#834 added solvent diffusion limited growth

examples/scripts/sei_growth.py

@@ -5,6 +5,7 @@
 # pb.settings.debug_mode = True
 
 options = {"sei": "reaction limited"}
+options = {"sei": "solvent-diffusion limited"}
 # options = {"sei": None}
 model = pb.lithium_ion.DFN(options)
 
@@ -41,27 +42,33 @@
 #     }
 # )
 
-parameter_values.update(
-    {
-        "Inner SEI reaction proportion": 0.5,
-        "Inner SEI partial molar volume [m3.mol-1]": 34.76e-6,
-        "Outer SEI partial molar volume [m3.mol-1]": 34.76e-6,
-        "SEI reaction exchange current density [A.m-2]": 1.5e-9,
-        "SEI resistance per unit thickness [Ohm.m-1]": 0,
-        "Outer SEI solvent diffusivity [m2.s-1]": 2.5e-22,
-        "Bulk solvent concentration [mol.m-3]": 2.636e3,
-        "Ratio of inner and outer SEI exchange current densities": 1,
-        "Inner SEI open-circuit potential [V]": 0.1,
-        "Outer SEI open-circuit potential [V]": 0.8,
-        "Inner SEI electron conducticity [S.m-1]": 8.95e-14,
-        "Inner SEI lithium interstitial diffusivity [m2.s-1]": 1e-15,
-        "Lithium interstitial reference concentration [mol.m-3]": 15,
-        "Initial inner SEI thickness [m]": 7.5e-9,
-        "Initial outer SEI thickness [m]": 7.5e-9,
-    }
-)
+# parameter_values.update(
+#     {
+#         "Inner SEI reaction proportion": 0.5,
+#         "Inner SEI partial molar volume [m3.mol-1]": 34.76e-7,
+#         "Outer SEI partial molar volume [m3.mol-1]": 34.76e-7,
+#         "SEI reaction exchange current density [A.m-2]": 1.5e-7,
+#         "SEI resistance per unit thickness [Ohm.m-1]": 1,
+#         "Outer SEI solvent diffusivity [m2.s-1]": 2.5e-22,
+#         "Bulk solvent concentration [mol.m-3]": 2.636e3,
+#         "Ratio of inner and outer SEI exchange current densities": 1,
+#         "Inner SEI open-circuit potential [V]": 0.1,
+#         "Outer SEI open-circuit potential [V]": 0.8,
+#         "Inner SEI electron conducticity [S.m-1]": 8.95e-14,
+#         "Inner SEI lithium interstitial diffusivity [m2.s-1]": 1e-15,
+#         "Lithium interstitial reference concentration [mol.m-3]": 15,
+#         "Initial inner SEI thickness [m]": 7.5e-9,
+#         "Initial outer SEI thickness [m]": 7.5e-9,
+#     }
+# )
 
 # parameter_values.update({"Current function [A]": 0})
+
+
+def my_sin(t):
+    return pb.sin(0.01 * t)
+
+
 parameter_values["Current function [A]"] = "[current data]US06"
 parameter_values["Current function [A]"] = 0
 
@@ -76,10 +83,11 @@
 hours = days * 24
 minutes = hours * 60
 seconds = minutes * 60
+
 t_eval = np.linspace(0, seconds, 100)
 
-# sim.solve(solver=solver)
-sim.solve(solver=solver, t_eval=t_eval)
+sim.solve(t_eval=t_eval, solver=solver)
+# sim.solve(solver=solver, t_eval=t_eval)
 sim.plot(
     [
         "Terminal voltage [V]",
@@ -99,9 +107,5 @@
             "X-averaged negative electrode sei interfacial current density [A.m-2]",
             "X-averaged negative electrode interfacial current density [A.m-2]",
         ],
-        [
-            "Negative electrode interfacial current density",
-            "Scaled negative electrode sei interfacial current density",
-        ],
     ]
 )

input/parameters/lithium-ion/seis/Example/parameters.csv

@@ -3,9 +3,9 @@ Name [units],Value,Reference,Notes
 ,,,
 # SEI properties,,,
 Inner SEI reaction proportion,0.5,,
-Inner SEI partial molar volume [m3.mol-1],34.76e-7, Ramadass (modified in pybamm),
-Outer SEI partial molar volume [m3.mol-1],34.76e-7, Ramadass (modified in pybamm),
-SEI reaction exchange current density [A.m-2],1.5E-7, Ramadass (modified in pybamm),
+Inner SEI partial molar volume [m3.mol-1],3e-6, Guess,
+Outer SEI partial molar volume [m3.mol-1],3e-6, Guess,
+SEI reaction exchange current density [A.m-2],1.5E-7, Guess,
 SEI resistance per unit thickness [Ohm.m-1],1, Ramadass,
 Outer SEI solvent diffusivity [m2.s-1],2.5E-22, Single paper,
 Bulk solvent concentration [mol.m-3],2.636E3, Ploehn paper,

pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py

@@ -80,6 +80,11 @@ def set_sei_submodel(self):
                 self.param, "Negative electrode"
             )
 
+        elif self.options["sei"] == "solvent-diffusion limited":
+            self.submodels["negative sei"] = pybamm.sei.SolventDiffusionLimited(
+                self.param, "Negative electrode"
+            )
+
         # positive electrode
         self.submodels["positive sei"] = pybamm.sei.NoSEI(
             self.param, "Positive electrode"

pybamm/models/submodels/sei/__init__.py

@@ -1,3 +1,4 @@
 from .base_sei import BaseModel
-from .reaction_limited import ReactionLimited
 from .no_sei import NoSEI
+from .reaction_limited import ReactionLimited
+from .solvent_diffusion_limited import SolventDiffusionLimited

pybamm/models/submodels/sei/solvent_diffusion_limited.py

@@ -0,0 +1,69 @@
+#
+# Class for solvent-diffusion limited SEI growth
+#
+import pybamm
+from .base_sei import BaseModel
+
+
+class SolventDiffusionLimited(BaseModel):
+    """Base class for solvent-diffusion limited SEI growth.
+
+    Parameters
+    ----------
+    param : parameter class
+        The parameters to use for this submodel
+    domain : str
+        The domain of the model either 'Negative' or 'Positive'
+
+
+    **Extends:** :class:`pybamm.particle.BaseParticle`
+    """
+
+    def __init__(self, param, domain):
+        super().__init__(param, domain)
+
+    def get_fundamental_variables(self):
+        L_inner = pybamm.standard_variables.L_inner
+        L_outer = pybamm.standard_variables.L_outer
+
+        variables = self._get_standard_thickness_variables(L_inner, L_outer)
+
+        return variables
+
+    def get_coupled_variables(self, variables):
+        L_sei_outer = variables["Outer negative electrode sei thickness"]
+
+        C_sei = pybamm.sei_parameters.C_sei_solvent
+
+        j_sei = -1 / (C_sei * L_sei_outer)
+
+        alpha = 0.5
+        j_inner = alpha * j_sei
+        j_outer = (1 - alpha) * j_sei
+
+        variables.update(self._get_standard_reaction_variables(j_inner, j_outer))
+
+        return variables
+
+    def set_rhs(self, variables):
+        L_inner = variables["Inner " + self.domain.lower() + " sei thickness"]
+        L_outer = variables["Outer " + self.domain.lower() + " sei thickness"]
+        j_inner = variables[
+            "Inner " + self.domain.lower() + " sei interfacial current density"
+        ]
+        j_outer = variables[
+            "Outer " + self.domain.lower() + " sei interfacial current density"
+        ]
+
+        v_bar = pybamm.sei_parameters.v_bar
+
+        self.rhs = {L_inner: -j_inner, L_outer: -v_bar * j_outer}
+
+    def set_initial_conditions(self, variables):
+        L_inner = variables["Inner " + self.domain.lower() + " sei thickness"]
+        L_outer = variables["Outer " + self.domain.lower() + " sei thickness"]
+
+        L_inner_0 = pybamm.sei_parameters.L_inner_0
+        L_outer_0 = pybamm.sei_parameters.L_outer_0
+
+        self.initial_conditions = {L_inner: L_inner_0, L_outer: L_outer_0}

pybamm/parameters/sei_parameters.py

@@ -57,13 +57,17 @@ def alpha(m_ratio, phi_s, phi_e, U_inner, U_outer):
 a_p = pybamm.standard_parameters_lithium_ion.a_p_dim
 L_x = pybamm.standard_parameters_lithium_ion.L_x
 
-I_typ = pybamm.electrical_parameters.I_typ
+i_typ = pybamm.electrical_parameters.i_typ
 
 C_sei_reaction = (
     F * L_sei_0_dim / (m_sei_dimensional * tau_discharge * V_bar_inner_dimensional)
 ) * pybamm.exp(-(F * U_n_ref / (2 * R * T_ref)))
 
-R_sei = F * I_typ * R_sei_dimensional * L_sei_0_dim / (a_n * L_x)
+C_sei_solvent = L_sei_0_dim ** 2 / (
+    c_sol_dimensional * V_bar_inner_dimensional * D_sol_dimensional * tau_discharge
+)
+
+R_sei = F * i_typ * R_sei_dimensional * L_sei_0_dim / (a_n * L_x)
 
 v_bar = V_bar_outer_dimensional / V_bar_inner_dimensional
 
@@ -72,9 +76,9 @@ def alpha(m_ratio, phi_s, phi_e, U_inner, U_outer):
 
 # ratio of SEI reaction scale to intercalation reaction
 Gamma_SEI_n = (F * L_sei_0_dim * a_n * L_x) / (
-    V_bar_inner_dimensional * I_typ * tau_discharge
+    V_bar_inner_dimensional * i_typ * tau_discharge
 )
 
 Gamma_SEI_p = (F * L_sei_0_dim * a_p * L_x) / (
-    V_bar_inner_dimensional * I_typ * tau_discharge
+    V_bar_inner_dimensional * i_typ * tau_discharge
 )