💡 Exam tip: Conductance increases ~2% per °C. Always report conductance at 25°C reference temperature. Used to estimate TDS: TDS (mg/L) ≈ SC₂₅ × 0.65.

Turbidity and TSS Relationship

TSS (mg/L) ≈ Turbidity (NTU) × k

Units: mg/L

Variables

kSite-specific correlation factor (typically 1.5–3.0 for secondary effluent)

💡 Exam tip: Turbidity is not a direct substitute for TSS but can be used for real-time process control. Establish a site-specific correlation by running paired TSS/turbidity measurements over several weeks.

Fecal Coliform Log Reduction

Log reduction = log₁₀(C_in ÷ C_eff)

Units: log units

Variables

C_inInfluent fecal coliform count (CFU/100 mL)

C_effEffluent fecal coliform count (CFU/100 mL)

Worked Example

Influent FC = 10,000,000 CFU/100 mL, effluent FC = 200 CFU/100 mL. What is the log reduction?

Log reduction = log₁₀(10,000,000 ÷ 200) = log₁₀(50,000) = 4.7

Answer: 4.7 log reduction

💡 Exam tip: Ontario requires ≥ 4-log reduction of fecal coliforms for Class IV effluent. UV and chlorination both achieve this. E. coli < 200 CFU/100 mL is a common effluent limit.