A link is required to translate between biological based and physical or chemical mediated processes to develop plant-wide modeling of wastewater treatment. This model mediates the interaction between the Modified Activated Sludge Model 2d (ASM2d) and the Modified Anaerobic Digestor Model 1 (ADM1).
The model relies on the following key assumptions:
- supports only liquid phase
- supports only Modified ASM2d to Modified ADM1 translations
.. index:: pair: watertap.unit_models.translators.translator_adm1_asm2d;translator_asm2d_adm1
.. currentmodule:: watertap.unit_models.translators.translator_asm2d_adm1
The translator degrees of freedom are the inlet feed state variables:
- temperature
- pressure
- volumetric flowrate
- solute compositions
This model provides two ports:
- inlet
- outlet
| Description | Symbol | Indices |
|---|---|---|
| Time | t | [0] |
| Inlet/outlet | x | ['in', 'out'] |
| Phases | p | ['Liq'] |
| Inlet Components | j_{in} | ['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'] |
| Outlet Components | j_{out} | ['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'] |
| Ion | j_{in} | ['S_cat', 'S_an'] 1 |
| Zero Flow Components | z | ['S_fa', 'S_h2', 'S_ch4', 'X_su', 'X_aa', 'X_fa', 'X_c4', 'X_pro', 'X_ac', 'X_h2'] |
- Notes
- 1 "Ion" is a subset of "Outlet Components" and uses the same symbol j_in.
| Description | Symbol | Parameter Name | Value | Units |
|---|---|---|---|---|
| Soluble inerts from composites | f_{sI, xc} | f_sI_xc | 1e-9 | \text{dimensionless} |
| Particulate inerts from composites | f_{xI, xc} | f_xI_xc | 0.1 | \text{dimensionless} |
| Carbohydrates from composites | f_{ch, xc} | f_ch_xc | 0.275 | \text{dimensionless} |
| Proteins from composites | f_{pr, xc} | f_pr_xc | 0.275 | \text{dimensionless} |
| Lipids from composites | f_{li, xc} | f_li_xc | 0.35 | \text{dimensionless} |
| Valerate from polyhydroxyalkanoates | f_{XPHA, Sva} | f_XPHA_Sva | 0.1 | \text{dimensionless} |
| Butyrate from polyhydroxyalkanoates | f_{XPHA, Sbu} | f_XPHA_Sbu | 0.1 | \text{dimensionless} |
| Propionate from polyhydroxyalkanoates | f_{XPHA, Spro} | f_XPHA_Spro | 0.4 | \text{dimensionless} |
| Acetate from polyhydroxyalkanoates | f_{XPHA, Sac} | f_XPHA_Sac | 0.4 | \text{dimensionless} |
| Carbon content of polyhydroxyalkanoates | C_{PHA} | C_PHA | 0.025 | \text{dimensionless} |
| Description | Equation |
|---|---|
| Volumetric flow equality | F_{out} = F_{in} |
| Temperature balance | T_{out} = T_{in} |
| Pressure balance | P_{out} = P_{in} |
| Zero-flow component conversions | C_{z, out} = 0 |
| Anions balance | S_{an} = \frac{S_{IN, out}}{14} |
| Cations balance | S_{cat} = \frac{S_{IC, out}}{12} |
| COD demanding compounds in S_O2 | COD_{SO2} = S_{O2, in} / \frac{1 - Y_{H}}{Y_{H}} |
| S_O2 concentration | S_{O2, 1} = S_{O2, in} - \frac{1 - Y_{H}}{Y_{H}} * COD_{SO2} |
| S_A concentration | S_{A, 1} = S_{A, in} - \frac{COD_{SO2}}{Y_{H}} |
| S_NH4 concentration | S_{NH4, 1} = S_{NH4, in} - (i_{NBM} * COD_{SO2}) |
| S_PO4 concentration | S_{PO4, 1} = S_{PO4, in} - (i_{PBM} * COD_{SO2}) |
| S_IC concentration | S_{IC, 1} = S_{IC, in} + \frac{COD_{SO2} * i_{CSA}}{Y_{H}} + (COD_{SO2} * i_{CXB}) |
| X_H concentration | X_{H, 1} = X_{H, in} + COD_{SO2} |
| COD demanding compounds in S_NO3 | COD_{SNO3} = S_{NO3, in} / \frac{1 - Y_{H}}{i_{NOx, N2} * Y_{H}} |
| S_A concentration | S_{A, 2} = S_{A, 1} - \frac{COD_{SNO3}}{Y_{H}} |
| S_NH4 concentration | S_{NH4, 2} = S_{NH4, 1} - (COD_{SNO3} * i_{NBM}) |
| S_N2 concentration | S_{N2, 2} = S_{N2, in} + \frac{1 - Y_{H}}{i_{NOx, N2} * Y_{H}} * COD_{SNO3} |
| S_NO3 concentration | S_{NO3, 2} = S_{NO3, in} - \frac{1 - Y_{H}}{i_{NOx, N2} * Y_{H}} * COD_{SNO3} |
| S_PO4 concentration | S_{PO4, 2} = S_{PO4, 1} - (COD_{SNO3} * i_{PBM}) |
| S_IC concentration | S_{IC, 2} = S_{IC, 1} + \frac{COD_{SNO3} * i_{CSA}}{Y_{H}} + (COD_{SNO3} * i_{CXB}) |
| X_H concentration | X_{H, 2} = X_{H, 1} + COD_{SNO3} |
| Nitrogen demand for soluble inerts | S_{ND} = S_{F, in} * i_{NSF} |
| Phosphorus demand for soluble inerts | S_{PD} = S_{F, in} * i_{PSF} |
| Organic nitrogen from soluble inerts | SN_{org} = \frac{S_{ND}}{Ni[S_{aa}] * 14} |
| Monosaccharides mapping (if SN_{org} >= S_{F, in}) | S_{su} = in |
| Monosaccharides mapping (if SN_{org} < S_{F, in}) | S_{su} = \frac{S_{F, in} - SN_{org}}{1000} |
| Amino acids mapping (if SN_{org} >= S_{F, in}) | S_{aa} = \frac{S_{F, in}}{1000} |
| Amino acids mapping (if SN_{org} < S_{F, in}) | S_{aa} = \frac{SN_{org}}{1000} |
| S_F concentration | S_{F, 3} = S_{F, in} - (S_{su} * 1000) - (S_{aa} * 1000) |
| S_NH4 concentration | S_{NH4, 3} = S_{NH4, 2} + (S_{F, in} * i_{NSF}) - (S_{aa} * Ni[S_{aa}] * 1000 * 14) |
| S_PO4 concentration | S_{PO4, 3} = S_{PO4, 2} + (S_{F, in} * i_{PSF}) |
| S_IC concentration | S_{IC, 3} = S_{IC, 2} + (S_{F, in} * i_{CSF}) - (S_{su} * Ci[S_{su}] * 1000 * 12) - (S_{aa} * Ci[S_{aa}] * 1000 * 12) |
| Description | Equation |
|---|---|
| Biomass concentration | bio = X_{H, 2} + X_{PAO, in} + X_{AUT, in} |
| S_I concentration | S_{I, 4} = S_{I, in} + (bio * f_{sI, xc}) |
| S_NH4 concentration | S_{NH4, 4} = S_{NH4, 3} + (bio * i_{NBM}) - (bio * f_{sI, xc} * i_{NSI}) - (bio * f_{xI, xc} * i_{NSI}) - (bio * f_{pr, xc} * Ni[X_{pr}] * 14) |
| S_PO4 concentration | S_{PO4, 4} = S_{PO4, 3} + (bio * i_{PBM}) - (bio * f_{sI, xc} * i_{PSI}) - (bio * f_{xI, xc} * i_{PXI}) - (bio * f_{ch, xc} * Pi[X_{ch}] * 31) - (bio * f_{li, xc} * Pi[X_{li}] * 31) |
| S_IC concentration | S_{IC, 4} = S_{IC, 3} + (bio * i_{CXB}) - (bio * f_{sI, xc} * i_{CSI}) - (bio * f_{xI, xc} * i_{CXI}) - (bio * f_{pr, xc} * Ci[X_{pr}] * 12) - (bio * f_{ch, xc} * Ci[X_{ch}] * 12) - (bio * f_{li, xc} * Ci[X_{li}] * 12) |
| X_I concentration | X_{I, 4} = X_{I, in} + (bio * f_{xI, xc}) |
| X_H concentration | X_{H, 4} = 0 |
| X_PAO concentration | X_{PAO, 4} = 0 |
| X_AUT concentration | X_{AUT, 4} = 0 |
| Nitrogen demand for particulate inerts | X_{ND} = X_{S, in} * i_{NXS} |
| Phosphorus demand for particulate inerts | X_{PD} = X_{S, in} * i_{PXS} |
| Organic nitrogen from particulate inerts | XN_{org} = \frac{X_{ND}}{Ni[X_{pr}] * 14} |
| Carbohydrates mapping (if XN_{org} >= X_{S, in}) | X_{ch} = 0 |
| Carbohydrates mapping (if XN_{org} < X_{S, in}) | X_{ch} = \frac{(X_{S, in} - XN_{org}) * 0.4}{1000} |
| Protein mapping (if XN_{org} >= X_{S, in}) | X_{pr} = \frac{S_{F, 3}}{1000} |
| Protein mapping (if XN_{org} < X_{S, in}) | X_{pr} = \frac{XN_{org}}{1000} |
| Lipids mapping (if XN_{org} >= X_{S, in}) | X_{li} = 0 |
| Lipids mapping (if XN_{org} < X_{S, in}) | X_{li} = \frac{(X_{S, in} - XN_{org}) * 0.6}{1000} |
| S_NH4 concentration | S_{NH4, 5} = S_{NH4, 4} + (X_{S, in} * i_{NXS}) - (X_{pr} * Ni[X_{pr}] * 1000 * 14) |
| S_PO4 concentration | S_{PO4, 5} = S_{PO4, 4} + (X_{S, in} * i_{PXS}) - (X_{ch} * Pi[X_{ch}] * 1000 * 31) - (X_{li} * Pi[X_{li}] * 1000 * 31) |
| S_IC concentration | S_{IC, 5} = S_{IC, 4} + (S_{F, in} * i_{CXS}) - (X_{ch} * Ci[X_{ch}] * 1000 * 12) - (X_{pr} * Ci[X_{pr}] * 1000 * 12) - (X_{li} * Ci[X_{li}] * 1000 * 12) |
| X_S concentration | X_{S, 5} = 0 |
| X_PP concentration | X_{PP, 6} = 0 |
| X_PHA concentration | X_{PHA, 6} = 0 |
| S_va concentration | S_{va, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sva}}{1000} |
| S_bu concentration | S_{bu, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sbu}}{1000} |
| S_pro concentration | S_{pro, 6} = \frac{X_{PHA, 6} * f_{XPHA, Spro}}{1000} |
| S_ac concentration | S_{ac, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sac}}{1000} |
| S_PO4 concentration | S_{PO4, 6} = S_{PO4, 5} + X_{PP, in} |
| S_IC concentration | S_{IC, 6} = S_{IC, 5} + (X_{PHA, in} * C_{PHA}) - (S_{va, 6} * Ci[S_{va}] * 1000 * 12) - (S_{bu, 6} * Ci[S_{bu}] * 1000 * 12) - (S_{pro, 6} * Ci[S_{pro}] * 1000 * 12) - (S_{ac, 6} * Ci[S_{ac}] * 1000 * 12) |
| S_K concentration | S_{K, 6} = S_{K, in} + (K_{XPP} * X_{PP, in}) |
| S_Mg concentration | S_{Mg, 6} = S_{Mg, in} + (Mg_{XPP} * X_{PP, in}) |
| Description | Equation |
|---|---|
| Biomass concentration | bio = X_{H, 2} + X_{AUT, in} |
| S_I concentration | S_{I, 4} = S_{I, in} + (bio * f_{sI, xc}) |
| S_NH4 concentration | S_{NH4, 4} = S_{NH4, 3} + (bio * i_{NBM}) - (bio * f_{sI, xc} * i_{NSI}) - (bio * f_{xI, xc} * i_{NSI}) - (bio * f_{pr, xc} * Ni[X_{pr}] * 14) |
| S_PO4 concentration | S_{PO4, 4} = S_{PO4, 3} + (bio * i_{PBM}) - (bio * f_{sI, xc} * i_{PSI}) - (bio * f_{xI, xc} * i_{PXI}) - (bio * f_{ch, xc} * Pi[X_{ch}] * 31) - (bio * f_{li, xc} * Pi[X_{li}] * 31) |
| S_IC concentration | S_{IC, 4} = S_{IC, 3} + (bio * i_{CXB}) - (bio * f_{sI, xc} * i_{CSI}) - (bio * f_{xI, xc} * i_{CXI}) - (bio * f_{pr, xc} * Ci[X_{pr}] * 12) - (bio * f_{ch, xc} * Ci[X_{ch}] * 12) - (bio * f_{li, xc} * Ci[X_{li}] * 12) |
| X_I concentration | X_{I, 4} = X_{I, in} + (bio * f_{xI, xc}) |
| X_H concentration | X_{H, 4} = 0 |
| X_PAO concentration | X_{PAO, 4} = X_{PAO, in} |
| X_PP concentration | X_{PP, 4} = X_{PP, in} |
| X_PHA concentration | X_{PHA, 4} = X_{PHA, in} |
| X_AUT concentration | X_{AUT, 4} = 0 |
| Nitrogen demand for particulate inerts | X_{ND} = X_{S, in} * i_{NXS} |
| Phosphorus demand for particulate inerts | X_{PD} = X_{S, in} * i_{PXS} |
| Organic nitrogen from particulate inerts | XN_{org} = \frac{X_{ND}}{Ni[X_{pr}] * 14} |
| Carbohydrates mapping (if XN_{org} >= X_{S, in}) | X_{ch} = 0 |
| Carbohydrates mapping (if XN_{org} < X_{S, in}) | X_{ch} = \frac{(X_{S, in} - XN_{org}) * 0.4}{1000} |
| Protein mapping (if XN_{org} >= X_{S, in}) | X_{pr} = \frac{S_{F, 3}}{1000} |
| Protein mapping (if XN_{org} < X_{S, in}) | X_{pr} = \frac{XN_{org}}{1000} |
| Lipids mapping (if XN_{org} >= X_{S, in}) | X_{li} = 0 |
| Lipids mapping (if XN_{org} < X_{S, in}) | X_{li} = \frac{(X_{S, in} - XN_{org}) * 0.6}{1000} |
| S_NH4 concentration | S_{NH4, 5} = S_{NH4, 4} + (X_{S, in} * i_{NXS}) - (X_{pr} * Ni[X_{pr}] * 1000 * 14) |
| S_PO4 concentration | S_{PO4, 5} = S_{PO4, 4} + (X_{S, in} * i_{PXS}) - (X_{ch} * Pi[X_{ch}] * 1000 * 31) - (X_{li} * Pi[X_{li}] * 1000 * 31) |
| S_IC concentration | S_{IC, 5} = S_{IC, 4} + (S_{F, in} * i_{CXS}) - (X_{ch} * Ci[X_{ch}] * 1000 * 12) - (X_{pr} * Ci[X_{pr}] * 1000 * 12) - (X_{li} * Ci[X_{li}] * 1000 * 12) |
| X_S concentration | X_{S, 5} = 0 |
| X_PAO concentration | X_{PAO, 5} = X_{PAO, in} |
| X_PP concentration | X_{PP, 5} = X_{PP, in} |
| X_PHA concentration | X_{PHA, 5} = X_{PHA, in} |
| S_va concentration | S_{va, 6} = 0 |
| S_bu concentration | S_{bu, 6} = 0 |
| S_pro concentration | S_{pro, 6} = 0 |
| S_ac concentration | S_{ac, 6} = 0 |
| X_PAO concentration | X_{PAO, 6} = X_{PAO, in} |
| X_PP concentration | X_{PP, 6} = X_{PP, in} |
| X_PHA concentration | X_{PHA, 6} = X_{PHA, in} |
| S_va concentration | S_{va, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sva}}{1000} |
| S_bu concentration | S_{bu, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sbu}}{1000} |
| S_pro concentration | S_{pro, 6} = \frac{X_{PHA, 6} * f_{XPHA, Spro}}{1000} |
| S_ac concentration | S_{ac, 6} = \frac{X_{PHA, 6} * f_{XPHA, Sac}}{1000} |
| S_PO4 concentration | S_{PO4, 6} = S_{PO4, 5} + X_{PP, in} |
| S_IC concentration | S_{IC, 6} = S_{IC, 5} + (X_{PHA, in} * C_{PHA}) - (S_{va, 6} * Ci[S_{va}] * 1000 * 12) - (S_{bu, 6} * Ci[S_{bu}] * 1000 * 12) - (S_{pro, 6} * Ci[S_{pro}] * 1000 * 12) - (S_{ac, 6} * Ci[S_{ac}] * 1000 * 12) |
| S_K concentration | S_{K, 6} = S_{K, in} + (K_{XPP} * X_{PP, in}) |
| S_Mg concentration | S_{Mg, 6} = S_{Mg, in} + (Mg_{XPP} * X_{PP, in}) |
.. currentmodule:: watertap.unit_models.translators.translator_asm2d_adm1
.. autoclass:: TranslatorDataASM2dADM1
:members:
:noindex:
[1] Flores-Alsina, X., Solon, K., Mbamba, C.K., Tait, S., Gernaey, K.V., Jeppsson, U. and Batstone, D.J., 2016. Modelling phosphorus (P), sulfur (S) and iron (Fe) interactions for dynamic simulations of anaerobic digestion processes. Water Research, 95, pp.370-382. https://github.com/wwtmodels/Plant-Wide-Models