# Activated Sludge Models (ASM1, ASM2d, ASM3)

> **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)