This package is an extension of the base Activated Sludge Model no.2d (ASM2d) and implements properties and reactions of an activated sludge model for biological nutrient removal from wastewater using an activated sludge biological reactor with biological phosphorus removal as provided in Flores-Alsina, X. et al. (2016) [1].
Throughout this documentation, text in red has been removed in the Modified ASM2d model, text in lime has been added, and text in blue has been modified from its base ASM2d implementation.
- The following modifications have been made to the base ASM2d model as provided in [1]:
- adds inorganic carbon (S_IC), potassium (S_K), and magnesium (S_Mg) as solutes
- removes total suspended solids (X_TSS), metal-hydroxides (X_MeOH), metal-phosphate (X_MeP), alkalinity (S_ALK), and any variables or parameters associated with alkalinity
- removes the precipitation reaction (R20) and the re-dissolution reaction (R21)
- updates the Petersen matrix based on the above changes
- updates the rate expressions based on the above changes
- This Modified Activated Sludge Model no.2D (ASM2D) property/reaction package:
- supports 'H2O', 'S_A', 'S_F', 'S_I', S_N2, S_NH4, S_NO3, S_O2, S_PO4, S_K, S_Mg, S_IC, X_AUT, X_H, X_I, X_PAO, X_PHA, X_PP, and X_S as components
- supports only liquid phase
| Description | Symbol | Indices |
|---|---|---|
| Components | j | ['H2O', 'S_A', 'S_F', 'S_I', S_N2, S_NH4, S_NO3, S_O2, S_PO4, S_K, S_Mg, S_IC, X_AUT, X_H, X_I, X_PAO, X_PHA, X_PP, X_S] |
| Phases | p | ['Liq'] |
The modified ASM2D model includes 18 components as outlined in the table below. Red text indicates the component has been removed in the Modified ASM2d model, and lime text indicates the component has been added.
| Description | Symbol | Name in Model |
|---|---|---|
| Fermentation products, considered to be acetate | S_A | S_A |
| Fermentable, readily bio-degradable organic substrates | S_F | S_F |
| Inert soluble organic material | S_I | S_I |
| Dinitrogen, N2. SN2 is assumed to be the only nitrogenous product of denitrification | S_{N2} | S_N2 |
| Ammonium plus ammonia nitrogen | S_{NH4} | S_NH4 |
| Nitrate plus nitrite nitrogen (N03' + N02' -N); SN03 is assumed to include nitrate as well as nitrite nitrogen. | S_{NO3} | S_NO3 |
| Dissolved oxygen | S_{O2} | S_O2 |
| Inorganic soluble phosphorus, primarily ortho-phosphates | S_{PO4} | S_PO4 |
| Potassium | S_{K} | S_K |
| Magnesium | S_{Mg} | S_Mg |
| Inorganic carbon | S_{IC} | S_IC |
| Alkalinity, [mol HCO_3- per m^3] | S_{ALK} | S_ALK |
| Autotrophic nitrifying organisms | X_{AUT} | X_AUT |
| Heterotrophic organisms | X_H | X_H |
| Inert particulate organic material | X_I | X_I |
| Metal-hydroxides | X_{MeOH} | X_MeOH |
| Metal-phosphate | X_{MeP} | X_MeP |
| Phosphate-accumulating organisms | X_{PAO} | X_PAO |
| A cell internal storage product of phosphorus-accumulating organisms, primarily comprising poly-hydroxy-alkanoates (PHA) | X_{PHA} | X_PHA |
| Poly-phosphate | X_{PP} | X_PP |
| Slowly biodegradable substrates | X_S | X_S |
| Total suspended solids, TSS | X_{TSS} | X_TSS |
Red text indicates the state variable has been removed in the Modified ASM2d model.
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Total volumetric flowrate | Q | flow_vol | None | \text{m}^3\text{/s} |
| Temperature | T | temperature | None | \text{K} |
| Pressure | P | pressure | None | \text{Pa} |
| Component mass concentrations | C_j | conc_mass_comp | [j] | \text{kg/}\text{m}^3 |
| Molar alkalinity | A | alkalinity | None | \text{kmol HCO}_{3}^{-}\text{/m}^{3} |
Red text indicates the stoichiometric coefficient has been removed in the Modified ASM2d model, lime text indicates the stoichiometric coefficient has been added, and blue text indicates the coefficient has had its value changed from its base ASM2d implementation.
| Description | Symbol | Parameter | Default Value | Units |
|---|---|---|---|---|
| C content of inert soluble COD S_I | i_{CSI} | i_CSI | 0.36718 | \text{dimensionless} |
| C content of inert soluble COD S_F | i_{CSF} | i_CSF | 0.31843 | \text{dimensionless} |
| C content of inert soluble COD S_A | i_{CSA} | i_CSA | 0.375 | \text{dimensionless} |
| C content of inert soluble COD X_I | i_{CXI} | i_CXI | 0.36178 | \text{dimensionless} |
| C content of inert soluble COD X_S | i_{CXS} | i_CXS | 0.31843 | \text{dimensionless} |
| C content of inert soluble COD X_B | i_{CXB} | i_CXB | 0.36612 | \text{dimensionless} |
| N content of inert soluble COD S_I | i_{NSI} | i_NSI | 0.06003 | \text{dimensionless} |
| N content of fermentable substrate S_F | i_{NSF} | i_NSF | 0.03552 | \text{dimensionless} |
| N content of inert particulate COD X_I | i_{NXI} | i_NXI | 0.06003 | \text{dimensionless} |
| N content of slowly biodegradable substrate X_S | i_{NXS} | i_NXS | 0.03552 | \text{dimensionless} |
| N content of biomass, X_H, X_PAO, X_AUT | i_{NBM} | i_NBM | 0.08615 | \text{dimensionless} |
| P content of inert soluble COD S_I | i_{PSI} | i_PSI | 0.00 | \text{dimensionless} |
| P content of fermentable substrate, S_F | i_{PSF} | i_PSF | 0.00559 | \text{dimensionless} |
| P content of inert particulate COD X_I | i_{PXI} | i_PXI | 0.00649 | \text{dimensionless} |
| P content of slowly biodegradable substrate X_S | i_{PXS} | i_PXS | 0.00559 | \text{dimensionless} |
| P content of biomass, X_H, X_PAO, X_AUT | i_{PBM} | i_PBM | 0.02154 | \text{dimensionless} |
| TSS to COD ratio for X_I | i_{TSSXI} | i_TSSXI | 0.75 | \text{dimensionless} |
| TSS to COD ratio for X_S | i_{TSSXS} | i_TSSXS | 0.75 | \text{dimensionless} |
| TSS to COD ratio for biomass, X_H, X_PAO, X_AUT | i_{TSSBM} | i_TSSBM | 0.90 | \text{dimensionless} |
| Production of S_I in hydrolysis | f_{SI} | f_SI | 0 | \text{dimensionless} |
| Yield coefficient for heterotrophic biomass X_H | Y_{H} | Y_H | 0.625 | \text{dimensionless} |
| Fraction of inert COD generated in lysis | f_{XI} | f_XI | 0.1 | \text{dimensionless} |
| Yield coefficient for P accumulating organisms (biomass/PHA) | Y_{PAO} | Y_PAO | 0.625 | \text{dimensionless} |
| PP requirement (PO4 release) per PHA stored | Y_{PO4} | Y_PO4 | 0.0129 | \text{dimensionless} |
| PHA requirement for PP storage | Y_{PHA} | Y_PHA | 0.2 | \text{dimensionless} |
| Yield of autotrophic biomass per NO3- N | Y_{A} | Y_A | 0.24 | \text{dimensionless} |
| Potassium coefficient for polyphosphates | i_{KXPP} | i_KXPP | 0.4204 | \text{dimensionless} |
| Magnesium coefficient for polyphosphates | i_{MgXPP} | i_MgXPP | 0.2614 | \text{dimensionless} |
Red text indicates the parameter has been removed in the Modified ASM2d model, lime text indicates the parameter has been added, and blue text indicates the parameter has had its value changed from its base ASM2d implementation.
| Description | Symbol | Parameter | Value at 20°C | Units |
|---|---|---|---|---|
| Hydrolysis rate constant | K_H | K_H | 2.46 | \text{day}^{-1} |
| Anoxic hydrolysis reduction factor | hl_{NO3} | hl_NO3 | 0.6 | \text{dimensionless} |
| Anaerobic hydrolysis reduction factor | hl_{fe} | hl_fe | 0.40 | \text{dimensionless} |
| Saturation/inhibition coefficient for oxygen | KH_{O2} | K_O2 | 0.0002 | \text{kg O_2/}\text{m}^{3} |
| Saturation/inhibition coefficient for nitrate | KH_{NO3} | K_NO3 | 0.0005 | \text{kg N/}\text{m}^{3} |
| Saturation coefficient for particulate COD | KL_{X} | KL_X | 0.1 | \text{kg X_S/}\text{kg X_H} |
| Maximum growth rate on substrate | µ_H | mu_H | 4.23 | \text{kg X_S/}\text{kg X_H . day} |
| Maximum rate for fermentation | q_{fe} | q_fe | 2.11 | \text{kg S_F/}\text{kg X_H . day} |
| Rate constant for lysis and decay | b_H | b_H | 0.28 | \text{day}^{-1} |
| Saturation coefficient for growth on SF | K_F | K_F | 0.004 | \text{kg COD/}\text{m}^{3} |
| Saturation coefficient for fermentation of SF | K_{fe} | K_fe | 0.004 | \text{d}^{-1} |
| Saturation coefficient for growth on acetate SA | KH_A | KH_A | 0.004 | \text{kg COD/}\text{m}^{3} |
| Saturation coefficient for ammonium (nutrient) | KH_{NH4} | KH_NH4 | 0.00005 | \text{kg N/}\text{m}^{3} |
| Saturation coefficient for phosphate (nutrient) | KH_{PO4} | KH_PO4 | 0.00001 | \text{kg P/}\text{m}^{3} |
| Saturation coefficient for alkalinity (HCO3-) | K_{ALK} | K_ALK | 0.0001 | \text{kmol HCO_{3}^{-}/}\text{m}^{3} |
| Rate constant for storage of X_PHA (base Xpp) | q_{PHA} | q_PHA | 2.46 | \text{kg PHA/}\text{kg PAO . day} |
| Rate constant for storage of X_PP | q_{PP} | q_PP | 1.23 | \text{kg PP/}\text{kg PAO . day} |
| Maximum growth rate of PAO | µ_{PAO} | mu_PAO | 0.82 | \text{day}^{-1} |
| Rate for Lysis of X_PAO | b_{PAO} | b_PAO | 0.14 | \text{day}^{-1} |
| Rate for Lysis of X_PP | b_{PP} | b_PP | 0.14 | \text{day}^{-1} |
| Rate for Lysis of X_PHA | b_{PHA} | b_PHA | 0.14 | \text{day}^{-1} |
| Saturation coefficient for phosphorus in storage of PP | KP_P | KP_P | 0.0002 | \text{kg P/}\text{m}^3 |
| Saturation coefficient for poly-phosphate | KP_{PP} | KP_PP | 0.01 | \text{kg PP/}\text{kg PAO} |
| Maximum ratio of X_PP/X_PAO | K_{MAX} | K_MAX | 0.34 | \text{kg PP/}\text{kg PAO} |
| Inhibition coefficient for PP storage | KI_{PP} | KI_PP | 0.02 | \text{kg PP/}\text{kg PAO} |
| Saturation coefficient for PHA | KP_{PHA} | KP_PHA | 0.01 | \text{kg PHA/}\text{kg PAO} |
| Maximum growth rate of X_AUT | µ_{AUT} | mu_AUT | 0.61 | \text{day}^{-1} |
| Decay rate of X_AUT | b_{AUT} | b_AUT | 0.09 | \text{day}^{-1} |
| Rate constant for P precipitation | k_{PRE} | k_pre | 1000 | \text{m/}^{3}\text{kg Fe(OH)_3 . day} |
| Rate constant for redissolution | k_{RED} | k_red | 0.6 | \text{day}^{-1} |
| Reduction factor for denitrification | hH_{NO3} | hH_NO3 | 0.8 | \text{dimensionless} |
| Anoxic reduction factor for endogenous respiration | hH_{NO3, end} | hH_NO3_end | 0.5 | \text{dimensionless} |
| Reduction factor under anoxic conditions | hP_{NO3} | hP_NO3 | 0.6 | \text{dimensionless} |
| Anoxic reduction factor for decay of PAOs | hP_{NO3, end} | hP_NO3_end | 0.33 | \text{dimensionless} |
| Anoxic reduction factor for decay of PP | hPP_{NO3, end} | hPP_NO3_end | 0.33 | \text{dimensionless} |
| Anoxic reduction factor for decay of PHA | hPHA_{NO3, end} | hPHA_NO3_end | 0.33 | \text{dimensionless} |
| Anoxic reduction factor for decay of autotrophs | hAUT_{NO3, end} | hAUT_NO3_end | 0.33 | \text{dimensionless} |
| Description | Symbol | Variable | Index | Units |
|---|---|---|---|---|
| Fluid specific heat capacity | c_p | cp | None | \text{J/kg/K} |
| Mass density | \rho | dens_mass | [p] | \text{kg/}\text{m}^3 |
Equations marked "(with decay)" indicate that the decay of heterotrophs and autotrophs is dependent on the electron acceptor present. Equations marked "(without decay)" indicate that the decay of heterotrophs and autotrophs does not change.
Red text indicates the equation has been removed in the Modified ASM2d model, and blue text indicates the equation has been modified from its base ASM2d implementation.
| Description | Equation |
|---|---|
| Aerobic hydrolysis | \rho _1 = K_{H}(\frac{S_{O2}}{KL_{O2}+S_{O2}})(\frac{X_{S}/X_{H}}{KL_{X}+X_{S}/X_{H}})X_{H} |
| Anoxic hydrolysis | \rho _2 = K_{H}\eta _{NO3}(\frac{KL_{O2}}{KL_{O2}+S_{O2}})(\frac{S_{NO3}}{KL_{NO3}+S_{NO3}})(\frac{X_{S}/X_{H}}{KL_{X}+X_{S}/X_{H}})X_{H} |
| Anaerobic hydrolysis | \rho _3 = K_{H}\eta _{fe}(\frac{KL_{O2}}{KL_{O2}+S_{O2}})(\frac{KL_{NO3}}{KL_{NO3}+S_{NO3}})(\frac{X_{S}/X_{H}}{KL_{X}+X_{S}/X_{H}})X_{H} |
| Growth on fermentable substrates, S_F | \rho _4 = µ_{H}(\frac{S_{O2}}{KH_{O2}+S_{O2}})(\frac{S_{F}}{K_{F}+S_{F}})(\frac{S_{F}}{S_{F}+S_{A}})(\frac{S_{NH4}}{KH_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KH_{PO4}+S_{PO4}})X_{H} |
| Growth on fermentation products, S_A | \rho _5 = µ_{H}(\frac{S_{O2}}{KH_{O2}+S_{O2}})(\frac{S_{A}}{KH_{A}+S_{A}})(\frac{S_{A}}{S_{F}+S_{A}})(\frac{S_{NH4}}{KH_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KH_{PO4}+S_{PO4}})X_{H} |
| Denitrification with fermentable substrates, S_F | \rho _6 = µ_{H}hH_{NO3}(\frac{KH_{O2}}{KH_{O2}+S_{O2}})(\frac{S_{NO3}}{KH_{NO3}+S_{NO3}})(\frac{S_{F}}{K_{F}+S_{F}})(\frac{S_{F}}{S_{F}+S_{A}})(\frac{S_{NH4}}{KH_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KH_{PO4}+S_{PO4}})X_{H} |
| Denitrification with fermentation products, S_A | \rho _7 = µ_{H}hH_{NO3}(\frac{KH_{O2}}{KH_{O2}+S_{O2}})(\frac{S_{NO3}}{KH_{NO3}+S_{NO3}})(\frac{S_{A}}{KH_{A}+S_{A}})(\frac{S_{A}}{S_{F}+S_{A}})(\frac{S_{NH4}}{KH_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KH_{PO4}+S_{PO4}})X_{H} |
| Fermentation | \rho _8 = q_{fe}(\frac{KH_{O2}}{KH_{O2}+S_{O2}})(\frac{KH_{NO3}}{KH_{NO3}+S_{NO3}})(\frac{S_{F}}{K_{fe}+S_{F}})X_{H} |
| Lysis (without decay) | \rho _9 = b_{H}X_{H} |
| Lysis (with decay) | \rho _9 = b_{H}(\frac{S_{O2}}{KH_{O2}+S_{O2}})+hH_{NO3,end}(\frac{KH_{O2}}{KH_{O2}+S_{O2}})(\frac{S_{NO3}}{KH_{NO3}+S_{NO3}})X_{H} |
| Storage of X_PHA | \rho _{10} = q_{PHA}(\frac{S_{A}}{KP_{A}+S_{A}})(\frac{X_{PP}/X_{PAO}}{KP_{PP}+X_{PP}/X_{PAO}})X_{PAO} |
| Aerobic storage of X_PP | \rho _{11} = q_{PP}(\frac{S_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{PO4}}{KP_{P}+S_{PO4}})(\frac{X_{PHA}/X_{PAO}}{KP_{PHA}+X_{PHA}/X_{PAO}})(\frac{K_{MAX} - X_{PP}/X_{PAO}}{K_{IPP}+K_{MAX} - X_{PP}/X_{PAO}})X_{PAO} |
| Anoxic storage of X_PP | \rho _{12} = q_{PP}hP_{NO3}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})(\frac{S_{PO4}}{KP_{P}+S_{PO4}})(\frac{X_{PHA}/X_{PAO}}{KP_{PHA}+X_{PHA}/X_{PAO}})(\frac{K_{MAX} - X_{PP}/X_{PAO}}{K_{IPP}+K_{MAX} - X_{PP}/X_{PAO}})X_{PAO} |
| Aerobic growth on X_PHA | \rho _{13} = µ_{PAO}(\frac{S_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NH4}}{KP_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KP_{PO4}+S_{PO4}})(\frac{X_{PHA}/X_{PAO}}{KP_{PHA}+X_{PHA}/X_{PAO}})X_{PAO} |
| Anoxic growth on X_PHA | \rho _{14} = µ_{PAO}hP_{NO3}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})(\frac{S_{NH4}}{KP_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KP_{PO4}+S_{PO4}})(\frac{X_{PHA}/X_{PAO}}{KP_{PHA}+X_{PHA}/X_{PAO}})X_{PAO} |
| Lysis of X_PAO (without decay) | \rho _{15} = b_{PAO}X_{PAO} |
| Lysis of X_PAO (with decay) | \rho _{15} = b_{PAO}(\frac{S_{O2}}{KP_{O2}+S_{O2}})+hP_{NO3,end}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})X_{PAO} |
| Lysis of X_PP (without decay) | \rho _{16} = b_{PP}X_{PP} |
| Lysis of X_PP (with decay) | \rho _{16} = b_{PP}(\frac{S_{O2}}{KP_{O2}+S_{O2}})+hPP_{NO3,end}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})X_{PP} |
| Lysis of X_PHA (without decay) | \rho _{17} = b_{PHA}X_{PHA} |
| Lysis of X_PHA (with decay) | \rho _{17} = b_{PHA}(\frac{S_{O2}}{KP_{O2}+S_{O2}})+hPHA_{NO3,end}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})X_{PHA} |
| Aerobic growth of X_AUT | \rho _{18} = µ_{AUT}(\frac{S_{O2}}{KA_{O2}+S_{O2}})(\frac{S_{NH4}}{KA_{NH4}+S_{NH4}})(\frac{S_{PO4}}{KA_{PO4}+S_{PO4}})X_{AUT} |
| Lysis of X_AUT (without decay) | \rho _{19} = b_{AUT}X_{AUT} |
| Lysis of X_AUT (with decay) | \rho _{19} = b_{AUT}(\frac{S_{O2}}{KP_{O2}+S_{O2}})+hAUT_{NO3,end}(\frac{KP_{O2}}{KP_{O2}+S_{O2}})(\frac{S_{NO3}}{KP_{NO3}+S_{NO3}})X_{AUT} |
| Precipitation of phosphorus with ferric hydroxide | \rho _{20} = k_{PRE}S_{PO4}X_{MeOH} |
| Redissolution | \rho _{21} = k_{RED}X_{MeP}(\frac{S_{ALK}}{K_{ALK}+S_{ALK}}) |
A thorough scaling routine for the ASM2D property package has yet to be implemented.
.. currentmodule:: watertap.property_models.activated_sludge.modified_asm2d_properties
.. autoclass:: ModifiedASM2dParameterBlock
:members:
:noindex:
.. autoclass:: ModifiedASM2dParameterData
:members:
:noindex:
.. autoclass:: _ModifiedASM2dStateBlock
:members:
:noindex:
.. autoclass:: ModifiedASM2dStateBlockData
:members:
:noindex:
.. currentmodule:: watertap.property_models.activated_sludge.modified_asm2d_reactions
.. autoclass:: ModifiedASM2dReactionParameterBlock
:members:
:noindex:
.. autoclass:: ModifiedASM2dReactionParameterData
:members:
:noindex:
.. autoclass:: _ModifiedASM2dReactionBlock
:members:
:noindex:
.. autoclass:: ModifiedASM2dReactionBlockData
:members:
:noindex:
[1] X. Flores-Alsina, K. Solon, C.K. Mbamba, S. Tait, K.V. Gernaey, U. Jeppsson, D.J. Batstone, Modelling phosphorus (P), sulfur (S) and iron (Fe) interactions fordynamic simulations of anaerobic digestion processes, Water Research. 95 (2016) 370-382. https://www.sciencedirect.com/science/article/pii/S0043135416301397