Activated Sludge Models (ASM1, ASM2d, ASM3)
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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
- Aerobic growth of heterotrophs: S_S + S_O + S_NH → X_B,H (Monod kinetics)
- Anoxic growth of heterotrophs: S_S + S_NO + S_NH → X_B,H (denitrification)
- Aerobic growth of autotrophs: S_NH + S_O → X_B,A + S_NO (nitrification)
- Decay of heterotrophs: X_B,H → X_P + X_S (death-regeneration concept)
- Decay of autotrophs: X_B,A → X_P + X_S
- Ammonification of soluble organic nitrogen: S_ND → S_NH
- Hydrolysis of entrapped organics: X_S → S_S
- 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
- Henze, M. et al. (1987). "Activated Sludge Model No. 1" — IAWPRC Scientific and Technical Report No. 1
- Henze, M. et al. (1995). "Activated Sludge Model No. 2" — IAWQ Scientific and Technical Report No. 3
- Henze, M. et al. (1999). "Activated Sludge Model No. 2d" — Water Sci. Technol. 39(1), 165-182
- Gujer, W. et al. (1999). "Activated Sludge Model No. 3" — Water Sci. Technol. 39(1), 183-193
- Henze, M. et al. (2000). "Activated Sludge Models ASM1, ASM2, ASM2d and ASM3" — IWA Publishing, ISBN 9781900222242
- Jeppsson, U. (1996). "Modelling Aspects of Wastewater Treatment Processes" — Lund University PhD thesis (comprehensive ASM1 parameter listing)