Merge pull request pybamm-team#1073 from pybamm-team/issue-836-add-li…

…thium-plating Issue 836 add lithium plating
brosaplanella · Jun 24, 2020 · cc5d9f1 · cc5d9f1
2 parents 7da7414 + 64f89ba
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diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -7,6 +7,7 @@
 -   Added some new solvers for algebraic models ([#1059](https://github.com/pybamm-team/PyBaMM/pull/1059))
 -   Added `length_scales` attribute to models ([#1058](https://github.com/pybamm-team/PyBaMM/pull/1058))
 -   Added averaging in secondary dimensions ([#1057](https://github.com/pybamm-team/PyBaMM/pull/1057))
+-   Added SEI reaction based on Yang et. al. 2017 and reduction in porosity ([#1009](https://github.com/pybamm-team/PyBaMM/issues/1009)) 
 
 ## Optimizations
 

diff --git a/docs/source/models/submodels/interface/sei.rst b/docs/source/models/submodels/interface/sei.rst
@@ -20,4 +20,7 @@ SEI models
     :members:
 
 .. autoclass:: pybamm.sei.SolventDiffusionLimited
+    :members:
+
+.. autoclass:: pybamm.sei.EcReactionLimited
     :members:
diff --git a/examples/notebooks/Getting Started/Tutorial 2 - Setting Parameter Values.ipynb b/examples/notebooks/Getting Started/Tutorial 2 - Setting Parameter Values.ipynb
@@ -18,7 +18,15 @@
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
    "source": [
     "%pip install pybamm -q    # install PyBaMM if it is not installed\n",
     "import pybamm"
@@ -93,12 +101,12 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "2237d34280454f28ba40140a92f7504d",
+       "model_id": "4a4e0be8318b453ea00394c0f5dbdea5",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=3599.9999999999995, step=35.99999999999999),…"
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
       ]
      },
      "metadata": {},
@@ -201,12 +209,12 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "cbf8ad0de78e47f982f27d1e7e64c9c3",
+       "model_id": "fb29cf7606614252a6a459832fc76c6a",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=1747.0357219251337, step=17.470357219251337)…"
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=1747.0357219251334, step=17.470357219251333)…"
       ]
      },
      "metadata": {},
@@ -254,7 +262,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -265,22 +273,26 @@
        " 'Bulk solvent concentration [mol.m-3]': 2636.0,\n",
        " 'Cation transference number': 0.4,\n",
        " 'Cell capacity [A.h]': 0.680616,\n",
+       " 'Cell cooling surface area [m2]': 0.0569,\n",
+       " 'Cell volume [m3]': 7.8e-06,\n",
        " 'Current function [A]': 1.36,\n",
+       " 'EC diffusivity [m2.s-1]': 2e-18,\n",
+       " 'EC initial concentration in electrolyte [mol.m-3]': 4541.0,\n",
        " 'Edge heat transfer coefficient [W.m-2.K-1]': 0.3,\n",
        " 'Electrode height [m]': 0.13699999999999998,\n",
        " 'Electrode width [m]': 0.207,\n",
-       " 'Electrolyte conductivity [S.m-1]': <function electrolyte_conductivity_Capiglia1999 at 0x7f7dd1166400>,\n",
-       " 'Electrolyte diffusivity [m2.s-1]': <function electrolyte_diffusivity_Capiglia1999 at 0x7f7dd1166378>,\n",
+       " 'Electrolyte conductivity [S.m-1]': <function electrolyte_conductivity_Capiglia1999 at 0x1334bf560>,\n",
+       " 'Electrolyte diffusivity [m2.s-1]': <function electrolyte_diffusivity_Capiglia1999 at 0x1334bf3b0>,\n",
        " 'Initial concentration in electrolyte [mol.m-3]': 1000.0,\n",
        " 'Initial concentration in negative electrode [mol.m-3]': 19986.609595075,\n",
        " 'Initial concentration in positive electrode [mol.m-3]': 30730.755438556498,\n",
-       " 'Initial inner SEI thickness [m]': 7.5e-09,\n",
-       " 'Initial outer SEI thickness [m]': 7.5e-09,\n",
+       " 'Initial inner SEI thickness [m]': 2.5e-09,\n",
+       " 'Initial outer SEI thickness [m]': 2.5e-09,\n",
        " 'Initial temperature [K]': 298.15,\n",
        " 'Inner SEI electron conductivity [S.m-1]': 8.95e-14,\n",
        " 'Inner SEI lithium interstitial diffusivity [m2.s-1]': 1.0000000000000001e-20,\n",
        " 'Inner SEI open-circuit potential [V]': 0.1,\n",
-       " 'Inner SEI partial molar volume [m3.mol-1]': 3e-06,\n",
+       " 'Inner SEI partial molar volume [m3.mol-1]': 9.585e-05,\n",
        " 'Inner SEI reaction proportion': 0.5,\n",
        " 'Lithium interstitial reference concentration [mol.m-3]': 15.0,\n",
        " 'Lower voltage cut-off [V]': 3.105,\n",
@@ -294,17 +306,17 @@
        " 'Negative current collector thickness [m]': 2.5e-05,\n",
        " 'Negative electrode Bruggeman coefficient (electrode)': 1.5,\n",
        " 'Negative electrode Bruggeman coefficient (electrolyte)': 1.5,\n",
-       " 'Negative electrode OCP [V]': <function graphite_mcmb2528_ocp_Dualfoil1998 at 0x7f7dd1160d90>,\n",
-       " 'Negative electrode OCP entropic change [V.K-1]': <function graphite_entropic_change_Moura2016 at 0x7f7e28275d08>,\n",
+       " 'Negative electrode OCP [V]': <function graphite_mcmb2528_ocp_Dualfoil1998 at 0x1332dab90>,\n",
+       " 'Negative electrode OCP entropic change [V.K-1]': <function graphite_entropic_change_Moura2016 at 0x1332dae60>,\n",
        " 'Negative electrode active material volume fraction': 0.7,\n",
        " 'Negative electrode cation signed stoichiometry': -1.0,\n",
        " 'Negative electrode charge transfer coefficient': 0.5,\n",
        " 'Negative electrode conductivity [S.m-1]': 100.0,\n",
        " 'Negative electrode density [kg.m-3]': 1657.0,\n",
-       " 'Negative electrode diffusivity [m2.s-1]': <function graphite_mcmb2528_diffusivity_Dualfoil1998 at 0x7f7e29bc4510>,\n",
+       " 'Negative electrode diffusivity [m2.s-1]': <function graphite_mcmb2528_diffusivity_Dualfoil1998 at 0x1332aa170>,\n",
        " 'Negative electrode double-layer capacity [F.m-2]': 0.2,\n",
        " 'Negative electrode electrons in reaction': 1.0,\n",
-       " 'Negative electrode exchange-current density [A.m-2]': <function graphite_electrolyte_exchange_current_density_Dualfoil1998 at 0x7f7e28275bf8>,\n",
+       " 'Negative electrode exchange-current density [A.m-2]': <function graphite_electrolyte_exchange_current_density_Dualfoil1998 at 0x1332dad40>,\n",
        " 'Negative electrode porosity': 0.3,\n",
        " 'Negative electrode specific heat capacity [J.kg-1.K-1]': 700.0,\n",
        " 'Negative electrode surface area to volume ratio [m-1]': 180000.0,\n",
@@ -319,7 +331,7 @@
        " 'Number of cells connected in series to make a battery': 1.0,\n",
        " 'Number of electrodes connected in parallel to make a cell': 1.0,\n",
        " 'Outer SEI open-circuit potential [V]': 0.8,\n",
-       " 'Outer SEI partial molar volume [m3.mol-1]': 3e-06,\n",
+       " 'Outer SEI partial molar volume [m3.mol-1]': 9.585e-05,\n",
        " 'Outer SEI solvent diffusivity [m2.s-1]': 2.5000000000000002e-22,\n",
        " 'Positive current collector conductivity [S.m-1]': 35500000.0,\n",
        " 'Positive current collector density [kg.m-3]': 2707.0,\n",
@@ -329,17 +341,17 @@
        " 'Positive current collector thickness [m]': 2.5e-05,\n",
        " 'Positive electrode Bruggeman coefficient (electrode)': 1.5,\n",
        " 'Positive electrode Bruggeman coefficient (electrolyte)': 1.5,\n",
-       " 'Positive electrode OCP [V]': <function lico2_ocp_Dualfoil1998 at 0x7f7dd11661e0>,\n",
-       " 'Positive electrode OCP entropic change [V.K-1]': <function lico2_entropic_change_Moura2016 at 0x7f7dd1166268>,\n",
+       " 'Positive electrode OCP [V]': <function lico2_ocp_Dualfoil1998 at 0x1334bf050>,\n",
+       " 'Positive electrode OCP entropic change [V.K-1]': <function lico2_entropic_change_Moura2016 at 0x1334bf320>,\n",
        " 'Positive electrode active material volume fraction': 0.7,\n",
        " 'Positive electrode cation signed stoichiometry': -1.0,\n",
        " 'Positive electrode charge transfer coefficient': 0.5,\n",
        " 'Positive electrode conductivity [S.m-1]': 10.0,\n",
        " 'Positive electrode density [kg.m-3]': 3262.0,\n",
-       " 'Positive electrode diffusivity [m2.s-1]': <function lico2_diffusivity_Dualfoil1998 at 0x7f7e30e82268>,\n",
+       " 'Positive electrode diffusivity [m2.s-1]': <function lico2_diffusivity_Dualfoil1998 at 0x1332daf80>,\n",
        " 'Positive electrode double-layer capacity [F.m-2]': 0.2,\n",
        " 'Positive electrode electrons in reaction': 1.0,\n",
-       " 'Positive electrode exchange-current density [A.m-2]': <function lico2_electrolyte_exchange_current_density_Dualfoil1998 at 0x7f7dd1166158>,\n",
+       " 'Positive electrode exchange-current density [A.m-2]': <function lico2_electrolyte_exchange_current_density_Dualfoil1998 at 0x1334bf200>,\n",
        " 'Positive electrode porosity': 0.3,\n",
        " 'Positive electrode specific heat capacity [J.kg-1.K-1]': 700.0,\n",
        " 'Positive electrode surface area to volume ratio [m-1]': 150000.0,\n",
@@ -355,21 +367,24 @@
        " 'Reference OCP vs SHE in the negative electrode [V]': nan,\n",
        " 'Reference OCP vs SHE in the positive electrode [V]': nan,\n",
        " 'Reference temperature [K]': 298.15,\n",
+       " 'SEI kinetic rate constant [m.s-1]': 1e-12,\n",
+       " 'SEI open-circuit potential [V]': 0.4,\n",
        " 'SEI reaction exchange current density [A.m-2]': 1.5e-07,\n",
-       " 'SEI resistivity [Ohm.m]': 1000000.0,\n",
+       " 'SEI resistivity [Ohm.m]': 5000000.0,\n",
        " 'Separator Bruggeman coefficient (electrode)': 1.5,\n",
        " 'Separator Bruggeman coefficient (electrolyte)': 1.5,\n",
        " 'Separator density [kg.m-3]': 397.0,\n",
        " 'Separator porosity': 1.0,\n",
        " 'Separator specific heat capacity [J.kg-1.K-1]': 700.0,\n",
        " 'Separator thermal conductivity [W.m-1.K-1]': 0.16,\n",
        " 'Separator thickness [m]': 2.5e-05,\n",
+       " 'Total heat transfer coefficient [W.m-2.K-1]': 10.0,\n",
        " 'Typical current [A]': 0.680616,\n",
        " 'Typical electrolyte concentration [mol.m-3]': 1000.0,\n",
        " 'Upper voltage cut-off [V]': 4.7}"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -387,15 +402,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Electrolyte conductivity [S.m-1]\t<function electrolyte_conductivity_Capiglia1999 at 0x7f7dd1166400>\n",
-      "Electrolyte diffusivity [m2.s-1]\t<function electrolyte_diffusivity_Capiglia1999 at 0x7f7dd1166378>\n",
+      "EC initial concentration in electrolyte [mol.m-3]\t4541.0\n",
+      "Electrolyte conductivity [S.m-1]\t<function electrolyte_conductivity_Capiglia1999 at 0x1334bf560>\n",
+      "Electrolyte diffusivity [m2.s-1]\t<function electrolyte_diffusivity_Capiglia1999 at 0x1334bf3b0>\n",
       "Initial concentration in electrolyte [mol.m-3]\t1000.0\n",
       "Negative electrode Bruggeman coefficient (electrolyte)\t1.5\n",
       "Positive electrode Bruggeman coefficient (electrolyte)\t1.5\n",
@@ -432,7 +448,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.8"
+   "version": "3.7.7"
   }
  },
  "nbformat": 4,

diff --git a/examples/notebooks/models/lead-acid.ipynb b/examples/notebooks/models/lead-acid.ipynb
@@ -13,7 +13,7 @@
    "source": [
     "We compare a standard porous-electrode model for lead-acid batteries with two asymptotic reductions. For a more in-depth introduction to PyBaMM models, see the [SPM notebook](./SPM.ipynb). Further details on the models can be found in [[1]](#ref)\n",
     "\n",
-    "<a name=\"ref\">[1]</a> Sulzer, Valentin, S. Jon Chapman, Colin P. Please, David A. Howey, and Charles W. Monroe. \"Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: II. Asymptotic Analysis.\" arXiv preprint arXiv:1902.01774 (2019)."
+    "<a name=\"ref\">[1]</a> Sulzer, V., Chapman, S. J., Please, C. P., Howey, D. A., & Monroe, C. W. (2019). “Faster Lead-Acid Battery Simulations from Porous Electrode Theory:  II. Asymptotic Analysis”. Journal of The Electrochemical Society, 166(12), A2372-A2382."
    ]
   },
   {
@@ -430,4 +430,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}
diff --git a/examples/notebooks/using-model-options_thermal-example.ipynb b/examples/notebooks/using-model-options_thermal-example.ipynb
@@ -186,7 +186,7 @@
    "metadata": {},
    "source": [
     "## References\n",
-    "[1] SG Marquis, V Sulzer, R Timms, CP Please and SJ Chapman. “An asymptotic derivation of a single particle model with electrolyte”. In: arXiv preprint arXiv:1905.12553 (2019)."
+    "[1] Marquis, S. G., Sulzer, V.,  Timms, R.,  Please, C. P.,  &  Chapman, S. J. (2019). “An  asymptotic derivation of a single particle model with electrolyte”. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.0341915jes), 166(15), A3693-A3706. "
    ]
   },
   {
@@ -218,4 +218,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}
diff --git a/examples/notebooks/using-submodels.ipynb b/examples/notebooks/using-submodels.ipynb
@@ -590,7 +590,7 @@
    "metadata": {},
    "source": [
     "## References\n",
-    "[1] SG Marquis, V Sulzer, R Timms, CP Please and SJ Chapman. “An asymptotion derivation of a single particle model with electrolyte”. In: arXiv preprint arXiv:1905.12553 (2019).\n",
+    "[1] Marquis, S. G., Sulzer, V.,  Timms, R.,  Please, C. P.,  &  Chapman, S. J. (2019). “An  asymptotic derivation of a single particle model with electrolyte”. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.0341915jes), 166(15), A3693-A3706.\n",
     "\n",
     "[2] M Doyle, TF Fuller and J Newman. \"Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell.\" Journal of the Electrochemical Society 140.6 (1993): 1526-1533."
    ]
@@ -624,4 +624,4 @@
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}
diff --git a/examples/scripts/cycling_ageing_yang.py b/examples/scripts/cycling_ageing_yang.py
@@ -0,0 +1,51 @@
+import pybamm as pb
+
+pb.set_logging_level("INFO")
+options = {"sei": "ec reaction limited", "sei porosity change": True}
+param = pb.ParameterValues(chemistry=pb.parameter_sets.Ramadass2004)
+model = pb.lithium_ion.DFN(options)
+experiment = pb.Experiment(
+    [
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/10",
+        "Rest for 5 minutes",
+        "Discharge at 2 C until 2.8 V",
+        "Rest for 5 minutes",
+    ]
+    * 2
+    + [
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at C/3 until 2.8 V",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 1 C until 2.8 V",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 2 C until 2.8 V",
+        "Charge at 1 C until 4.2 V",
+        "Hold at 4.2 V until C/20",
+        "Rest for 30 minutes",
+        "Discharge at 3 C until 2.8 V",
+    ]
+)
+sim = pb.Simulation(model, experiment=experiment, parameter_values=param)
+sim.solve(solver=pb.CasadiSolver(mode="safe", dt_max=120))
+sim.plot(
+    [
+        "Current [A]",
+        "Total current density [A.m-2]",
+        "Terminal voltage [V]",
+        "Discharge capacity [A.h]",
+        "Electrolyte potential [V]",
+        "Electrolyte concentration [mol.m-3]",
+        "Total negative electrode sei thickness",
+        "Negative electrode porosity",
+        "X-averaged negative electrode porosity",
+        "Negative electrode sei interfacial current density [A.m-2]",
+        "X-averaged total negative electrode sei thickness [m]",
+    ]
+)
diff --git a/pybamm/__init__.py b/pybamm/__init__.py
@@ -162,7 +162,6 @@ def version(formatted=False):
 from .parameters import electrical_parameters
 from .parameters import thermal_parameters
 from .parameters import standard_parameters_lithium_ion, standard_parameters_lead_acid
-from .parameters import sei_parameters
 from .parameters import parameter_sets
 
 

diff --git a/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/README.md b/pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/README.md
@@ -0,0 +1,8 @@
+# Graphite anode parameters
+
+Parameters for a graphite anode, from the paper
+
+> Marquis, S. G., Sulzer, V.,  Timms, R.,  Please, C. P.,  &  Chapman, S. J. (2019). “An  asymptotic derivation of a single particle model with electrolyte”. [Journal of The Electrochemical Society](https://doi.org/10.1149/2.0341915jes), 166(15), A3693-A3706. 
+> P. Ramadass, Bala Haran, Parthasarathy M. Gomadam, Ralph White, and Branko N. Popov.["Development of First Principles Capacity Fade Model for Li-Ion Cells."](https://scholarcommons.sc.edu/cgi/viewcontent.cgi?article=1161&context=eche_facpub) (2004)
+
+and references therein.
diff --git a/...nodes/graphite_Ramadass2004/graphite_electrolyte_exchange_current_density_Ramadass2004.py b/...nodes/graphite_Ramadass2004/graphite_electrolyte_exchange_current_density_Ramadass2004.py
@@ -0,0 +1,37 @@
+from pybamm import exp, constants, standard_parameters_lithium_ion
+
+
+def graphite_electrolyte_exchange_current_density_Ramadass2004(c_e, c_s_surf, T):
+    """
+    Exchange-current density for Butler-Volmer reactions between graphite and LiPF6 in
+    EC:DMC.
+
+    References
+    ----------
+    .. [1] P. Ramadass, Bala Haran, Parthasarathy M. Gomadam, Ralph White, and Branko
+    N. Popov. "Development of First Principles Capacity Fade Model for Li-Ion Cells."
+    (2004)
+
+    Parameters
+    ----------
+    c_e : :class:`pybamm.Symbol`
+        Electrolyte concentration [mol.m-3]
+    c_s_surf : :class:`pybamm.Symbol`
+        Particle concentration [mol.m-3]
+    T : :class:`pybamm.Symbol`
+        Temperature [K]
+
+    Returns
+    -------
+    :class:`pybamm.Symbol`
+        Exchange-current density [A.m-2]
+    """
+    m_ref = 4.854 * 10 ** (-6)  # (A/m2)(mol/m3)**1.5
+    E_r = 37480
+    arrhenius = exp(E_r / constants.R * (1 / 298.15 - 1 / T))
+
+    c_n_max = standard_parameters_lithium_ion.c_n_max
+
+    return (
+        m_ref * arrhenius * c_e ** 0.5 * c_s_surf ** 0.5 * (c_n_max - c_s_surf) ** 0.5
+    )