Add Acid-Base Eq.Constraints to ADM1 Documentation

docs/technical_reference/property_models/ADM1.rst

@@ -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
 -------------------------
@@ -144,6 +146,8 @@ Kinetic Parameters
    "Acetate acid-base equilibrium constant, K_a_ac", ":math:`K_{a,ac}`", "K_a_ac", 1.74e-5, ":math:`\text{kmol/}\text{m}^3`"
    "Carbon dioxide acid-base equilibrium constant, K_a_co2", ":math:`K_{a,co2}`", "K_a_co2", 4.94e-7, ":math:`\text{kmol/}\text{m}^3`"
    "Inorganic nitrogen acid-base equilibrium constant, K_a_IN", ":math:`K_{a,IN}`", "K_a_IN", 1.11e-9, ":math:`\text{kmol/}\text{m}^3`"
+   "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`"
 
 Properties
 ----------
@@ -178,6 +182,26 @@ 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}}`"
 
+Acid-Base Equilibrium Constraints
+---------------------------------
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "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{K_{a,co2} * \frac{C_{S_{IC},ref}}{12}}{K_{a,co2} + S_{H}}`"
+   "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} + C_{ac} + C_{pro} + C_{bu} + C_{va} + 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::
@@ -194,12 +218,26 @@ The rules for pH inhibition of amino-acid-utilizing microorganisms (:math:`I_{pH
          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}\\
          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
 -------

docs/technical_reference/property_models/ASM1.rst

@@ -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
 -------------------------

docs/technical_reference/property_models/ASM2D.rst

@@ -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
 ---------------------------

docs/technical_reference/property_models/modified_ADM1.rst

@@ -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
 -------------------------
@@ -199,6 +201,8 @@ Kinetic Parameters
    ":lime:`Magnesium coefficient for polyphosphates, Mg_PP`", ":math:`Mg_{PP}`", "Mg_PP", 1/3, ":math:`\text{dimensionless}`"
    "Carbon dioxide acid-base equilibrium constant, K_a_co2", ":math:`K_{a,co2}`", "K_a_co2", 4.94e-7, ":math:`\text{kmol/}\text{m}^3`"
    "Inorganic nitrogen acid-base equilibrium constant, K_a_IN", ":math:`K_{a,IN}`", "K_a_IN", 1.11e-9, ":math:`\text{kmol/}\text{m}^3`"
+   "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`"
 
 Properties
 ----------
@@ -242,8 +246,31 @@ 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}}`"
 
+Acid-Base Equilibrium 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.
 
-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:
+.. csv-table::
+   :header: "Description", "Equation"
+
+   "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{K_{a,co2} * \frac{C_{S_{IC},ref}}{12}}{K_{a,co2} + S_{H}}`"
+   "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} + C_{ac} + C_{pro} + C_{bu} + C_{va} + 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::
 
@@ -259,13 +286,28 @@ The rules for pH inhibition of amino-acid-utilizing microorganisms (:math:`I_{pH
          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}\\
          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::
 

watertap/property_models/anaerobic_digestion/adm1_reactions.py

@@ -1241,25 +1241,25 @@ def _rxn_rate(self):
         self.conc_mass_va = pyo.Var(
             initialize=0.01159624,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of va-",
+            doc="mass concentration of va-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_bu = pyo.Var(
             initialize=0.0132208,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of bu-",
+            doc="mass concentration of bu-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_pro = pyo.Var(
             initialize=0.015742,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of pro-",
+            doc="mass concentration of pro-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_ac = pyo.Var(
             initialize=0.1972,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of ac-",
+            doc="mass concentration of ac-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mol_hco3 = pyo.Var(
@@ -1454,7 +1454,7 @@ def concentration_of_nh4_rule(self):
 
         self.concentration_of_nh4 = pyo.Constraint(
             rule=concentration_of_nh4_rule,
-            doc="constraint concentration of pro-",
+            doc="constraint concentration of nh4",
         )
 
         def S_OH_rule(self):
@@ -1482,7 +1482,7 @@ def S_H_rule(self):
 
         self.S_H_cons = pyo.Constraint(
             rule=S_H_rule,
-            doc="constraint concentration of pro-",
+            doc="constraint concentration of H",
         )
 
         def rule_pH(self):

watertap/property_models/anaerobic_digestion/modified_adm1_reactions.py

@@ -1812,25 +1812,25 @@ def _rxn_rate(self):
         self.conc_mass_va = pyo.Var(
             initialize=0.01159624,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of va-",
+            doc="mass concentration of va-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_bu = pyo.Var(
             initialize=0.0132208,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of bu-",
+            doc="mass concentration of bu-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_pro = pyo.Var(
             initialize=0.015742,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of pro-",
+            doc="mass concentration of pro-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mass_ac = pyo.Var(
             initialize=0.1972,
             domain=pyo.NonNegativeReals,
-            doc="molar concentration of ac-",
+            doc="mass concentration of ac-",
             units=pyo.units.kg / pyo.units.m**3,
         )
         self.conc_mol_hco3 = pyo.Var(