Issue 729 ecker params

CHANGELOG.md

@@ -3,11 +3,15 @@
 ## Features
 
 -   Store variable slices in model for inspection ([#925](https://github.com/pybamm-team/PyBaMM/pull/925))
+-   Added LiNiCoO2 parameter set from Ecker et. al. ([#922](https://github.com/pybamm-team/PyBaMM/pull/922))
 -   Made t_plus (optionally) a function of electrolyte concentration, and added (1 + dlnf/dlnc) to models ([#921](https://github.com/pybamm-team/PyBaMM/pull/921))
 -   Added `DummySolver` for empty models ([#915](https://github.com/pybamm-team/PyBaMM/pull/915))
 -   Added functionality to broadcast to edges ([#891](https://github.com/pybamm-team/PyBaMM/pull/891))
 -   Reformatted and cleaned up `QuickPlot` ([#886](https://github.com/pybamm-team/PyBaMM/pull/886))
 -   Added thermal effects to lead-acid models ([#885](https://github.com/pybamm-team/PyBaMM/pull/885))
+-   Add new symbols `VariableDot`, representing the derivative of a variable wrt time,
+    and `StateVectorDot`, representing the derivative of a state vector wrt time
+    ([#858](https://github.com/pybamm-team/PyBaMM/issues/858))
 -   Added a helper function for info on function parameters ([#881](https://github.com/pybamm-team/PyBaMM/pull/881))
 -   Added additional notebooks showing how to create and compare models ([#877](https://github.com/pybamm-team/PyBaMM/pull/877))
 -   Added `Minimum`, `Maximum` and `Sign` operators

examples/notebooks/compare-comsol-discharge-curve.ipynb

@@ -214,7 +214,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.6"
+   "version": "3.6.9"
   }
  },
  "nbformat": 4,

examples/notebooks/models/DFN.ipynb

@@ -271,7 +271,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.6.9"
   }
  },
  "nbformat": 4,

pybamm/CITATIONS.txt

@@ -135,3 +135,37 @@ year={2020}
   doi          = {10.5281/zenodo.3597656},
   url          = {https://doi.org/10.5281/zenodo.3597656}
 }
+
+@article{ecker2015i,
+  title={Parameterization of a physico-chemical model of a lithium-ion battery i. determination of parameters},
+  author={Ecker, Madeleine and Tran, Thi Kim Dung and Dechent, Philipp and K{\"a}bitz, Stefan and Warnecke, Alexander and Sauer, Dirk Uwe},
+  journal={Journal of the Electrochemical Society},
+  volume={162},
+  number={9},
+  pages={A1836--A1848},
+  year={2015},
+  publisher={The Electrochemical Society}
+}
+
+@article{ecker2015ii,
+  title={Parameterization of a physico-chemical model of a lithium-ion battery ii. model validation},
+  author={Ecker, Madeleine and K{\"a}bitz, Stefan and Laresgoiti, Izaro and Sauer, Dirk Uwe},
+  journal={Journal of The Electrochemical Society},
+  volume={162},
+  number={9},
+  pages={A1849--A1857},
+  year={2015},
+  publisher={The Electrochemical Society}
+}
+
+@article{richardson2020,
+title = "Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation",
+journal = "Electrochimica Acta",
+volume = "339",
+pages = "135862",
+year = "2020",
+issn = "0013-4686",
+doi = "https://doi.org/10.1016/j.electacta.2020.135862",
+url = "http://www.sciencedirect.com/science/article/pii/S0013468620302541",
+author = "G. Richardson and I. Korotkin and R. Ranom and M. Castle and J.M. Foster",
+}

pybamm/expression_tree/symbol.py

@@ -737,7 +737,7 @@ def shape(self):
                 )
                 # Pick a y that won't cause RuntimeWarnings
                 y = np.linspace(0.1, 0.9, min_y_size)
-            evaluated_self = self.evaluate(0, y, y)
+            evaluated_self = self.evaluate(0, y, y, inputs="shape test")
 
         # Return shape of evaluated object
         if isinstance(evaluated_self, numbers.Number):

pybamm/input/discharge_data/Ecker_1C.csv

@@ -0,0 +1,31 @@
+20.3084233101775,4.10984760218981
+137.255118370379,4.06170981679401
+247.454888715569,4.02086563524606
+393.638257540821,3.98148017446767
+530.825726746058,3.94063599291972
+670.262170856298,3.91146157752832
+820.943489491555,3.87499355828908
+955.88198379179,3.84581914289769
+1097.56740280703,3.81226856519758
+1243.75077163228,3.79038775365404
+1383.18721574253,3.76121333826264
+1529.37058456778,3.73641508517996
+1666.55805377301,3.7247453190234
+1808.24347278826,3.70578194901899
+1947.6799168985,3.69848834517114
+2087.11636100874,3.68827729978416
+2231.05075492899,3.67514881285803
+2379.48309865925,3.66056160516233
+2521.16851767449,3.63576335207965
+2658.35598687973,3.60075405360997
+2802.29038079997,3.55407498898374
+2939.47785000521,3.51031336589665
+3081.16326902045,3.47384534665741
+3225.0976629407,3.43008372357031
+3344.29333290591,3.38194593817451
+3470.23592758612,3.30755117892646
+3553.44799907126,3.21273432890442
+3616.41929641137,3.11500003734325
+3652.40289489144,3.01872446655165
+3688.3864933715,2.89910936344693
+3715.37419223154,2.76636577341609

pybamm/input/discharge_data/Ecker_5C.csv

@@ -0,0 +1,33 @@
+0,4.00772806063782
+2.10996257174233,3.9630519063978
+9.53641973294314,3.90466605332464
+22.2674891521443,3.85148732048119
+40.7157517827462,3.80418814691602
+60.9764236014983,3.75781321732131
+82.7105988252504,3.72697310974463
+103.708022346502,3.69851401469471
+126.547325124005,3.67723564231538
+149.386627901507,3.65476333775538
+175.172937489009,3.63351237271449
+204.643005589013,3.60393814158189
+277.21304828527,3.55566182788309
+341.310446402776,3.51924603989306
+391.409562172782,3.4910575923102
+409.091603032784,3.47331305363065
+430.457402405285,3.45679670630482
+454.401832736538,3.43791647603876
+477.60951136529,3.41067186867334
+499.712062440292,3.38938664445941
+530.287258094045,3.35265909799465
+551.653057466548,3.32539736104271
+574.123984392801,3.29098230875862
+594.384656211552,3.25535276879001
+615.013703881554,3.214950926016
+634.169248146556,3.17572931175344
+650.377785601557,3.11737737526159
+664.37606794906,3.06736240853066
+677.63759859406,3.00540126815833
+685.373491470311,2.94219480684576
+693.846136049062,2.87660733300644
+701.213653074063,2.79787632742773
+706.002539140314,2.71195774734383

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/README.md

@@ -0,0 +1,12 @@
+# Graphite anode parameters
+
+Parameters for a graphite anode, from the papers:
+
+> 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.
+
+>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.
+
+The fits to data for the electrode and electrolyte properties are those provided
+by Dr. Simon O’Kane in the paper:
+
+> Richardson, Giles, et. al. "Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation." Electrochemica Acta 339 (2020): 135862

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_diffusivity_Ecker2015.py

@@ -0,0 +1,42 @@
+from pybamm import exp
+
+
+def graphite_diffusivity_Ecker2015(sto, T, T_inf, E_D_s, R_g):
+    """
+    Graphite diffusivity as a function of stochiometry [1, 2, 3].
+
+    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.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    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 = 8.4e-13 * exp(-11.3 * sto) + 8.2e-15
+    arrhenius = exp(-E_D_s / (R_g * T)) * exp(E_D_s / (R_g * 296))
+
+    return D_ref * arrhenius

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

@@ -0,0 +1,46 @@
+from pybamm import exp
+from scipy import constants
+
+
+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
+    ----------
+    .. [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.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    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
+    """
+
+    k_ref = 1.995 * 1e-10
+
+    # multiply by Faraday's constant to get correct units
+    F = constants.physical_constants["Faraday constant"][0]
+    m_ref = F * k_ref
+
+    arrhenius = exp(-E_r / (R_g * T)) * exp(E_r / (R_g * T_inf))
+
+    return m_ref * arrhenius

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_ocp_Ecker2015.csv

@@ -0,0 +1,41 @@
+0.0015151515151514694, 1.4325153374233128
+0.0060606060606061, 0.8619631901840491
+0.010606060606060619, 0.7914110429447854
+0.016666666666666607, 0.6595092024539877
+0.021212121212121238, 0.5797546012269938
+0.022727272727272707, 0.5245398773006136
+0.030303030303030276, 0.4754601226993864
+0.039393939393939315, 0.4141104294478526
+0.045454545454545414, 0.3680981595092023
+0.05303030303030298, 0.3312883435582821
+0.06666666666666665, 0.28220858895705514
+0.07878787878787874, 0.24846625766871155
+0.08939393939393936, 0.2239263803680982
+0.10151515151515145, 0.22085889570552153
+0.12727272727272732, 0.21165644171779152
+0.14242424242424245, 0.2024539877300613
+0.15909090909090917, 0.19938650306748462
+0.17727272727272725, 0.19325153374233128
+0.19393939393939397, 0.18404907975460127
+0.21363636363636362, 0.1809815950920246
+0.23333333333333328, 0.17177914110429437
+0.25757575757575757, 0.16564417177914104
+0.2787878787878788, 0.16257668711656437
+0.303030303030303, 0.15337423312883436
+0.32878787878787885, 0.14110429447852746
+0.35151515151515156, 0.13496932515337412
+0.3712121212121211, 0.13190184049079745
+0.39242424242424234, 0.128834355828221
+0.5681818181818183, 0.1257668711656441
+0.5878787878787879, 0.12269938650306744
+0.6060606060606062, 0.1165644171779141
+0.6272727272727272, 0.10122699386503076
+0.6545454545454545, 0.0950920245398772
+0.6742424242424243, 0.0950920245398772
+0.6939393939393939, 0.08895705521472386
+0.7181818181818183, 0.08895705521472386
+0.7393939393939393, 0.08588957055214719
+0.8909090909090911, 0.08282208588957074
+0.956060606060606, 0.08272208588957074
+0.9772727272727273, 0.07975460122699385
+1, 0.07055214723926384

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/graphite_ocp_Ecker2015_function.py

@@ -0,0 +1,62 @@
+from pybamm import exp, tanh
+
+
+def graphite_ocp_Ecker2015_function(sto):
+    """
+    Graphite OCP as a function of stochiometry [1, 2, 3].
+
+    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.
+    .. [3] Richardson, Giles, et. al. "Generalised single particle models for
+    high-rate operation of graded lithium-ion electrodes: Systematic derivation
+    and validation." Electrochemica Acta 339 (2020): 135862
+
+    Parameters
+    ----------
+    sto: :class: `numpy.Array`
+        Electrode stochiometry
+
+    Returns
+    -------
+    : double
+        Open circuit potential
+    """
+
+    # Graphite Anode from Ecker, Kabitz, Laresgoiti et al.
+    # Analytical fit (WebPlotDigitizer + gnuplot)
+    a = 0.716502
+    b = 369.028
+    c = 0.12193
+    d = 35.6478
+    e = 0.0530947
+    g = 0.0169644
+    h = 27.1365
+    i = 0.312832
+    j = 0.0199313
+    k = 28.5697
+    m = 0.614221
+    n = 0.931153
+    o = 36.328
+    p = 1.10743
+    q = 0.140031
+    r = 0.0189193
+    s = 21.1967
+    t = 0.196176
+
+    u_eq = (
+        a * exp(-b * sto)
+        + c * exp(-d * (sto - e))
+        - r * tanh(s * (sto - t))
+        - g * tanh(h * (sto - i))
+        - j * tanh(k * (sto - m))
+        - n * exp(o * (sto - p))
+        + q
+    )
+
+    return u_eq

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/measured_graphite_diffusivity_Ecker2015.csv

@@ -0,0 +1,23 @@
+0.04291659469592768,2.5318983605709854e-13
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