Electrolyte overpotentials

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Features
 
+-   Added the electrolyte overpotential and Ohmic losses for full conductivity, including surface form ([#1350](https://github.com/pybamm-team/PyBaMM/pull/1350))
 -   Added functionality to `Citations` to print formatted citations ([#1340](https://github.com/pybamm-team/PyBaMM/pull/1340))
 -   Updated the way events are handled in `CasadiSolver` for more accurate event location ([#1328](https://github.com/pybamm-team/PyBaMM/pull/1328))
 -   Added error message if initial conditions are outside the bounds of a variable ([#1326](https://github.com/pybamm-team/PyBaMM/pull/1326))

pybamm/models/full_battery_models/base_battery_model.py

@@ -848,12 +848,10 @@ def set_voltage_variables(self):
 
         # Battery-wide variables
         V_dim = self.variables["Terminal voltage [V]"]
-        eta_e_av = self.variables.get("X-averaged electrolyte ohmic losses", 0)
-        eta_c_av = self.variables.get("X-averaged concentration overpotential", 0)
-        eta_e_av_dim = self.variables.get("X-averaged electrolyte ohmic losses [V]", 0)
-        eta_c_av_dim = self.variables.get(
-            "X-averaged concentration overpotential [V]", 0
-        )
+        eta_e_av = self.variables["X-averaged electrolyte ohmic losses"]
+        eta_c_av = self.variables["X-averaged concentration overpotential"]
+        eta_e_av_dim = self.variables["X-averaged electrolyte ohmic losses [V]"]
+        eta_c_av_dim = self.variables["X-averaged concentration overpotential [V]"]
         num_cells = pybamm.Parameter(
             "Number of cells connected in series to make a battery"
         )

pybamm/models/submodels/electrolyte_conductivity/base_electrolyte_conductivity.py

@@ -291,6 +291,74 @@ def _get_whole_cell_variables(self, variables):
 
         return variables
 
+    def _get_electrolyte_overpotentials(self, variables):
+        """
+        A private function to obtain the electrolyte overpotential and Ohmic losses.
+        Note: requires 'variables' to contain the potential, electrolyte concentration
+        and temperature the subdomains: 'negative electrode', 'separator', and
+        'positive electrode'.
+
+        Parameters
+        ----------
+        variables : dict
+            The variables that have been set in the rest of the model.
+
+        Returns
+        -------
+        variables : dict
+            The variables including the whole-cell electrolyte potentials
+            and currents.
+        """
+        param = self.param
+
+        phi_e_n = variables["Negative electrolyte potential"]
+        phi_e_p = variables["Positive electrolyte potential"]
+
+        c_e_n = variables["Negative electrolyte concentration"]
+        c_e_s = variables["Separator electrolyte concentration"]
+        c_e_p = variables["Positive electrolyte concentration"]
+
+        T_n = variables["Negative electrode temperature"]
+        T_s = variables["Separator temperature"]
+        T_p = variables["Positive electrode temperature"]
+
+        # concentration overpotential
+        indef_integral_n = pybamm.IndefiniteIntegral(
+            param.chi(c_e_n, T_n)
+            * (1 + param.Theta * T_n)
+            * pybamm.grad(c_e_n)
+            / c_e_n,
+            pybamm.standard_spatial_vars.x_n,
+        )
+        indef_integral_s = pybamm.IndefiniteIntegral(
+            param.chi(c_e_s, T_s)
+            * (1 + param.Theta * T_s)
+            * pybamm.grad(c_e_s)
+            / c_e_s,
+            pybamm.standard_spatial_vars.x_s,
+        )
+        indef_integral_p = pybamm.IndefiniteIntegral(
+            param.chi(c_e_p, T_p)
+            * (1 + param.Theta * T_p)
+            * pybamm.grad(c_e_p)
+            / c_e_p,
+            pybamm.standard_spatial_vars.x_p,
+        )
+
+        integral_n = indef_integral_n
+        integral_s = indef_integral_s + pybamm.boundary_value(integral_n, "right")
+        integral_p = indef_integral_p + pybamm.boundary_value(integral_s, "right")
+
+        eta_c_av = pybamm.x_average(integral_p) - pybamm.x_average(integral_n)
+
+        delta_phi_e_av = (
+            pybamm.x_average(phi_e_p) - pybamm.x_average(phi_e_n) - eta_c_av
+        )
+
+        variables.update(self._get_split_overpotential(eta_c_av, delta_phi_e_av))
+
+        return variables
+
     def set_boundary_conditions(self, variables):
         phi_e = variables["Electrolyte potential"]
         self.boundary_conditions = {

pybamm/models/submodels/electrolyte_conductivity/full_conductivity.py

@@ -45,6 +45,7 @@ def get_coupled_variables(self, variables):
         )
 
         variables.update(self._get_standard_current_variables(i_e))
+        variables.update(self._get_electrolyte_overpotentials(variables))
 
         return variables
 

pybamm/models/submodels/electrolyte_conductivity/surface_potential_form/full_surface_form_conductivity.py

@@ -95,6 +95,7 @@ def get_coupled_variables(self, variables):
 
         if self.domain == "Positive":
             variables.update(self._get_whole_cell_variables(variables))
+            variables.update(self._get_electrolyte_overpotentials(variables))
 
         return variables
 

tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_full_conductivity.py

@@ -12,13 +12,19 @@ def test_public_functions(self):
         param = pybamm.LithiumIonParameters()
         a = pybamm.Scalar(1)
         surf = "electrode surface area to volume ratio"
+        a_n = pybamm.FullBroadcast(a, "negative electrode", "current collector")
+        a_s = pybamm.FullBroadcast(a, "separator", "current collector")
+        a_p = pybamm.FullBroadcast(a, "positive electrode", "current collector")
+
         variables = {
             "Electrolyte tortuosity": a,
-            "Electrolyte concentration": pybamm.FullBroadcast(
-                a,
-                ["negative electrode", "separator", "positive electrode"],
-                "current collector",
-            ),
+            "Electrolyte concentration": pybamm.Concatenation(a_n, a_s, a_p),
+            "Negative electrolyte concentration": a_n,
+            "Separator electrolyte concentration": a_s,
+            "Positive electrolyte concentration": a_p,
+            "Negative electrode temperature": a_n,
+            "Separator temperature": a_s,
+            "Positive electrode temperature": a_p,
             "Negative "
             + surf: pybamm.FullBroadcast(a, "negative electrode", "current collector"),
             "Positive "
@@ -28,7 +34,7 @@ def test_public_functions(self):
                 ["negative electrode", "separator", "positive electrode"],
                 "current collector",
             ),
-            "Cell temperature": a,
+            "Cell temperature": pybamm.Concatenation(a_n, a_s, a_p),
         }
         submodel = pybamm.electrolyte_conductivity.Full(param)
         std_tests = tests.StandardSubModelTests(submodel, variables)

tests/unit/test_models/test_submodels/test_electrolyte_conductivity/test_surface_form/test_full_surface_form_conductivity.py

@@ -31,9 +31,11 @@ def test_public_functions(self):
             "Electrolyte potential": pybamm.Concatenation(a_n, a_s, a_p),
             "Negative electrode temperature": a_n,
             "Separator temperature": a_s,
+            "Separator electrolyte concentration": a_s,
             "Positive electrode temperature": a_p,
             "Negative electrode potential": a_n,
             "Positive electrode potential": a_p,
+            "Positive electrolyte concentration": a_p,
         }
 
         spf = pybamm.electrolyte_conductivity.surface_potential_form
@@ -50,8 +52,12 @@ def test_public_functions(self):
             ),
             "Negative electrolyte potential": a_n,
             "Negative electrolyte current density": a_n,
+            "Negative electrolyte concentration": a_n,
+            "Negative electrode temperature": a_n,
             "Separator electrolyte potential": a_s,
             "Separator electrolyte current density": a_s,
+            "Separator electrolyte concentration": a_s,
+            "Separator temperature": a_s,
             "Positive electrode porosity": a_p,
             "Positive electrolyte tortuosity": a_p,
             "Positive electrode tortuosity": a_p,