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Design Calculations ​

Comprehensive UK-standard design calculations for wastewater treatment processes, covering primary sedimentation, biological filtration, settling tanks, chemical dosing, and sludge handling.

Overview ​

This section provides detailed design methodologies following UK water industry standards (PS208, PS211, PS221). Each calculation includes:

  • Design equations with full derivations
  • UK water industry standards and compliance criteria
  • Worked examples with realistic values
  • Parameter tables with acceptable ranges
  • Related calculation dependencies

Design Calculation Topics ​

Primary Tanks ​

Primary sedimentation tank design per PS208 standards.

Key Parameters:

  • Surface Overflow Rate: 1.0-1.2 m/h at DWF
  • Retention time: 2-4 hours
  • N-1 capacity requirements
  • Sludge production estimates

Standards: UK PS208, UK operator guidelines

Biofilters ​

Trickling filter (biofilter) design per PS211 standards.

Key Parameters:

  • BOD loading: 0.07 kgBOD/m³/d maximum
  • Ammonia loading: 0.015 kgN/m³/d maximum
  • Wetting rate: 0.04-0.75 m³/m²/h
  • Recirculation requirements

Standards: UK PS211, biological treatment design

Humus Tanks ​

Secondary settling tank design per PS221 standards.

Key Parameters:

  • Hydraulic loading: 1.0 m³/m²/h (all tanks), 2.0 m³/m²/h (N-1)
  • Minimum HRT: 2 hours at maximum flow
  • Minimum SWD: 2.0 m
  • Humus sludge capture

Standards: UK PS221, UK operator design criteria

Chemical Dosing ​

Phosphorus removal using ferric sulphate with UK operator molar ratios.

Key Parameters:

  • Fe:P molar ratios: 1.5-2.2 (typical 1.66)
  • Dosing stages: primary, secondary, tertiary
  • Storage requirements: 28 days supply
  • Chemical sludge production

Standards: UK operator operational guidelines

Alkalinity Balance ​

Alkalinity consumption and supplementation for biological nutrient removal.

Key Parameters:

  • Nitrification: 7.14 kg CaCO₃/kg NH₄-N
  • Chemical dosing: 0.75 kg CaCO₃/kg Fe
  • Minimum effluent alkalinity: 50 mg/L CaCO₃
  • Sodium bicarbonate supplementation

Standards: Biological treatment chemistry

Sludge Production ​

Comprehensive sludge handling including production, thickening, and storage.

Key Parameters:

  • Primary sludge: 40-60% SS removal
  • Biological yield: 0.4-0.6 kgSS/kgBOD
  • Storage: 14 days (UK operator), 4 days buffer
  • Thickening targets: 3-6% DS

Standards: UK operator sludge management

Flow and Load ​

Hydraulic flow and pollutant load calculations for design basis.

Key Parameters:

  • Population equivalent: 60g BOD/person/day (UK)
  • DWF, 3DWF, 6DWF calculations
  • Formula A (PS201) for FFT
  • Diurnal flow factors

Standards: UK PS201, UK operator flow basis

Design Process Workflow ​

1. Flow and Load Basis ​

Start with Flow and Load calculations to establish:

  • Design population (PE)
  • Dry Weather Flow (DWF)
  • Full Flow to Treatment (FFT via Formula A)
  • Pollutant loads (BOD, SS, NH₄-N, TP)

2. Primary Treatment ​

Use Primary Tanks to design:

  • Tank geometry (radial or rectangular)
  • Verify PS208 compliance (upflow velocity, HRT)
  • Check N-1 capacity
  • Calculate primary sludge production

3. Biological Treatment ​

Design biofilters using Biofilters:

  • Media volume based on BOD/NH₃ loading rates
  • Recirculation requirements for wetting rate
  • Temperature correction for efficiency
  • Biomass production estimates

4. Secondary Settling ​

Size humus tanks per Humus Tanks:

  • Surface area for hydraulic loading
  • Verify PS221 compliance and N-1 capacity
  • Humus sludge capture calculations

5. Phosphorus Removal (if required) ​

Apply Chemical Dosing:

  • Determine dosing stage and Fe:P ratio
  • Calculate chemical consumption
  • Size storage tanks (28 days)
  • Account for chemical sludge

6. Alkalinity Assessment ​

Check Alkalinity Balance:

  • Calculate nitrification consumption
  • Add chemical dosing consumption
  • Verify effluent alkalinity ≥ 50 mg/L
  • Size sodium bicarbonate dosing if needed

7. Sludge Management ​

Complete design with Sludge Production:

  • Combine all sludge sources
  • Calculate mixed sludge properties
  • Design storage tanks (14 days UK operator)
  • Assess liquor return impact

Key UK Standards Referenced ​

PS208 - Primary Sedimentation Tanks ​

  • Maximum upflow velocity: 1.2 m/h (DWF), 2.0 m/h (FFT)
  • Minimum retention time: 2 hours
  • Minimum sidewater depth: 2.5 m
  • N-1 compliance requirements

PS211 - Biological Filters ​

  • Maximum BOD loading: 0.07 kgBOD/m³/d
  • Maximum ammonia loading: 0.015 kgN/m³/d
  • Wetting rate range: 0.04-0.75 m³/m²/h

PS221 - Humus Tanks ​

  • Maximum HLR (all tanks): 1.0 m³/m²/h
  • Maximum HLR (N-1): 2.0 m³/m²/h
  • Minimum HRT: 2 hours
  • Minimum SWD: 2.0 m

PS201 - Storm Flow Calculations ​

  • Formula A: QFA = DWF + 1.36P + 3.18√P
  • FFT determination
  • Storm tank sizing

UK operator Operational Guidelines ​

  • Fe:P molar ratios for phosphorus removal
  • Sludge storage requirements (14 days)
  • Alkalinity management criteria

Calculation Interdependencies ​

┌─────────────────┐
│ Flow and Load   │ ← Start here: establish design basis
└────────┬────────┘
         │
         ├──→ ┌─────────────────┐
         │    │ Primary Tanks   │ → Primary effluent quality
         │    └────────┬────────┘
         │             │
         ├──→ ┌───────▼─────────┐
         │    │ Biofilters      │ → Biomass production
         │    └────────┬────────┘
         │             │
         ├──→ ┌───────▼─────────┐
         │    │ Humus Tanks     │ → Humus sludge
         │    └─────────────────┘
         │
         ├──→ ┌─────────────────┐
         │    │ Chemical Dosing │ → Chemical sludge, Fe dose
         │    └────────┬────────┘
         │             │
         └──→ ┌───────▼─────────┐
              │ Alkalinity      │ → NaHCO₃ requirement
              └─────────────────┘
                      │
              ┌───────▼─────────┐
              │ Sludge Handling │ → Final storage design
              └─────────────────┘

Common Design Values (UK Practice) ​

Population Equivalent ​

  • UK standard: 60g BOD/person/day
  • EU standard: 54g BOD/person/day
  • Per capita flow: 120-150 L/hd/d (domestic)

Diurnal Factors ​

  • Peak flow factor: 1.5-2.5 × average
  • Minimum flow factor: 0.33-0.50 × average
  • FMEAN factor: 1.6 (UK operator standard)

Removal Efficiencies ​

  • Primary tanks: 30-40% BOD, 50-60% SS
  • Primary + chemical: 40% BOD, 60% SS, 70% TP
  • Biofilters: 85% BOD, 85% NH₃
  • Overall target: BOD ≤ 20 mg/L, SS ≤ 30 mg/L, NH₄-N ≤ 3 mg/L

Sludge Characteristics ​

  • Primary sludge: 3-5% DS
  • Humus sludge: 2% DS
  • Mixed sludge: 2-4% DS (before thickening)
  • Thickened sludge: 3-6% DS

Compliance Verification ​

When completing a design, verify compliance across all calculations:

  1. Hydraulic compliance:

    • Primary tanks: PS208 upflow velocities and HRT
    • Biofilters: PS211 wetting rate range
    • Humus tanks: PS221 hydraulic loading and HRT

  2. Loading rate compliance:

    • Biofilter BOD loading ≤ 0.07 kgBOD/m³/d
    • Biofilter NH₃ loading ≤ 0.015 kgN/m³/d

  3. N-1 redundancy:

    • Primary tanks operable with one tank out
    • Humus tanks operable with one tank out
    • Blending tanks: minimum 2 for redundancy

  4. Effluent quality targets:

    • BOD ≤ 20 mg/L (or consent limit)
    • SS ≤ 30 mg/L (or consent limit)
    • NH₄-N ≤ 3 mg/L (or consent limit)
    • TP ≤ 1 mg/L (if P removal required)
    • Alkalinity ≥ 50 mg/L CaCO₃

  5. Storage adequacy:

    • Chemical storage: 28 days minimum
    • Sludge storage: 14 days minimum (UK operator)
    • Buffer tanks: 4 days typical

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