A link is required to translate between biological and physically- or chemically-mediated processes
to develop whole-plant modeling of wastewater treatment. This model mediates the interaction between
the Activated Sludge Model 1 (ASM1) and the Anaerobic Digestor Model 1 (ADM1).
The model relies on the following key assumptions:
supports only liquid phase
supports only ASM1 to ADM1 translations
.. index::
pair: watertap.unit_models.translators.translator_asm1_adm1;translator_asm1_adm1
.. currentmodule:: watertap.unit_models.translators.translator_asm1_adm1
The translator degrees of freedom are the inlet feed state variables:
temperature
pressure
volumetric flowrate
solute compositions
cations
anions
This model provides two ports:
Description
Symbol
Indices
Time
t
[0]
Inlet/outlet
x
['in', 'out']
Phases
p
['Liq']
Inlet Components
j
['H2O', 'S_I', 'S_S', 'X_I', 'X_S', 'X_BH', 'X_BA', 'X_P', 'S_O', 'S_NO', 'S_NH', 'S_ND', 'X_ND', 'S_ALK']
Ion
j
['S_cat', 'S_an'] *
Outlet 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']
Notes
* Ion" is a subset of "Component" and uses the same symbol j.
Additional documentation on the ASM1 property model can be found here: Activated Sludge Model 1 Documentation
Description
Symbol
Variable
Soluble inert organic matter, S_I
S_I
S_I
Readily biodegradable substrate, S_S
S_S
S_S
Particulate inert organic matter, X_I
X_I
X_I
Slowly biodegradable substrate, X_S
X_S
X_S
Active heterotrophic biomass, X_BH
X_{BH}
X_BH
Active autotrophic biomass, X_BA
X_{BA}
X_BA
Particulate products arising from biomass decay, X_P
X_P
X_P
Oxygen, S_O
S_O
S_O
Nitrate and nitrite nitrogen, S_NO
S_{NO}
S_NO
{NH_{4}}^{+} + NH_{3} Nitrogen, S_NH
S_{NH}
S_NH
Soluble biodegradable organic nitrogen, S_ND
S_{ND}
S_ND
Particulate biodegradable organic nitrogen, X_ND
X_{ND}
X_ND
Alkalinity, S_ALK
S_{ALK}
S_ALK
Additional documentation on the ADM1 property model can be found here: Anaerobic Digestion Model 1 Documentation
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. The amount of CO_2 dissolved in the liquid phase is equivalent to S_{IC} - S_{HCO3^{-}} .
Description
Symbol
Parameter Name
Value
Units
Nitrogen fraction in particulate products
i_{xe}
i_xe
0.06
\text{dimensionless}
Nitrogen fraction in biomass
i_{xb}
i_xb
0.08
\text{dimensionless}
Anaerobic degradable fraction of X_I and:math:X_P
f_{xI}
f_xI
0.05
\text{dimensionless}
Equations and Relationships
Description
Equation
Pressure balance
P_{out} = P_{in}
Temperature balance
T_{out} = T_{in}
Volumetric flow equality
F_{out} = F_{in}
The total incoming COD is reduced in a step-wise manner until the COD demand has been satisfied. The reduction is based on a
hierarchy of ASM1 state variables such that S_s is reduced by the COD demand first. If there is insufficient
S_s present, then S_s is reduced to zero and the remaining demand is subtracted from X_s . If necessary, X_{BH} and X_{BA} may also need to be reduced.
Description
Equation
COD demand
COD_{demand} = S_{o} + 2.86S_{NO}
Readily biodegradable substrate remaining (step 1)
S_{S, inter} = S_{S} - COD_{demand}
Slowly biodegradable substrate remaining (step 2)
X_{S, inter} = X_{S} - COD_{demand, 2}
Active heterotrophic biomass remaining (step 3)
X_{BH, inter} = X_{BH} - COD_{demand, 3}
Active autotrophic biomass remaining (step 4)
X_{BA, inter} = X_{BA} - COD_{demand, 4}
Soluble COD
COD_{s} = S_{I} + S_{S, inter}
Particulate COD
COD_{p} = X_{I} + X_{S, inter} + X_{BH, inter} + X_{BA, inter} + X_{P}
Total COD
COD_{t} = COD_{s} + COD_{p}
The Total incoming Kjeldahl nitrogen is calculated with components updated in the anaerobic environment.
Description
Equation
Total Kjeldahl nitrogen
TKN = S_{NH} + S_{ND} + X_{ND} + i_{xb}(X_{BH, inter} + X_{BA, inter}) + i_{xe}(X_{I} + X_{P})
S_{nd} and S_s Mapping Equations
Figure 1. Schematic illustration of S_{nd} and S_s mapping (Copp et al. 2006)
Description
Equation
Required soluble COD
ReqCOD_{s} = \frac{S_{ND}}{N_{aa} * 14}
Amino acids mapping (if S_{S,inter} > ReqCOD_{s} )
S_{aa} = ReqCOD_{s}
Amino acids mapping (if S_{S,inter} \leq ReqCOD_{s} )
S_{aa} = S_{S, inter}
Monosaccharides mapping step A (if S_{S,inter} > ReqCOD_{s} )
S_{su, A} = S_{S, inter} - ReqCOD_{s}
Monosaccharides mapping step A (if S_{S,inter} \leq ReqCOD_{s} )
S_{su, A} = 0
COD remaining from step A
COD_{remain, A} = COD_{t} - S_{S,inter}
Organic nitrogen pool remaining from step A
OrgN_{remain, A} = TKN - (S_{aa} * N_{aa} * 14) - S_{NH}
Soluble Inert COD Mapping Equations
Figure 2. Schematic illustration of soluble inert COD mapping (Copp et al. 2006)
Description
Equation
Required soluble inert organic nitrogen
OrgN_{s, req} = S_{I} * N_{I} * 14
Soluble inert mapping step B (if OrgN_{remain, A} > OrgN_{s, req} )
S_{I, ADM1} = S_{I}
Soluble inert mapping step B (if OrgN_{remain, A} \leq OrgN_{s, req} )
S_{I, ADM1} = \frac{OrgN_{remain, A}}{N_{I} * 14}
Monosaccharides mapping step B (if OrgN_{remain, A} > OrgN_{s, req} )
S_{su} = S_{su, A}
Monosaccharides mapping step B (if OrgN_{remain, A} \leq OrgN_{s, req} )
S_{su} = S_{su, A} + S_{I} - S_{I, ADM1}
COD remaining from step B
COD_{remain, B} = COD_{remain, A} - S_{I}
Organic nitrogen pool remaining from step B
OrgN_{remain, B} = OrgN_{remain, A} - (S_{I, ADM1} * N_{I} * 14)
Particulate Inert COD Mapping Equations
Figure 3. Schematic illustration of particulate inert COD mapping (Copp et al. 2006)
Description
Equation
Required particulate inert material
OrgN_{x, req} = f_{xi} * (X_{P} + X_{I}) * N_{I} * 14
Particulate inert mapping step C (if OrgN_{remain, B} > OrgN_{x, req} )
X_{I, ADM1} = f_{xi} * (X_{P} + X_{I})
Particulate inert mapping step C (if OrgN_{remain, B} \leq OrgN_{x, req} )
X_{I, ADM1} = \frac{OrgN_{remain, B}}{N_{I} * 14}
COD remaining from step C
COD_{remain, C} = COD_{remain, B} - X_{I, ADM1}
Organic nitrogen pool remaining from step C
OrgN_{remain, C} = OrgN_{remain, B} - (X_{I_ADM1} * N_{I} * 14)
Final COD and TKN Mapping Equations
Figure 4. Schematic illustration of final COD and TKN mapping (Copp et al. 2006)
Description
Equation
Required soluble COD
COD_{Xc, req} = \frac{OrgN_{remain, C}}{N_{xc} * 14}
Composites mapping (if COD_{remain, C} > COD_{Xc, req} )
X_{C} = COD_{Xc, req}
Composites mapping (if COD_{remain, C} \leq COD_{Xc, req} )
X_{C} = COD_{remain, C}
Carbohydrates mapping (if COD_{remain, C} > COD_{Xc, req} )
X_{ch} = \frac{f_{ch, xc} (COD_{remain, C} - X_{C})}{f_{ch, xc} - f_{li, xc}}
Carbohydrates mapping (if COD_{remain, C} \leq COD_{Xc, req} )
X_{ch} = 0
Lipids mapping (if COD_{remain, C} > COD_{Xc, req} )
X_{li} = \frac{f_{li, xc} (COD_{remain, C} - X_{C})}{f_{ch, xc} - f_{li, xc}}
Lipdis mapping (if COD_{remain, C} \leq COD_{Xc, req} )
X_{li} = 0
Inorganic nitrogen mapping (if COD_{remain, C} > COD_{Xc, req} )
S_{IN} = S_{NH, in}
Inorganic nitrogen mapping (if COD_{remain, C} \leq COD_{Xc, req} )
S_{IN} = S_{NH, in} + (OrgN_{remain, C} - X_{C} * N_{xc} * 14)
Anions balance
S_{an} = \frac{S_{IN}}{14}
Cations balance
S_{cat} = \frac{S_{IC}}{12}
.. currentmodule:: watertap.unit_models.translators.translator_asm1_adm1
.. autoclass:: TranslatorDataASM1ADM1
:members:
:noindex:
[1] Copp J. and Jeppsson, U., Rosen, C., 2006.
Towards an ASM1 - ADM1 State Variable Interface for Plant-Wide Wastewater Treatment Modeling.
Proceedings of the Water Environment Federation, 2003, pp 498-510.
https://www.accesswater.org/publications/proceedings/-290550/towards-an-asm1---adm1-state-variable-interface-for-plant-wide-wastewater-treatment-modeling