Note
Go to the end to download the full example code
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 >= 3.0, matplotlib >= 2.0
0.0 [1. 0. 0. 0. 0. 0.]
1e-14 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
2e-14 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
4e-14 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
8e-14 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
1.6e-13 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
3.2e-13 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
6.4e-13 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
1.28e-12 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
2.56e-12 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
5.12e-12 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
1.024e-11 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
2.048e-11 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
4.096e-11 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
8.192e-11 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
1.6384e-10 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
3.2768e-10 [6.25191227e-02 9.15971219e-01 3.13969632e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
6.5536e-10 [6.25191227e-02 9.15971219e-01 3.13969631e-04 2.08341959e-02
1.20497585e-04 2.40995170e-04]
1.31072e-09 [6.25191226e-02 9.15971219e-01 3.13969630e-04 2.08341958e-02
1.20497585e-04 2.40995170e-04]
2.62144e-09 [6.25191224e-02 9.15971219e-01 3.13969629e-04 2.08341958e-02
1.20497585e-04 2.40995169e-04]
5.24288e-09 [6.25191220e-02 9.15971220e-01 3.13969626e-04 2.08341956e-02
1.20497584e-04 2.40995168e-04]
1.048576e-08 [6.25191212e-02 9.15971221e-01 3.13969619e-04 2.08341954e-02
1.20497583e-04 2.40995166e-04]
2.097152e-08 [6.25191196e-02 9.15971223e-01 3.13969606e-04 2.08341948e-02
1.20497581e-04 2.40995162e-04]
4.194304e-08 [6.25191165e-02 9.15971227e-01 3.13969580e-04 2.08341938e-02
1.20497577e-04 2.40995155e-04]
6.291456e-08 [6.25191134e-02 9.15971232e-01 3.13969555e-04 2.08341928e-02
1.20497573e-04 2.40995147e-04]
8.388608e-08 [6.25191102e-02 9.15971236e-01 3.13969529e-04 2.08341917e-02
1.20497569e-04 2.40995139e-04]
1.2582912e-07 [6.25191040e-02 9.15971244e-01 3.13969477e-04 2.08341896e-02
1.20497562e-04 2.40995123e-04]
1.6777216e-07 [6.25190977e-02 9.15971253e-01 3.13969425e-04 2.08341876e-02
1.20497554e-04 2.40995108e-04]
2.097152e-07 [6.25190915e-02 9.15971261e-01 3.13969374e-04 2.08341855e-02
1.20497546e-04 2.40995092e-04]
2.9360128e-07 [6.25190790e-02 9.15971278e-01 3.13969270e-04 2.08341813e-02
1.20497531e-04 2.40995061e-04]
4.6137344000000005e-07 [6.25190540e-02 9.15971311e-01 3.13969064e-04 2.08341730e-02
1.20497500e-04 2.40994999e-04]
7.9691776e-07 [6.25190040e-02 9.15971379e-01 3.13968650e-04 2.08341563e-02
1.20497437e-04 2.40994875e-04]
1.4680064e-06 [6.25189039e-02 9.15971513e-01 3.13967824e-04 2.08341230e-02
1.20497313e-04 2.40994626e-04]
2.81018368e-06 [6.25187039e-02 9.15971782e-01 3.13966171e-04 2.08340563e-02
1.20497064e-04 2.40994128e-04]
5.4945382399999995e-06 [6.25183037e-02 9.15972321e-01 3.13962865e-04 2.08339230e-02
1.20496567e-04 2.40993133e-04]
8.1788928e-06 [6.25179036e-02 9.15972859e-01 3.13959559e-04 2.08337896e-02
1.20496069e-04 2.40992138e-04]
1.086324736e-05 [6.25175035e-02 9.15973397e-01 3.13956253e-04 2.08336563e-02
1.20495571e-04 2.40991143e-04]
1.354760192e-05 [6.25171033e-02 9.15973936e-01 3.13952947e-04 2.08335229e-02
1.20495074e-04 2.40990148e-04]
1.891631104e-05 [6.25163031e-02 9.15975012e-01 3.13946335e-04 2.08332563e-02
1.20494079e-04 2.40988157e-04]
2.428502016e-05 [6.25155029e-02 9.15976089e-01 3.13939724e-04 2.08329896e-02
1.20493084e-04 2.40986167e-04]
2.965372928e-05 [6.25147026e-02 9.15977165e-01 3.13933112e-04 2.08327229e-02
1.20492089e-04 2.40984177e-04]
3.50224384e-05 [6.25139024e-02 9.15978242e-01 3.13926501e-04 2.08324562e-02
1.20491094e-04 2.40982187e-04]
4.5759856640000004e-05 [6.25123020e-02 9.15980394e-01 3.13913279e-04 2.08319229e-02
1.20489104e-04 2.40978207e-04]
5.4656377630337116e-05 [6.25109760e-02 9.15982178e-01 3.13902325e-04 2.08314810e-02
1.20487455e-04 2.40974910e-04]
6.355289862067423e-05 [6.25096500e-02 9.15983962e-01 3.13891371e-04 2.08310392e-02
1.20485806e-04 2.40971613e-04]
7.244941961101134e-05 [6.25083241e-02 9.15985746e-01 3.13880417e-04 2.08305973e-02
1.20484158e-04 2.40968316e-04]
8.134594060134845e-05 [6.25069982e-02 9.15987529e-01 3.13869464e-04 2.08301554e-02
1.20482509e-04 2.40965019e-04]
9.024246159168556e-05 [6.25056723e-02 9.15989313e-01 3.13858512e-04 2.08297136e-02
1.20480861e-04 2.40961722e-04]
0.00010803550357235979 [6.25030205e-02 9.15992880e-01 3.13836609e-04 2.08288299e-02
1.20477565e-04 2.40955129e-04]
0.000125828545553034 [6.25003689e-02 9.15996447e-01 3.13814708e-04 2.08279463e-02
1.20474268e-04 2.40948537e-04]
0.00014362158753370823 [6.24977174e-02 9.16000014e-01 3.13792809e-04 2.08270627e-02
1.20470973e-04 2.40941945e-04]
0.00016141462951438246 [6.24950659e-02 9.16003581e-01 3.13770911e-04 2.08261791e-02
1.20467677e-04 2.40935354e-04]
0.00017920767149505668 [6.24924146e-02 9.16007148e-01 3.13749016e-04 2.08252955e-02
1.20464382e-04 2.40928764e-04]
0.0001970007134757309 [6.24897633e-02 9.16010714e-01 3.13727123e-04 2.08244120e-02
1.20461087e-04 2.40922174e-04]
0.00023258679743707935 [6.24844611e-02 9.16017847e-01 3.13683343e-04 2.08226451e-02
1.20454498e-04 2.40908996e-04]
0.0002575762995598795 [6.24807380e-02 9.16022855e-01 3.13652605e-04 2.08214044e-02
1.20449872e-04 2.40899744e-04]
0.0002825658016826796 [6.24770151e-02 9.16027864e-01 3.13621870e-04 2.08201637e-02
1.20445247e-04 2.40890493e-04]
0.0003075553038054797 [6.24732923e-02 9.16032872e-01 3.13591140e-04 2.08189231e-02
1.20440622e-04 2.40881244e-04]
0.0003325448059282798 [6.24695698e-02 9.16037879e-01 3.13560413e-04 2.08176826e-02
1.20435998e-04 2.40871995e-04]
0.0003575343080510799 [6.24658474e-02 9.16042887e-01 3.13529691e-04 2.08164421e-02
1.20431374e-04 2.40862748e-04]
0.00038252381017388 [6.24621252e-02 9.16047894e-01 3.13498973e-04 2.08152017e-02
1.20426751e-04 2.40853503e-04]
0.0004075133122966801 [6.24584032e-02 9.16052901e-01 3.13468258e-04 2.08139614e-02
1.20422129e-04 2.40844258e-04]
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1.20417507e-04 2.40835015e-04]
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1.20412886e-04 2.40825773e-04]
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1.20408266e-04 2.40816532e-04]
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1.20403646e-04 2.40807292e-04]
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1.20399027e-04 2.40798054e-04]
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1.20394409e-04 2.40788817e-04]
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1.20389791e-04 2.40779581e-04]
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1.20380557e-04 2.40761114e-04]
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1.20375941e-04 2.40751882e-04]
0.0006823978356474816 [6.24174737e-02 9.16107960e-01 3.13130665e-04 2.08003218e-02
1.20371326e-04 2.40742651e-04]
0.0007073873377702818 [6.24137539e-02 9.16112964e-01 3.13099999e-04 2.07990822e-02
1.20366711e-04 2.40733422e-04]
0.0007323768398930819 [6.24100343e-02 9.16117967e-01 3.13069337e-04 2.07978427e-02
1.20362097e-04 2.40724194e-04]
0.0007573663420158821 [6.24063150e-02 9.16122971e-01 3.13038679e-04 2.07966032e-02
1.20357483e-04 2.40714967e-04]
0.0007823558441386822 [6.24025958e-02 9.16127974e-01 3.13008025e-04 2.07953638e-02
1.20352871e-04 2.40705741e-04]
0.0008073453462614824 [6.23988768e-02 9.16132977e-01 3.12977374e-04 2.07941245e-02
1.20348258e-04 2.40696517e-04]
0.0008323348483842825 [6.23951580e-02 9.16137979e-01 3.12946728e-04 2.07928852e-02
1.20343647e-04 2.40687294e-04]
0.0008573243505070827 [6.23914393e-02 9.16142981e-01 3.12916086e-04 2.07916460e-02
1.20339036e-04 2.40678072e-04]
0.0008823138526298828 [6.23877209e-02 9.16147984e-01 3.12885448e-04 2.07904069e-02
1.20334426e-04 2.40668852e-04]
0.000904804404540403 [6.23843745e-02 9.16152485e-01 3.12857877e-04 2.07892917e-02
1.20330277e-04 2.40660554e-04]
0.0009272949564509231 [6.23810282e-02 9.16156987e-01 3.12830310e-04 2.07881765e-02
1.20326129e-04 2.40652258e-04]
0.0009497855083614432 [6.23776820e-02 9.16161488e-01 3.12802745e-04 2.07870615e-02
1.20321981e-04 2.40643962e-04]
0.0009722760602719633 [6.23743361e-02 9.16165989e-01 3.12775184e-04 2.07859464e-02
1.20317834e-04 2.40635668e-04]
0.0009947666121824833 [6.23709902e-02 9.16170490e-01 3.12747626e-04 2.07848314e-02
1.20313687e-04 2.40627375e-04]
0.0010172571640930034 [6.23676445e-02 9.16174990e-01 3.12720072e-04 2.07837165e-02
1.20309541e-04 2.40619083e-04]
0.0010397477160035236 [6.23642990e-02 9.16179491e-01 3.12692520e-04 2.07826016e-02
1.20305396e-04 2.40610791e-04]
0.0010622382679140437 [6.23609536e-02 9.16183991e-01 3.12664972e-04 2.07814868e-02
1.20301251e-04 2.40602501e-04]
0.0010847288198245638 [6.23576084e-02 9.16188491e-01 3.12637427e-04 2.07803720e-02
1.20297106e-04 2.40594212e-04]
0.001107219371735084 [6.23542633e-02 9.16192991e-01 3.12609886e-04 2.07792573e-02
1.20292962e-04 2.40585924e-04]
0.001129709923645604 [6.23509184e-02 9.16197490e-01 3.12582347e-04 2.07781426e-02
1.20288818e-04 2.40577637e-04]
0.0011522004755561241 [6.23475736e-02 9.16201990e-01 3.12554812e-04 2.07770280e-02
1.20284675e-04 2.40569350e-04]
0.0011746910274666443 [6.23442290e-02 9.16206489e-01 3.12527280e-04 2.07759134e-02
1.20280533e-04 2.40561065e-04]
0.0011971815793771644 [6.23408845e-02 9.16210988e-01 3.12499751e-04 2.07747989e-02
1.20276391e-04 2.40552781e-04]
0.0012196721312876845 [6.23375402e-02 9.16215486e-01 3.12472226e-04 2.07736844e-02
1.20272249e-04 2.40544498e-04]
0.0012421626831982046 [6.23341960e-02 9.16219985e-01 3.12444704e-04 2.07725699e-02
1.20268108e-04 2.40536216e-04]
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1.20263968e-04 2.40527935e-04]
0.0012871437870192448 [6.23275081e-02 9.16228982e-01 3.12389669e-04 2.07703412e-02
1.20259828e-04 2.40519655e-04]
0.001309634338929765 [6.23241644e-02 9.16233479e-01 3.12362156e-04 2.07692269e-02
1.20255688e-04 2.40511376e-04]
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1.20251549e-04 2.40503098e-04]
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0.0013771059946613253 [6.23141341e-02 9.16246972e-01 3.12279638e-04 2.07658844e-02
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0.0015570304099454862 [6.22873933e-02 9.16282943e-01 3.12059732e-04 2.07569732e-02
1.20210188e-04 2.40420375e-04]
0.0015795209618560064 [6.22840514e-02 9.16287439e-01 3.12032258e-04 2.07558595e-02
1.20206054e-04 2.40412108e-04]
0.0016020115137665265 [6.22807096e-02 9.16291934e-01 3.12004788e-04 2.07547459e-02
1.20201921e-04 2.40403843e-04]
0.0016245020656770466 [6.22773680e-02 9.16296429e-01 3.11977321e-04 2.07536323e-02
1.20197789e-04 2.40395578e-04]
0.0016469926175875667 [6.22740265e-02 9.16300924e-01 3.11949857e-04 2.07525187e-02
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0.001714464273319127 [6.22640030e-02 9.16314407e-01 3.11867484e-04 2.07491785e-02
1.20181265e-04 2.40362529e-04]
0.0017347057700385952 [6.22609962e-02 9.16318452e-01 3.11842778e-04 2.07481765e-02
1.20177548e-04 2.40355096e-04]
0.0017549472667580633 [6.22579895e-02 9.16322496e-01 3.11818074e-04 2.07471745e-02
1.20173832e-04 2.40347663e-04]
0.0017751887634775314 [6.22549830e-02 9.16326541e-01 3.11793373e-04 2.07461726e-02
1.20170116e-04 2.40340231e-04]
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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.kinetics.net_production_rates
soln.append(TDY=reactor.thermo.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).Y)
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.Y[:,j], label=gas.species_name(j))
ax[0, 1].legend(fontsize=8, loc='best')
ax[0, 1].set(xlabel='Distance (m)', ylabel='Mass 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.Y[:,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='Mass 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()
Total running time of the script: (0 minutes 0.771 seconds)