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Add Acid-Base Eq.Constraints to ADM1 Documentation (#1013)
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* Update documentation and minor corrections to reaction files

* Resolve formatting issues

* Resolve more formatting issues

* Resolve the remaining formatting issues

* Refine documentation

* Specify KW as water dissociation constant

* Address Adam's comments

* Add Class Documentation section

* Fix syntax errors in ASM property models

---------

Co-authored-by: Adam Atia <[email protected]>
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@MarcusHolly @adam-a-a
MarcusHolly and adam-a-a authored May 19, 2023
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62 changes: 53 additions & 9 deletions docs/technical_reference/property_models/ADM1.rst
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Expand Up @@ -59,10 +59,12 @@ State variables
"Total volumetric flowrate", ":math:`Q`", "flow_vol", "None", ":math:`\text{m}^3\text{/s}`"
"Temperature", ":math:`T`", "temperature", "None", ":math:`\text{K}`"
"Pressure", ":math:`P`", "pressure", "None", ":math:`\text{Pa}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[p]", ":math:`\text{kg/}\text{m}^3`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[j]", ":math:`\text{kg/}\text{m}^3`"
"Anions in molar concentrations", ":math:`M_a`", "anions", "None", ":math:`\text{kmol/}\text{m}^3`"
"Cations in molar concentrations", ":math:`M_c`", "cations", "None", ":math:`\text{kmol/}\text{m}^3`"
"Component pressure", ":math:`P_{j,sat}`", "pressure_sat", "[p]", ":math:`\text{Pa}`"
"Component pressure", ":math:`P_{j,sat}`", "pressure_sat", "[j]", ":math:`\text{Pa}`"
"Reference temperature", ":math:`T_{ref}`", "temperature_ref", "None", ":math:`\text{K}`"
"Reference component mass concentrations", ":math:`C_{j,ref}`", "conc_mass_comp_ref", "[j]", ":math:`\text{kg/}\text{m}^3`"

Stoichiometric Parameters
-------------------------
Expand Down Expand Up @@ -137,7 +139,7 @@ Kinetic Parameters
"First-order decay rate for X_pro, k_dec_X_pro", ":math:`k_{dec,X_{pro}}`", "k_dec_X_pro", 0.02, ":math:`\text{d}^{-1}`"
"First-order decay rate for X_ac, k_dec_X_ac", ":math:`k_{dec,X_{ac}}`", "k_dec_X_ac", 0.02, ":math:`\text{d}^{-1}`"
"First-order decay rate for X_h2, k_dec_X_h2", ":math:`k_{dec,X_{h2}}`", "k_dec_X_h2", 0.02, ":math:`\text{d}^{-1}`"
"Dissociation constant, KW", ":math:`KW`", "KW", 2.08e-14, ":math:`(\text{kmol/}\text{m}^3)^2`"
"Water dissociation constant, KW", ":math:`KW`", "KW", 2.08e-14, ":math:`(\text{kmol/}\text{m}^3)^2`"
"Valerate acid-base equilibrium constant, K_a_va", ":math:`K_{a,va}`", "K_a_va", 1.38e-5, ":math:`\text{kmol/}\text{m}^3`"
"Butyrate acid-base equilibrium constant, K_a_bu", ":math:`K_{a,bu}`", "K_a_bu", 1.5e-5, ":math:`\text{kmol/}\text{m}^3`"
"Propionate acid-base equilibrium constant, K_a_pro", ":math:`K_{a,pro}`", "K_a_bu", 1.32e-5, ":math:`\text{kmol/}\text{m}^3`"
Expand Down Expand Up @@ -178,31 +180,73 @@ Process Rate Equations
"Decay of X_ac", ":math:`\rho_{18} = k_{dec, X_{ac}} C_{X_{ac}}`"
"Decay of X_h2", ":math:`\rho_{19} = k_{dec, X_{h2}} C_{X_{h2}}`"

Additional Variables
--------------------
.. csv-table::
:header: "Description", "Symbol", "Parameter", "Value at 20 C", "Units"

"Molar concentration of hydrogen, S_H", ":math:`S_{H}`", "S_H", 3.4e-8, ":math:`\text{kmol/}\text{m}^3`"
"Molar concentration of hydroxide, S_OH", ":math:`S_{OH}`", "S_OH", 3.4e-8, ":math:`\text{kmol/}\text{m}^3`"

Additional Constraints
----------------------
.. csv-table::
:header: "Description", "Equation"

"Water dissociation constant constraint", ":math:`KW = 10^{-14} exp{(\frac{55900}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"CO2 acid-base equilibrium constraint", ":math:`K_{a,co2} = 10^{-6.35} exp{(\frac{7646}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"Nitrogen acid-base equilibrium constraint", ":math:`K_{a,IN} = 10^{-9.25} exp{(\frac{51965}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"Mass concentration of valerate, va-", ":math:`C_{va} = \frac{K_{a,va} * C_{va,ref}}{K_{a,va} + S_{H}}`"
"Mass concentration of butyrate, bu-", ":math:`C_{bu} = \frac{K_{a,bu} * C_{bu,ref}}{K_{a,bu} + S_{H}}`"
"Mass concentration of propionate, pro-", ":math:`C_{pro} = \frac{K_{a,pro} * C_{pro,ref}}{K_{a,pro} + S_{H}}`"
"Mass concentration of acetate, ac-", ":math:`C_{ac} = \frac{K_{a,ac} * C_{ac,ref}}{K_{a,ac} + S_{H}}`"
"Molar concentration of bicarbonate, HCO3", ":math:`M_{hco3} = \frac{K_{a,co2} * \frac{C_{S_{IC},ref}}{12}}{K_{a,co2} + S_{H}}`"
"Molar concentration of ammonia, NH3", ":math:`M_{nh3} = \frac{K_{a,IN} * \frac{C_{S_{IN},ref}}{14}}{K_{a,IN} + S_{H}}`"
"Molar concentration of carbon dioxide, CO2", ":math:`M_{co2} = \frac{C_{S_{IC},ref}}{12} - M_{hco3}`"
"Molar concentration of ammonium, NH4+", ":math:`M_{nh4} = \frac{C_{S_{IN},ref}}{14} - M_{nh3}`"
"Molar concentration of hydrogen, H+", ":math:`S_{H} = M_{hco3} + \frac{C_{ac}}{64} + \frac{C_{pro}}{112} + \frac{C_{bu}}{160} + \frac{C_{va}}{208} + S_{OH} + M_{a} - M_{c} - M_{nh4}`"
"Molar concentration of hydroxide, OH-", ":math:`S_{OH} = \frac{KW}{S_{H}}`"
"pH of solution", ":math:`pH = -log_{10}(S_{H})`"

The rules for pH inhibition of amino-acid-utilizing microorganisms (:math:`I_{pH,aa}`), acetate-utilizing microorganisms (:math:`I_{pH,ac}`), and hydrogen-utilizing microorganisms (:math:`I_{pH,h2}`) are:

.. math::
I_{pH,aa}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2} & \text{for } pH \le pH_{UL,aa}\\
\exp{(-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2)} & \text{for } pH \le pH_{UL,aa}\\
1 & \text{for } pH > pH_{UL,aa}
\end{cases}
I_{pH,ac}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2} & \text{for } pH \le pH_{UL,ac}\\
\exp{(-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2)} & \text{for } pH \le pH_{UL,ac}\\
1 & \text{for } pH > pH_{UL,ac}
\end{cases}
I_{pH,aa}=
I_{pH,h2}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2} & \text{for } pH \le pH_{UL,h2}\\
\exp{(-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2)} & \text{for } pH \le pH_{UL,h2}\\
1 & \text{for } pH > pH_{UL,h2}
\end{cases}
The rules for inhibition related to secondary substrate (:math:`I_{IN,lim}`), hydrogen inhibition attributed to long chain fatty acids (:math:`I_{h2,fa}`), hydrogen inhibition attributed to valerate and butyrate uptake (:math:`I_{h2,c4}`), hydrogen inhibition attributed to propionate uptake (:math:`I_{h2,pro}`), ammonia inibition attributed to acetate uptake (:math:`I_{nh3}`), are:

.. math::
I_{IN,lim} = \frac{1}{1 + \frac{K_{S_{IN}}}{C_{S_{IN}}/14}}
I_{h2, fa}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,fa}}}
I_{h2, c4}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,c4}}}
I_{h2, pro}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,pro}}}
I_{nh3}= \frac{1}{1 + \frac{M_{nh3}}{K_{I,nh3}}}
Classes
-------
Class Documentation
-------------------
.. currentmodule:: watertap.property_models.anaerobic_digestion.adm1_properties

.. autoclass:: ADM1ParameterBlock
Expand Down
42 changes: 40 additions & 2 deletions docs/technical_reference/property_models/ASM1.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -42,8 +42,8 @@ State variables
"Total volumetric flowrate", ":math:`Q`", "flow_vol", "None", ":math:`\text{m}^3\text{/s}`"
"Temperature", ":math:`T`", "temperature", "None", ":math:`\text{K}`"
"Pressure", ":math:`P`", "pressure", "None", ":math:`\text{Pa}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[p]", ":math:`\text{kg/}\text{m}^3`"
"Alkalinity in molar concentration", ":math:`A`", "alkalinity", "[p]", ":math:`\text{kmol HCO}_{3}^{-}\text{/m}^{3}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[j]", ":math:`\text{kg/}\text{m}^3`"
"Alkalinity in molar concentration", ":math:`A`", "alkalinity", "None", ":math:`\text{kmol HCO}_{3}^{-}\text{/m}^{3}`"

Stoichiometric Parameters
-------------------------
Expand Down Expand Up @@ -103,6 +103,44 @@ Scaling
-------
Scaling for the ASM1 property package has yet to be implemented.

Class Documentation
-------------------
.. currentmodule:: watertap.property_models.activated_sludge.asm1_properties

.. autoclass:: ASM1ParameterBlock
:members:
:noindex:

.. autoclass:: ASM1ParameterData
:members:
:noindex:

.. autoclass:: _ASM1StateBlock
:members:
:noindex:

.. autoclass:: ASM1StateBlockData
:members:
:noindex:

.. currentmodule:: watertap.property_models.activated_sludge.asm1_reactions

.. autoclass:: ASM1ReactionParameterBlock
:members:
:noindex:

.. autoclass:: ASM1ReactionParameterData
:members:
:noindex:

.. autoclass:: _ASM1ReactionBlock
:members:
:noindex:

.. autoclass:: ASM1ReactionBlockData
:members:
:noindex:


References
----------
Expand Down
41 changes: 39 additions & 2 deletions docs/technical_reference/property_models/ASM2D.rst
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Expand Up @@ -57,8 +57,8 @@ State variables
"Total volumetric flowrate", ":math:`Q`", "flow_vol", "None", ":math:`\text{m}^3\text{/s}`"
"Temperature", ":math:`T`", "temperature", "None", ":math:`\text{K}`"
"Pressure", ":math:`P`", "pressure", "None", ":math:`\text{Pa}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[p]", ":math:`\text{kg/}\text{m}^3`"
"Molar alkalinity", ":math:`A`", "alkalinity", "[p]", ":math:`\text{kmol HCO}_{3}^{-}\text{/m}^{3}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[j]", ":math:`\text{kg/}\text{m}^3`"
"Molar alkalinity", ":math:`A`", "alkalinity", "None", ":math:`\text{kmol HCO}_{3}^{-}\text{/m}^{3}`"

Stoichiometric Coefficients
---------------------------
Expand Down Expand Up @@ -164,6 +164,43 @@ Scaling
-------
A thorough scaling routine for the ASM2D property package has yet to be implemented.

Class Documentation
-------------------
.. currentmodule:: watertap.property_models.activated_sludge.asm2d_properties

.. autoclass:: ASM2dParameterBlock
:members:
:noindex:

.. autoclass:: ASM2dParameterData
:members:
:noindex:

.. autoclass:: _ASM2dStateBlock
:members:
:noindex:

.. autoclass:: ASM2dStateBlockData
:members:
:noindex:

.. currentmodule:: watertap.property_models.activated_sludge.asm2d_reactions

.. autoclass:: ASM2dReactionParameterBlock
:members:
:noindex:

.. autoclass:: ASM2dReactionParameterData
:members:
:noindex:

.. autoclass:: _ASM2dReactionBlock
:members:
:noindex:

.. autoclass:: ASM2dReactionBlockData
:members:
:noindex:

References
----------
Expand Down
70 changes: 59 additions & 11 deletions docs/technical_reference/property_models/modified_ADM1.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -86,10 +86,12 @@ State variables
"Total volumetric flowrate", ":math:`Q`", "flow_vol", "None", ":math:`\text{m}^3\text{/s}`"
"Temperature", ":math:`T`", "temperature", "None", ":math:`\text{K}`"
"Pressure", ":math:`P`", "pressure", "None", ":math:`\text{Pa}`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[p]", ":math:`\text{kg/}\text{m}^3`"
"Component mass concentrations", ":math:`C_j`", "conc_mass_comp", "[j]", ":math:`\text{kg/}\text{m}^3`"
"Anions in molar concentrations", ":math:`M_a`", "anions", "None", ":math:`\text{kmol/}\text{m}^3`"
"Cations in molar concentrations", ":math:`M_c`", "cations", "None", ":math:`\text{kmol/}\text{m}^3`"
"Component pressure", ":math:`P_{j,sat}`", "pressure_sat", "[p]", ":math:`\text{Pa}`"
"Component pressure", ":math:`P_{j,sat}`", "pressure_sat", "[j]", ":math:`\text{Pa}`"
"Reference temperature", ":math:`T_{ref}`", "temperature_ref", "None", ":math:`\text{K}`"
"Reference component mass concentrations", ":math:`C_{j,ref}`", "conc_mass_comp_ref", "[j]", ":math:`\text{kg/}\text{m}^3`"

Stoichiometric Parameters
-------------------------
Expand Down Expand Up @@ -174,7 +176,7 @@ Kinetic Parameters
"First-order decay rate for X_pro, k_dec_X_pro", ":math:`k_{dec,X_{pro}}`", "k_dec_X_pro", 0.02, ":math:`\text{d}^{-1}`"
"First-order decay rate for X_ac, k_dec_X_ac", ":math:`k_{dec,X_{ac}}`", "k_dec_X_ac", 0.02, ":math:`\text{d}^{-1}`"
"First-order decay rate for X_h2, k_dec_X_h2", ":math:`k_{dec,X_{h2}}`", "k_dec_X_h2", 0.02, ":math:`\text{d}^{-1}`"
"Dissociation constant, KW", ":math:`KW`", "KW", 2.08e-14, ":math:`(\text{kmol/}\text{m}^3)^2`"
"Water dissociation constant, KW", ":math:`KW`", "KW", 2.08e-14, ":math:`(\text{kmol/}\text{m}^3)^2`"
"Valerate acid-base equilibrium constant, K_a_va", ":math:`K_{a,va}`", "K_a_va", 1.38e-5, ":math:`\text{kmol/}\text{m}^3`"
"Butyrate acid-base equilibrium constant, K_a_bu", ":math:`K_{a,bu}`", "K_a_bu", 1.5e-5, ":math:`\text{kmol/}\text{m}^3`"
"Propionate acid-base equilibrium constant, K_a_pro", ":math:`K_{a,pro}`", "K_a_bu", 1.32e-5, ":math:`\text{kmol/}\text{m}^3`"
Expand Down Expand Up @@ -242,30 +244,76 @@ Process Rate Equations
":lime:`Lysis of X_PP`", ":math:`\rho_{24} = b_{PP} C_{X_{PP}}`"
":lime:`Lysis of X_PHA`", ":math:`\rho_{25} = b_{PHA} C_{X_{PHA}}`"

Additional Variables
--------------------
.. csv-table::
:header: "Description", "Symbol", "Parameter", "Value at 20 C", "Units"

The rules for pH inhibition of amino-acid-utilizing microorganisms (:math:`I_{pH,aa}`), acetate-utilizing microorganisms (:math:`I_{pH,ac}`), hydrogen-utilizing microorganisms (:math:`I_{pH,h2}`) are:
"Molar concentration of hydrogen, S_H", ":math:`S_{H}`", "S_H", 3.4e-8, ":math:`\text{kmol/}\text{m}^3`"
"Molar concentration of hydroxide, S_OH", ":math:`S_{OH}`", "S_OH", 3.4e-8, ":math:`\text{kmol/}\text{m}^3`"

Additional Constraints
----------------------
:lime:`Lime` text indicates the equation has been added, and :blue:`blue` text indicates the equation has been modified from its base ADM1 implementation.

.. csv-table::
:header: "Description", "Equation"

"Water dissociation constant constraint", ":math:`KW = 10^{-14} exp{(\frac{55900}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"CO2 acid-base equilibrium constraint", ":math:`K_{a,co2} = 10^{-6.35} exp{(\frac{7646}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"Nitrogen acid-base equilibrium constraint", ":math:`K_{a,IN} = 10^{-9.25} exp{(\frac{51965}{R} * (\frac{1}{T_{ref}} - \frac{1}{T}))}`"
"Mass concentration of valerate, va-", ":math:`C_{va} = \frac{K_{a,va} * C_{va,ref}}{K_{a,va} + S_{H}}`"
"Mass concentration of butyrate, bu-", ":math:`C_{bu} = \frac{K_{a,bu} * C_{bu,ref}}{K_{a,bu} + S_{H}}`"
"Mass concentration of propionate, pro-", ":math:`C_{pro} = \frac{K_{a,pro} * C_{pro,ref}}{K_{a,pro} + S_{H}}`"
"Mass concentration of acetate, ac-", ":math:`C_{ac} = \frac{K_{a,ac} * C_{ac,ref}}{K_{a,ac} + S_{H}}`"
"Molar concentration of bicarbonate, HCO3", ":math:`M_{hco3} = \frac{K_{a,co2} * \frac{C_{S_{IC},ref}}{12}}{K_{a,co2} + S_{H}}`"
"Molar concentration of ammonia, NH3", ":math:`M_{nh3} = \frac{K_{a,IN} * \frac{C_{S_{IN},ref}}{14}}{K_{a,IN} + S_{H}}`"
"Molar concentration of carbon dioxide, CO2", ":math:`M_{co2} = \frac{C_{S_{IC},ref}}{12} - M_{hco3}`"
"Molar concentration of ammonium, NH4+", ":math:`M_{nh4} = \frac{C_{S_{IN},ref}}{14} - M_{nh3}`"
":lime:`Molar concentration of magnesium, Mg`", ":math:`M_{Mg} = \frac{C_{X_{PP},ref}}{300.41}`"
":lime:`Molar concentration of potassium, K`", ":math:`M_{K} = \frac{C_{X_{PP},ref}}{300.41}`"
":blue:`Molar concentration of hydrogen, H+`", ":math:`S_{H} = M_{hco3} + \frac{C_{ac}}{64} + \frac{C_{pro}}{112} + \frac{C_{bu}}{160} + \frac{C_{va}}{208} + S_{OH} + M_{a} - M_{c} - M_{nh4} - M_{Mg} - M_{K}`"
"Molar concentration of hydroxide, OH-", ":math:`S_{OH} = \frac{KW}{S_{H}}`"
"pH of solution", ":math:`pH = -log_{10}(S_{H})`"

The rules for inhibition of amino-acid-utilizing microorganisms (:math:`I_{pH,aa}`), acetate-utilizing microorganisms (:math:`I_{pH,ac}`), hydrogen-utilizing microorganisms (:math:`I_{pH,h2}`) are:

.. math::
I_{pH,aa}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2} & \text{for } pH \le pH_{UL,aa}\\
\exp{(-3 (\frac{pH - pH_{UL,aa}}{pH_{UL,aa} - pH_{LL,aa}})^2)} & \text{for } pH \le pH_{UL,aa}\\
1 & \text{for } pH > pH_{UL,aa}
\end{cases}
I_{pH,ac}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2} & \text{for } pH \le pH_{UL,ac}\\
\exp{(-3 (\frac{pH - pH_{UL,ac}}{pH_{UL,ac} - pH_{LL,ac}})^2)} & \text{for } pH \le pH_{UL,ac}\\
1 & \text{for } pH > pH_{UL,ac}
\end{cases}
I_{pH,aa}=
I_{pH,h2}=
\begin{cases}
\exp{-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2} & \text{for } pH \le pH_{UL,h2}\\
\exp{(-3 (\frac{pH - pH_{UL,h2}}{pH_{UL,h2} - pH_{LL,h2}})^2)} & \text{for } pH \le pH_{UL,h2}\\
1 & \text{for } pH > pH_{UL,h2}
\end{cases}
The rules for hydrogen sulfide inhibition factors are shown below; however, since :math:`Z_{h2s}` is assumed to be 0, all of these inhibition factors are negligible
The rules for inhibition related to secondary substrate (:math:`I_{IN,lim}`), hydrogen inhibition attributed to long chain fatty acids (:math:`I_{h2,fa}`), hydrogen inhibition attributed to valerate and butyrate uptake (:math:`I_{h2,c4}`), hydrogen inhibition attributed to propionate uptake (:math:`I_{h2,pro}`), ammonia inibition attributed to acetate uptake (:math:`I_{nh3}`), are:

.. math::
I_{IN,lim} = \frac{1}{1 + \frac{K_{S_{IN}}}{C_{S_{IN}}/14}}
I_{h2, fa}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,fa}}}
I_{h2, c4}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,c4}}}
I_{h2, pro}= \frac{1}{1 + \frac{C_{S_{h2}}}{K_{I,h2,pro}}}
I_{nh3}= \frac{1}{1 + \frac{M_{nh3}}{K_{I,nh3}}}
:lime:`The rules for hydrogen sulfide inhibition factors are shown below; however, since` :math:`Z_{h2s}` :lime:`is assumed to be 0, all of these inhibition factors are negligible.`

.. math::
Expand All @@ -277,8 +325,8 @@ The rules for hydrogen sulfide inhibition factors are shown below; however, sinc
I_{h2s, pro}= \frac{1}{1 + \frac{Z_{h2s}}{K_{I,h2s,pro}}}
Classes
-------
Class Documentation
-------------------
.. currentmodule:: watertap.property_models.anaerobic_digestion.modified_adm1_properties

.. autoclass:: ModifiedADM1ParameterBlock
Expand Down
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