Activated Sludge Model nr. 1 (ASM1)
The original source of the activated sludge model is (Henze et al., 1987). This model has been tested and extended since, so that we decided to further include the information 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_OHO=1)This works for all parameters below and just add multiples for every to overwrite.
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, and the some of the process equations have a division by 0 if all states are 0!
States
| Name | Description | Particle Size |
|---|---|---|
| $\mathtt{S\_B}\left( t \right)$ | Soluble biodegradable organics | soluble |
| $\mathtt{S\_U}\left( t \right)$ | Soluble nondegradable organics | soluble |
| $\mathtt{S\_O2}\left( t \right)$ | Dissolved oxygen | soluble |
| $\mathtt{XC\_B}\left( t \right)$ | Particulate and colloidal biodegradable organics | particulate,colloidal |
| $\mathtt{X\_UInf}\left( t \right)$ | Particulate nonbiodegradable organics from the influent | particulate |
| $\mathtt{X\_UE}\left( t \right)$ | Particulate nonbiodegradable endogenous products | particulate |
| $\mathtt{S\_NHx}\left( t \right)$ | Ammonia (NH4 + NH3) | soluble |
| $\mathtt{S\_NOx}\left( t \right)$ | Nitrate and nitrite (NO3 + NO2) (considered to be NO3 only for stoichiometry) | soluble |
| $\mathtt{XC\_BN}\left( t \right)$ | Particulate and colloidal biodegradable organic N | particulate,colloidal |
| $\mathtt{S\_BN}\left( t \right)$ | Soluble biodegradable organic N | soluble |
| $\mathtt{X\_OHO}\left( t \right)$ | Ordinary heterotrophic organisms | particulate |
| $\mathtt{X\_ANO}\left( t \right)$ | 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 | $\frac{\mathtt{m\_OHOMax} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_B}\left( t \right) \mathtt{S\_O2}\left( t \right) \mathtt{S\_NHx}\left( t \right)}{\left( \mathtt{K\_NHxOHO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right) \left( \mathtt{K\_SBOHO} + \mathtt{S\_B}\left( t \right) \right)}$ |
| $\mathtt{g\_hAn}\left( t \right)$ | Anoxic growth of heterotrophs | $\frac{\mathtt{K\_O2OHO} \mathtt{m\_OHOMax} \mathtt{n\_mOHOAx} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_B}\left( t \right) \mathtt{S\_NHx}\left( t \right) \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NHxOHO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right) \left( \mathtt{K\_SBOHO} + \mathtt{S\_B}\left( t \right) \right)}$ |
| $\mathtt{g\_aO2}\left( t \right)$ | Aerobic growth of autotrophs | $\frac{\mathtt{m\_ANOMax} \mathtt{X\_ANO}\left( t \right) \mathtt{S\_O2}\left( t \right) \mathtt{S\_NHx}\left( t \right)}{\left( \mathtt{K\_NHxANO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_O2ANO} + \mathtt{S\_O2}\left( t \right) \right)}$ |
| $\mathtt{d\_h}\left( t \right)$ | Decay of heterotrophs | $\mathtt{b\_OHO} \mathtt{X\_OHO}\left( t \right)$ |
| $\mathtt{d\_a}\left( t \right)$ | Decay of autotrophs | $\mathtt{b\_ANO} \mathtt{X\_ANO}\left( t \right)$ |
| $\mathtt{am\_N}\left( t \right)$ | Ammonification of soluble organic Nitrogen | $\mathtt{q\_am} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_BN}\left( t \right)$ |
| $\mathtt{ho}\left( t \right)$ | Hydrolysis of entrapped organics | $\frac{\mathtt{q\_XCBSBhyd} \left( \frac{\mathtt{K\_O2OHO} \mathtt{n\_qhydAx} \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right)} + \frac{\mathtt{S\_O2}\left( t \right)}{\mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right)} \right) \mathtt{XC\_B}\left( t \right)}{\mathtt{K\_XCBhyd} + \frac{\mathtt{XC\_B}\left( t \right)}{\mathtt{X\_OHO}\left( t \right)}}$ |
| $\mathtt{ho\_N}\left( t \right)$ | Hydrolysis of entrapped organic nitrogen | $\frac{\mathtt{q\_XCBSBhyd} \left( \frac{\mathtt{K\_O2OHO} \mathtt{n\_qhydAx} \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right)} + \frac{\mathtt{S\_O2}\left( t \right)}{\mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right)} \right) \mathtt{XC\_BN}\left( t \right)}{\mathtt{K\_XCBhyd} + \frac{\mathtt{XC\_B}\left( t \right)}{\mathtt{X\_OHO}\left( t \right)}}$ |
Stoichiometric Matrix
| $\mathtt{S\_B}\left( t \right)$ | $\mathtt{S\_U}\left( t \right)$ | $\mathtt{S\_O2}\left( t \right)$ | $\mathtt{XC\_B}\left( t \right)$ | $\mathtt{X\_UInf}\left( t \right)$ | $\mathtt{X\_UE}\left( t \right)$ | $\mathtt{S\_NHx}\left( t \right)$ | $\mathtt{S\_NOx}\left( t \right)$ | $\mathtt{XC\_BN}\left( t \right)$ | $\mathtt{S\_BN}\left( t \right)$ | $\mathtt{X\_OHO}\left( t \right)$ | $\mathtt{X\_ANO}\left( t \right)$ | $\mathtt{S\_Alk}\left( t \right)$ | $\mathtt{S\_N2}\left( t \right)$ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $\frac{-1}{\mathtt{Y\_OHO}}$ | $0$ | $\frac{-1 + \mathtt{Y\_OHO}}{\mathtt{Y\_OHO}}$ | $0$ | $0$ | $0$ | $- \mathtt{i\_NXBio}$ | $0$ | $0$ | $0$ | $1$ | $0$ | $- \mathtt{i\_ChargeSNHx} \mathtt{i\_NXBio}$ | $0$ | $\mathtt{g\_hO2}\left( t \right) = \frac{\mathtt{m\_OHOMax} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_B}\left( t \right) \mathtt{S\_O2}\left( t \right) \mathtt{S\_NHx}\left( t \right)}{\left( \mathtt{K\_NHxOHO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right) \left( \mathtt{K\_SBOHO} + \mathtt{S\_B}\left( t \right) \right)}$ |
| $\frac{-1}{\mathtt{Y\_OHO}}$ | $0$ | $0$ | $0$ | $0$ | $0$ | $- \mathtt{i\_NXBio}$ | $\frac{-1 + \mathtt{Y\_OHO}}{\mathtt{Y\_OHO} \mathtt{i\_NO3N2}}$ | $0$ | $0$ | $1$ | $0$ | $\frac{\left( -1 + \mathtt{Y\_OHO} \right) \mathtt{i\_ChargeSNOx}}{\mathtt{Y\_OHO} \mathtt{i\_NO3N2}} - \mathtt{i\_ChargeSNHx} \mathtt{i\_NXBio}$ | $\frac{1 - \mathtt{Y\_OHO}}{\mathtt{Y\_OHO} \mathtt{i\_NO3N2}}$ | $\mathtt{g\_hAn}\left( t \right) = \frac{\mathtt{K\_O2OHO} \mathtt{m\_OHOMax} \mathtt{n\_mOHOAx} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_B}\left( t \right) \mathtt{S\_NHx}\left( t \right) \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NHxOHO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right) \left( \mathtt{K\_SBOHO} + \mathtt{S\_B}\left( t \right) \right)}$ |
| $0$ | $0$ | $\frac{\mathtt{Y\_ANO} + \mathtt{i\_CODNO3}}{\mathtt{Y\_ANO}}$ | $0$ | $0$ | $0$ | $- \mathtt{i\_NXBio} + \frac{-1}{\mathtt{Y\_ANO}}$ | $\frac{1}{\mathtt{Y\_ANO}}$ | $0$ | $0$ | $0$ | $1$ | $\frac{\mathtt{i\_ChargeSNOx}}{\mathtt{Y\_ANO}} + \mathtt{i\_ChargeSNHx} \left( - \mathtt{i\_NXBio} + \frac{-1}{\mathtt{Y\_ANO}} \right)$ | $0$ | $\mathtt{g\_aO2}\left( t \right) = \frac{\mathtt{m\_ANOMax} \mathtt{X\_ANO}\left( t \right) \mathtt{S\_O2}\left( t \right) \mathtt{S\_NHx}\left( t \right)}{\left( \mathtt{K\_NHxANO} + \mathtt{S\_NHx}\left( t \right) \right) \left( \mathtt{K\_O2ANO} + \mathtt{S\_O2}\left( t \right) \right)}$ |
| $0$ | $0$ | $0$ | $1 - \mathtt{f\_XUBiolys}$ | $0$ | $\mathtt{f\_XUBiolys}$ | $0$ | $0$ | $\mathtt{i\_NXBio} - \mathtt{f\_XUBiolys} \mathtt{i\_NXUE}$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $\mathtt{d\_h}\left( t \right) = \mathtt{b\_OHO} \mathtt{X\_OHO}\left( t \right)$ |
| $0$ | $0$ | $0$ | $1 - \mathtt{f\_XUBiolys}$ | $0$ | $\mathtt{f\_XUBiolys}$ | $0$ | $0$ | $\mathtt{i\_NXBio} - \mathtt{f\_XUBiolys} \mathtt{i\_NXUE}$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $\mathtt{d\_a}\left( t \right) = \mathtt{b\_ANO} \mathtt{X\_ANO}\left( t \right)$ |
| $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $\mathtt{i\_ChargeSNHx}$ | $0$ | $\mathtt{am\_N}\left( t \right) = \mathtt{q\_am} \mathtt{X\_OHO}\left( t \right) \mathtt{S\_BN}\left( t \right)$ |
| $1$ | $0$ | $0$ | $-1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{ho}\left( t \right) = \frac{\mathtt{q\_XCBSBhyd} \left( \frac{\mathtt{K\_O2OHO} \mathtt{n\_qhydAx} \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right)} + \frac{\mathtt{S\_O2}\left( t \right)}{\mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right)} \right) \mathtt{XC\_B}\left( t \right)}{\mathtt{K\_XCBhyd} + \frac{\mathtt{XC\_B}\left( t \right)}{\mathtt{X\_OHO}\left( t \right)}}$ |
| $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $1$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{ho\_N}\left( t \right) = \frac{\mathtt{q\_XCBSBhyd} \left( \frac{\mathtt{K\_O2OHO} \mathtt{n\_qhydAx} \mathtt{S\_NOx}\left( t \right)}{\left( \mathtt{K\_NOxOHO} + \mathtt{S\_NOx}\left( t \right) \right) \left( \mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right) \right)} + \frac{\mathtt{S\_O2}\left( t \right)}{\mathtt{K\_O2OHO} + \mathtt{S\_O2}\left( t \right)} \right) \mathtt{XC\_BN}\left( t \right)}{\mathtt{K\_XCBhyd} + \frac{\mathtt{XC\_B}\left( t \right)}{\mathtt{X\_OHO}\left( t \right)}}$ |
Composition Matrix
| $\mathtt{S\_B}\left( t \right)$ | $\mathtt{S\_U}\left( t \right)$ | $\mathtt{S\_O2}\left( t \right)$ | $\mathtt{XC\_B}\left( t \right)$ | $\mathtt{X\_UInf}\left( t \right)$ | $\mathtt{X\_UE}\left( t \right)$ | $\mathtt{S\_NHx}\left( t \right)$ | $\mathtt{S\_NOx}\left( t \right)$ | $\mathtt{XC\_BN}\left( t \right)$ | $\mathtt{S\_BN}\left( t \right)$ | $\mathtt{X\_OHO}\left( t \right)$ | $\mathtt{X\_ANO}\left( t \right)$ | $\mathtt{S\_Alk}\left( t \right)$ | $\mathtt{S\_N2}\left( t \right)$ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| COD | $1$ | $1$ | $-1$ | $1$ | $1$ | $1$ | $0$ | $\mathtt{i\_CODNO3}$ | $0$ | $0$ | $1$ | $1$ | $0$ | $\mathtt{i\_CODN2}$ |
| N | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{i\_NXUE}$ | $1$ | $1$ | $1$ | $1$ | $\mathtt{i\_NXBio}$ | $\mathtt{i\_NXBio}$ | $0$ | $1$ |
| Charge | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $\mathtt{i\_ChargeSNHx}$ | $\mathtt{i\_ChargeSNOx}$ | $0$ | $0$ | $0$ | $0$ | $-1$ | $0$ |
Parameters
| Name | Description | Default Value | Unit | Temperature |
|---|---|---|---|---|
| $\mathtt{Y\_OHO}$ | Yield for XOHO growth | $0.67$ | gXOHO/gXCB | 20 |
| $\mathtt{f\_XUBiolys}$ | Fraction of XU generated in biomass decay | $0.08$ | gramXU/gramXBio1 | 20 |
| $\mathtt{Y\_ANO}$ | Yield of XANO growth per SNO3 | $0.24$ | gramXAUT/gramSNO3 | 20 |
| $\mathtt{i\_NXBio}$ | N content of biomass (XOHO, XPAO, XANO) | $0.086$ | gramN/gramXBio | 20 |
| $\mathtt{i\_NXUE}$ | N content of products from biomass | $0.06$ | gramN/gramXUE | 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 |
| $\mathtt{i\_ChargeSNHx}$ | Conversion factor for NHx in charge | $\frac{1}{\mathtt{M\_N}}$ | Charge/gramN | 20 |
| $\mathtt{i\_ChargeSNOx}$ | Conversion factor for NO3 in charge | $\frac{-1}{\mathtt{M\_N}}$ | Charge/gramN | 20 |
| $\mathtt{q\_XCBSBhyd}$ | Maximum specific hydrolysis rate of particulate and soluble biodegradable organics | $3$ | gramXCB/gramXOHO/d | 20 |
| $\mathtt{K\_XCBhyd}$ | Saturation coefficient for XB/XOHO | $0.03$ | gramXCB/gramXOHO | 20 |
| $\mathtt{n\_qhydAx}$ | Correction factor for hydrolysis under anoxic conditions | $0.4$ | - | 20 |
| $\mathtt{m\_OHOMax}$ | Maximum growth rate of XOHO | $6$ | per day | 20 |
| $\mathtt{n\_mOHOAx}$ | Reduction factor for anoxic growth of XOHO | $0.8$ | - | 20 |
| $\mathtt{K\_SBOHO}$ | Half-saturation coefficient for SB | $20$ | gramSB/m^3 | 20 |
| $\mathtt{b\_OHO}$ | Decay rate for XOHO | $0.62$ | per day | 20 |
| $\mathtt{K\_O2OHO}$ | Half-saturation coefficient for SO2 XOHO | $0.2$ | gramSO2/m^3 | 20 |
| $\mathtt{K\_NOxOHO}$ | Half-saturation coefficient for SNOx XOHO | $0.5$ | gramSNOx/m^3 | 20 |
| $\mathtt{K\_NHxOHO}$ | Half-saturation coefficient for NH4* | $0.05$ | gramSNHx/m^3 | 20 |
| $\mathtt{m\_ANOMax}$ | Maximum growth rate of XANO | $0.8$ | per day | 20 |
| $\mathtt{b\_ANO}$ | Decay rate for XANO | $0.15$ | per day | 20 |
| $\mathtt{q\_am}$ | Rate constant for ammonification | $0.08$ | m^3/gramXCB,N/day | 20 |
| $\mathtt{K\_O2ANO}$ | Half-saturation coefficient for SO2 for XANO | $0.4$ | gramSO2/m^3 | 20 |
| $\mathtt{K\_NHxANO}$ | Half-saturation coefficient for SNHx for XANO | $1$ | gramSNHx/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.