# Tutorial 10: Fluid Flow Simulation

```{note}
This tutorial is available as a Python script [`examples/10_flow_simulation.py`](https://github.com/GeoBrain-Project/geobrain/blob/main/examples/10_flow_simulation.py) and an interactive Jupyter notebook [`examples/notebooks/10_flow_simulation.ipynb`](https://github.com/GeoBrain-Project/geobrain/blob/main/examples/notebooks/10_flow_simulation.ipynb).
```

Simulate oil-water two-phase fluid flow through porous media using
GeoBrain's differentiable reservoir simulator.

## What You Will Learn

- Set up a reservoir model with `ReservoirModel`
- Configure grid, rock properties, PVT data, and relative permeability
- Add production and injection wells
- Run flow simulation with `FlowPropagator`
- Visualize production curves and pressure/saturation maps

## Key Concepts

**Two-phase flow** simulation solves the coupled pressure and saturation
equations on a reservoir grid. GeoBrain's flow module is fully differentiable,
enabling gradient-based history matching and optimization of well placement
or injection strategy.

Water is injected through an injector well to maintain reservoir pressure and
displace oil toward the producer. The simulator solves pressure and transport
equations at each time step, updating the saturation front as it advances
through the heterogeneous permeability field. Production curves record the
oil rate, water rate, and water cut at the producer over time.

## Code

```python
from geobrain.physics.flow import ReservoirModel, FlowPropagator, Well

model = ReservoirModel(
    grid=grid_config,
    rock=rock_props,
    pvt=pvt_data,
)

model.add_well(Well(name='INJ1', type='injector', ...))
model.add_well(Well(name='PROD1', type='producer', ...))

propagator = FlowPropagator(model)
result = propagator.run(n_steps=100, dt=1.0)
```

## Results

The pressure and saturation fields evolve as injected water displaces oil
toward the production well. The maps below show snapshots at key time steps.

```{figure} ../../examples/figs/10_state_maps.png
:width: 100%
:name: fig-10-state-maps

Pressure and saturation maps at key time steps.
```

Production curves capture the time history of oil rate, water rate, and water
cut at the producer. Water breakthrough is visible as the oil rate declines
and the water cut rises sharply.

```{figure} ../../examples/figs/10_production_curves.png
:width: 100%
:name: fig-10-production-curves

Production curves: oil rate, water rate, and water cut.
```

The following figure illustrates the full reservoir state evolution, tracking
how the saturation front progresses through the domain at selected time steps.

```{figure} ../../examples/figs/10_key_time_steps.png
:width: 100%
:name: fig-10-key-time-steps

Reservoir state evolution at key time steps.
```

## Full Example

See [`examples/10_flow_simulation.py`](https://github.com/GeoBrain-Project/geobrain/blob/main/examples/10_flow_simulation.py).