This package 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 Henze, M. et al. (1999) [1].
This 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_ALK, X_AUT, X_H, X_I, X_MeOH, X_MeP, X_PAO, X_PHA, X_PP, X_S, and X_TSS as components
supports only liquid phase
Limitations of the model, as noted in [1], are as follows:
valid for municipal wastewater only
overflow of fermentation products (considered to be acetate) to the aeration tank cannot be modeled
influent wastewater requires sufficient concentrations of magnesium and potassium
pH should be near neutral
temperature in the range of 10-25°C
Description
Symbol
Indices
Components
j ['H2O', 'S_A', 'S_F', 'S_I', S_N2, S_NH4, S_NO3, S_O2, S_PO4, S_ALK, X_AUT, X_H, X_I, X_MeOH, X_MeP, X_PAO, X_PHA, X_PP, X_S, X_TSS]
Phases
p ['Liq']
The ASM2D model includes 19 components as outlined in the table below.
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.
NH_4 NH_4
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
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
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}
Stoichiometric Coefficients The table below provides typical values for stoichiometric coefficients (from Table 9 of reference).
Description
Symbol
Parameter
Default Value
Units
N content of inert soluble COD S_I
i_{NSI} i_NSI
0.01
\text{dimensionless} N content of fermentable substrate S_F
i_{NSF} i_NSF
0.03
\text{dimensionless} N content of inert particulate COD X_I
i_{NXI} i_NXI
0.02
\text{dimensionless} N content of slowly biodegradable substrate X_S
i_{NXS} i_NXS
0.08
\text{dimensionless} N content of biomass, X_H, X_PAO, X_AUT
i_{NBM} i_NBM
0.07
\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_{SF} i_SF
0.01
\text{dimensionless} P content of inert particulate COD X_I
i_{PXI} i_PXI
0.01
\text{dimensionless} P content of slowly biodegradable substrate X_S
i_{PXS} i_PXS
0.01
\text{dimensionless} P content of biomass, X_H, X_PAO, X_AUT
i_{PBM} i_PBM
0.02
\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
0.40
\text{dimensionless} PHA requirement for PP storage
Y_{PHA} Y_PHA
0
\text{dimensionless} Yield of autotrophic biomass per NO3- N
Y_{A} Y_A
0.24
\text{dimensionless}
Description
Symbol
Parameter
Value at 20°C
Units
Hydrolysis rate constant
K_H K_H
3
\text{day}^{-1} Anoxic hydrolysis reduction factor
\eta _{NO3} eta_NO3
0.6
\text{dimensionless} Anaerobic hydrolysis reduction factor
\eta _{fe} eta_fe
0.40
\text{dimensionless} Saturation/inhibition coefficient for oxygen
K_{O2} K_O2
0.0002
\text{kg O_2/}\text{m}^{3} Saturation/inhibition coefficient for nitrate
K_{NO3} K_NO3
0.0005
\text{kg N/}\text{m}^{3} Saturation coefficient for particulate COD
K_{X} K_X
0.1
\text{kg X_S/}\text{kg X_H} Maximum growth rate on substrate
µ_H mu_H
6
\text{kg X_S/}\text{kg X_H . day} Maximum rate for fermentation
q_{fe} q_fe
3
\text{kg S_F/}\text{kg X_H . day} Rate constant for lysis and decay
b_H b_H
0.4
\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
K_A K_A
0.004
\text{kg COD/}\text{m}^{3} Saturation coefficient for ammonium (nutrient)
K_{NH4} K_NH4
0.00005
\text{kg N/}\text{m}^{3} Saturation coefficient for phosphate (nutrient)
K_P K_P
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
3
\text{kg PHA/}\text{kg PAO . day} Rate constant for storage of X_PP
q_{PP} q_PP
1.5
\text{kg PP/}\text{kg PAO . day} Maximum growth rate of PAO
µ_{PAO} mu_PAO
1
\text{day}^{-1} Rate for Lysis of X_PAO
b_{PAO} b_PAO
0.2
\text{day}^{-1} Rate for Lysis of X_PP
b_{PP} b_PP
0.2
\text{day}^{-1} Rate for Lysis of X_PHA
b_{PHA} b_PHA
0.2
\text{day}^{-1} Saturation coefficient for phosphorus in storage of PP
K_{PS} K_PS
0.0002
\text{kg P/}\text{m}^3 Saturation coefficient for poly-phosphate
K_{PP} K_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
K_{IPP} K_IPP
0.02
\text{kg PP/}\text{kg PAO} Saturation coefficient for PHA
K_{PHA} K_PHA
0.01
\text{kg PHA/}\text{kg PAO} Maximum growth rate of X_AUT
µ_{AUT} mu_AUT
1
\text{day}^{-1} Decay rate of X_AUT
b_{AUT} b_{AUT}
0.15
\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}
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
Description
Equation
Aerobic hydrolysis
\rho _1 = K_{H}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{X_{S}/X_{H}}{K_{X}+X_{S}/X_{H}})X_{H} Anoxic hydrolysis
\rho _2 = K_{H}\eta _{NO3}(\frac{K_{O2}}{K_{O2}+S_{O2}})(\frac{S_{NO3}}{K_{NO3}+S_{NO3}})(\frac{X_{S}/X_{H}}{K_{X}+X_{S}/X_{H}})X_{H} Anaerobic hydrolysis
\rho _3 = K_{H}\eta _{fe}(\frac{K_{O2}}{K_{O2}+S_{O2}})(\frac{K_{NO3}}{K_{NO3}+S_{NO3}})(\frac{X_{S}/X_{H}}{K_{X}+X_{S}/X_{H}})X_{H} Growth on fermentable substrates, S_F
\rho _4 = µ_{H}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{S_{F}}{K_{F}+S_{F}})(\frac{S_{F}}{S_{F}+S_{A}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{H} Growth on fermentation products, S_A
\rho _5 = µ_{H}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{S_{A}}{K_{A}+S_{A}})(\frac{S_{A}}{S_{F}+S_{A}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{H} Denitrification with fermentable substrates, S_F
\rho _6 = µ_{H}\eta _{NO3}(\frac{K_{O2}}{K_{O2}+S_{O2}})(\frac{S_{NO3}}{K_{NO3}+S_{NO3}})(\frac{S_{F}}{K_{F}+S_{F}})(\frac{S_{F}}{S_{F}+S_{A}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{H} Denitrification with fermentation products, S_A
\rho _7 = µ_{H}\eta _{NO3}(\frac{K_{O2}}{K_{O2}+S_{O2}})(\frac{S_{NO3}}{K_{NO3}+S_{NO3}})(\frac{S_{A}}{K_{A}+S_{A}})(\frac{S_{A}}{S_{F}+S_{A}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{H} Fermentation
\rho _8 = q_{fe}(\frac{K_{O2}}{K_{O2}+S_{O2}})(\frac{K_{NO3}}{K_{NO3}+S_{NO3}})(\frac{S_{F}}{K_{F}+S_{F}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{H} Lysis
\rho _9 = b_{H}X_{H} Storage of X_PHA
\rho _{10} = q_{PHA}(\frac{S_{A}}{K_{A}+S_{A}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})(\frac{X_{PP}/X_{PAO}}{K_{PP}+X_{PP}/X_{PAO}})X_{PAO} Aerobic storage of X_PP
\rho _{11} = q_{PP}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{S_{PO4}}{K_{PS}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})(\frac{X_{PHA}/X_{PAO}}{K_{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} = \rho _{11}\eta _{NO3}(\frac{K_{O2}}{S_{O2}})(\frac{S_{NO3}}{K_{NO3}+S_{NO3}}) Aerobic growth on X_PHA
\rho _{13} = µ_{PAO}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})(\frac{X_{PHA}/X_{PAO}}{K_{PHA}+X_{PHA}/X_{PAO}})X_{PAO} Anoxic growth on X_PHA
\rho _{14} = \rho _{13}\eta _{NO3}(\frac{K_{O2}}{S_{O2}})(\frac{S_{NO3}}{K_{NO3}+S_{NO3}}) Lysis of X_PAO
\rho _{15} = b_{PAO}X_{PAO}(\frac{S_{ALK}}{K_{ALK}+S_{ALK}}) Lysis of X_PP
\rho _{16} = b_{PP}X_{PP}(\frac{S_{ALK}}{K_{ALK}+S_{ALK}}) Lysis of X_PHA
\rho _{17} = b_{PHA}X_{PHA}(\frac{S_{ALK}}{K_{ALK}+S_{ALK}}) Aerobic growth of X_AUT
\rho _{18} = µ_{AUT}(\frac{S_{O2}}{K_{O2}+S_{O2}})(\frac{S_{NH4}}{K_{NH4}+S_{NH4}})(\frac{S_{PO4}}{K_{P}+S_{PO4}})(\frac{S_{ALK}}{K_{ALK}+S_{ALK}})X_{AUT} Lysis of X_AUT
\rho _{19} = k_{AUT}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.asm2d_properties
.. autoclass:: ASM2dParameterBlock
:members:
:noindex:
.. autoclass:: ASM2dParameterData
:members:
:noindex:
.. autoclass:: _ASM2dStateBlock
:members:
:noindex:
.. autoclass:: ASM2dStateBlockData
:members:
:noindex:
.. currentmodule:: watertap.property_models.activated_sludge.asm2d_reactions
.. autoclass:: ASM2dReactionParameterBlock
:members:
:noindex:
.. autoclass:: ASM2dReactionParameterData
:members:
:noindex:
.. autoclass:: _ASM2dReactionBlock
:members:
:noindex:
.. autoclass:: ASM2dReactionBlockData
:members:
:noindex:
[1] M. Henze, W. Gujer, T. Mino, T. Matsuo, M.C. Wentzel, G. v. R. Marais, M.C.M. Van Loosdrecht, Activated sludge model No.2D, ASM2D, Water Science and Technology. 39 (1999) 165–182. https://doi.org/10.1016/S0273-1223(98)00829-4 .