gaspype/examples/sofc_methane.md

SOFC with Methane

This example shows a 1D isothermal SOFC (Solid oxide fuel cell) model.

The operating parameters chosen here are not necessarily realistic due to constraints not included in this model. Under the example condition the formation of solid carbon is for example very likely. A pre-reforming step is typically applied when operating on methane.

import gaspype as gp
from gaspype.constants import R, F
import numpy as np
import matplotlib.pyplot as plt

Calculate equilibrium compositions for fuel and air sides in counter flow along the fuel flow direction:

fuel_utilization = 0.90
air_utilization = 0.5
t = 800 + 273.15  # K
p = 1e5  # Pa

fs = gp.fluid_system('H2, H2O, O2, CH4, CO, CO2')
feed_fuel = gp.fluid({'CH4': 1, 'H2O': 0.1}, fs)

o2_full_conv = np.sum(gp.elements(feed_fuel)[['H', 'C' ,'O']] * [1/4, 1, -1/2])

feed_air = gp.fluid({'O2': 1, 'N2': 4}) * o2_full_conv * fuel_utilization / air_utilization

conversion = np.linspace(0, fuel_utilization, 32)
perm_oxygen = o2_full_conv * conversion * gp.fluid({'O2': 1})

fuel_side = gp.equilibrium(feed_fuel + perm_oxygen, t, p)
air_side  = gp.equilibrium(feed_air  - perm_oxygen, t, p)

Plot compositions of the fuel and air side:

fig, ax = plt.subplots()
ax.set_xlabel("Conversion")
ax.set_ylabel("Molar fraction")
ax.plot(conversion, fuel_side.get_x(), '-')
ax.legend(fuel_side.species)

fig, ax = plt.subplots()
ax.set_xlabel("Conversion")
ax.set_ylabel("Molar fraction")
ax.plot(conversion, air_side.get_x(), '-')
ax.legend(air_side.species)

Calculation of the oxygen partial pressures:

o2_fuel_side = gp.oxygen_partial_pressure(fuel_side, t, p)
o2_air_side = air_side.get_x('O2') * p

Plot oxygen partial pressures:

fig, ax = plt.subplots()
ax.set_xlabel("Conversion")
ax.set_ylabel("Oxygen partial pressure / Pa")
ax.set_yscale('log')
ax.plot(conversion, np.stack([o2_fuel_side, o2_air_side], axis=1), '-')
ax.legend(['o2_fuel_side', 'o2_air_side'])

Calculation of the local nernst potential between fuel and air side:

z_O2 = 4  # Number of electrons transferred per O2 molecule
nernst_voltage = R*t / (z_O2*F) * np.log(o2_air_side/o2_fuel_side)

Plot nernst potential:

fig, ax = plt.subplots()
ax.set_xlabel("Conversion")
ax.set_ylabel("Voltage / V")
ax.plot(conversion, nernst_voltage, '-')
print(np.min(nernst_voltage))

The model uses between each node a constant conversion. Because current density depends strongly on the position along the cell the constant conversion does not relate to a constant distance.

To calculate the local current density (node_current) as well as the total cell current (terminal_current) the (relative) physical distance between the nodes (dz) must be calculated:

cell_voltage = 0.77  # V
ASR = 0.2  # Ohm*cm²

node_current = (nernst_voltage - cell_voltage) / ASR  # A/cm² (Current density at each node)

current = (node_current[1:] + node_current[:-1]) / 2  # A/cm² (Average current density between the nodes)

dz = 1/current / np.sum(1/current)  # Relative distance between each node

terminal_current = np.sum(current * dz) # A/cm² (Total cell current per cell area)

print(f'Terminal current: {terminal_current:.2f} A/cm²')

Plot the local current density:

z_position = np.concatenate([[0], np.cumsum(dz)])  # Relative position of each node

fig, ax = plt.subplots()
ax.set_xlabel("Relative cell position")
ax.set_ylabel("Current density / A/cm²")
ax.plot(z_position, node_current, '-')