> ## Documentation Index
> Fetch the complete documentation index at: https://mintlify.com/pybamm-team/PyBaMM/llms.txt
> Use this file to discover all available pages before exploring further.

# Lead-Acid Models

> Physics-based lead-acid battery models in PyBaMM, including the Full porous-electrode model, the Leading-Order Quasi-Static (LOQS) model, and BasicFull.

PyBaMM includes a set of physics-based models for lead-acid batteries derived from the Newman-Tiedemann porous-electrode framework. All models are available under the `pybamm.lead_acid` namespace.

<Note>
  Lead-acid models use `pybamm.LeadAcidParameters` and default to the `Sulzer2019` parameter set. Unlike lithium-ion models, there are no particles: the electrode active material is modelled as a solid reactant with no diffusion.
</Note>

## Available models

| Model       | Electrolyte diffusion              | Spatial resolution | Use case                          |
| ----------- | ---------------------------------- | ------------------ | --------------------------------- |
| `Full`      | Full (spatially resolved)          | Full 1D            | High-fidelity simulation          |
| `LOQS`      | Leading-order (spatially averaged) | 0D / 1D            | Fast simulation, parameter sweeps |
| `BasicFull` | Full                               | Full 1D            | Education and model exploration   |

***

## Models

<Tabs>
  <Tab title="Full">
    ### Full model

    The `Full` model is a porous-electrode model for lead-acid batteries based on the Newman-Tiedemann framework as described in Sulzer et al. (2019). It resolves spatial distributions of electrolyte concentration and potential, electrode potential, and porosity across the cell sandwich.

    **When to use:** High-accuracy simulations where spatial gradients in electrolyte concentration and porosity are important, including during high-rate discharge or charge.

    **Reference:** Sulzer, V., et al. (2019). *Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model*. Journal of The Electrochemical Society.

    ```python theme={null}
    import pybamm

    model = pybamm.lead_acid.Full()
    print(model.name)  # 'Full model'

    param = model.default_parameter_values  # Sulzer2019
    sim = pybamm.Simulation(model, parameter_values=param)
    sim.solve([0, 3600])
    sim.plot()
    ```
  </Tab>

  <Tab title="LOQS">
    ### Leading-Order Quasi-Static model

    The `LOQS` model is derived by an asymptotic expansion in the applied current, retaining only the leading-order terms. Electrolyte concentration and porosity are spatially uniform (x-averaged). This makes the model significantly faster than the Full model.

    **When to use:** Rapid simulations, state estimation, parameter identification, or any case where spatial gradients in the electrolyte are secondary.

    **Reference:** Sulzer, V., et al. (2019). *Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part II. Asymptotic Analysis*. Journal of The Electrochemical Society.

    <Note>
      The LOQS model does not use a Jacobian by default when `dimensionality=0`. This makes it particularly efficient for 0D simulations.
    </Note>

    ```python theme={null}
    import pybamm

    model = pybamm.lead_acid.LOQS()
    print(model.name)  # 'LOQS model'

    sim = pybamm.Simulation(model)
    sim.solve([0, 3600])
    sim.plot()
    ```
  </Tab>

  <Tab title="BasicFull">
    ### BasicFull

    The `BasicFull` model implements the same physics as `Full` but in a single self-contained class, making the governing equations directly visible. It does not use the submodel architecture and is less flexible, but is easier to read and modify for educational purposes.

    **When to use:** Understanding the governing equations, developing new models, or teaching. For production use, prefer `pybamm.lead_acid.Full`.

    **Reference:** Sulzer, V., et al. (2019). *Faster Lead-Acid Battery Simulations from Porous-Electrode Theory: Part I. Physical Model*. Journal of The Electrochemical Society.

    ```python theme={null}
    import pybamm

    model = pybamm.lead_acid.BasicFull()
    print(model.name)  # 'Basic full model'

    sim = pybamm.Simulation(model)
    sim.solve([0, 3600])
    sim.plot()
    ```
  </Tab>
</Tabs>

***

## Lead-acid specific options

<AccordionGroup>
  <Accordion title="Hydrolysis (oxygen evolution)">
    Lead-acid cells produce oxygen at the positive plate during overcharge via electrolyte hydrolysis. Enabling this option adds oxygen diffusion and reaction submodels.

    | Option         | Values              | Default   |
    | -------------- | ------------------- | --------- |
    | `"hydrolysis"` | `"false"`, `"true"` | `"false"` |

    <Warning>
      When `"hydrolysis"` is `"true"`, `"surface form"` cannot be `"false"`. Use `"algebraic"` or `"differential"` instead.
    </Warning>

    ```python theme={null}
    model = pybamm.lead_acid.Full(
        options={
            "hydrolysis": "true",
            "surface form": "algebraic",
        }
    )
    ```
  </Accordion>

  <Accordion title="Convection">
    Gas evolution during charge drives electrolyte convection. This can be modelled with a uniform transverse or fully resolved transverse convection model.

    | Option         | Values                                                | Default  |
    | -------------- | ----------------------------------------------------- | -------- |
    | `"convection"` | `"none"`, `"uniform transverse"`, `"full transverse"` | `"none"` |

    ```python theme={null}
    model = pybamm.lead_acid.Full(
        options={"convection": "uniform transverse"}
    )
    ```
  </Accordion>

  <Accordion title="Thermal">
    | Option      | Values                                               | Default        |
    | ----------- | ---------------------------------------------------- | -------------- |
    | `"thermal"` | `"isothermal"`, `"lumped"`, `"x-lumped"`, `"x-full"` | `"isothermal"` |

    ```python theme={null}
    model = pybamm.lead_acid.Full(
        options={"thermal": "lumped"}
    )
    ```
  </Accordion>

  <Accordion title="Operating mode">
    Control how the external circuit condition is applied. The LOQS model supports callable operating modes via an algebraic constraint.

    | Option             | Values                                                                  | Default     |
    | ------------------ | ----------------------------------------------------------------------- | ----------- |
    | `"operating mode"` | `"current"`, `"voltage"`, `"power"`, `"resistance"`, `"CCCV"`, callable | `"current"` |

    ```python theme={null}
    model = pybamm.lead_acid.LOQS(
        options={"operating mode": "voltage"}
    )
    ```
  </Accordion>
</AccordionGroup>

### Example with options

```python theme={null}
import pybamm

# Full lead-acid model with oxygen evolution and uniform convection
model = pybamm.lead_acid.Full(
    options={
        "hydrolysis": "true",
        "surface form": "algebraic",
        "convection": "uniform transverse",
        "thermal": "isothermal",
    }
)

param = model.default_parameter_values  # Sulzer2019
sim = pybamm.Simulation(model, parameter_values=param)
sim.solve([0, 3600])
sim.plot()
```

<Tip>
  Call `pybamm.print_citations()` after running a simulation to get the full citation list for the models and parameters used.
</Tip>