116 lines
3.3 KiB
Markdown
116 lines
3.3 KiB
Markdown
# SOFC with Methane
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This example shows a 1D isothermal SOFC (Solid oxide fuel cell) model.
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The operating parameters chosen here are not necessary realistic.
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```python
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import gaspype as gp
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from gaspype.constants import R, F
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import numpy as np
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import matplotlib.pyplot as plt
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```
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Calculation of the local equilibrium compositions on the fuel and air
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side in counter flow along the fuel flow direction:
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```python
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fuel_utilization = 0.90
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air_utilization = 0.5
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t = 800 + 273.15 # K
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p = 1e5 # Pa
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fs = gp.fluid_system('H2, H2O, O2, CH4, CO, CO2')
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feed_fuel = gp.fluid({'CH4': 1, 'H2O': 0.1}, fs)
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o2_full_conv = np.sum(gp.elements(feed_fuel)[['H', 'C' ,'O']] * [1/4, 1, -1/2])
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feed_air = gp.fluid({'O2': 1, 'N2': 4}) * o2_full_conv * fuel_utilization / air_utilization
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conversion = np.linspace(0, fuel_utilization, 32)
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perm_oxygen = o2_full_conv * conversion * gp.fluid({'O2': 1})
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fuel_side = gp.equilibrium(feed_fuel + perm_oxygen, t, p)
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air_side = gp.equilibrium(feed_air - perm_oxygen, t, p)
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```
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Plot compositions of the fuel and air side:
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```python
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fig, ax = plt.subplots()
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ax.set_xlabel("Conversion")
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ax.set_ylabel("Molar fraction")
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ax.plot(conversion, fuel_side.get_x(), '-')
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ax.legend(fuel_side.species)
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fig, ax = plt.subplots()
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ax.set_xlabel("Conversion")
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ax.set_ylabel("Molar fraction")
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ax.plot(conversion, air_side.get_x(), '-')
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ax.legend(air_side.species)
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```
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Calculation of the oxygen partial pressures:
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```python
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o2_fuel_side = gp.oxygen_partial_pressure(fuel_side, t, p)
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o2_air_side = air_side.get_x('O2') * p
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```
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Plot oxygen partial pressures:
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```python
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fig, ax = plt.subplots()
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ax.set_xlabel("Conversion")
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ax.set_ylabel("Oxygen partial pressure / Pa")
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ax.set_yscale('log')
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ax.plot(conversion, np.stack([o2_fuel_side, o2_air_side], axis=1), '-')
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ax.legend(['o2_fuel_side', 'o2_air_side'])
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```
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Calculation of the local nernst potential between fuel and air side:
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```python
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z_O2 = 4
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nernst_voltage = R*t / (z_O2*F) * np.log(o2_air_side/o2_fuel_side)
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```
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Plot nernst potential:
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```python
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fig, ax = plt.subplots()
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ax.set_xlabel("Conversion")
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ax.set_ylabel("Voltage / V")
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ax.plot(conversion, nernst_voltage, '-')
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print(np.min(nernst_voltage))
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```
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The model uses between each node a constant conversion. Because
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current density depends strongly on the position along the cell
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the constant conversion does not relate to a constant distance.
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To calculate the local current density (**node_current**) as well
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as the total cell current (**terminal_current**) the (relative)
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physical distance between the nodes (**dz**) must be calculated:
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```python
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cell_voltage = 0.77 # V
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ASR = 0.2 # Ohm*cm²
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node_current = (nernst_voltage - cell_voltage) / ASR # mA/cm² (Current density at each node)
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current = (node_current[1:] + node_current[:-1]) / 2 # mA/cm² (Average current density between the nodes)
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dz = 1/current / np.sum(1/current) # Relative distance between each node
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terminal_current = np.sum(current * dz) # mA/cm² (Total cell current per cell area)
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print(f'Terminal current: {terminal_current:.2f} A/cm²')
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```
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Plot the local current density:
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```python
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z_position = np.concatenate([[0], np.cumsum(dz)]) # Relative position of each node
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fig, ax = plt.subplots()
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ax.set_xlabel("Relative cell position")
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ax.set_ylabel("Current density / A/cm²")
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ax.plot(z_position, node_current, '-')
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```
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