Activated Sludge Model No. 1 (ASM1)
The original source of the activated sludge model is (Henze et al., 1987). This model has been tested and extended ever since, such that we decided to further include the updates from (Hauduc et al., 2010) and (Corominas et al., 2010). The goal was to provide these models in a machine readable form with a mass balance that sums up to zero.
Create a process with this model using
Process("ASM1")Add keyword arguments to overwrite the default values of the parameters, e.g.
Process("ASM1"; Y_H = 1)Such keyword arguments can be provided for all parameters listed below. Multiple keyword arguments can be provided if multiple parameters are to be set to different values.
When using this Model, one needs to set the initial state/initial condition in the corresponding reactor. This is because the default values are all 0, which leads to a division by 0 for some of the process equations!
States
| Name | Description | Particle Size |
|---|---|---|
| $\mathtt{S\_S}\left( t \right)$ | Soluble biodegradable organics | soluble |
| $\mathtt{S\_I}\left( t \right)$ | Soluble nondegradable organics | soluble |
| $\mathtt{S\_O}\left( t \right)$ | Dissolved oxygen | soluble |
| $\mathtt{X\_S}\left( t \right)$ | Particulate and colloidal biodegradable organics | particulate,colloidal |
| $\mathtt{X\_I}\left( t \right)$ | Particulate nonbiodegradable organics from the influent | particulate |
| $\mathtt{X\_P}\left( t \right)$ | Particulate nonbiodegradable endogenous products | particulate |
| $\mathtt{S\_NH}\left( t \right)$ | Ammonia (NH4 + NH3) | soluble |
| $\mathtt{S\_NO}\left( t \right)$ | Nitrate and nitrite (NO3 + NO2) (considered to be NO3 only for stoichiometry) | soluble |
| $\mathtt{X\_ND}\left( t \right)$ | Particulate and colloidal biodegradable organic N | particulate,colloidal |
| $\mathtt{S\_ND}\left( t \right)$ | Soluble biodegradable organic N | soluble |
| $\mathtt{X\_BH}\left( t \right)$ | Ordinary heterotrophic organisms | particulate |
| $\mathtt{X\_BA}\left( t \right)$ | Autotrophic nitrifying organisms (NH4+ to NO3-) | particulate |
| $\mathtt{S\_ALK}\left( t \right)$ | Alkalinity (HCO3-) | soluble |
| $\mathtt{S\_N2}\left( t \right)$ | Dissolved nitrogen (gas, N2) | soluble |
Process Rates
| Name | Description | Equation |
|---|---|---|
| $\mathtt{g\_hO2}\left( t \right)$ | Aerobic growth of heterotrophs | $\frac{\mathtt{mu\_H} \mathtt{S\_O}\left( t \right) \mathtt{S\_NH}\left( t \right) \mathtt{X\_BH}\left( t \right) \mathtt{S\_S}\left( t \right)}{\left( \mathtt{K\_NHH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right) \left( \mathtt{K\_S} + \mathtt{S\_S}\left( t \right) \right)}$ |
| $\mathtt{g\_hAn}\left( t \right)$ | Anoxic growth of heterotrophs | $\frac{\mathtt{K\_OH} \mathtt{eta\_g} \mathtt{mu\_H} \mathtt{S\_NH}\left( t \right) \mathtt{S\_NO}\left( t \right) \mathtt{X\_BH}\left( t \right) \mathtt{S\_S}\left( t \right)}{\left( \mathtt{K\_NHH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right) \left( \mathtt{K\_S} + \mathtt{S\_S}\left( t \right) \right)}$ |
| $\mathtt{g\_aO2}\left( t \right)$ | Aerobic growth of autotrophs | $\frac{\mathtt{mu\_A} \mathtt{S\_O}\left( t \right) \mathtt{S\_NH}\left( t \right) \mathtt{X\_BA}\left( t \right)}{\left( \mathtt{K\_NH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_OA} + \mathtt{S\_O}\left( t \right) \right)}$ |
| $\mathtt{d\_h}\left( t \right)$ | Decay of heterotrophs | $\mathtt{b\_H} \mathtt{X\_BH}\left( t \right)$ |
| $\mathtt{d\_a}\left( t \right)$ | Decay of autotrophs | $\mathtt{b\_A} \mathtt{X\_BA}\left( t \right)$ |
| $\mathtt{am\_N}\left( t \right)$ | Ammonification of soluble organic nitrogen | $\mathtt{k\_a} \mathtt{S\_ND}\left( t \right) \mathtt{X\_BH}\left( t \right)$ |
| $\mathtt{ho}\left( t \right)$ | Hydrolysis of entrapped organics | $\frac{\mathtt{k\_h} \left( \frac{\mathtt{K\_OH} \mathtt{eta\_h} \mathtt{S\_NO}\left( t \right)}{\left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right)} + \frac{\mathtt{S\_O}\left( t \right)}{\mathtt{K\_OH} + \mathtt{S\_O}\left( t \right)} \right) \mathtt{X\_S}\left( t \right)}{\mathtt{K\_X} + \frac{\mathtt{X\_S}\left( t \right)}{\mathtt{X\_BH}\left( t \right)}}$ |
| $\mathtt{ho\_N}\left( t \right)$ | Hydrolysis of entrapped organic nitrogen | $\frac{\mathtt{k\_h} \left( \frac{\mathtt{K\_OH} \mathtt{eta\_h} \mathtt{S\_NO}\left( t \right)}{\left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right)} + \frac{\mathtt{S\_O}\left( t \right)}{\mathtt{K\_OH} + \mathtt{S\_O}\left( t \right)} \right) \mathtt{X\_ND}\left( t \right)}{\mathtt{K\_X} + \frac{\mathtt{X\_S}\left( t \right)}{\mathtt{X\_BH}\left( t \right)}}$ |
Stoichiometric Matrix
| $\mathtt{S\_S}\left( t \right)$ | $\mathtt{S\_I}\left( t \right)$ | $\mathtt{S\_O}\left( t \right)$ | $\mathtt{X\_S}\left( t \right)$ | $\mathtt{X\_I}\left( t \right)$ | $\mathtt{X\_P}\left( t \right)$ | $\mathtt{S\_NH}\left( t \right)$ | $\mathtt{S\_NO}\left( t \right)$ | $\mathtt{X\_ND}\left( t \right)$ | $\mathtt{S\_ND}\left( t \right)$ | $\mathtt{X\_BH}\left( t \right)$ | $\mathtt{X\_BA}\left( t \right)$ | $\mathtt{S\_ALK}\left( t \right)$ | $\mathtt{S\_N2}\left( t \right)$ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $\frac{-1}{\mathtt{Y\_H}}$ | $0$ | $\frac{-1 + \mathtt{Y\_H}}{\mathtt{Y\_H}}$ | $0$ | $0$ | $0$ | $- \mathtt{i\_XB}$ | $0$ | $0$ | $0$ | $1$ | $0$ | $- \mathtt{i\_ChargeSNH} \mathtt{i\_XB}$ | $0$ | $\mathtt{g\_hO2}\left( t \right) = \frac{\mathtt{mu\_H} \mathtt{S\_O}\left( t \right) \mathtt{S\_NH}\left( t \right) \mathtt{X\_BH}\left( t \right) \mathtt{S\_S}\left( t \right)}{\left( \mathtt{K\_NHH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right) \left( \mathtt{K\_S} + \mathtt{S\_S}\left( t \right) \right)}$ |
| $\frac{-1}{\mathtt{Y\_H}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $- \mathtt{i\_XB}$ | $\frac{-1 + \mathtt{Y\_H}}{\mathtt{Y\_H} \mathtt{i\_NO3N2}}$ | $0$ | $0$ | $1$ | $0$ | $\frac{\left( -1 + \mathtt{Y\_H} \right) \mathtt{i\_ChargeSNO}}{\mathtt{Y\_H} \mathtt{i\_NO3N2}} - \mathtt{i\_ChargeSNH} \mathtt{i\_XB}$ | $\frac{1 - \mathtt{Y\_H}}{\mathtt{Y\_H} \mathtt{i\_NO3N2}}$ | $\mathtt{g\_hAn}\left( t \right) = \frac{\mathtt{K\_OH} \mathtt{eta\_g} \mathtt{mu\_H} \mathtt{S\_NH}\left( t \right) \mathtt{S\_NO}\left( t \right) \mathtt{X\_BH}\left( t \right) \mathtt{S\_S}\left( t \right)}{\left( \mathtt{K\_NHH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right) \left( \mathtt{K\_S} + \mathtt{S\_S}\left( t \right) \right)}$ |
| $0$ | $0$ | $\frac{\mathtt{Y\_A} + \mathtt{i\_CODNO3}}{\mathtt{Y\_A}}$ | $0$ | $0$ | $0$ | $- \mathtt{i\_XB} + \frac{-1}{\mathtt{Y\_A}}$ | $\frac{1}{\mathtt{Y\_A}}$ | $0$ | $0$ | $0$ | $1$ | $\frac{\mathtt{i\_ChargeSNO}}{\mathtt{Y\_A}} + \mathtt{i\_ChargeSNH} \left( - \mathtt{i\_XB} + \frac{-1}{\mathtt{Y\_A}} \right)$ | $0$ | $\mathtt{g\_aO2}\left( t \right) = \frac{\mathtt{mu\_A} \mathtt{S\_O}\left( t \right) \mathtt{S\_NH}\left( t \right) \mathtt{X\_BA}\left( t \right)}{\left( \mathtt{K\_NH} + \mathtt{S\_NH}\left( t \right) \right) \left( \mathtt{K\_OA} + \mathtt{S\_O}\left( t \right) \right)}$ |
| $0$ | $0$ | $0$ | $1 - \mathtt{f\_P}$ | $0$ | $\mathtt{f\_P}$ | $0$ | $0$ | $\mathtt{i\_XB} - \mathtt{f\_P} \mathtt{i\_XB}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $\mathtt{d\_h}\left( t \right) = \mathtt{b\_H} \mathtt{X\_BH}\left( t \right)$ |
| $0$ | $0$ | $0$ | $1 - \mathtt{f\_P}$ | $0$ | $\mathtt{f\_P}$ | $0$ | $0$ | $\mathtt{i\_XB} - \mathtt{f\_P} \mathtt{i\_XB}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $\mathtt{d\_a}\left( t \right) = \mathtt{b\_A} \mathtt{X\_BA}\left( t \right)$ |
| $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $\mathtt{i\_ChargeSNH}$ | $0$ | $\mathtt{am\_N}\left( t \right) = \mathtt{k\_a} \mathtt{S\_ND}\left( t \right) \mathtt{X\_BH}\left( t \right)$ |
| $1$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{ho}\left( t \right) = \frac{\mathtt{k\_h} \left( \frac{\mathtt{K\_OH} \mathtt{eta\_h} \mathtt{S\_NO}\left( t \right)}{\left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right)} + \frac{\mathtt{S\_O}\left( t \right)}{\mathtt{K\_OH} + \mathtt{S\_O}\left( t \right)} \right) \mathtt{X\_S}\left( t \right)}{\mathtt{K\_X} + \frac{\mathtt{X\_S}\left( t \right)}{\mathtt{X\_BH}\left( t \right)}}$ |
| $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $1$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{ho\_N}\left( t \right) = \frac{\mathtt{k\_h} \left( \frac{\mathtt{K\_OH} \mathtt{eta\_h} \mathtt{S\_NO}\left( t \right)}{\left( \mathtt{K\_NO} + \mathtt{S\_NO}\left( t \right) \right) \left( \mathtt{K\_OH} + \mathtt{S\_O}\left( t \right) \right)} + \frac{\mathtt{S\_O}\left( t \right)}{\mathtt{K\_OH} + \mathtt{S\_O}\left( t \right)} \right) \mathtt{X\_ND}\left( t \right)}{\mathtt{K\_X} + \frac{\mathtt{X\_S}\left( t \right)}{\mathtt{X\_BH}\left( t \right)}}$ |
Composition Matrix
| $\mathtt{S\_S}\left( t \right)$ | $\mathtt{S\_I}\left( t \right)$ | $\mathtt{S\_O}\left( t \right)$ | $\mathtt{X\_S}\left( t \right)$ | $\mathtt{X\_I}\left( t \right)$ | $\mathtt{X\_P}\left( t \right)$ | $\mathtt{S\_NH}\left( t \right)$ | $\mathtt{S\_NO}\left( t \right)$ | $\mathtt{X\_ND}\left( t \right)$ | $\mathtt{S\_ND}\left( t \right)$ | $\mathtt{X\_BH}\left( t \right)$ | $\mathtt{X\_BA}\left( t \right)$ | $\mathtt{S\_ALK}\left( t \right)$ | $\mathtt{S\_N2}\left( t \right)$ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COD | $1$ | $1$ | $-1$ | $1$ | $1$ | $1$ | $0$ | $\mathtt{i\_CODNO3}$ | $0$ | $0$ | $1$ | $1$ | $0$ | $\mathtt{i\_CODN2}$ |
| N | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{i\_XB}$ | $1$ | $1$ | $1$ | $1$ | $\mathtt{i\_XB}$ | $\mathtt{i\_XB}$ | $0$ | $1$ |
| Charge | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{i\_ChargeSNH}$ | $\mathtt{i\_ChargeSNO}$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $0$ |
Parameters
| Name | Description | Default Value | Unit | Temperature |
|---|---|---|---|---|
| $\mathtt{Y\_H}$ | Yield for X_BH growth | $0.67$ | gXBH/gXS | 20 |
| $\mathtt{f\_P}$ | Fraction of XU generated in biomass decay | $0.08$ | gramXU/gramXBio1 | 20 |
| $\mathtt{Y\_A}$ | Yield of X_BA growth per SNO3 | $0.24$ | gramXAUT/gramSNO3 | 20 |
| $\mathtt{i\_XB}$ | N content of biomass (XBH, XPAO, XBA) | $0.086$ | gramN/gramXBio | 20 |
| $\mathtt{i\_XP}$ | N content of products from biomass | $0.06$ | gramN/gramX_P | 20 |
| $\mathtt{i\_NO3N2}$ | Conversion factor for NO3 reduction to N2 | $\frac{ - 3 \mathtt{COD\_O} - \mathtt{COD\_neg}}{\mathtt{M\_N}}$ | gramCOD/gramN | 20 |
| $\mathtt{i\_CODNO3}$ | Conversion factor for NO3 in COD | $\frac{\mathtt{COD\_N} + 3 \mathtt{COD\_O} + \mathtt{COD\_neg}}{\mathtt{M\_N}}$ | gramCOD/gramN | 20 |
| $\mathtt{i\_CODN2}$ | Conversion factor for N2 in COD | $\frac{\mathtt{COD\_N}}{\mathtt{M\_N}}$ | gramCOD/gramN | 20 |
| $\mathtt{i\_ChargeSNH}$ | Conversion factor for NHx in charge | $\frac{1}{\mathtt{M\_N}}$ | Charge/gramN | 20 |
| $\mathtt{i\_ChargeSNO}$ | Conversion factor for NO3 in charge | $\frac{-1}{\mathtt{M\_N}}$ | Charge/gramN | 20 |
| $\mathtt{k\_h}$ | Maximum specific hydrolysis rate of particulate and soluble biodegradable organics | $3$ | gramXS/gramXBH/d | 20 |
| $\mathtt{K\_X}$ | Saturation coefficient for XB/X_BH | $0.03$ | gramXS/gramXBH | 20 |
| $\mathtt{eta\_h}$ | Correction factor for hydrolysis under anoxic conditions | $0.4$ | - | 20 |
| $\mathtt{mu\_H}$ | Maximum growth rate of X_BH | $6$ | per day | 20 |
| $\mathtt{eta\_g}$ | Reduction factor for anoxic growth of X_BH | $0.8$ | - | 20 |
| $\mathtt{K\_S}$ | Half-saturation coefficient for S_S | $20$ | gramS_S/m^3 | 20 |
| $\mathtt{b\_H}$ | Decay rate for X_BH | $0.62$ | per day | 20 |
| $\mathtt{K\_OH}$ | Half-saturation coefficient for SO XBH | $0.2$ | gramS_O/m^3 | 20 |
| $\mathtt{K\_NO}$ | Half-saturation coefficient for SNO XBH | $0.5$ | gramS_NO/m^3 | 20 |
| $\mathtt{K\_NHH}$ | Half-saturation coefficient for NH4* | $0.05$ | gramS_NH/m^3 | 20 |
| $\mathtt{mu\_A}$ | Maximum growth rate of X_BA | $0.8$ | per day | 20 |
| $\mathtt{b\_A}$ | Decay rate for X_BA | $0.15$ | per day | 20 |
| $\mathtt{k\_a}$ | Rate constant for ammonification | $0.08$ | m^3/gramX_S,N/day | 20 |
| $\mathtt{K\_OA}$ | Half-saturation coefficient for SO for XBA | $0.4$ | gramS_O/m^3 | 20 |
| $\mathtt{K\_NH}$ | Half-saturation coefficient for SNH for XBA | $1$ | gramS_NH/m^3 | 20 |
| $\mathtt{COD\_neg}$ | Theoretical COD of negative charge | $8$ | gramCOD/mol | |
| $\mathtt{COD\_pos}$ | Theoretical COD of positive charge | $-8$ | gramCOD/mol | |
| $\mathtt{COD\_C}$ | Theoretical COD of molar carbon | $32$ | gramCOD/mol | |
| $\mathtt{COD\_N}$ | Theoretical COD of molar nitrogen | $-24$ | gramCOD/mol | |
| $\mathtt{COD\_H}$ | Theoretical COD of molar hydrogen | $8$ | gramCOD/mol | |
| $\mathtt{COD\_O}$ | Theoretical COD of molar oxygen | $-16$ | gramCOD/mol | |
| $\mathtt{COD\_S}$ | Theoretical COD of molar sulphur | $48$ | gramCOD/mol | |
| $\mathtt{COD\_P}$ | Theoretical COD of molar phosphorus | $40$ | gramCOD/mol | |
| $\mathtt{COD\_Fe}$ | Theoretical COD of molar iron | $24$ | gramCOD/mol | |
| $\mathtt{M\_N}$ | atomic molar mass of nitrogen | $14$ | gram/mol |
References
- Corominas, L.; Rieger, L.; Takács, I.; Ekama, G.; Hauduc, H.; Vanrolleghem, P. A.; Oehmen, A.; Gernaey, K. V.; van Loosdrecht, M. C. and Comeau, Y. (2010). New framework for standardized notation in wastewater treatment modelling. Water Science and Technology 61, 841–857.
- Hauduc, H.; Rieger, L.; Takács, I.; Héduit, A.; Vanrolleghem, P. A. and Gillot, S. (2010). A systematic approach for model verification: application on seven published activated sludge models. Water Science and Technology 61, 825–839.
- Henze, M.; Grady, C. L.; Gujer, W.; Marais, G. and Matsuo, T. (1987). A general model for single-sludge wastewater treatment systems. Water Research 21, 505–515.