Modified ADM1 Property Package

.red {color:red} .lime {color:lime} .blue {color:blue}

This package is an extension of the base Anaerobic Digestion Model no.1 (ADM1) and implements properties and reactions of an anaerobic digestion model for wastewater treatment using an anaerobic digester as provided in Batstone, D. J. et al. (2002) and Rosen and Jeppsson (2006).

Throughout this documentation, text in red has been removed in the Modified ADM1 model, text in lime has been added, and text in blue has been modified from its base ADM1 implementation.

The following modifications have been made to the base ADM1 model as provided in Flores-Alsina, X. et al. (2016):

tracks inorganic phosphorus (S_IP), polyhydroxyalkanoates (X_PHA), polyphosphates (X_PP), phosphorus accumulating organisms (X_PAO), potassium (S_K), and magnesium (S_Mg)
removes the composite material variable (X_C) and the associated disintegration reaction
adds 7 additional reactions

This modified 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_IP', 'S_I', 'X_ch', 'X_pr', 'X_li', 'X_su', 'X_aa', 'X_fa', 'X_c4', 'X_pro', 'X_ac', 'X_h2', 'X_I', 'X_PHA', 'X_PP', 'X_PAO', 'S_K', 'S_Mg', 'S_cat', 'S_an', and 'S_co2' as components
supports only liquid and vapor phase
only makes changes to the liquid phase modelling

Sets

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_IP', 'S_I', 'X_ch', 'X_pr', 'X_li', 'X_su', 'X_aa', 'X_fa', 'X_c4', 'X_pro', 'X_ac', 'X_h2', 'X_I', 'X_PHA', 'X_PP', 'X_PAO', 'S_K', 'S_Mg', 'S_cat', 'S_an', 'S_co2']
Phases	p	['Liq', 'Vap']

Components

Red text indicates the component has been removed in the Modified ADM1 model, and lime text indicates the component has been added.

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
Inorganic phosphorus, S_IP	S_IP	S_IP
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
Polyhydroxyalkanoates, X_PHA	X_PHA	X_PHA
Polyphosphates, X_PP	X_PP	X_PP
Phosphorus accumulating organisms, X_PAO	X_PAO	X_PAO
Potassium, S_K	S_K	S_K
Magnesium, S_Mg	S_Mg	S_Mg
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. The amount of CO2 dissolved in the liquid phase is equivalent to S_IC - S_HCO3-.

State variables

Description	Symbol	Variable	Index	Units
Total volumetric flowrate	Q	flow_vol	None	m³/s
Temperature	T	temperature	None	K
Pressure	P	pressure	None	Pa
Component mass concentrations	C_j	conc_mass_comp	[j]	kg/m³
Anions in molar concentrations	M_a	anions	None	kmol/m³
Cations in molar concentrations	M_c	cations	None	kmol/m³
Component carbon content	Ci	Ci_dict	[j]	kmol/kg
Component nitrogen content	Ni	Ni_dict	[j]	kmol/kg
Component phosphorus content	Pi	Pi_dict	[j]	kmol/kg
Component pressure	P_j, sat	pressure_sat	[j]	Pa
Reference temperature	T_ref	temperature_ref	None	K
Reference component mass concentrations	C_j, ref	conc_mass_comp_ref	[j]	kg/m³

Stoichiometric Parameters

Red text indicates the parameter has been removed in the Modified ADM1 model, and lime text indicates the parameter has been added.

Description	Symbol	Parameter	Value at 20 C	Units
Soluble inerts from composites, f_sI_xc	f_sI, xc	f_sI_xc	0.1	dimensionless
Particulate inerts from composites, f_xI_xc	f_xI, xc	f_xI_xc	0.2	dimensionless
Carbohydrates from composites, f_ch_xc	f_ch, xc	f_ch_xc	0.2	dimensionless
Proteins from composites, f_pr_xc	f_pr, xc	f_pr_xc	0.2	dimensionless
Lipids from composites, f_li_xc	f_li, xc	f_li_xc	0.3	dimensionless
Nitrogen content of composites, N_xc	N_xc	N_xc	0.0376/14	kmol-N/kg-COD
Nitrogen content of inerts, N_I	N_I	N_I	0.06/14	kmol-N/kg-COD
Nitrogen in amino acids and proteins, N_aa	N_aa	N_aa	0.007	kmol-N/kg-COD
Nitrogen content in bacteria, N_bac	N_bac	N_bac	0.08/14	kmol-N/kg-COD
Reference component mass concentration of hydrogen sulfide, Z_h2s	Z_h2s	Z_h2s	0	kg/m³
Fraction of inert particulate organics from biomass, f_xi_xb	f_xi, xb	f_xi_xb	0.1	dimensionless
Fraction of carbohydrates from biomass, f_ch_xb	f_ch, xb	f_ch_xb	0.275	dimensionless
Fraction of lipids from biomass, f_li_xb	f_li, xb	f_li_xb	0.35	dimensionless
Fraction of proteins from biomass, f_pr_xb	f_pr, xb	f_pr_xb	0.275	dimensionless
Fraction of soluble inerts from biomass, f_si_xb	f_si, xb	f_si_xb	0	dimensionless
Fatty acids from lipids, f_fa_li	f_fa, li	f_fa_li	0.95	dimensionless
Hydrogen from sugars, f_h2_su	f_h2, su	f_h2_su	0.19	dimensionless
Butyrate from sugars, f_bu_su	f_bu, su	f_bu_su	0.13	dimensionless
Propionate from sugars, f_pro_su	f_pro, su	f_pro_su	0.27	dimensionless
Acetate from sugars, f_ac_su	f_ac, su	f_ac_su	0.41	dimensionless
Hydrogen from amino acids, f_h2_aa	f_h2, aa	f_h2_aa	0.06	dimensionless
Valerate from amino acids, f_va_aa	f_va, aa	f_va_aa	0.23	dimensionless
Butyrate from amino acids, f_bu_aa	f_bu, aa	f_bu_aa	0.26	dimensionless
Propionate from amino acids, f_pro_aa	f_pro, aa	f_pro_aa	0.05	dimensionless
Acetate from amino acids, f_ac_aa	f_ac, aa	f_ac_aa	0.4	dimensionless
Yield of biomass on sugar substrate, Y_su	Y_su	Y_su	0.1	kg-COD X/kg-COD S
Yield of biomass on amino acid substrate, Y_aa	Y_aa	Y_aa	0.08	kg-COD X/kg-COD S
Yield of biomass on fatty acid substrate, Y_fa	Y_fa	Y_fa	0.06	kg-COD X/kg-COD S
Yield of biomass on valerate and butyrate substrate, Y_c4	Y_c4	Y_c4	0.06	kg-COD X/kg-COD S
Yield of biomass on propionate substrate, Y_pro	Y_pro	Y_pro	0.04	kg-COD X/kg-COD S
Yield of biomass on acetate substrate, Y_ac	Y_ac	Y_ac	0.05	kg-COD X/kg-COD S
Yield of hydrogen per biomass, Y_h2	Y_h2	Y_h2	0.06	kg-COD X/kg-COD S

Kinetic Parameters

Red text indicates the parameter has been removed in the Modified ADM1 model, and lime text indicates the parameter has been added.

Description	Symbol	Parameter	Value at 20 C	Units
First-order kinetic parameter for disintegration, k_dis	k_dis	k_dis	0.5	d^− 1
First-order kinetic parameter for hydrolysis of carbohydrates, k_hyd_ch	k_hyd, ch	k_hyd_ch	10	d^− 1
First-order kinetic parameter for hydrolysis of proteins, k_hyd_pr	k_hyd, pr	k_hyd_pr	10	d^− 1
First-order kinetic parameter for hydrolysis of lipids, k_hyd_li	k_hyd, li	k_hyd_li	10	d^− 1
Water dissociation constant, pK_W	pK_W	pKW	14	dimensionless
Process inhibition term, I	I	I	1	dimensionless
Inhibition parameter for inorganic nitrogen, K_S_IN	K_{S_IN}	K_S_IN	1e-4	kmol/m³
Monod maximum specific uptake rate of sugars, k_m_su	k_{m_su}	k_m_su	30	d^− 1
Half saturation value for uptake of sugars, K_S_su	K_{S_su}	K_S_su	0.5	kg/m³
Upper limit of pH for uptake rate of amino acids, pH_UL_aa	pH_UL, aa	pH_UL_aa	5.5	dimensionless
Lower limit of pH for uptake rate of amino acids, pH_LL_aa	pH_LL, aa	pH_LL_aa	4	dimensionless
Monod maximum specific uptake rate of amino acids, k_m_aa	k_{m_aa}	k_m_aa	50	d^− 1
Half saturation value for uptake of amino acids, K_S_aa	K_{S_aa}	K_S_aa	0.3	kg/m³
Monod maximum specific uptake rate of fatty acids, k_m_fa	k_{m_fa}	k_m_fa	6	d^− 1
Half saturation value for uptake of fatty acids, K_S_fa	K_{S_fa}	K_S_fa	0.4	kg/m³
Inhibition parameter for hydrogen during uptake of fatty acids, K_I_h2_fa	K_{I, h2_fa}	K_I_h2_fa	5e-6	kg/m³
Monod maximum specific uptake rate of valerate and butyrate, k_m_c4	k_{m_c4}	k_m_c4	20	d^− 1
Half saturation value for uptake of valerate and butyrate, K_S_c4	K_{S_c4}	K_S_c4	0.2	kg/m³
Inhibition parameter for hydrogen during uptake of valerate and butyrate, K_I_h2_c4	K_{I, h2_c4}	K_I_h2_c4	1e-5	kg/m³
Monod maximum specific uptake rate of propionate, k_m_pro	k_{m_pro}	k_m_pro	13	d^− 1
Half saturation value for uptake of propionate, K_S_pro	K_{S_pro}	K_S_pro	0.1	kg/m³
Inhibition parameter for hydrogen during uptake of propionate, K_I_h2_pro	K_{I, h2_pro}	K_I_h2_pro	3.5e-6	kg/m³
Monod maximum specific uptake rate of acetate, k_m_ac	k_{m_ac}	k_m_ac	8	d^− 1
Half saturation value for uptake of acetate, K_S_ac	K_{S_ac}	K_S_ac	0.15	kg/m³
Inhibition parameter for ammonia during uptake of acetate, K_I_nh3	K_I, nh3	K_I_nh3	0.0018	kg/m³
Upper limit of pH for uptake rate of acetate, pH_UL_ac	pH_UL, ac	pH_UL_ac	7	dimensionless
Lower limit of pH for uptake rate of acetate, pH_LL_ac	pH_LL, ac	pH_LL_ac	6	dimensionless
Monod maximum specific uptake rate of hydrogen, k_m_h2	k_{m_h2}	k_m_h2	35	d^− 1
Half saturation value for uptake of hydrogen, K_S_h2	K_{S_h2}	K_S_h2	7e-6	kg/m³
Upper limit of pH for uptake rate of hydrogen, pH_UL_h2	pH_UL, h2	pH_UL_h2	6	dimensionless
Lower limit of pH for uptake rate of hydrogen, pH_LL_h2	pH_LL, h2	pH_LL_h2	5	dimensionless
First-order decay rate for X_su, k_dec_X_su	k_{dec, X_su}	k_dec_X_su	0.02	d^− 1
First-order decay rate for X_aa, k_dec_X_aa	k_{dec, X_aa}	k_dec_X_aa	0.02	d^− 1
First-order decay rate for X_fa, k_dec_X_fa	k_{dec, X_fa}	k_dec_X_fa	0.02	d^− 1
First-order decay rate for X_c4, k_dec_X_c4	k_{dec, X_c4}	k_dec_X_c4	0.02	d^− 1
First-order decay rate for X_pro, k_dec_X_pro	k_{dec, X_pro}	k_dec_X_pro	0.02	d^− 1
First-order decay rate for X_ac, k_dec_X_ac	k_{dec, X_ac}	k_dec_X_ac	0.02	d^− 1
First-order decay rate for X_h2, k_dec_X_h2	k_{dec, X_h2}	k_dec_X_h2	0.02	d^− 1
Valerate acid-base equilibrium constant, K_a_va	K_a, va	K_a_va	1.38e-5	kmol/m³
Butyrate acid-base equilibrium constant, K_a_bu	K_a, bu	K_a_bu	1.5e-5	kmol/m³
Propionate acid-base equilibrium constant, K_a_pro	K_a, pro	K_a_bu	1.32e-5	kmol/m³
Acetate acid-base equilibrium constant, K_a_ac	K_a, ac	K_a_ac	1.74e-5	kmol/m³
50% inhibitory concentration of H2S on acetogens, K_I_h2s_ac	K_{I, h2s_ac}	K_I_h2s_ac	460e-3	kg/m³
50% inhibitory concentration of H2S on c4 degraders, K_I_h2s_c4	K_{I, h2s_c4}	K_I_h2s_c4	481e-3	kg/m³
50% inhibitory concentration of H2S on hydrogenotrophic methanogens, K_I_h2s_h2	K_{I, h2s_h2}	K_I_h2s_h2	481e-3	kg/m³
50% inhibitory concentration of H2S on propionate degraders, K_I_h2s_pro	K_{I, h2s_pro}	K_I_h2s_pro	481e-3	kg/m³
Phosphorus limitation for inorganic phosphorus, K_S_IP	K_s, IP	K_S_IP	2e-5	kmol/m³
Lysis rate of phosphorus accumulating organisms, b_PAO	b_PAO	b_PAO	0.2	d^− 1
Lysis rate of polyhydroxyalkanoates, b_PHA	b_PHA	b_PHA	0.2	d^− 1
Lysis rate of polyphosphates, b_PP	b_PP	b_PP	0.2	d^− 1
Yield of acetate on polyhydroxyalkanoates, f_ac_PHA	f_ac, PHA	f_ac_PHA	0.4	dimensionless
Yield of butyrate on polyhydroxyalkanoates, f_bu_PHA	f_bu, PHA	f_bu_PHA	0.1	dimensionless
Yield of propionate on polyhydroxyalkanoates, f_pro_PHA	f_pro, PHA	f_pro_PHA	0.4	dimensionless
Yield of valerate on polyhydroxyalkanoates, f_va_PHA	f_va, PHA	f_va_PHA	0.1	dimensionless
Saturation coefficient for acetate, K_A	K_A	K_A	4e-3	kg/m³
Saturation coefficient for polyphosphate, K_PP	K_PP	k_PP	0.32e-3	dimensionless
Rate constant for storage of polyhydroxyalkanoates, q_PHA	q_PHA	q_PHA	3	d^− 1
Yield of biomass on phosphate (kmol P/kg COD), Y_PO4	Y_PO4	Y_PO4	12.903e-3	dimensionless
Potassium coefficient for polyphosphates, K_PP	K_PP	K_PP	1/3	dimensionless
Magnesium coefficient for polyphosphates, Mg_PP	Mg_PP	Mg_PP	1/3	dimensionless
Carbon dioxide acid-base equilibrium constant, pK_a_co2	pK_a, co2	pK_a_co2	6.35	dimensionless
Inorganic nitrogen acid-base equilibrium constant, pK_a_IN	pK_a, IN	pK_a_IN	9.25	dimensionless

Properties

Description	Symbol	Variable	Index	Units
Fluid specific heat capacity	c_p	cp	None	J/kg/K
Mass density	ρ	dens_mass	[p]	kg/m³

Process Rate Equations

Red text indicates the equation has been removed in the Modified ADM1 model, lime text indicates the equation has been added, and blue text indicates the equation has been modified from its base ADM1 implementation.

Description	Equation
Disintegration	ρ₁ = k_disC_{X_c}
Hydrolysis of carbohydrates	ρ₁ = k_hyd, chC_{X_ch}
Hydrolysis of proteins	ρ₂ = k_hyd, prC_{X_pr}
Hydrolysis of lipids	ρ₃ = k_hyd, liC_{X_li}
Uptake of sugars	$\rho_4 = k_{m_{su}} \frac{C_{S_{su}}}{K_{S_{su}}+C_{S_{su}}} C_{X_{su}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa}$
Uptake of amino acids	$\rho_5 = k_{m_{aa}} \frac{C_{S_{aa}}}{K_{S_{aa}}+C_{S_{aa}}} C_{X_{aa}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa}$
Uptake of long chain fatty acids (LCFAs)	$\rho_6 = k_{m_{fa}} \frac{C_{S_{fa}}}{K_{S_{fa}}+C_{S_{fa}}} C_{X_{fa}} \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{fa}}} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa}$
Uptake of valerate	$\rho_7 = k_{m_{c4}} \frac{C_{S_{va}}}{K_{S_{c4}}+C_{S_{va}}} C_{X_{c4}} \frac{C_{S_{va}}}{C_{S_{bu}} + C_{S_{va}}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{c4}}} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa} I_{h2s, c4}$
Uptake of butyrate	$\rho_8 = k_{m_{c4}} \frac{C_{S_{bu}}}{K_{S_{c4}}+C_{S_{bu}}} C_{X_{c4}} \frac{C_{S_{bu}}}{C_{S_{bu}} + C_{S_{va}}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{c4}}} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa} I_{h2s, c4}$
Uptake of propionate	$\rho_9 = k_{m_{pro}} \frac{C_{S_{pro}}}{K_{S_{pro}}+C_{S_{pro}}} C_{X_{pro}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{S_{h2}}/K_{I,h2_{pro}}} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,aa} I_{h2s, pro}$
Uptake of acetate	$\rho_{10} = k_{m_{ac}} \frac{C_{S_{ac}}}{K_{S_{ac}}+C_{S_{ac}}} C_{X_{ac}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + C_{NH3}/K_{I,nh3}} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,ac} I_{h2s, ac}$
Uptake of hydrogen	$\rho_{11} = k_{m_{h2}} \frac{C_{S_{h2}}}{K_{S_{h2}}+C_{S_{h2}}} C_{X_{h2}} \cdot \frac{1}{1 + K_{S_{IN}}/C_{S_{IN}}/14} \cdot \frac{1}{1 + K_{S_{IP}}/C_{S_{IP}}/31} I_{pH,h2} I_{h2s, h2}$
Decay of X_su	ρ₁₂ = k_{dec, X_su}C_{X_su}
Decay of X_aa	ρ₁₃ = k_{dec, X_aa}C_{X_aa}
Decay of X_fa	ρ₁₄ = k_{dec, X_fa}C_{X_fa}
Decay of X_c4	ρ₁₅ = k_{dec, X_c4}C_{X_c4}
Decay of X_pro	ρ₁₆ = k_{dec, X_pro}C_{X_pro}
Decay of X_ac	ρ₁₇ = k_{dec, X_ac}C_{X_ac}
Decay of X_h2	ρ₁₈ = k_{dec, X_h2}C_{X_h2}
Storage of S_va in X_PHA	$\rho_{19} = q_{PHA} \frac{C_{S_{va}}}{K_{A} + C_{S{va}}} \cdot \frac{C_{X_{PP}} / C_{X_{PAO}}}{K_{PP} + \frac{C_{X_{PP}}}{C_{X_{PAO}}}} C_{X_{PAO}} \frac{C_{S_{va}}}{C_{S_{va}} + C_{S_{bu}} + C_{S_{pro}} + C_{S_{ac}}}$
Storage of S_bu in X_PHA	$\rho_{20} = q_{PHA} \frac{C_{S_{bu}}}{K_{A} + C_{S{bu}}} \cdot \frac{C_{X_{PP}} / C_{X_{PAO}}}{K_{PP} + \frac{C_{X_{PP}}}{C_{X_{PAO}}}} C_{X_{PAO}} \frac{C_{S_{bu}}}{C_{S_{va}} + C_{S_{bu}} + C_{S_{pro}} + C_{S_{ac}}}$
Storage of S_pro in X_PHA	$\rho_{21} = q_{PHA} \frac{C_{S_{pro}}}{K_{A} + C_{S{pro}}} \cdot \frac{C_{X_{PP}} / C_{X_{PAO}}}{K_{PP} + \frac{C_{X_{PP}}}{C_{X_{PAO}}}} C_{X_{PAO}} \frac{C_{S_{pro}}}{C_{S_{va}} + C_{S_{bu}} + C_{S_{pro}} + C_{S_{ac}}}$
Storage of S_ac in X_PHA	$\rho_{22} = q_{PHA} \frac{C_{S_{ac}}}{K_{A} + C_{S{ac}}} \cdot \frac{C_{X_{PP}} / C_{X_{PAO}}}{K_{PP} + \frac{C_{X_{PP}}}{C_{X_{PAO}}}} C_{X_{PAO}} \frac{C_{S_{ac}}}{C_{S_{va}} + C_{S_{bu}} + C_{S_{pro}} + C_{S_{ac}}}$
Lysis of X_PAO	ρ₂₃ = b_PAOC_{X_PAO}
Lysis of X_PP	ρ₂₄ = b_PPC_{X_PP}
Lysis of X_PHA	ρ₂₅ = b_PHAC_{X_PHA}

Additional Variables

Description	Symbol	Parameter	Value at 20 C	Units
pH of solution	pH	pH	7	dimensionless
Mass concentration of valerate, va-	C_va	conc_mass_va	0.011	kg/m³
Mass concentration of butyrate, bu-	C_bu	conc_mass_bu	0.013	kg/m³
Mass concentration of propionate, pro-	C_pro	conc_mass_pro	0.016	kg/m³
Mass concentration of acetate, ac-	C_ac	conc_mass_ac	0.2	kg/m³
Molar concentration of bicarbonate, HCO3	M_hco3	conc_mol_hco3	0.14	kmol/m³
Molar concentration of ammonia, NH3	M_nh3	conc_mol_nh3	0.0041	kmol/m³
Molar concentration of carbon dioxide, CO2	M_co2	conc_mol_co2	0.0099	kmol/m³
Molar concentration of ammonium, NH4	M_nh4	conc_mol_nh4	0.1261	kmol/m³
Molar concentration of magnesium, Mg	M_Mg	conc_mol_Mg	4.5822e-5	kmol/m³
Molar concentration of potassium, K	M_K	conc_mol_K	0.010934	kmol/m³

Additional Constraints

Lime text indicates the equation has been added, and blue text indicates the equation has been modified from its base ADM1 implementation.

Description	Equation
Water dissociation constant constraint	$log(10^{-pK_{W}}) = log(10^{-14}) + (\frac{55900}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))$
CO2 acid-base equilibrium constraint	$log(10^{-pK_{a,co2}}) = log(10^{-6.35}) + (\frac{7646}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))$
Nitrogen acid-base equilibrium constraint	$log(10^{-pK_{a,IN}}) = log(10^{-9.25}) + (\frac{51965}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))$
pH of solution	pH = − log(S_H)
Mass concentration of valerate, va-	$C_{va,ref} = C_{va} (1 + \frac{S_{H}}{K_{a,va}})$
Mass concentration of butyrate, bu-	$C_{bu,ref} = C_{bu} (1 + \frac{S_{H}}{K_{a,bu}})$
Mass concentration of propionate, pro-	$C_{pro,ref} = C_{pro} (1 + \frac{S_{H}}{K_{a,pro}})$
Mass concentration of acetate, ac-	$C_{ac,ref} = C_{ac} (1 + \frac{S_{H}}{K_{a,ac}})$
Molar concentration of bicarbonate, HCO3	pK_a, co2 = log(M_co2) − log(M_hco3) + pH
Molar concentration of ammonia, NH3	pK_a, IN = log(M_nh4) − log(M_nh3) + pH
Molar concentration of carbon dioxide, CO2	$M_{co2} = \frac{C_{S_{IC},ref}}{12} - M_{hco3}$
Molar concentration of ammonium, NH4+	$M_{nh4} = \frac{C_{S_{IN},ref}}{14} - M_{nh3}$
Molar concentration of hydrogen, H+	$S_{H} = M_{hco3} + \frac{C_{ac}}{64} + \frac{C_{pro}}{112} + \frac{C_{bu}}{160} + \frac{C_{va}}{208} + 10^{pH - pK_{W}} + M_{a} - M_{c} - M_{nh4} - M_{Mg} - M_{K}$
Molar concentration of magnesium, Mg	$M_{Mg} = \frac{C_{X_{PP},ref}}{300.41}$
Molar concentration of potassium, K	$M_{K} = \frac{C_{X_{PP},ref}}{300.41}$

The rules for inhibition of amino-acid-utilizing microorganisms (I_pH, aa), acetate-utilizing microorganisms (I_pH, ac), hydrogen-utilizing microorganisms (I_pH, h2) are:

$$\begin{aligned} I_{pH,aa}= \begin{cases} \exp{(-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2)} & \text{for } pH \le pH_{UL,aa}\\\ 1 & \text{for } pH > pH_{UL,aa} \end{cases} \end{aligned}$$$$\begin{aligned} I_{pH,ac}= \begin{cases} \exp{(-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2)} & \text{for } pH \le pH_{UL,ac}\\\ 1 & \text{for } pH > pH_{UL,ac} \end{cases} \end{aligned}$$$$\begin{aligned} I_{pH,h2}= \begin{cases} \exp{(-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2)} & \text{for } pH \le pH_{UL,h2}\\\ 1 & \text{for } pH > pH_{UL,h2} \end{cases} \end{aligned}$$

The rules for inhibition related to secondary substrate (I_IN, lim), hydrogen inhibition attributed to long chain fatty acids (I_h2, fa), hydrogen inhibition attributed to valerate and butyrate uptake (I_h2, c4), hydrogen inhibition attributed to propionate uptake (I_h2, pro), ammonia inibition attributed to acetate uptake (I_nh3), are:

$$I_{IN,lim} = \frac{1}{1 + \frac{K_{S_{IN}}}{C_{S_{IN}}/14}}$$$$I_{h2, fa}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,fa}}}$$$$I_{h2, c4}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,c4}}}$$$$I_{h2, pro}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,pro}}}$$$$I_{nh3}= \frac{1}{1 + \frac{M_{nh3}}{K_{I,nh3}}}$$

The rules for hydrogen sulfide inhibition factors are shown below; however, since Z_h2s is assumed to be 0, all of these inhibition factors are negligible.

$$I_{h2s, ac} = \frac{1}{1 + \frac{Z_{h2s}}{K_{I,h2s,ac}}}$$$$I_{h2s, c4}= \frac{1}{1 + \frac{Z_{h2s}}{K_{I,h2s,c4}}}$$$$I_{h2s, h2}= \frac{1}{1 + \frac{Z_{h2s}}{K_{I,h2s,h2}}}$$$$I_{h2s, pro}= \frac{1}{1 + \frac{Z_{h2s}}{K_{I,h2s,pro}}}$$

Class Documentation

watertap.property_models.anaerobic_digestion.modified_adm1_properties

ModifiedADM1ParameterBlock

ModifiedADM1ParameterData

_ModifiedADM1StateBlock

ModifiedADM1StateBlockData

watertap.property_models.anaerobic_digestion.adm1_properties_vapor

ADM1_vaporParameterBlock

ADM1_vaporParameterData

_ADM1_vaporStateBlock

ADM1_vaporStateBlockData

watertap.property_models.anaerobic_digestion.modified_adm1_reactions

ModifiedADM1ReactionParameterBlock

ModifiedADM1ReactionParameterData

_ModifiedADM1ReactionBlock

ModifiedADM1ReactionBlockData

References

[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

[3] X. Flores-Alsina, K. Solon, C.K. Mbamba, S. Tait, K.V. Gernaey, U. Jeppsson, D.J. Batstone, 2016. Modelling phosphorus (P), sulfur (S) and iron (Fe) interactions for dynamic simulations of anaerobic digestion processes, Water Research. 95 370-382. https://www.sciencedirect.com/science/article/pii/S0043135416301397

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Modified ADM1 Property Package

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Modified ADM1 Property Package

Sets

Components

State variables

Stoichiometric Parameters

Kinetic Parameters

Properties

Process Rate Equations

Additional Variables

Additional Constraints

Class Documentation

References