Source code for pybop.models.lithium_ion.weppner_huggins

import warnings

import numpy as np
from pybamm import DummySolver, Parameter, ParameterValues, citations
from pybamm import lithium_ion as pybamm_lithium_ion
from pybamm import t as pybamm_t



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class BaseWeppnerHuggins(pybamm_lithium_ion.BaseModel):
    """
    WeppnerHuggins Model for GITT. Credit: pybamm-param team.

    This model can be used with PyBOP through the `pybop.WeppnerHuggins` class.

    Parameters
    ----------
    name : str, optional
        The name of the model.
    **model_kwargs : optional
        Valid PyBaMM model option keys and their values, for example:
        parameter_set : pybamm.ParameterValues or dict, optional
            The parameters for the model. If None, default parameters provided by PyBaMM are used.
        geometry : dict, optional
            The geometry definitions for the model. If None, default geometry from PyBaMM is used.
        submesh_types : dict, optional
            The types of submeshes to use. If None, default submesh types from PyBaMM are used.
        var_pts : dict, optional
            The discretization points for each variable in the model. If None, default points from PyBaMM are used.
        spatial_methods : dict, optional
            The spatial methods used for discretization. If None, default spatial methods from PyBaMM are used.
        solver : pybamm.Solver, optional
            The solver to use for simulating the model. If None, the default solver from PyBaMM is used.
    """

    def __init__(self, name="Weppner & Huggins model", **model_kwargs):
        # Model kwargs (build, options) are not implemented, keeping here for consistent interface
        if model_kwargs is not dict(build=True):
            unused_kwargs_warning = "The input model_kwargs are not currently used by the Weppner & Huggins model."
            warnings.warn(unused_kwargs_warning, UserWarning, stacklevel=2)

        super().__init__({}, name)

        citations.register("""
            @article{Weppner1977,
            title={{Determination of the kinetic parameters
            of mixed-conducting electrodes and application to the system Li3Sb}},
            author={Weppner, W and Huggins, R A},
            journal={Journal of The Electrochemical Society},
            volume={124},
            number={10},
            pages={1569},
            year={1977},
            publisher={IOP Publishing}
            }
        """)

        # `self.param` is a class containing all the relevant parameters and functions for
        # this model. These are purely symbolic at this stage, and will be set by the
        # `ParameterValues` class when the model is processed.
        self.options["working electrode"] = "positive"

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        self._summary_variables = []



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        t = pybamm_t

        ######################
        # Parameters
        ######################


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        d_s = Parameter("Positive particle diffusivity [m2.s-1]")



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        c_s_max = Parameter("Maximum concentration in positive electrode [mol.m-3]")



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        i_app = self.param.current_density_with_time



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        U = Parameter("Reference OCP [V]")



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        U_prime = Parameter("Derivative of the OCP wrt stoichiometry [V]")



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        epsilon = Parameter("Positive electrode active material volume fraction")



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        r_particle = Parameter("Positive particle radius [m]")



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        a = 3 * (epsilon / r_particle)



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        l_w = self.param.p.L


        ######################
        # Governing equations
        ######################

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        u_surf = (
            (2 / (np.pi**0.5))
            * (i_app / ((d_s**0.5) * a * self.param.F * l_w))
            * (t**0.5)
        )

        # Linearised voltage

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        V = U + (U_prime * u_surf) / c_s_max

        ######################
        # (Some) variables
        ######################
        self.variables = {
            "Voltage [V]": V,
            "Time [s]": t,
        }

        # Set the built property on creation to prevent unnecessary model rebuilds

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        self._built = True


    @property

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    def default_geometry(self):
        return {}


    @property

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    def default_parameter_values(self):
        parameter_values = ParameterValues("Xu2019")
        parameter_values.update(
            {
                "Reference OCP [V]": 4.1821,
                "Derivative of the OCP wrt stoichiometry [V]": -1.38636,
            },
            check_already_exists=False,
        )
        return parameter_values


    @property

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    def default_submesh_types(self):
        return {}


    @property

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    def default_var_pts(self):
        return {}


    @property

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    def default_spatial_methods(self):
        return {}


    @property

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    def default_solver(self):
        return DummySolver()