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:
- inlet
- outlet
| 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} |
| 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}) |
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} |
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) |
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) |
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