This package implements properties and reactions of an anaerobic digestion model for industrial wastewater treatment from food and beverage production using an anaerobic digester as provided in
Batstone, D. J. et al. (2002) and Rosen and Jeppsson (2006) .
This Anaerobic Digestion Model no.1 (ADM1) property/reaction package:
supports 'H2O', 'S_su', 'S_aa', 'S_fa', 'S_va', 'S_bu', 'S_pro', 'S_ac', 'S_h2', 'S_ch4', 'S_IC', 'S_IN', 'S_I', 'X_c', 'X_ch', 'X_pr', 'X_li', 'X_su', 'X_aa', 'X_fa', 'X_c4', 'X_pro', 'X_ac', 'X_h2', 'X_I', 'S_cat', 'S_an', and 'S_co2' as components
supports only liquid and vapor phase
Description
Symbol
Indices
Components
j ['H2O', 'S_su', 'S_aa', 'S_fa', 'S_va', 'S_bu', 'S_pro', 'S_ac', 'S_h2', 'S_ch4', 'S_IC', 'S_IN', 'S_I', 'X_c', 'X_ch', 'X_pr', 'X_li', 'X_su', 'X_aa', 'X_fa', 'X_c4', 'X_pro', 'X_ac', 'X_h2', 'X_I', 'S_cat', 'S_an', 'S_co2']
Phases
p ['Liq', 'Vap']
Description
Symbol
Variable
Monosaccharides, S_su
S_{su} S_su
Amino acids, S_aa
S_{aa} S_aa
Long chain fatty acids, S_fa
S_{fa} S_fa
Total valerate, S_va
S_{va} S_va
Total butyrate, S_bu
S_{bu} S_bu
Total propionate, S_pro
S_{pro} S_pro
Total acetate, S_ac
S_{ac} S_ac
Hydrogen gas, S_h2
S_{h2} S_h2
Methane gas, S_ch4
S_{ch4} S_ch4
Inorganic carbon, S_IC
S_{IC} S_IC
Inorganic nitrogen, S_IN
S_{IN} S_IN
Soluble inerts, S_I
S_I S_I
Composites, X_c
X_c X_c
Carbohydrates, X_ch
X_{ch} X_ch
Proteins, X_pr
X_{pr} X_pr
Lipids, X_li
X_{li} X_li
Sugar degraders, X_su
X_{su} X_su
Amino acid degraders, X_aa
X_{aa} X_aa
Long chain fatty acid (LCFA) degraders, X_fa
X_{fa} X_fa
Valerate and butyrate degraders, X_c4
X_{c4} X_c4
Propionate degraders, X_pro
X_{pro} X_pro
Acetate degraders, X_ac
X_{ac} X_ac
Hydrogen degraders, X_h2
X_{h2} X_h2
Particulate inerts, X_I
X_I X_I
Total cation equivalents concentration, S_cat
S_{cat} S_cat
Total anion equivalents concentration, S_an
S_{an} S_an
Carbon dioxide, S_co2
S_{co2} S_co2
NOTE: S_h2 and S_ch4 have vapor phase and liquid phase, S_co2 only has vapor phase, and the other components only have liquid phase
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
[p]
\text{kg/}\text{m}^3 Anions in molar concentrations
M_a anions
None
\text{kmol/}\text{m}^3 Cations in molar concentrations
M_c cations
None
\text{kmol/}\text{m}^3 Water pressure
P_{w,sat} p_w_sat
None
\text{Pa} Component pressure
P_{j,sat} p_sat
[p]
\text{Pa}
Stoichiometric Parameters
Description
Symbol
Parameter
Value at 20 C
Units
Soluble inerts from composites, f_sI_xc
f_{sI,xc} f_sI_xc
0.1
\text{dimensionless} Particulate inerts from composites, f_xI_xc
f_{xI,xc} f_xI_xc
0.2
\text{dimensionless} Carbohydrates from composites, f_ch_xc
f_{ch,xc} f_ch_xc
0.2
\text{dimensionless} Proteins from composites, f_pr_xc
f_{pr,xc} f_pr_xc
0.2
\text{dimensionless} Lipids from composites, f_li_xc
f_{li,xc} f_li_xc
0.3
\text{dimensionless} Nitrogen content of composites, N_xc
N_{xc} N_xc
0.0376/14
\text{kmol-N/}\text{kg-COD} Nitrogen content of inerts, N_I
N_I N_I
0.06/14
\text{kmol-N/}\text{kg-COD} Nitrogen in amino acids and proteins, N_aa
N_{aa} N_aa
0.007
\text{kmol-N/}\text{kg-COD} Nitrogen content in bacteria, N_bac
N_{bac} N_bac
0.08/14
\text{kmol-N/}\text{kg-COD} Fatty acids from lipids, f_fa_li
f_{fa,li} f_fa_li
0.95
\text{dimensionless} Hydrogen from sugars, f_h2_su
f_{h2,su} f_h2_su
0.19
\text{dimensionless} Butyrate from sugars, f_bu_su
f_{bu,su} f_bu_su
0.13
\text{dimensionless} Propionate from sugars, f_pro_su
f_{pro,su} f_pro_su
0.27
\text{dimensionless} Acetate from sugars, f_ac_su
f_{ac,su} f_ac_su
0.41
\text{dimensionless} Hydrogen from amino acids, f_h2_aa
f_{h2,aa} f_h2_aa
0.06
\text{dimensionless} Valerate from amino acids, f_va_aa
f_{va,aa} f_va_aa
0.23
\text{dimensionless} Butyrate from amino acids, f_bu_aa
f_{bu,aa} f_bu_aa
0.26
\text{dimensionless} Propionate from amino acids, f_pro_aa
f_{pro,aa} f_pro_aa
0.05
\text{dimensionless} Acetate from amino acids, f_ac_aa
f_{ac,aa} f_ac_aa
0.4
\text{dimensionless} Yield of biomass on sugar substrate, Y_su
Y_{su} Y_su
0.1
\text{kg-COD X/}\text{kg-COD S} Yield of biomass on amino acid substrate, Y_aa
Y_{aa} Y_aa
0.08
\text{kg-COD X/}\text{kg-COD S} Yield of biomass on fatty acid substrate, Y_fa
Y_{fa} Y_fa
0.06
\text{kg-COD X/}\text{kg-COD S} Yield of biomass on valerate and butyrate substrate, Y_c4
Y_{c4} Y_c4
0.06
\text{kg-COD X/}\text{kg-COD S} Yield of biomass on propionate substrate, Y_pro
Y_{pro} Y_pro
0.04
\text{kg-COD X/}\text{kg-COD S} Yield of biomass on acetate substrate, Y_ac
Y_{ac} Y_ac
0.05
\text{kg-COD X/}\text{kg-COD S} Yield of hydrogen per biomass, Y_h2
Y_{h2} Y_h2
0.06
\text{kg-COD X/}\text{kg-COD S}
Description
Symbol
Parameter
Value at 20 C
Units
First-order kinetic parameter for disintegration, k_dis
k_{dis} k_dis
0.5
\text{d}^{-1} First-order kinetic parameter for hydrolysis of carbohydrates, k_hyd_ch
k_{hyd,ch} k_hyd_ch
10
\text{d}^{-1} First-order kinetic parameter for hydrolysis of proteins, k_hyd_pr
k_{hyd,pr} k_hyd_pr
10
\text{d}^{-1} First-order kinetic parameter for hydrolysis of lipids, k_hyd_li
k_{hyd,li} k_hyd_li
10
\text{d}^{-1} Inhibition parameter for inorganic nitrogen, K_S_IN
K_{S_{IN}} K_S_IN
1e-4
\text{kmol/}\text{m}^3 Monod maximum specific uptake rate of sugars, k_m_su
k_{m_{su}} k_m_su
30
\text{d}^{-1} Half saturation value for uptake of sugars, K_S_su
K_{S_{su}} K_S_su
0.5
\text{kg/}\text{m}^3 Upper limit of pH for uptake rate of amino acids, pH_UL_aa
pH_{UL,aa} pH_UL_aa
5.5
\text{dimensionless} Lower limit of pH for uptake rate of amino acids, pH_LL_aa
pH_{LL,aa} pH_LL_aa
4
\text{dimensionless} Monod maximum specific uptake rate of amino acids, k_m_aa
k_{m_{aa}} k_m_aa
50
\text{d}^{-1} Half saturation value for uptake of amino acids, K_S_aa
K_{S_{aa}} K_S_aa
0.3
\text{kg/}\text{m}^3 Monod maximum specific uptake rate of fatty acids, k_m_fa
k_{m_{fa}} k_m_fa
6
\text{d}^{-1} Half saturation value for uptake of fatty acids, K_S_fa
K_{S_{fa}} K_S_fa
0.4
\text{kg/}\text{m}^3 Inhibition parameter for hydrogen during uptake of fatty acids, K_I_h2_fa
K_{I,h2_{fa}} K_I_h2_fa
5e-6
\text{kg/}\text{m}^3 Monod maximum specific uptake rate of valerate and butyrate, k_m_c4
k_{m_{c4}} k_m_c4
20
\text{d}^{-1} Half saturation value for uptake of valerate and butyrate, K_S_c4
K_{S_{c4}} K_S_c4
0.2
\text{kg/}\text{m}^3 Inhibition parameter for hydrogen during uptake of valerate and butyrate, K_I_h2_c4
K_{I,h2_{c4}} K_I_h2_c4
1e-5
\text{kg/}\text{m}^3 Monod maximum specific uptake rate of propionate, k_m_pro
k_{m_{pro}} k_m_pro
13
\text{d}^{-1} Half saturation value for uptake of propionate, K_S_pro
K_{S_{pro}} K_S_pro
0.1
\text{kg/}\text{m}^3 Inhibition parameter for hydrogen during uptake of propionate, K_I_h2_pro
K_{I,h2_{pro}} K_I_h2_pro
3.5e-6
\text{kg/}\text{m}^3 Monod maximum specific uptake rate of acetate, k_m_ac
k_{m_{ac}} k_m_ac
8
\text{d}^{-1} Half saturation value for uptake of acetate, K_S_ac
K_{S_{ac}} K_S_ac
0.15
\text{kg/}\text{m}^3 Inhibition parameter for ammonia during uptake of acetate, K_I_nh3
K_{I,nh3} K_I_nh3
0.0018
\text{kg/}\text{m}^3 Upper limit of pH for uptake rate of acetate, pH_UL_ac
pH_{UL,ac} pH_UL_ac
7
\text{dimensionless} Lower limit of pH for uptake rate of acetate, pH_LL_ac
pH_{LL,ac} pH_LL_ac
6
\text{dimensionless} Monod maximum specific uptake rate of hydrogen, k_m_h2
k_{m_{h2}} k_m_h2
35
\text{d}^{-1} Half saturation value for uptake of hydrogen, K_S_h2
K_{S_{h2}} K_S_h2
7e-6
\text{kg/}\text{m}^3 Upper limit of pH for uptake rate of hydrogen, pH_UL_h2
pH_{UL,h2} pH_UL_h2
6
\text{dimensionless} Lower limit of pH for uptake rate of hydrogen, pH_LL_h2
pH_{LL,h2} pH_LL_h2
5
\text{dimensionless} First-order decay rate for X_su, k_dec_X_su
k_{dec,X_{su}} k_dec_X_su
0.02
\text{d}^{-1} First-order decay rate for X_aa, k_dec_X_aa
k_{dec,X_{aa}} k_dec_X_aa
0.02
\text{d}^{-1} First-order decay rate for X_fa, k_dec_X_fa
k_{dec,X_{fa}} k_dec_X_fa
0.02
\text{d}^{-1} First-order decay rate for X_c4, k_dec_X_c4
k_{dec,X_{c4}} k_dec_X_c4
0.02
\text{d}^{-1} First-order decay rate for X_pro, k_dec_X_pro
k_{dec,X_{pro}} k_dec_X_pro
0.02
\text{d}^{-1} First-order decay rate for X_ac, k_dec_X_ac
k_{dec,X_{ac}} k_dec_X_ac
0.02
\text{d}^{-1} First-order decay rate for X_h2, k_dec_X_h2
k_{dec,X_{h2}} k_dec_X_h2
0.02
\text{d}^{-1} Dissociation constant, KW
KW KW
2.08e-14
(\text{kmol/}\text{m}^3)^2 Valerate acid-base equilibrium constant, K_a_va
K_{a,va} K_a_va
1.38e-5
\text{kmol/}\text{m}^3 Butyrate acid-base equilibrium constant, K_a_bu
K_{a,bu} K_a_bu
1.5e-5
\text{kmol/}\text{m}^3 Propionate acid-base equilibrium constant, K_a_pro
K_{a,pro} K_a_bu
1.32e-5
\text{kmol/}\text{m}^3 Acetate acid-base equilibrium constant, K_a_ac
K_{a,ac} K_a_ac
1.74e-5
\text{kmol/}\text{m}^3 Carbon dioxide acid-base equilibrium constant, K_a_co2
K_{a,co2} K_a_co2
4.94e-7
\text{kmol/}\text{m}^3 Inorganic nitrogen acid-base equilibrium constant, K_a_IN
K_{a,IN} K_a_IN
1.11e-9
\text{kmol/}\text{m}^3
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
Disintegration
\rho_1 = k_{dis} C_{X_c} Hydrolysis of carbohydrates
\rho_2 = k_{hyd,ch} C_{X_{ch}} Hydrolysis of proteins
\rho_3 = k_{hyd,pr} C_{X_{pr}} Hydrolysis of lipids
\rho_4 = k_{hyd,li} C_{X_{li}} Uptake of sugars
\rho_5 = k_{m_{su}} \frac{C_{S_{su}}}{K_{S_{su}}+C_{S_{su}}} C_{X_{su}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} I_{pH,aa} Uptake of amino acids
\rho_6 = k_{m_{aa}} \frac{C_{S_{aa}}}{K_{S_{aa}}+C_{S_{aa}}} C_{X_{aa}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} I_{pH,aa} Uptake of long chain fatty acids (LCFAs)
\rho_7 = k_{m_{fa}} \frac{C_{S_{fa}}}{K_{S_{fa}}+C_{S_{fa}}} C_{X_{fa}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{fa}}} I_{pH,aa} Uptake of valerate
\rho_8 = k_{m_{c4}} \frac{C_{S_{va}}}{K_{S_{c4}}+C_{S_{va}}} C_{X_{c4}} \frac{C_{S_{va}}}{C_{S_{bu}} + C_{S_{va}}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{c4}}} I_{pH,aa} Uptake of butyrate
\rho_9 = k_{m_{c4}} \frac{C_{S_{bu}}}{K_{S_{c4}}+C_{S_{bu}}} C_{X_{c4}} \frac{C_{S_{bu}}}{C_{S_{bu}} + C_{S_{va}}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{c4}}} I_{pH,aa} Uptake of propionate
\rho_{10} = k_{m_{pro}} \frac{C_{S_{pro}}}{K_{S_{pro}}+C_{S_{pro}}} C_{X_{pro}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{pro}}} I_{pH,aa} Uptake of acetate
\rho_{11} = k_{m_{ac}} \frac{C_{S_{ac}}}{K_{S_{ac}}+C_{S_{ac}}} C_{X_{ac}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{NH3}/K_{I,nh3}} I_{pH,ac} Uptake of hydrogen
\rho_{12} = k_{m_{h2}} \frac{C_{S_{h2}}}{K_{S_{h2}}+C_{S_{h2}}} C_{X_{h2}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} I_{pH,h2} Decay of X_su
\rho_{13} = k_{dec, X_{su}} C_{X_{su}} Decay of X_aa
\rho_{14} = k_{dec, X_{aa}} C_{X_{aa}} Decay of X_fa
\rho_{15} = k_{dec, X_{fa}} C_{X_{fa}} Decay of X_c4
\rho_{16} = k_{dec, X_{c4}} C_{X_{c4}} Decay of X_pro
\rho_{17} = k_{dec, X_{pro}} C_{X_{pro}} Decay of X_ac
\rho_{18} = k_{dec, X_{ac}} C_{X_{ac}} Decay of X_h2
\rho_{19} = k_{dec, X_{h2}} C_{X_{h2}}
The rules for pH inhibition of amino-acid-utilizing microorganisms (I_{pH,aa} ), acetate-utilizing microorganisms (I_{pH,ac} ), and hydrogen-utilizing microorganisms (I_{pH,h2} ) are:
I_{pH,aa}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2} & \text{for } pH \le pH_{UL,aa}\\
1 & \text{for } pH > pH_{UL,aa}
\end{cases}
I_{pH,ac}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2} & \text{for } pH \le pH_{UL,ac}\\
1 & \text{for } pH > pH_{UL,ac}
\end{cases}
I_{pH,aa}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2} & \text{for } pH \le pH_{UL,h2}\\
1 & \text{for } pH > pH_{UL,h2}
\end{cases}
.. currentmodule:: watertap.property_models.anaerobic_digestion.adm1_properties
.. autoclass:: ADM1ParameterBlock
:members:
:noindex:
.. autoclass:: ADM1ParameterData
:members:
:noindex:
.. autoclass:: _ADM1StateBlock
:members:
:noindex:
.. autoclass:: ADM1StateBlockData
:members:
:noindex:
.. currentmodule:: watertap.property_models.anaerobic_digestion.adm1_properties_vapor
.. autoclass:: ADM1_vaporParameterBlock
:members:
:noindex:
.. autoclass:: ADM1_vaporParameterData
:members:
:noindex:
.. autoclass:: _ADM1_vaporStateBlock
:members:
:noindex:
.. autoclass:: ADM1_vaporStateBlockData
:members:
:noindex:
.. currentmodule:: watertap.property_models.anaerobic_digestion.adm1_reactions
.. autoclass:: ADM1ReactionParameterBlock
:members:
:noindex:
.. autoclass:: ADM1ReactionParameterData
:members:
:noindex:
.. autoclass:: _ADM1ReactionBlock
:members:
:noindex:
.. autoclass:: ADM1ReactionBlockData
:members:
:noindex:
[1] Batstone, D.J., Keller, J., Angelidaki, I., Kalyuzhnyi, S.V., Pavlostathis, S.G., Rozzi, A., Sanders, W.T.M., Siegrist, H.A. and Vavilin, V.A., 2002.
The IWA anaerobic digestion model no 1 (ADM1).
Water Science and technology, 45(10), pp.65-73.
https://iwaponline.com/wst/article-abstract/45/10/65/6034
[2] Rosen, C. and Jeppsson, U., 2006.
Aspects on ADM1 Implementation within the BSM2 Framework.
Department of Industrial Electrical Engineering and Automation, Lund University, Lund, Sweden, pp.1-35.
https://www.iea.lth.se/WWTmodels_download/TR_ADM1.pdf