ASM1 to ADM1 Translator

Introduction

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 Digester Model 1 (ADM1).

The model relies on the following key assumptions:

• supports only liquid phase

• supports only ASM1 to ADM1 translations

Degrees of Freedom

The translator degrees of freedom are the inlet feed state variables:

• temperature

• pressure

• volumetric flowrate

• solute compositions

• cations

• anions

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	\(j\)	[‘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.

ASM1 Components

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

ADM1 Components

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 \(S_{IC} - S_{HCO3^{-}}\) .

Parameters

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	\(F_{out} = F_{in}\)

COD Equations

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	\(COD_{t} = COD_{s} + COD_{p}\)

TKN Equation

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 \(S_{S,inter} ≤ ReqCOD_{s}\))	\(S_{aa} = S_{S, inter}\)
Monosaccharides mapping step A (if \(S_{S,inter} > ReqCOD_{s}\))	\(S_{su, A} = S_{S, inter} - ReqCOD_{s}\)
Monosaccharides mapping step A (if \(S_{S,inter} ≤ ReqCOD_{s}\))	\(S_{su, A} = 0\)
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 \(OrgN_{remain, A} ≤ OrgN_{s, req}\))	\(S_{I, ADM1} = \frac{OrgN_{remain, A}}{N_{I} * 14}\)
Monosaccharides mapping step B (if \(OrgN_{remain, A} > OrgN_{s, req}\))	\(S_{su} = S_{su, A}\)
Monosaccharides mapping step B (if \(OrgN_{remain, A} ≤ OrgN_{s, req}\))	\(S_{su} = S_{su, A} + S_{I} - S_{I, ADM1}\)
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 \(OrgN_{remain, B} ≤ OrgN_{x, req}\))	\(X_{I, ADM1} = \frac{OrgN_{remain, B}}{N_{I} * 14}\)
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 \(COD_{remain, C} ≤ COD_{Xc, req}\))	\(X_{C} = COD_{remain, C}\)
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 \(COD_{remain, C} ≤ COD_{Xc, req}\))	\(X_{ch} = 0\)
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 \(COD_{remain, C} ≤ COD_{Xc, req}\))	\(X_{li} = 0\)
Inorganic nitrogen mapping (if \(COD_{remain, C} > COD_{Xc, req}\))	\(S_{IN} = S_{NH, in}\)
Inorganic nitrogen mapping (if \(COD_{remain, C} ≤ COD_{Xc, req}\))	\(S_{IN} = S_{NH, in} + (OrgN_{remain, C} - X_{C} * N_{xc} * 14)\)
Anions balance	\(S_{an} = \frac{S_{IN}}{14}\)
Cations balance	\(S_{cat} = \frac{S_{IC}}{12}\)

Classes

class watertap.unit_models.translators.translator_asm1_adm1.TranslatorDataASM1ADM1(component)

Translator block representing the ASM1/ADM1 interface

build()

Begin building model. :param None:

Returns:

None

initialize_build(state_args_in=None, state_args_out=None, outlvl=0, solver=None, optarg=None)

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] 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