Merge pull request #824 from pybamm-team/issue-821-add-NCA-set

Issue 821 add nca set

examples/scripts/compare_lithium_ion.py

@@ -26,7 +26,7 @@
 
 # load parameter values and process models and geometry
 param = models[0].default_parameter_values
-param["Current function [A]"] = 1.0
+param["Current function [A]"] = 1
 
 for model in models:
     param.process_model(model)

examples/scripts/nca_parameters.py

@@ -0,0 +1,11 @@
+import pybamm as pb
+
+pb.set_logging_level("INFO")
+model = pb.lithium_ion.DFN()
+
+chemistry = pb.parameter_sets.NCA_Kim2011
+parameter_values = pb.ParameterValues(chemistry=chemistry)
+
+sim = pb.Simulation(model, parameter_values=parameter_values, C_rate=1)
+sim.solve()
+sim.plot()

input/parameters/lithium-ion/anodes/graphite_Kim2011/README.md

@@ -0,0 +1,7 @@
+# Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A. (2011). Multi-domain modeling of lithium-ion batteries encompassing multi-physics in varied length scales. Journal of The Electrochemical Society, 158(8), A955-A969.
+
+Note, only an effective cell volumetric heat capacity is provided in the paper. We therefore used the values for the density and specific heat capacity reported in the Marquis2019 parameter set in each region and multiplied each density by the ratio of the volumetric heat capacity provided in smith to the calculated value. This ensures that the values produce the same effective cell volumetric heat capacity. This works fine for x-lumped thermal models but not for x-full thermal models. We do the same for the planar effective thermal conductivity.

input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_diffusivity_Kim2011.py

@@ -0,0 +1,37 @@
+from pybamm import exp
+
+
+def graphite_diffusivity_Kim2011(sto, T, T_inf, E_D_s, R_g):
+    """
+        Graphite diffusivity [1].
+
+        References
+        ----------
+        .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+        (2011). Multi-domain modeling of lithium-ion batteries encompassing
+        multi-physics in varied length scales. Journal of The Electrochemical
+        Society, 158(8), A955-A969.
+
+        Parameters
+        ----------
+        sto: :class: `numpy.Array`
+            Electrode stochiometry
+        T: :class: `numpy.Array`
+            Dimensional temperature
+        T_inf: double
+            Reference temperature
+        E_D_s: double
+            Solid diffusion activation energy
+        R_g: double
+            The ideal gas constant
+
+        Returns
+        -------
+        : double
+            Solid diffusivity
+   """
+
+    D_ref = 9 * 10 ** (-14)
+    arrhenius = exp(E_D_s / R_g * (1 / T_inf - 1 / T))
+
+    return D_ref * arrhenius

input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_electrolyte_reaction_rate_Kim2011.py

@@ -0,0 +1,48 @@
+from pybamm import exp
+
+
+def graphite_electrolyte_reaction_rate_Kim2011(T, T_inf, E_r, R_g):
+    """
+    Reaction rate for Butler-Volmer reactions between graphite and LiPF6 in EC:DMC
+    [1].
+
+    References
+    ----------
+    .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+    (2011). Multi-domain modeling of lithium-ion batteries encompassing
+    multi-physics in varied length scales. Journal of The Electrochemical
+    Society, 158(8), A955-A969.
+
+    Parameters
+    ----------
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_r: double
+        Reaction activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    :`numpy.Array`
+        Reaction rate
+    """
+
+    i0_ref = 36  # reference exchange current density at 100% SOC
+    sto = 0.36  # stochiometry at 100% SOC
+    c_s_n_max = 2.87 * 10 ** 4  # max electrode concentration
+    c_s_n_ref = sto * c_s_n_max  # reference electrode concentration
+    c_e_ref = 1.2 * 10 ** 3  # reference electrolyte concentration
+    alpha = 0.5  # charge transfer coefficient
+
+    m_ref = (
+        2
+        * i0_ref
+        / (c_e_ref ** alpha * (c_s_n_max - c_s_n_ref) ** alpha * c_s_n_ref ** alpha)
+    )
+
+    arrhenius = exp(E_r / R_g * (1 / T_inf - 1 / T))
+
+    return m_ref * arrhenius

input/parameters/lithium-ion/anodes/graphite_Kim2011/graphite_ocp_Kim2011.py

@@ -0,0 +1,29 @@
+from pybamm import exp, tanh
+
+
+def graphite_ocp_Kim2011(sto):
+    """
+       Graphite Open Circuit Potential (OCP) as a function of the stochiometry [1].
+
+       References
+       ----------
+       .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+       (2011). Multi-domain modeling of lithium-ion batteries encompassing
+       multi-physics in varied length scales. Journal of The Electrochemical
+       Society, 158(8), A955-A969.
+       """
+
+    u_eq = (
+        0.124
+        + 1.5 * exp(-70 * sto)
+        - 0.0351 * tanh((sto - 0.286) / 0.083)
+        - 0.0045 * tanh((sto - 0.9) / 0.119)
+        - 0.035 * tanh((sto - 0.99) / 0.05)
+        - 0.0147 * tanh((sto - 0.5) / 0.034)
+        - 0.102 * tanh((sto - 0.194) / 0.142)
+        - 0.022 * tanh((sto - 0.98) / 0.0164)
+        - 0.011 * tanh((sto - 0.124) / 0.0226)
+        + 0.0155 * tanh((sto - 0.105) / 0.029)
+    )
+
+    return u_eq

input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv

@@ -0,0 +1,38 @@
+Name [units],Value,Reference,Notes
+# Empty rows and rows starting with ‘#’ will be ignored,,,
+,,,
+# Electrode properties,,,
+Negative electrode conductivity [S.m-1],100,,
+Maximum concentration in negative electrode [mol.m-3],2.87E4,,
+Negative electrode diffusivity [m2.s-1],[function]graphite_diffusivity_Kim2011,,
+Negative electrode OCP [V],[function]graphite_ocp_Kim2011,
+,,,
+# Microstructure,,,
+Negative electrode porosity,0.4,,
+Negative electrode active material volume fraction,0.51,,
+Negative particle radius [m],5.083E-7,,
+Negative particle distribution in x,1,,
+Negative electrode surface area density [m-1],3.01E6,,
+Negative electrode Bruggeman coefficient (electrolyte),2,,
+Negative electrode Bruggeman coefficient (electrode),2,,
+,,,
+# Interfacial reactions,,,
+Negative electrode cation signed stoichiometry,-1,,
+Negative electrode electrons in reaction,1,,
+Reference OCP vs SHE in the negative electrode [V],,,
+Negative electrode charge transfer coefficient,0.5,,
+Negative electrode double-layer capacity [F.m-2],0.2,Not reported in Kim2011,
+,,,
+# Density,,,
+Negative electrode density [kg.m-3],2136.43638,1657 * 1.28934,
+,,,
+# Thermal parameters,,,
+Negative electrode specific heat capacity [J.kg-1.K-1],700,,
+Negative electrode thermal conductivity [W.m-1.K-1],1.1339,1.7 * 0.667,
+Negative electrode OCP entropic change [V.K-1],0,,
+,,,
+# Activation energies,,,
+Reference temperature [K],298.15,25C,
+Negative electrode reaction rate,[function]graphite_electrolyte_reaction_rate_Kim2011,,
+Negative reaction rate activation energy [J.mol-1],3E4,,
+Negative solid diffusion activation energy [J.mol-1],4E3,,

input/parameters/lithium-ion/cathodes/nca_Kim2011/README.md

@@ -0,0 +1,8 @@
+# Nickel Cobalt Aluminium (NCA) cathode parameters
+
+Parameters for an NCA cathode, from the paper
+
+> Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A. (2011). Multi-domain modeling of lithium-ion batteries encompassing multi-physics in varied length scales. Journal of The Electrochemical Society, 158(8), A955-A969.
+
+Note, only an effective cell volumetric heat capacity is provided in the paper. We therefore used the values for the density and specific heat capacity reported in the Marquis2019 parameter set in each region and multiplied each density by the ratio of the volumetric heat capacity provided in smith to the calculated value. This ensures that the values produce the same effective cell volumetric heat capacity. This works fine for x-lumped thermal models but not for x-full thermal models. We do the same for the planar effective thermal conductivity.
+

input/parameters/lithium-ion/cathodes/nca_Kim2011/nca_diffusivity_Kim2011.py

@@ -0,0 +1,37 @@
+from pybamm import exp
+
+
+def nca_diffusivity_Kim2011(sto, T, T_inf, E_D_s, R_g):
+    """
+    NCA diffusivity as a function of stochiometry [1].
+
+    References
+    ----------
+    .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+    (2011). Multi-domain modeling of lithium-ion batteries encompassing
+    multi-physics in varied length scales. Journal of The Electrochemical
+    Society, 158(8), A955-A969.
+
+    Parameters
+    ----------
+    sto: :class: `numpy.Array`
+        Electrode stochiometry
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_D_s: double
+        Solid diffusion activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    : double
+        Solid diffusivity
+    """
+
+    D_ref = 3 * 10 ** (-15)
+    arrhenius = exp(E_D_s / R_g * (1 / T_inf - 1 / T))
+
+    return D_ref * arrhenius

input/parameters/lithium-ion/cathodes/nca_Kim2011/nca_electrolyte_reaction_rate_Kim2011.py

@@ -0,0 +1,46 @@
+from pybamm import exp
+
+
+def nca_electrolyte_reaction_rate_Kim2011(T, T_inf, E_r, R_g):
+    """
+    Reaction rate for Butler-Volmer reactions between NCA and LiPF6 in EC:DMC
+    [1].
+
+     References
+    ----------
+    .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+    (2011). Multi-domain modeling of lithium-ion batteries encompassing
+    multi-physics in varied length scales. Journal of The Electrochemical
+    Society, 158(8), A955-A969.
+
+    Parameters
+    ----------
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_r: double
+        Reaction activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    : double
+        Reaction rate
+    """
+    i0_ref = 4  # reference exchange current density at 100% SOC
+    sto = 0.41  # stochiometry at 100% SOC
+    c_s_max = 4.9 * 10 ** 4  # max electrode concentration
+    c_s_ref = sto * c_s_max  # reference electrode concentration
+    c_e_ref = 1.2 * 10 ** 3  # reference electrolyte concentration
+    alpha = 0.5  # charge transfer coefficient
+
+    m_ref = (
+        2
+        * i0_ref
+        / (c_e_ref ** alpha * (c_s_max - c_s_ref) ** alpha * c_s_ref ** alpha)
+    )
+    arrhenius = exp(E_r / R_g * (1 / T_inf - 1 / T))
+
+    return m_ref * arrhenius

input/parameters/lithium-ion/cathodes/nca_Kim2011/nca_ocp_Kim2011_data.csv

@@ -0,0 +1,75 @@
+0.370214428274133, 4.210440859985937
+0.37577436378229034, 4.198214873372019
+0.3836904770360269, 4.182142025684674
+0.3918959828337426, 4.165163132847251
+0.40106922140226364, 4.149604765177982
+0.40686180736573874, 4.138286599370602
+0.4116896199858422, 4.129799619141419
+0.4194137255876832, 4.115653556008545
+0.4266554445178383, 4.10292308566477
+0.4329304171529992, 4.090189327068291
+0.4396907358872798, 4.0802916864290655
+0.44548430832656627, 4.070390757537136
+0.4532103868800297, 4.059079168235163
+0.45852157264763016, 4.050593832132332
+0.4628660121202365, 4.042105207776797
+0.4710764502970082, 4.032212499516627
+0.47638763606460877, 4.023727163413795
+0.4836313279463863, 4.013831166900922
+0.48942490038567266, 4.0039302380089925
+0.4981187117099415, 3.994039173875174
+0.5077763099017708, 3.979899687247709
+0.5164711077018508, 3.971425860029342
+0.5280592390562348, 3.9530412391609326
+0.537716837248064, 3.938901752533467
+0.5493089145056929, 3.9261860793268606
+0.5565516199116592, 3.914872845898536
+0.5671749779226715, 3.8993194106083244
+0.5768345490661232, 3.88801439781176
+0.5869745339296383, 3.872459318395196
+0.5961487589739706, 3.8583181876413786
+0.6087065960507823, 3.844188565772025
+0.6159493014567486, 3.832875332343701
+0.6246431127810175, 3.822984268209883
+0.6352684437436521, 3.8102653067505723
+0.6463781343295951, 3.798965226333064
+0.660386090848898, 3.784840536842767
+0.6763275399581893, 3.7707224238578783
+0.6917856159199836, 3.756602666746637
+0.7038630392767319, 3.7467231114972837
+0.7246372333851825, 3.7312042028604644
+0.7391305360036051, 3.71991563132742
+0.7531414519503417, 3.710042652583475
+0.7676347545687643, 3.698754081050431
+0.7797121779255124, 3.6888745258010776
+0.7917886148064496, 3.677577733636274
+0.8043484248348838, 3.6662825855978216
+0.8144923556016439, 3.65639645384306
+0.8260854193350838, 3.645098017551904
+0.8357449904785356, 3.6337930047553395
+0.8463732808686039, 3.6253257540423807
+0.8560318655362443, 3.612603504330366
+0.8652100364838214, 3.604131321238351
+0.8739028613322789, 3.5928230201890825
+0.8840477785748505, 3.5843541253497717
+0.8927425763749305, 3.5758802981314046
+0.9024031339941933, 3.5659925222502906
+0.9125490377125759, 3.5589408643264306
+0.9222105818076499, 3.5504703253607675
+0.9338056184927125, 3.5420063629005125
+0.9482959616837011, 3.526466080621117
+0.957951586923908, 3.5094921201627503
+0.965192319378252, 3.495344412903525
+0.9709740541078039, 3.4684366410261873
+0.9743448419547373, 3.450024070009794
+0.976744937603432, 3.425939263078894
+0.9805892338397507, 3.393355967034346
+0.9820196237660176, 3.36501616110439
+0.9834510001680955, 3.3380935920898844
+0.9848843495217959, 3.3140054969062804
+0.9858323527763772, 3.287081283765423
+0.987258796799399, 3.2530725301736645
+0.9896421223593032, 3.204894695680104
+0.9905703960976598, 3.1496257442302342
+0.9915055751666949, 3.104277451188519
+0.9933828386354436, 3.023501523513243

input/parameters/lithium-ion/cathodes/nca_Kim2011/nca_ocp_Kim2011_function.py

@@ -0,0 +1,37 @@
+from pybamm import exp
+
+
+def nca_ocp_Kim2011_function(sto):
+    """
+    NCA open-circuit potential (OCP) [1]. Fit in paper seems wrong to using
+    nca_ocp_Kim2011_data.csv instead.
+    References
+    ----------
+    .. [1] Kim, G. H., Smith, K., Lee, K. J., Santhanagopalan, S., & Pesaran, A.
+    (2011). Multi-domain modeling of lithium-ion batteries encompassing
+    multi-physics in varied length scales. Journal of The Electrochemical
+    Society, 158(8), A955-A969.
+
+    Parameters
+    ----------
+    sto: double
+       Stochiometry of material (li-fraction)
+
+    """
+
+    u_eq = (
+        1.68 * sto ** 10
+        - 2.222 * sto ** 9
+        + 15.056 * sto ** 8
+        - 23.488 * sto ** 7
+        + 81.246 * sto ** 6
+        - 344.566 * sto ** 5
+        + 621.3475 * sto ** 4
+        - 544.774 * sto ** 3
+        + 264.427 * sto ** 2
+        - 66.3691 * sto
+        + 11.8058
+        - 0.61386 * exp(5.8201 * sto ** 136.4)
+    )
+
+    return u_eq