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Activated Sludge Models (ASM1, ASM2d, ASM3)

Note

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Used by: biological-process-engineer agent, reactor node, monster node Validation: Verified against IWA publications, WaterTAP documentation, and peer-reviewed literature

ASM1 — Activated Sludge Model No. 1

Source: Henze, M., Grady, C.P.L., Gujer, W., Marais, G.v.R., Matsuo, T. (1987). IAWPRC Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment.

Published: IWA Scientific and Technical Report No. 1

13 Components (State Variables)

Symbol	Description	Type
S_I	Soluble inert organic matter	Soluble
S_S	Readily biodegradable substrate	Soluble
X_I	Particulate inert organic matter	Particulate
X_S	Slowly biodegradable substrate	Particulate
X_B,H	Active heterotrophic biomass	Particulate
X_B,A	Active autotrophic biomass	Particulate
X_P	Particulate products from biomass decay	Particulate
S_O	Dissolved oxygen	Soluble
S_NO	Nitrate and nitrite nitrogen	Soluble
S_NH	Ammonium nitrogen (NH₄⁺-N)	Soluble
S_ND	Soluble biodegradable organic nitrogen	Soluble
X_ND	Particulate biodegradable organic nitrogen	Particulate
S_ALK	Alkalinity (molar units)	Soluble

8 Processes

1. Aerobic growth of heterotrophs: S_S + S_O + S_NH → X_B,H (Monod kinetics)
2. Anoxic growth of heterotrophs: S_S + S_NO + S_NH → X_B,H (denitrification)
3. Aerobic growth of autotrophs: S_NH + S_O → X_B,A + S_NO (nitrification)
4. Decay of heterotrophs: X_B,H → X_P + X_S (death-regeneration concept)
5. Decay of autotrophs: X_B,A → X_P + X_S
6. Ammonification of soluble organic nitrogen: S_ND → S_NH
7. Hydrolysis of entrapped organics: X_S → S_S
8. Hydrolysis of entrapped organic nitrogen: X_ND → S_ND

Key Kinetic Parameters (default values at 20°C)

Parameter	Symbol	Default	Unit	Description
Max. heterotrophic growth rate	μ_H	6.0	d⁻¹
Half-saturation (substrate)	K_S	20.0	g COD/m³
Half-saturation (oxygen, het.)	K_O,H	0.2	g O₂/m³
Half-saturation (nitrate)	K_NO	0.5	g NO₃-N/m³
Heterotrophic decay rate	b_H	0.62	d⁻¹
Max. autotrophic growth rate	μ_A	0.8	d⁻¹
Half-saturation (ammonia)	K_NH	1.0	g NH₃-N/m³
Half-saturation (oxygen, aut.)	K_O,A	0.4	g O₂/m³
Autotrophic decay rate	b_A	0.05	d⁻¹
Anoxic reduction factor	η_g	0.8	—
Hydrolysis rate	k_h	3.0	g X_S/(g X_B,H · d)
Yield (heterotrophic)	Y_H	0.67	g COD/g COD
Yield (autotrophic)	Y_A	0.24	g COD/g N
Fraction to X_P	f_P	0.08	—

Temperature Correction

Arrhenius-type: k(T) = k(20) · θ^(T-20)

Common θ values:

• Heterotrophic growth: θ = 1.072
• Autotrophic growth: θ = 1.103 (nitrifiers are very temperature-sensitive)
• Decay: θ = 1.04

Presentation Format

The model is presented in the Petersen matrix (also called Gujer matrix) format, where rows are processes and columns are components. Each cell contains the stoichiometric coefficient for how a process affects a component.

ASM2d — Activated Sludge Model No. 2d

Source: Henze, M., Gujer, W., Mino, T., Matsuo, T., Wentzel, M.C., Marais, G.v.R., van Loosdrecht, M.C.M. (1999)

Published: IWA Scientific and Technical Report No. 3; also Water Science & Technology 39(1), 165-182

Key Extensions over ASM1

• Adds biological phosphorus removal by phosphorus accumulating organisms (PAOs)
• Includes denitrifying PAOs (simultaneous P-removal and denitrification)
• 19 components, 21 processes
• Models storage of poly-hydroxy-alkanoates (PHA) and polyphosphate (poly-P) by PAOs
• Includes fermentation of readily biodegradable substrate

Additional Components (beyond ASM1)

• S_F: Fermentable, readily biodegradable substrate
• S_A: Fermentation products (acetate)
• S_PO4: Soluble ortho-phosphate
• X_PAO: Phosphorus accumulating organisms
• X_PP: Poly-phosphate stored by PAOs
• X_PHA: Poly-hydroxy-alkanoates stored by PAOs

ASM3 — Activated Sludge Model No. 3

Source: Gujer, W., Henze, M., Mino, T., van Loosdrecht, M.C.M. (1999); updated in Henze et al. (2001)

Published: IWA Scientific and Technical Report No. 9

Key Differences from ASM1

• Replaces death-regeneration with endogenous respiration (conceptually simpler)
• Introduces storage polymers (X_STO) for heterotrophic biomass — substrate is first stored, then used for growth
• 13 state variables, 12 reactions
• More suitable for dynamic simulation and control applications
• Eliminates the problematic simultaneous storage/growth ambiguity in ASM1

Storage-Based Metabolism

In ASM3, heterotrophs first store readily biodegradable substrate as internal storage products (X_STO), then grow on these stored products. This two-step process better reflects observed biological behavior.

Choosing Between Models

Criterion	ASM1	ASM2d	ASM3
Carbon & nitrogen	Yes	Yes	Yes
Phosphorus removal	No	Yes	Via separate Bio-P module
Computational cost	Low	High	Medium
Calibration effort	Low	High	Medium
Best for	Carbon/N only WWTPs	Bio-P plants	Dynamic control

Authoritative References

1. Henze, M. et al. (1987). "Activated Sludge Model No. 1" — IAWPRC Scientific and Technical Report No. 1
2. Henze, M. et al. (1995). "Activated Sludge Model No. 2" — IAWQ Scientific and Technical Report No. 3
3. Henze, M. et al. (1999). "Activated Sludge Model No. 2d" — Water Sci. Technol. 39(1), 165-182
4. Gujer, W. et al. (1999). "Activated Sludge Model No. 3" — Water Sci. Technol. 39(1), 183-193
5. Henze, M. et al. (2000). "Activated Sludge Models ASM1, ASM2, ASM2d and ASM3" — IWA Publishing, ISBN 9781900222242
6. Jeppsson, U. (1996). "Modelling Aspects of Wastewater Treatment Processes" — Lund University PhD thesis (comprehensive ASM1 parameter listing)