Sludge Production - Calculation and Storage

Comprehensive sludge handling calculations covering production from all sources, thickening, storage requirements, and liquor return streams. Based on UK water industry sludge management standards.

Sludge Sources in Wastewater Treatment

Primary Sludge

Origin: Gravity settling in primary sedimentation tanks

Characteristics:

• Dry solids (DS): 3-5% (typical 4%)
• Volatile solids (VS): 65-75% of DS
• Specific gravity: 1.02-1.05
• Color: Grey to brown
• Odor: Unpleasant (organic matter, H₂S if septic)

Production:

Primary_solids = TSS_removed = TSS_inf × (E_SS / 100)

Where typical SS removal = 50%

Humus Sludge (Biological Sludge from Biofilters)

Origin: Sloughed biomass from biofilter media, captured in humus tanks

Characteristics:

• Dry solids: 1.5-2.5% (typical 2%)
• Volatile solids: 70-80% of DS
• Specific gravity: 1.005-1.015
• Color: Brown (aerobic)
• Odor: Earthy, musty

Production:

Humus_solids = Biomass_biofilter × E_capture

Where typical capture efficiency = 85%

Tertiary Sludge

Origin: Enhanced filtration or additional settling

Characteristics:

• Dry solids: 1-3%
• Mainly fine biological solids
• Low in quantity (typically 5-10% of total)

Chemical Sludge

Origin: Precipitation from ferric or aluminum dosing for P removal

Characteristics:

• Dry solids: Depends on dosing stage (3-6% if co-settled with primary)
• Volatile solids: 20-40% of DS (lower than biological, due to Fe(OH)₃ or Al(OH)₃)
• Specific gravity: 1.05-1.15 (denser than biological)
• Color: Orange-brown (Fe), greyish-white (Al)

Production:

Chemical_solids = Fe_dose × 2.3 (kgSS per kg Fe)

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Design Equations

Sludge Solids and Flow Calculations

Dry Solids Mass

Formula:

DS_mass = TSS_load × (Removal_efficiency / 100)

Example:

TSS_load = 350 kgSS/d
Removal_efficiency = 50% (primary)

DS_mass = 350 × 0.50 = 175 kgDS/d

Sludge Flow from Solids and %DS

Formula:

Sludge_flow = (DS_mass / 1000) / (DS% / 100)

Where:

• Sludge_flow = sludge volumetric flow (m³/d)
• DS_mass = dry solids production (kg/d)
• DS% = percent dry solids (%, e.g., 3% = 0.03 fraction)

Derivation:

Sludge contains DS% dry solids by weight.
Assuming density ≈ 1000 kg/m³ (close to water):
Volume (m³) = Mass (kg) / 1000
Total sludge mass = DS_mass / (DS%/100)
Total sludge volume = (DS_mass / (DS%/100)) / 1000
Simplifies to: Sludge_flow = (DS_mass / 1000) / (DS% / 100)

Example:

DS_mass = 175 kg/d
DS% = 3%

Sludge_flow = (175 / 1000) / 0.03 = 5.83 m³/d

Alternative (concentration basis):

Sludge concentration (mg/L) = DS% × 10,000
Sludge concentration = 3 × 10,000 = 30,000 mg/L

Sludge_flow = DS_mass (kg/d) × 1000 / Concentration (mg/L)
Sludge_flow = 175 × 1000 / 30,000 = 5.83 m³/d

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Combining Multiple Sludge Sources

Weighted Average %DS

When mixing sludges of different %DS:

Formula:

Mixed_DS% = Σ(Flow_i × DS%_i) / Σ(Flow_i)

Example:

Primary sludge: 50 m³/d at 5% DS
Humus sludge: 50 m³/d at 2% DS

Mixed_DS% = (50 × 5 + 50 × 2) / (50 + 50)
Mixed_DS% = (250 + 100) / 100 = 3.5%

Total Solids Mass

Formula:

Total_DS = Σ(Flow_i × DS%_i × 10)

Example:

Total_DS = (50 × 5 × 10) + (50 × 2 × 10)
Total_DS = 2,500 + 1,000 = 3,500 kgDS/d

Verification:

Mixed_flow = 100 m³/d
Mixed_DS% = 3.5%
Total_DS = 100 × 3.5 × 10 = 3,500 kgDS/d ✓

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Thickening Calculations

Thickening concentrates sludge to reduce volume.

Target %DS After Thickening

Typical thickening targets:

• Primary sludge: 4-6% DS (from 3-5%)
• Biological sludge: 3-5% DS (from 1.5-2.5%)
• Mixed sludge: 4-6% DS (from 2-4%)

Thickened Sludge Flow

Mass balance (solids conserved):

Input_DS_mass = Thickened_DS_mass

Input_flow × Input_DS% = Thickened_flow × Target_DS%

Thickened_flow = (Input_flow × Input_DS%) / Target_DS%

Example:

Input: 100 m³/d at 2% DS
Target: 3% DS

Thickened_flow = (100 × 2) / 3 = 66.67 m³/d

Volume reduction:

Volume_reduction = Input_flow - Thickened_flow
Volume_reduction = 100 - 66.67 = 33.33 m³/d (33% reduction)

Liquor Flow from Thickening

Formula:

Liquor_flow = Input_flow - Thickened_flow

Example:

Liquor_flow = 100 - 66.67 = 33.33 m³/d

This liquor (supernatant) is returned to the inlet works and must be accounted for in the mass balance.

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Liquor Return Loads

Liquor from sludge thickening carries pollutants back to treatment.

Typical Liquor Concentrations

Parameter	Concentration (mg/L)	Range (mg/L)
TSS	500	300-800
BOD	750	500-1,200
NH₄-N	100	50-200
TP	10	5-20

Higher NH₄-N: Biological degradation in sludge releases ammonia

Pollutant Load Calculation

Formula:

Load_return = (Concentration × Liquor_flow) / 1000

Example:

Liquor_flow = 33.33 m³/d
NH₄-N concentration = 100 mg/L

NH₄_load_return = (100 × 33.33) / 1000 = 3.33 kgN/d

Impact on treatment:

Influent NH₄-N = 30 mg/L, Q = 1000 m³/d
Influent load = (30 × 1000) / 1000 = 30 kgN/d

Total load to treatment = 30 + 3.33 = 33.33 kgN/d
Increase = 3.33 / 30 × 100 = 11% increase from liquor return

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Storage Tank Sizing

UK operator Storage Standards

Tank Type	Capacity (days)	Purpose
Sludge storage	14	Main operational buffer
Buffer tank	4	Short-term fluctuations
Blending tank	18 hours	Homogenization before dewatering

Minimum: 2 blending tanks for N-1 redundancy

Storage Volume Calculation

Formula:

Volume = Flow × Days × (1 + Freeboard)

Where:

• Freeboard = typically 10% (0.10)

Example (storage tank):

Thickened_flow = 67 m³/d
Storage_days = 14 (UK operator standard)
Freeboard = 10%

Volume = 67 × 14 × 1.10 = 1,031.8 m³

Select: 1,050 m³ tank

Example (buffer tank):

Volume = 67 × 4 × 1.10 = 294.8 m³

Select: 300 m³ tank

Example (blending tank, per tank):

Blending_hours = 18 hours
Blending_days = 18 / 24 = 0.75 days

Volume_per_tank = 67 × 0.75 × 1.10 = 55.3 m³

For 2 tanks: Total blending = 110.6 m³
Select: 2 × 60 m³ tanks

Total Tank Volume

Formula:

Total_volume = Storage + Buffer + Blending

Example:

Total = 1,050 + 300 + 110 = 1,460 m³

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Worked Example - Complete Sludge Assessment

Design Basis

• Population: 5,000 PE
• DWF: 600 m³/d
• Primary sludge: 105 kgDS/d at 5% DS
• Humus sludge: 85 kgDS/d at 2% DS (from biofilter, 85% capture of 100 kgSS/d biomass)
• Chemical sludge (if using Fe for P): 44 kgDS/d at 5% DS (co-settled with primary)

Step 1: Calculate Individual Sludge Flows

Primary + chemical (combined in primary tank):

Combined_DS = 105 + 44 = 149 kgDS/d
DS% = 5%

Primary_flow = (149 / 1000) / 0.05 = 2.98 m³/d

Humus sludge:

Humus_DS = 85 kgDS/d
DS% = 2%

Humus_flow = (85 / 1000) / 0.02 = 4.25 m³/d

Step 2: Calculate Mixed Sludge Properties

Total flow:

Mixed_flow = 2.98 + 4.25 = 7.23 m³/d

Total solids:

Total_DS = 149 + 85 = 234 kgDS/d

Weighted average %DS:

Mixed_DS% = (2.98 × 5 + 4.25 × 2) / 7.23
Mixed_DS% = (14.9 + 8.5) / 7.23 = 3.24%

Step 3: Thicken to Target %DS

Target: 4% DS (UK operator typical)

Thickened flow:

Thickened_flow = (7.23 × 3.24) / 4.0
Thickened_flow = 23.43 / 4.0 = 5.86 m³/d

Liquor flow:

Liquor_flow = 7.23 - 5.86 = 1.37 m³/d

Step 4: Calculate Liquor Return Loads

Using typical concentrations:

TSS return:

TSS_load = (500 mg/L × 1.37 m³/d) / 1000 = 0.69 kgSS/d

BOD return:

BOD_load = (750 × 1.37) / 1000 = 1.03 kgBOD/d
(~0.3% of influent BOD, minimal impact)

NH₄-N return:

NH₄_load = (100 × 1.37) / 1000 = 0.14 kgN/d
(~0.4% of influent NH₄-N, minimal impact for this small works)

Step 5: Design Storage Tanks

Sludge storage (14 days):

Storage = 5.86 × 14 × 1.10 = 90.0 m³

Select: 100 m³ tank

Buffer tank (4 days):

Buffer = 5.86 × 4 × 1.10 = 25.8 m³

Select: 30 m³ tank

Blending tanks (18 hours each, 2 tanks):

Blending_per_tank = 5.86 × 0.75 × 1.10 = 4.83 m³

Select: 2 × 5 m³ tanks (total 10 m³)

Total capacity:

Total = 100 + 30 + 10 = 140 m³

Step 6: Calculate Specific Gravity

Typical mixed sludge:

SG = 1.02 (range 1.01-1.05 for 3-5% DS)

Design Summary

Parameter	Value	Notes
Primary + chemical sludge	2.98 m³/d at 5% DS	149 kgDS/d
Humus sludge	4.25 m³/d at 2% DS	85 kgDS/d
Mixed sludge	7.23 m³/d at 3.24% DS	234 kgDS/d
Thickened sludge	5.86 m³/d at 4% DS
Liquor return	1.37 m³/d	19% of mixed flow
Liquor NH₄-N load	0.14 kgN/d	0.4% of influent
Storage tank	100 m³	14 days
Buffer tank	30 m³	4 days
Blending tanks	2 × 5 m³	18 hours per tank
Total storage	140 m³
Specific gravity	1.02	Typical for 3-4% DS
Compliance status	OK	✓ Meets UK operator standards

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Biological Sludge Yield Coefficients

For biological treatment processes, sludge production is calculated using yield coefficients.

ASM1-Based Yields (Activated Sludge)

Formula:

Y_obs = Y / (1 + k_d × SRT)

Where:

• Y_obs = observed yield (kgSS/kgBOD removed)
• Y = true yield (kgSS/kgBOD), typically 0.4-0.6
• k_d = decay coefficient (1/d), typically 0.05-0.10
• SRT = solids retention time (days)

Example (activated sludge):

Y = 0.5 kgSS/kgBOD
k_d = 0.08 /d
SRT = 10 days

Y_obs = 0.5 / (1 + 0.08 × 10) = 0.5 / 1.8 = 0.28 kgSS/kgBOD

Biofilter Biomass Yield

Typical biofilter yield:

Y = 0.7 kgSS/kgBOD removed

Higher than activated sludge due to fixed film (lower decay).

Example:

BOD_removed = 100 kgBOD/d
Y = 0.7

Biomass = 100 × 0.7 = 70 kgSS/d

Humus sludge (after capture):

Humus_capture = 85% (typical)
Humus_sludge = 70 × 0.85 = 59.5 kgSS/d

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UK Water Company Variations

UK Industry Practice

• Sludge storage: 14 days minimum (strictly enforced)
• Buffer tank: 4 days typical
• Blending tanks: 2 minimum (N-1 redundancy)
• Thickening target: 4-6% DS

UK Industry Practice

• Sludge storage: 10-14 days depending on site
• Prefer gravity thickening for primary sludge
• DAF (Dissolved Air Flotation) for biological sludge
• Centrifuge thickening for mixed sludge

UK Industry Practice

• Sludge storage: 14 days minimum
• Often use picket fence thickeners
• Polymer dosing common for thickening (5-15 kg/tonne DS)
• Target 5% DS for dewatering feed

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Thickening Technologies

Gravity Thickening

Best for: Primary sludge, mixed sludge

Mechanism: Gravity settling with slow agitation (picket fence)

Performance:

• Inlet: 2-4% DS
• Outlet: 4-8% DS
• Solids capture: 90-95%

Design:

Surface_area = DS_load / Solids_loading_rate

Where typical solids loading = 30-50 kgDS/m²/d

Dissolved Air Flotation (DAF)

Best for: Biological sludge (humus, WAS)

Mechanism: Micro air bubbles attach to floc, float to surface

Performance:

• Inlet: 0.5-2% DS
• Outlet: 3-6% DS
• Solids capture: 90-98%

Design:

Surface_area = Flow / Hydraulic_loading_rate

Where typical HLR = 4-8 m/h

Centrifuge Thickening

Best for: Mixed sludge, high throughput

Mechanism: Centrifugal force separates solids

Performance:

• Inlet: 1-4% DS
• Outlet: 4-8% DS
• Solids capture: 85-95% (with polymer)

Polymer dosing: 2-5 kg polymer/tonne DS

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Dewatering Targets and Methods

Dewatering Technologies

Technology	Cake %DS	Polymer Dose	Relative Cost
Belt press	15-25%	3-8 kg/tonne	Medium
Centrifuge	18-30%	5-10 kg/tonne	High (CAPEX), Low (OPEX)
Filter press	25-40%	5-15 kg/tonne	Low (CAPEX), Medium (OPEX)
Screw press	15-25%	2-5 kg/tonne	Low-Medium

Cake Production

Formula:

Cake_mass = DS_feed / (Cake_DS% / 100)

Example:

DS_feed = 234 kg/d (thickened at 4% DS)
Cake_DS% = 22% (belt press)

Cake_mass = 234 / 0.22 = 1,064 kg/d ≈ 1.06 tonnes/d

Annual production:

Annual = 1.06 × 365 = 387 tonnes/year

Disposal Routes

UK options:

• Agricultural land spreading: Most common, requires treatment/certification
• Incineration: Large works, energy recovery
• Landfill: Decreasing (landfill tax), last resort
• Anaerobic digestion: Large works, biogas production

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Common Sludge Issues

Poor Thickening Performance

Symptoms:

• Low %DS in thickened sludge
• Solids carryover to liquor

Causes:

• Excessive polymer dose (dispersion)
• Insufficient polymer dose (poor floc)
• Hydraulic overload

Solutions:

• Optimize polymer dose via jar testing
• Reduce feed rate
• Check equipment (picket fence rotation, DAF air supply)

High Liquor Return Loads

Symptoms:

• Significant NH₄-N or BOD return
• Treatment performance declining

Causes:

• Poor thickening (dilute liquor with high organics)
• Septicity in storage (anaerobic breakdown)

Solutions:

• Improve thickening performance
• Reduce storage time (< 7 days in tank before thickening)
• Aerate storage tanks (if biological sludge)

Storage Tank Odor

Symptoms:

• H₂S odor from sludge storage
• Complaints from neighbors

Causes:

• Anaerobic conditions in stored sludge
• High temperature (summer)

Solutions:

• Cover tanks with odor treatment (biofilter/scrubber)
• Reduce storage time
• Lime stabilization (raise pH > 12)
• Ferric chloride addition (binds H₂S)

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Related Calculations

• Primary Tanks: Primary sludge production
• Biofilters: Biomass production
• Chemical Dosing: Chemical sludge production
• Alkalinity Balance: Liquor NH₄-N impact

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References

• UK operator Sludge Management Standards: Storage and treatment requirements
• WRc/UKWIR: Sludge treatment and disposal best practice
• CIWEM Handbook: Sludge thickening and dewatering

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