Plug flow reactor: silicon nitride deposition

A 1-D steady state plug-flow reactor demonstrating silicon nitride (Si3N4) deposition from ammonia (NH3) and silicon tetrafluoride (SiF4).

Assumes a constant temperature, frictionless, cylindrical reactor.

Based off the Jupyter notebook created by Yuanjie Jiang, which corresponds to the original example from:

R.S. Larson. “PLUG: A FORTRAN program for the analysis of PLUG flow reactors with gas-phase and surface chemistry”, Sandia Report SAND-96-8211, 1996. https://doi.org/10.2172/204257

The results are somewhat different from those in the Larson report in part due to the fact that this example does not include the frictional pressure drop.

Requires: cantera >= 3.2, matplotlib >= 2.0

Tags: Python catalysis plug flow reactor reactor network surface chemistry

0.0 [1. 0. 0. 0. 0. 0.]
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0.37327940811611804 [3.94093543e-02 9.46709274e-01 1.60824388e-04 1.31329771e-02
 1.95856727e-04 3.91713454e-04]
0.3758414162417212 [3.92804669e-02 9.46882394e-01 1.60136412e-04 1.30900260e-02
 1.95658787e-04 3.91317575e-04]
0.3784034243673243 [3.91519450e-02 9.47055021e-01 1.59451830e-04 1.30471967e-02
 1.95461879e-04 3.90923758e-04]
0.38352744061853056 [3.88959951e-02 9.47398796e-01 1.58092759e-04 1.29619026e-02
 1.95071129e-04 3.90142258e-04]
0.3886514568697368 [3.86414986e-02 9.47740608e-01 1.56747008e-04 1.28770929e-02
 1.94684422e-04 3.89368845e-04]
0.393775473120943 [3.83884498e-02 9.48080465e-01 1.55414410e-04 1.27927656e-02
 1.94301707e-04 3.88603414e-04]
0.39889948937214925 [3.81368426e-02 9.48418375e-01 1.54094804e-04 1.27089187e-02
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0.4040235056233555 [3.78866713e-02 9.48754346e-01 1.52788029e-04 1.26255503e-02
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0.4091475218745617 [3.76379299e-02 9.49088387e-01 1.51493927e-04 1.25426585e-02
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0.4193955543769742 [3.71447135e-02 9.49750708e-01 1.48943128e-04 1.23782965e-02
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0.42964358687938664 [3.66571465e-02 9.50405405e-01 1.46441199e-04 1.22158171e-02
 1.91730200e-04 3.83460400e-04]
0.4398916193817991 [3.61751821e-02 9.51052540e-01 1.43986969e-04 1.20552048e-02
 1.91028590e-04 3.82057180e-04]
0.45013965188421157 [3.56987737e-02 9.51692180e-01 1.41579308e-04 1.18964440e-02
 1.90341021e-04 3.80682041e-04]
0.46038768438662403 [3.52278745e-02 9.52324388e-01 1.39217118e-04 1.17395191e-02
 1.89667144e-04 3.79334288e-04]
0.4706357168890365 [3.47624380e-02 9.52949228e-01 1.36899337e-04 1.15844147e-02
 1.89006624e-04 3.78013247e-04]
0.48088374939144896 [3.43024177e-02 9.53566765e-01 1.34624936e-04 1.14311151e-02
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0.4911317818938614 [3.38477672e-02 9.54177062e-01 1.32392915e-04 1.12796050e-02
 1.87724357e-04 3.75448714e-04]
0.5013798143962739 [3.33984402e-02 9.54780183e-01 1.30202308e-04 1.11298690e-02
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0.5116278468986863 [3.29543905e-02 9.55376191e-01 1.28052176e-04 1.09818916e-02
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0.5218758794010988 [3.25155719e-02 9.55965149e-01 1.25941607e-04 1.08356574e-02
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0.5321239119035113 [3.20819385e-02 9.56547121e-01 1.23869718e-04 1.06911512e-02
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0.5423719444059237 [3.16534443e-02 9.57122170e-01 1.21835650e-04 1.05483575e-02
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0.5526199769083362 [3.12300433e-02 9.57690358e-01 1.19838569e-04 1.04072612e-02
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0.5628680094107487 [3.08116900e-02 9.58251748e-01 1.17877667e-04 1.02678470e-02
 1.83612362e-04 3.67224724e-04]
0.5731160419131611 [3.03983386e-02 9.58806403e-01 1.15952156e-04 1.01300996e-02
 1.83069032e-04 3.66138065e-04]
0.5833640744155736 [2.99899437e-02 9.59354383e-01 1.14061273e-04 9.99400397e-03
 1.82535974e-04 3.65071949e-04]
0.593612106917986 [2.95864598e-02 9.59895752e-01 1.12204273e-04 9.85954491e-03
 1.82012955e-04 3.64025910e-04]

import numpy as np
import cantera as ct
import matplotlib.pyplot as plt

mech = 'SiF4_NH3_mec.yaml'

# import the model for gas-Si-N interface and adjacent bulk phases
gas_si_n_interface = ct.Interface(mech, 'SI3N4')
gas = gas_si_n_interface.adjacent['gas']

# Set the initial conditions
T0 = 1713  # K
p0 = 2 * ct.one_atm / 760.0  # Pa ~2Torr
gas.TPX = T0, p0, "SiF4:0.1427, NH3:0.8573"
gas_si_n_interface.TP = T0, p0
D = 5.08e-2  # diameter of the tube [m]
Ac = np.pi * D**2 / 4  # cross section of the tube [m]
u0 = 11.53  # m/s initial velocity of the flow

reactor = ct.FlowReactor(gas)
reactor.area = Ac
reactor.mass_flow_rate = gas.density * u0 * Ac
reactor.energy_enabled = False

rsurf = ct.ReactorSurface(gas_si_n_interface, reactor)
net = ct.ReactorNet([reactor])
soln = ct.SolutionArray(gas, extra=['x', 'speed', 'surf_coverages', 'N_dep', 'Si_dep'])
kN = gas_si_n_interface.kinetics_species_index('N(D)')
kSi = gas_si_n_interface.kinetics_species_index('Si(D)')

# Integrate the reactor network
while net.distance < 0.6:
    print(net.distance, rsurf.coverages)
    net.step()
    wdot = rsurf.phase.net_production_rates
    soln.append(TDY=reactor.phase.TDY,
                x=net.distance,
                speed=reactor.speed,
                surf_coverages=rsurf.coverages,
                N_dep=wdot[kN],
                Si_dep=wdot[kSi])

# Plot the results
plt.rcParams['figure.constrained_layout.use'] = True
f, ax = plt.subplots(2, 3, figsize=(9,6))

# plot the temperature profile along the flow direction
ax[0, 0].plot(soln.x, soln.T[:], color='C3')
ax[0, 0].set(xlabel='Distance (m)', ylabel='Temperature (K)', title='Gas properties')

# plot the pressure of the gas along the flow direction
ax_p = ax[0,0].twinx()
ax_p.plot(soln.x, soln.P, color='C2')
ax_p.set(ylabel='Pressure (Pa)')

# plot gas velocity along the flow direction
h_vel = ax[1, 0].plot(soln.x, soln.speed, color='C0', label='velocity')
ax[1, 0].set(xlabel='Distance (m)', ylabel='Velocity (m/s)')

# plot gas density along the flow direction
ax_rho = ax[1,0].twinx()
h_rho = ax_rho.plot(soln.x, soln.density / 1000, color='C1', label='density')
ax_rho.set(ylabel=r'Density ($\mathregular{g/cm^3}$)')
ax_rho.legend(handles=h_vel+h_rho)

# plot major and minor gas species separately
minor_idx = []
major_idx = []
for i, name in enumerate(gas.species_names):
    mean = np.mean(soln(name).X)
    if mean >= 0.001:
        major_idx.append(i)
    elif mean >= 1e-10:
        minor_idx.append(i)

# plot major gas species along the flow direction
for j in major_idx:
    ax[0, 1].plot(soln.x, soln.X[:,j], label=gas.species_name(j))
ax[0, 1].legend(fontsize=8, loc='best')
ax[0, 1].set(xlabel='Distance (m)', ylabel='Mole Fraction',
             title='Gas phase major species')

# plot minor gas species along the flow direction
for k, i in enumerate(minor_idx):
    style = '-' if k < 10 else '--'
    ax[1, 1].plot(soln.x, soln.X[:,i], label=gas.species_name(i), linestyle=style)
ax[1, 1].legend(fontsize=7.5, loc='best')
ax[1, 1].set(xlabel='Distance (m)', ylabel='Mole Fraction',
             title='Gas phase minor species')

# plot the site fraction of the surface species along the flow direction
for i, name in enumerate(gas_si_n_interface.species_names):
    ax[0, 2].plot(soln.x, soln.surf_coverages[:, i], label=name)
ax[0, 2].legend(fontsize=8)
ax[0, 2].set(xlabel='Distance (m)', ylabel='Site Fraction', title='Surface species')

# plot the surface deposition of N and Si
ax[1, 2].plot(soln.x, soln.N_dep, label='N(D)')
ax[1, 2].plot(soln.x, soln.Si_dep, label='Si(D)')
ax[1, 2].set(xlabel='Distance (m)', ylabel='Deposition Rate (kmol/m$^2$/s)',
             title='Bulk deposition')
ax[1, 2].legend()

plt.show()