gaspype/examples/thermodynamic_carbon_activity.md

# Carbon Activity

This example shows the equilibrium calculation for solid carbon.


```python
import gaspype as gp
import numpy as np
import matplotlib.pyplot as plt
```

Setting temperatures and pressure:


```python
t_range = np.array([600, 700, 800, 900, 1100, 1500])  # °C

p = 1e5  # Pa

fs = gp.fluid_system(['H2', 'H2O', 'CO2', 'CO', 'CH4'])
```

Equilibrium calculation for methane steam mixtures:


```python
ratio = np.linspace(0.01, 1.5, num=128)

fl = gp.fluid({'CH4': 1}, fs) + ratio * gp.fluid({'H2O': 1}, fs)
```

gaspype.carbon_activity supports currently only 0D fluids therefore we build this helper function:


```python
def partial_c_activity(fl: gp.fluid, t: float, p: float):
    fls = fl.array_composition.shape

    eq_fl = gp.equilibrium(fl, t, p)

    ret = np.zeros(fls[0])
    for i in range(fls[0]):
        ret[i] = gp.carbon_activity(gp.fluid(eq_fl.array_composition[i,:], fs), t, p)

    return ret
```

Now we use the helper function to calculate the carbon activitx for all
compositions in equilibrium_h2o times all temperatures in t_range:


```python
carbon_activity = np.vstack([partial_c_activity(fl, tc + 273.15, p) for tc in t_range])
```

Plot carbon activities, a activity of > 1 means there is thermodynamically the formation of sold carbon favored.


```python
fig, ax = plt.subplots(figsize=(6, 4), dpi=120)
ax.set_xlabel("H2O/CH4")
ax.set_ylabel("carbon activity")
ax.set_ylim(1e-1, 1e3)
ax.set_yscale('log')
ax.plot(ratio, carbon_activity.T)
ax.hlines(1, np.min(ratio), np.max(ratio), colors='k', linestyles='dashed')
ax.legend([f'{tc} °C' for tc in t_range])
```