ASM2d to ADM1 Translator
Introduction
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 Digester Model 1 (ADM1).
The model relies on the following key assumptions:
supports only liquid phase
supports only Modified ASM2d to Modified ADM1 translations
Degrees of Freedom
The translator degrees of freedom are the inlet feed state variables:
temperature
pressure
volumetric flowrate
solute compositions
Ports
This model provides two ports:
inlet
outlet
Sets
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.
Parameters
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 |
\(\text{dimensionless}\) |
Equations and Relationships
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 |
\(S_{IC, 3} = S_{IC, 2} + (S_{F, in} * i_{CSF}) - (S_{su} * Ci[S_{su}] * 1000 * 12) - (S_{aa} * Ci[S_{aa}] * 1000 * 12)\) |
Equations and Relationships (with biological phosphorus removal)
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 |
\(S_{Mg, 6} = S_{Mg, in} + (Mg_{XPP} * X_{PP, in})\) |
Equations and Relationships (without biological phosphorus removal)
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 |
\(S_{Mg, 6} = S_{Mg, in} + (Mg_{XPP} * X_{PP, in})\) |
Classes
- class watertap.unit_models.translators.translator_asm2d_adm1.TranslatorDataASM2dADM1(component)[source]
Translator block representing the ASM2d/ADM1 interface
- build()[source]
Begin building model. :param None:
- Returns:
None
- initialize_build(state_args_in=None, state_args_out=None, outlvl=0, solver=None, optarg=None)[source]
This method calls the initialization method of the state blocks.
- Keyword Arguments:
state_args_in – a dict of arguments to be passed to the inlet property package (to provide an initial state for initialization (see documentation of the specific property package) (default = None).
state_args_out – a dict of arguments to be passed to the outlet property package (to provide an initial state for initialization (see documentation of the specific property package) (default = None).
outlvl – sets output level of initialization routine
optarg – solver options dictionary object (default=None, use default solver options)
solver – str indicating which solver to use during initialization (default = None, use default solver)
- Returns:
None
References
[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