#729 added electrolyte conductivity

Author: Scottmar93

input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Dualfoil1998.py input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_electrolyte_reaction_rate_Ecker2015.py

@@ -1,13 +1,18 @@
 import autograd.numpy as np
 
 
-def graphite_electrolyte_reaction_rate_Dualfoil1998(T, T_inf, E_r, R_g):
+def graphite_electrolyte_reaction_rate_Ecker2015(T, T_inf, E_r, R_g):
     """
     Reaction rate for Butler-Volmer reactions between graphite and LiPF6 in EC:DMC.
 
     References
     ----------
-    .. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+    .. [1] 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.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
 
     Parameters
     ----------
@@ -25,7 +30,7 @@ def graphite_electrolyte_reaction_rate_Dualfoil1998(T, T_inf, E_r, R_g):
     :`numpy.Array`
         Reaction rate
     """
-    m_ref = 2 * 10 ** (-5)
+    m_ref = 2.79 * 10 ** (-6)
     arrhenius = np.exp(E_r / R_g * (1 / T_inf - 1 / T))
 
     return m_ref * arrhenius

input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_entropic_change_Moura2016.py

@@ -30,7 +30,7 @@ Negative electrode thermal conductivity [W.m-1.K-1],N/A,,
 Negative electrode OCP entropic change [V.K-1],N/A,,
 ,,,
 # Activation energies,,,
-Reference temperature [K],298.15,25C,
-Negative electrode reaction rate,ADD,,
+Reference temperature [K],296.15,23C,
+Negative electrode reaction rate,[function]graphite_electrolyte_reaction_rate_Ecker2015,,
 Negative reaction rate activation energy [J.mol-1],53400,,
 Negative solid diffusion activation energy [J.mol-1],3.03E+04,,

input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_diffusivity_Dualfoil1998.py

@@ -10,7 +10,7 @@ Positive electrode OCP [V],[data]nco_ocp_Ecker2015,,
 # Microstructure,,,
 Positive electrode porosity,0.296,,
 Positive particle radius [m],1E-05,,
-Positive electrode surface area density [m-1],ADD,,
+Positive electrode surface area density [m-1],188455,,
 Positive electrode Bruggeman coefficient,N/A,,
 ,,,
 # Interfacial reactions,,,
@@ -30,7 +30,7 @@ Positive electrode thermal conductivity [W.m-1.K-1],N/A,,
 Positive electrode OCP entropic change [V.K-1],N/A,,
 ,,,
 # Activation energies,,,
-Reference temperature [K],298.15,25C,
-Positive electrode reaction rate,ADD,,
+Reference temperature [K],296.15,25C,
+Positive electrode reaction rate,[function]nco_electrolyte_reaction_rate_Ecker2015,,
 Positive reaction rate activation energy [J.mol-1],4.36E+04,,
 Positive solid diffusion activation energy [J.mol-1],8.06E+04,,

input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_mcmb2528_ocp_Dualfoil1998.py

@@ -0,0 +1,48 @@
+import autograd.numpy as np
+
+
+def electrolyte_conductivity_Capiglia1999(c_e, T, T_inf, E_k_e, R_g):
+    """
+    Conductivity of LiPF6 in EC:DMC as a function of ion concentration [1, 2].
+
+    References
+    ----------
+    .. [1] 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.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
+
+    Parameters
+    ----------
+    c_e: :class: `numpy.Array`
+        Dimensional electrolyte concentration
+    T: :class: `numpy.Array`
+        Dimensional temperature
+    T_inf: double
+        Reference temperature
+    E_k_e: double
+        Electrolyte conductivity activation energy
+    R_g: double
+        The ideal gas constant
+
+    Returns
+    -------
+    :`numpy.Array`
+        Solid diffusivity
+    """
+
+    x = c_e / 1000
+
+    # in mS / cm
+    sigma_e = 2.667 * x ** 3 - 12.983 * x ** 2 + 17.919 * x + 1.726
+
+    # convert to S / m
+    sigma_e = sigma_e / 10
+
+    # In Ecker paper there is factor of 1/T out the front but this doesn't
+    # make much sense so just going to leave it out for now
+    arrhenius = np.exp(E_k_e / R_g * (1 / T_inf - 1 / T))
+
+    return sigma_e * arrhenius

input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv

@@ -3,15 +3,17 @@
 
 def electrolyte_diffusivity_Capiglia1999(c_e, T, T_inf, E_D_e, R_g):
     """
-    Diffusivity of LiPF6 in EC:DMC as a function of ion concentration. The original data
-    is from [1]. The fit from Dualfoil [2].
+    Diffusivity of LiPF6 in EC:DMC as a function of ion concentration [1, 2].
 
     References
     ----------
-    .. [1] C Capiglia et al. 7Li and 19F diffusion coefficients and thermal
-    properties of non-aqueous electrolyte solutions for rechargeable lithium batteries.
-    Journal of power sources 81 (1999): 859-862.
-    .. [2] http://www.cchem.berkeley.edu/jsngrp/fortran.html
+    .. [1] 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.
+    .. [2] Ecker, Madeleine, et al. "Parameterization of a physico-chemical model of
+    a lithium-ion battery ii. model validation." Journal of The Electrochemical
+    Society 162.9 (2015): A1849-A1857.
+l
 
     Parameters
     ----------