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
| 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'] |
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
| 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} |
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 | \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} |
| Reference component mass concentration of hydrogen sulfide, Z_h2s | Z_{h2s} | Z_h2s | 0 | \text{kg/}\text{m}^3 |
| Fraction of inert particulate organics from biomass, f_xi_xb | f_{xi,xb} | f_xi_xb | 0.1 | \text{dimensionless} |
| Fraction of carbohydrates from biomass, f_ch_xb | f_{ch,xb} | f_ch_xb | 0.275 | \text{dimensionless} |
| Fraction of lipids from biomass, f_li_xb | f_{li,xb} | f_li_xb | 0.35 | \text{dimensionless} |
| Fraction of proteins from biomass, f_pr_xb | f_{pr,xb} | f_pr_xb | 0.275 | \text{dimensionless} |
| Fraction of soluble inerts from biomass, f_si_xb | f_{si,xb} | f_si_xb | 0 | \text{dimensionless} |
| 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} |
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 | \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 |
| 50% inhibitory concentration of H2S on acetogens, K_I_h2s_ac | K_{I,h2s_{ac}} | K_I_h2s_ac | 460e-3 | \text{kg/}\text{m}^3 |
| 50% inhibitory concentration of H2S on c4 degraders, K_I_h2s_c4 | K_{I,h2s_{c4}} | K_I_h2s_c4 | 481e-3 | \text{kg/}\text{m}^3 |
| 50% inhibitory concentration of H2S on hydrogenotrophic methanogens, K_I_h2s_h2 | K_{I,h2s_{h2}} | K_I_h2s_h2 | 481e-3 | \text{kg/}\text{m}^3 |
| 50% inhibitory concentration of H2S on propionate degraders, K_I_h2s_pro | K_{I,h2s_{pro}} | K_I_h2s_pro | 481e-3 | \text{kg/}\text{m}^3 |
| Phosphorus limitation for inorganic phosphorus, K_S_IP | K_{s,IP} | K_S_IP | 2e-5 | \text{kmol/}\text{m}^3 |
| Lysis rate of phosphorus accumulating organisms, b_PAO | b_{PAO} | b_PAO | 0.2 | \text{d}^{-1} |
| Lysis rate of polyhydroxyalkanoates, b_PHA | b_{PHA} | b_PHA | 0.2 | \text{d}^{-1} |
| Lysis rate of polyphosphates, b_PP | b_{PP} | b_PP | 0.2 | \text{d}^{-1} |
| Yield of acetate on polyhydroxyalkanoates, f_ac_PHA | f_{ac,PHA} | f_ac_PHA | 0.4 | \text{dimensionless} |
| Yield of butyrate on polyhydroxyalkanoates, f_bu_PHA | f_{bu,PHA} | f_bu_PHA | 0.1 | \text{dimensionless} |
| Yield of propionate on polyhydroxyalkanoates, f_pro_PHA | f_{pro,PHA} | f_pro_PHA | 0.4 | \text{dimensionless} |
| Yield of valerate on polyhydroxyalkanoates, f_va_PHA | f_{va,PHA} | f_va_PHA | 0.1 | \text{dimensionless} |
| Saturation coefficient for acetate, K_A | K_{A} | K_A | 4e-3 | \text{kg/}\text{m}^3 |
| Saturation coefficient for polyphosphate, K_PP | K_{PP} | k_PP | 0.32e-3 | \text{dimensionless} |
| Rate constant for storage of polyhydroxyalkanoates, q_PHA | q_{PHA} | q_PHA | 3 | \text{d}^{-1} |
| Yield of biomass on phosphate (kmol P/kg COD), Y_PO4 | Y_{PO4} | Y_PO4 | 12.903e-3 | \text{dimensionless} |
| Potassium coefficient for polyphosphates, K_PP | K_{PP} | K_PP | 1/3 | \text{dimensionless} |
| Magnesium coefficient for polyphosphates, Mg_PP | Mg_{PP} | Mg_PP | 1/3 | \text{dimensionless} |
| 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 |
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 | \rho_1 = k_{dis} C_{X_c} |
| Hydrolysis of carbohydrates | \rho_1 = k_{hyd,ch} C_{X_{ch}} |
| Hydrolysis of proteins | \rho_2 = k_{hyd,pr} C_{X_{pr}} |
| Hydrolysis of lipids | \rho_3 = k_{hyd,li} C_{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 | \rho_{12} = k_{dec, X_{su}} C_{X_{su}} |
| Decay of X_aa | \rho_{13} = k_{dec, X_{aa}} C_{X_{aa}} |
| Decay of X_fa | \rho_{14} = k_{dec, X_{fa}} C_{X_{fa}} |
| Decay of X_c4 | \rho_{15} = k_{dec, X_{c4}} C_{X_{c4}} |
| Decay of X_pro | \rho_{16} = k_{dec, X_{pro}} C_{X_{pro}} |
| Decay of X_ac | \rho_{17} = k_{dec, X_{ac}} C_{X_{ac}} |
| Decay of X_h2 | \rho_{18} = 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 | \rho_{23} = b_{PAO} C_{X_{PAO}} |
| Lysis of X_PP | \rho_{24} = b_{PP} C_{X_{PP}} |
| Lysis of X_PHA | \rho_{25} = b_{PHA} C_{X_{PHA}} |
The rules for pH inhibition of amino-acid-utilizing microorganisms (I_{pH,aa}), acetate-utilizing microorganisms (I_{pH,ac}), 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}
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}}}
.. currentmodule:: watertap.property_models.anaerobic_digestion.modified_adm1_properties
.. autoclass:: ModifiedADM1ParameterBlock
:members:
:noindex:
.. autoclass:: ModifiedADM1ParameterData
:members:
:noindex:
.. autoclass:: _ModifiedADM1StateBlock
:members:
:noindex:
.. autoclass:: ModifiedADM1StateBlockData
: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.modified_adm1_reactions
.. autoclass:: ModifiedADM1ReactionParameterBlock
:members:
:noindex:
.. autoclass:: ModifiedADM1ReactionParameterData
:members:
:noindex:
.. autoclass:: _ModifiedADM1ReactionBlock
:members:
:noindex:
.. autoclass:: ModifiedADM1ReactionBlockData
: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
[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