Added throughput variables for degradation sudies

CHANGELOG.md

@@ -1,5 +1,9 @@
 # [Unreleased](https://github.com/pybamm-team/PyBaMM/)
 
+## Features
+
+-   Addew new cumulative variables `Throughput capacity [A.h]` and `Throughput energy [W.h]` to standard variables and summary variables, to assist with degradation studies. `Time [s]` and `Time [h]` also added to summary variables. ([#2249](https://github.com/pybamm-team/PyBaMM/pull/2249)) 
+
 ## Bug fixes
 
 -   Added new parameter `Ratio of lithium moles to SEI moles` (short name z_sei) to fix a bug where this number was incorrectly hardcoded to 1. ([#2222](https://github.com/pybamm-team/PyBaMM/pull/2222))

pybamm/input/parameters/lithium_ion/electrolytes/lipf6_OKane2022/README.md

@@ -0,0 +1,7 @@
+# LiPF6 electrolyte parameters
+
+Parameters for a LiPF6 electrolyte, from the paper
+
+> Simon O'Kane, Weilong Ai, Ganesh Madabattula, Diego Alonso-Alvarez, Robert Timms, Valentin Sulzer, Jacqueline Edge, Billy Wu, Gregory Offer, and Monica Marinescu. ["Lithium-ion battery degradation: how to model it."](https://pubs.rsc.org/en/content/articlelanding/2022/cp/d2cp00417h) Physical Chemistry: Chemical Physics 24 (2022): 7909-7922
+
+and references therein.

pybamm/input/parameters/lithium_ion/electrolytes/lipf6_OKane2022/electrolyte_conductivity_Nyman2008_arrhenius.py

@@ -0,0 +1,41 @@
+from pybamm import exp, constants
+
+
+def electrolyte_conductivity_Nyman2008_arrhenius(c_e, T):
+    """
+    Conductivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
+    comes from [1], with Arrhenius temperature dependence added from [2].
+
+    References
+    ----------
+    .. [1] A. Nyman, M. Behm, and G. Lindbergh, "Electrochemical characterisation and
+    modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte,"
+    Electrochim. Acta, vol. 53, no. 22, pp. 6356–6365, 2008.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery i. determination of parameters." Journal of the
+    Electrochemical Society 162.9 (2015): A1836-A1848.
+
+    Parameters
+    ----------
+    c_e: :class:`pybamm.Symbol`
+        Dimensional electrolyte concentration
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    sigma_e = (
+        0.1297 * (c_e / 1000) ** 3 - 2.51 * (c_e / 1000) ** 1.5 + 3.329 * (c_e / 1000)
+    )
+
+    # Nyman et al. (2008) does not provide temperature dependence
+    # So use temperature dependence from Ecker et al. (2015) instead
+
+    E_sigma_e = 17000
+    arrhenius = exp(E_sigma_e / constants.R * (1 / 298.15 - 1 / T))
+
+    return sigma_e * arrhenius

pybamm/input/parameters/lithium_ion/electrolytes/lipf6_OKane2022/electrolyte_diffusivity_Nyman2008_arrhenius.py

@@ -0,0 +1,39 @@
+from pybamm import exp, constants
+
+
+def electrolyte_diffusivity_Nyman2008_arrhenius(c_e, T):
+    """
+    Diffusivity of LiPF6 in EC:EMC (3:7) as a function of ion concentration. The data
+    comes from [1], with Arrhenius temperature dependence added from [2].
+
+    References
+    ----------
+    .. [1] A. Nyman, M. Behm, and G. Lindbergh, "Electrochemical characterisation and
+    modelling of the mass transport phenomena in LiPF6-EC-EMC electrolyte,"
+    Electrochim. Acta, vol. 53, no. 22, pp. 6356–6365, 2008.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery i. determination of parameters." Journal of the
+    Electrochemical Society 162.9 (2015): A1836-A1848.
+
+    Parameters
+    ----------
+    c_e: :class:`pybamm.Symbol`
+        Dimensional electrolyte concentration
+    T: :class:`pybamm.Symbol`
+        Dimensional temperature
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Solid diffusivity
+    """
+
+    D_c_e = 8.794e-11 * (c_e / 1000) ** 2 - 3.972e-10 * (c_e / 1000) + 4.862e-10
+
+    # Nyman et al. (2008) does not provide temperature dependence
+    # So use temperature dependence from Ecker et al. (2015) instead
+
+    E_D_c_e = 17000
+    arrhenius = exp(E_D_c_e / constants.R * (1 / 298.15 - 1 / T))
+
+    return D_c_e * arrhenius

pybamm/input/parameters/lithium_ion/electrolytes/lipf6_OKane2022/parameters.csv

@@ -0,0 +1,10 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrolyte properties,,,
+Typical electrolyte concentration [mol.m-3],1000,Chen 2020,
+Initial concentration in electrolyte [mol.m-3],1000,Chen 2020,
+Cation transference number,0.2594,Chen 2020,
+1 + dlnf/dlnc,1,,
+Electrolyte diffusivity [m2.s-1],[function]electrolyte_diffusivity_Nyman2008_arrhenius,OKane 2022, 
+Electrolyte conductivity [S.m-1],[function]electrolyte_conductivity_Nyman2008_arrhenius,OKane 2022, 

pybamm/input/parameters/lithium_ion/lithium_platings/okane2022_Li_plating/README.md

@@ -2,6 +2,8 @@
 
 Some example parameters for lithium plating from the paper:
 
-> O’Kane, S. E. J., Ai, W., Madabattula, G., Alonso-Alvarez, D., Timms, R, Sulzer, V., Edge, J. S., Wu, B., Offer, G. J., & Marinescu, M. (2022) Lithium-ion battery degradation: how to model it. Physical Chemistry: Chemical Physics, accepted.
+> Simon O'Kane, Weilong Ai, Ganesh Madabattula, Diego Alonso-Alvarez, Robert Timms, Valentin Sulzer, Jacqueline Edge, Billy Wu, Gregory Offer, and Monica Marinescu. ["Lithium-ion battery degradation: how to model it."](https://pubs.rsc.org/en/content/articlelanding/2022/cp/d2cp00417h) Physical Chemistry: Chemical Physics 24 (2022): 7909-7922
+
+and references therein.
 
 Note: this parameter set does not claim to be representative of the true parameter values. These are merely the parameter values that were used in the referenced papers.

pybamm/input/parameters/lithium_ion/negative_electrodes/graphite_OKane2022/README.md

@@ -1,6 +1,6 @@
 # LG M50 Graphite anode parameters
 
-Parameters for a LG M50 graphite anode, from the paper
+Parameters for an LG M50 graphite negative electrode, from the paper
 
 > Simon O'Kane, Weilong Ai, Ganesh Madabattula, Diego Alonso-Alvarez, Robert Timms, Valentin Sulzer, Jacqueline Edge, Billy Wu, Gregory Offer, and Monica Marinescu. ["Lithium-ion battery degradation: how to model it."](https://pubs.rsc.org/en/content/articlelanding/2022/cp/d2cp00417h) Physical Chemistry: Chemical Physics 24 (2022): 7909-7922
 

pybamm/input/parameters/lithium_ion/seis/OKane2022/README.md

@@ -1,12 +1,9 @@
 # SEI parameters
 
-Some example parameters for SEI growth from the papers:
+Parameters for SEI growth from the paper
 
-> Ramadass, P., Haran, B., Gomadam, P. M., White, R., & Popov, B. N. (2004). Development of first principles capacity fade model for Li-ion cells. Journal of the Electrochemical Society, 151(2), A196-A203.
-> Ploehn, H. J., Ramadass, P., & White, R. E. (2004). Solvent diffusion model for aging of lithium-ion battery cells. Journal of The Electrochemical Society, 151(3), A456-A462.
-> Single, F., Latz, A., & Horstmann, B. (2018). Identifying the mechanism of continued growth of the solid–electrolyte interphase. ChemSusChem, 11(12), 1950-1955.
-> Safari, M., Morcrette, M., Teyssot, A., & Delacour, C. (2009). Multimodal Physics-Based Aging Model for Life Prediction of Li-Ion Batteries. Journal of The Electrochemical Society, 156(3), 
-> Yang, X., Leng, Y., Zhang, G., Ge, S., Wang, C. (2017). Modeling of lithium plating induced aging of lithium-ion batteries: Transition from linear to nonlinear aging. Journal of Power Sources, 360, 28-40.
-> Waldmann, T., Wilka, M., Kasper, M., Fleischammer M., Wohlfahrt-Mehrens M. (2014). Temperature dependent ageing mechanisms in Lithium-ion batteris: A Post-Mortem study. Journal of Power Sources, 262, 129-135.
+> Simon O'Kane, Weilong Ai, Ganesh Madabattula, Diego Alonso-Alvarez, Robert Timms, Valentin Sulzer, Jacqueline Edge, Billy Wu, Gregory Offer, and Monica Marinescu. ["Lithium-ion battery degradation: how to model it."](https://pubs.rsc.org/en/content/articlelanding/2022/cp/d2cp00417h) Physical Chemistry: Chemical Physics 24 (2022): 7909-7922
 
-Note: this parameter set does not claim to be representative of the true parameter values. Instead these are parameter values that were used to fit SEI models to observed experimental data in the referenced papers.
+and references therein.
+
+Note: this parameter set does not claim to be representative of the true parameter values. These are merely the parameter values that were used in the referenced papers.

pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py

@@ -185,6 +185,10 @@ def set_summary_variables(self):
         Sets the default summary variables.
         """
         summary_variables = [
+            "Time [s]",
+            "Time [h]",
+            "Throughput capacity [A.h]",
+            "Throughput energy [W.h]",
             "Positive electrode capacity [A.h]",
             # LAM, LLI
             "Loss of active material in positive electrode [%]",

pybamm/models/standard_variables.py

@@ -11,6 +11,10 @@ def __init__(self):
         self.Q_Ah = pybamm.Variable("Discharge capacity [A.h]")
         self.Q_Wh = pybamm.Variable("Discharge energy [W.h]")
 
+        # Throughput capacity and energy (cumulative)
+        self.Qt_Ah = pybamm.Variable("Throughput capacity [A.h]")
+        self.Qt_Wh = pybamm.Variable("Throughput energy [W.h]")
+
         # Electrolyte concentration
         self.c_e_n = pybamm.Variable(
             "Negative electrolyte concentration",

pybamm/models/submodels/external_circuit/base_external_circuit.py

@@ -12,29 +12,50 @@ def __init__(self, param, options):
 
     def get_fundamental_variables(self):
         Q_Ah = pybamm.standard_variables.Q_Ah
-        variables = {"Discharge capacity [A.h]": Q_Ah}
+        Qt_Ah = pybamm.standard_variables.Qt_Ah
+        variables = {
+            "Discharge capacity [A.h]": Q_Ah,
+            "Throughput capacity [A.h]": Qt_Ah,
+        }
         if self.options["calculate discharge energy"] == "true":
             Q_Wh = pybamm.standard_variables.Q_Wh
-            variables.update({"Discharge energy [W.h]": Q_Wh})
+            Qt_Wh = pybamm.standard_variables.Qt_Wh
+            variables.update({
+                "Discharge energy [W.h]": Q_Wh,
+                "Throughput energy [W.h]": Qt_Wh,
+            })
+        else:
+            variables.update({
+                "Discharge energy [W.h]": pybamm.Scalar(0),
+                "Throughput energy [W.h]": pybamm.Scalar(0),
+            })
         return variables
 
     def set_initial_conditions(self, variables):
         Q_Ah = variables["Discharge capacity [A.h]"]
+        Qt_Ah = variables["Throughput capacity [A.h]"]
         self.initial_conditions[Q_Ah] = pybamm.Scalar(0)
+        self.initial_conditions[Qt_Ah] = pybamm.Scalar(0)
         if self.options["calculate discharge energy"] == "true":
             Q_Wh = variables["Discharge energy [W.h]"]
+            Qt_Wh = variables["Throughput energy [W.h]"]
             self.initial_conditions[Q_Wh] = pybamm.Scalar(0)
+            self.initial_conditions[Qt_Wh] = pybamm.Scalar(0)
 
     def set_rhs(self, variables):
-        # ODE for discharge capacity
+        # ODEs for discharge capacity and throughput capacity
         Q_Ah = variables["Discharge capacity [A.h]"]
+        Qt_Ah = variables["Throughput capacity [A.h]"]
         I = variables["Current [A]"]
 
         self.rhs[Q_Ah] = I * self.param.timescale / 3600
+        self.rhs[Qt_Ah] = abs(I) * self.param.timescale / 3600
         if self.options["calculate discharge energy"] == "true":
             Q_Wh = variables["Discharge energy [W.h]"]
+            Qt_Wh = variables["Throughput energy [W.h]"]
             V = variables["Terminal voltage [V]"]
             self.rhs[Q_Wh] = I * V * self.param.timescale / 3600
+            self.rhs[Qt_Wh] = abs(I * V) * self.param.timescale / 3600
 
 
 class LeadingOrderBaseModel(BaseModel):
@@ -45,8 +66,16 @@ def __init__(self, param, options):
 
     def get_fundamental_variables(self):
         Q_Ah = pybamm.Variable("Leading-order discharge capacity [A.h]")
-        variables = {"Discharge capacity [A.h]": Q_Ah}
+        Qt_Ah = pybamm.Variable("Leading-order throughput capacity [A.h]")
+        variables = {
+            "Discharge capacity [A.h]": Q_Ah,
+            "Throughput capacity [A.h]": Qt_Ah,
+        }
         if self.options["calculate discharge energy"] == "true":
             Q_Wh = pybamm.Variable("Leading-order discharge energy [W.h]")
-            variables.update({"Discharge energy [W.h]": Q_Wh})
+            Qt_Wh = pybamm.Variable("Leading-order throughput energy [W.h]")
+            variables.update({
+                "Discharge energy [W.h]": Q_Wh,
+                "Throughput energy [W.h]": Qt_Wh,
+            })
         return variables

pybamm/parameters/parameter_sets.py

@@ -239,7 +239,7 @@
     "negative electrode": "graphite_OKane2022",
     "separator": "separator_Chen2020",
     "positive electrode": "nmc_OKane2022",
-    "electrolyte": "lipf6_Nyman2008",
+    "electrolyte": "lipf6_OKane2022",
     "experiment": "1C_discharge_from_full_Chen2020",
     "sei": "OKane2022",
     "lithium plating": "okane2022_Li_plating",