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 >= 3.2, matplotlib >= 2.0
0.0 [1. 0. 0. 0. 0. 0.]
1e-14 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
2e-14 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
4e-14 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
8e-14 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
1.6e-13 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
3.2e-13 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
6.4e-13 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
1.28e-12 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
2.56e-12 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
5.12e-12 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
1.024e-11 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
2.048e-11 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
4.096e-11 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
8.192e-11 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
1.6384e-10 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
3.2768e-10 [6.24965089e-02 9.15639902e-01 3.13856066e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
6.5536e-10 [6.24965089e-02 9.15639903e-01 3.13856065e-04 2.08266599e-02
2.41024213e-04 4.82048426e-04]
1.31072e-09 [6.24965088e-02 9.15639903e-01 3.13856065e-04 2.08266599e-02
2.41024213e-04 4.82048425e-04]
2.62144e-09 [6.24965087e-02 9.15639903e-01 3.13856064e-04 2.08266599e-02
2.41024212e-04 4.82048425e-04]
5.24288e-09 [6.24965085e-02 9.15639903e-01 3.13856063e-04 2.08266598e-02
2.41024212e-04 4.82048424e-04]
1.048576e-08 [6.24965081e-02 9.15639903e-01 3.13856059e-04 2.08266597e-02
2.41024211e-04 4.82048422e-04]
2.097152e-08 [6.24965074e-02 9.15639905e-01 3.13856053e-04 2.08266594e-02
2.41024209e-04 4.82048418e-04]
4.194304e-08 [6.24965058e-02 9.15639907e-01 3.13856040e-04 2.08266589e-02
2.41024205e-04 4.82048410e-04]
8.388608e-08 [6.24965027e-02 9.15639911e-01 3.13856014e-04 2.08266579e-02
2.41024197e-04 4.82048395e-04]
1.2582912e-07 [6.24964996e-02 9.15639915e-01 3.13855988e-04 2.08266568e-02
2.41024190e-04 4.82048379e-04]
1.6777216e-07 [6.24964964e-02 9.15639919e-01 3.13855963e-04 2.08266558e-02
2.41024182e-04 4.82048364e-04]
2.5165824e-07 [6.24964902e-02 9.15639928e-01 3.13855911e-04 2.08266537e-02
2.41024166e-04 4.82048333e-04]
3.3554432e-07 [6.24964839e-02 9.15639936e-01 3.13855859e-04 2.08266516e-02
2.41024151e-04 4.82048301e-04]
5.0331648e-07 [6.24964714e-02 9.15639953e-01 3.13855756e-04 2.08266475e-02
2.41024120e-04 4.82048239e-04]
6.7108864e-07 [6.24964590e-02 9.15639970e-01 3.13855653e-04 2.08266433e-02
2.41024089e-04 4.82048177e-04]
1.00663296e-06 [6.24964340e-02 9.15640004e-01 3.13855447e-04 2.08266350e-02
2.41024026e-04 4.82048053e-04]
1.6777216e-06 [6.24963840e-02 9.15640071e-01 3.13855034e-04 2.08266183e-02
2.41023902e-04 4.82047804e-04]
3.01989888e-06 [6.24962841e-02 9.15640206e-01 3.13854208e-04 2.08265850e-02
2.41023653e-04 4.82047307e-04]
5.704253439999999e-06 [6.24960842e-02 9.15640475e-01 3.13852557e-04 2.08265184e-02
2.41023156e-04 4.82046312e-04]
8.388608e-06 [6.24958844e-02 9.15640745e-01 3.13850905e-04 2.08264518e-02
2.41022658e-04 4.82045317e-04]
1.107296256e-05 [6.24956846e-02 9.15641014e-01 3.13849254e-04 2.08263852e-02
2.41022161e-04 4.82044322e-04]
1.375731712e-05 [6.24954847e-02 9.15641284e-01 3.13847602e-04 2.08263186e-02
2.41021663e-04 4.82043327e-04]
1.912602624e-05 [6.24950850e-02 9.15641823e-01 3.13844300e-04 2.08261854e-02
2.41020668e-04 4.82041337e-04]
2.449473536e-05 [6.24946853e-02 9.15642362e-01 3.13840997e-04 2.08260522e-02
2.41019674e-04 4.82039347e-04]
2.986344448e-05 [6.24942857e-02 9.15642902e-01 3.13837694e-04 2.08259190e-02
2.41018679e-04 4.82037357e-04]
3.52321536e-05 [6.24938860e-02 9.15643441e-01 3.13834392e-04 2.08257859e-02
2.41017684e-04 4.82035368e-04]
4.596957184e-05 [6.24930866e-02 9.15644519e-01 3.13827787e-04 2.08255195e-02
2.41015694e-04 4.82031388e-04]
5.487142348601705e-05 [6.24924239e-02 9.15645413e-01 3.13822311e-04 2.08252986e-02
2.41014045e-04 4.82028089e-04]
6.37732751320341e-05 [6.24917612e-02 9.15646307e-01 3.13816835e-04 2.08250778e-02
2.41012395e-04 4.82024790e-04]
7.267512677805114e-05 [6.24910985e-02 9.15647201e-01 3.13811360e-04 2.08248570e-02
2.41010746e-04 4.82021491e-04]
8.157697842406819e-05 [6.24904359e-02 9.15648095e-01 3.13805885e-04 2.08246361e-02
2.41009096e-04 4.82018193e-04]
9.047883007008523e-05 [6.24897732e-02 9.15648989e-01 3.13800409e-04 2.08244153e-02
2.41007447e-04 4.82014894e-04]
0.00010828253336211933 [6.24884479e-02 9.15650777e-01 3.13789459e-04 2.08239736e-02
2.41004148e-04 4.82008297e-04]
0.0001260862366541534 [6.24871226e-02 9.15652564e-01 3.13778510e-04 2.08235320e-02
2.41000850e-04 4.82001700e-04]
0.0001438899399461875 [6.24857973e-02 9.15654352e-01 3.13767561e-04 2.08230903e-02
2.40997552e-04 4.81995103e-04]
0.00016169364323822158 [6.24844721e-02 9.15656140e-01 3.13756612e-04 2.08226487e-02
2.40994253e-04 4.81988507e-04]
0.00017949734653025567 [6.24831468e-02 9.15657928e-01 3.13745664e-04 2.08222071e-02
2.40990955e-04 4.81981911e-04]
0.00019730104982228975 [6.24818216e-02 9.15659715e-01 3.13734716e-04 2.08217655e-02
2.40987658e-04 4.81975315e-04]
0.00023290845640635795 [6.24791713e-02 9.15663290e-01 3.13712823e-04 2.08208823e-02
2.40981062e-04 4.81962125e-04]
0.00025791096888530323 [6.24773104e-02 9.15665801e-01 3.13697451e-04 2.08202621e-02
2.40976432e-04 4.81952864e-04]
0.0002829134813642485 [6.24754496e-02 9.15668311e-01 3.13682080e-04 2.08196420e-02
2.40971802e-04 4.81943603e-04]
0.0003079159938431938 [6.24735887e-02 9.15670821e-01 3.13666711e-04 2.08190219e-02
2.40967172e-04 4.81934343e-04]
0.0003329185063221391 [6.24717280e-02 9.15673331e-01 3.13651342e-04 2.08184018e-02
2.40962542e-04 4.81925084e-04]
0.00035792101880108436 [6.24698672e-02 9.15675841e-01 3.13635974e-04 2.08177817e-02
2.40957912e-04 4.81915825e-04]
0.00038292353128002965 [6.24680066e-02 9.15678351e-01 3.13620607e-04 2.08171617e-02
2.40953283e-04 4.81906567e-04]
0.00040792604375897493 [6.24661460e-02 9.15680861e-01 3.13605241e-04 2.08165416e-02
2.40948655e-04 4.81897309e-04]
0.0004329285562379202 [6.24642854e-02 9.15683371e-01 3.13589877e-04 2.08159216e-02
2.40944026e-04 4.81888052e-04]
0.0004579310687168655 [6.24624249e-02 9.15685881e-01 3.13574513e-04 2.08153016e-02
2.40939398e-04 4.81878796e-04]
0.0004829335811958108 [6.24605644e-02 9.15688391e-01 3.13559150e-04 2.08146816e-02
2.40934770e-04 4.81869541e-04]
0.0005079360936747561 [6.24587039e-02 9.15690900e-01 3.13543788e-04 2.08140616e-02
2.40930143e-04 4.81860286e-04]
0.0005329386061537014 [6.24568436e-02 9.15693410e-01 3.13528428e-04 2.08134417e-02
2.40925516e-04 4.81851031e-04]
0.0005579411186326466 [6.24549832e-02 9.15695919e-01 3.13513068e-04 2.08128217e-02
2.40920889e-04 4.81841777e-04]
0.0005829436311115919 [6.24531229e-02 9.15698429e-01 3.13497709e-04 2.08122018e-02
2.40916262e-04 4.81832524e-04]
0.0006079461435905371 [6.24512627e-02 9.15700938e-01 3.13482351e-04 2.08115819e-02
2.40911636e-04 4.81823272e-04]
0.0006329486560694823 [6.24494025e-02 9.15703448e-01 3.13466995e-04 2.08109620e-02
2.40907010e-04 4.81814020e-04]
0.0006579511685484275 [6.24475424e-02 9.15705957e-01 3.13451639e-04 2.08103421e-02
2.40902384e-04 4.81804769e-04]
0.0006829536810273728 [6.24456823e-02 9.15708466e-01 3.13436284e-04 2.08097222e-02
2.40897759e-04 4.81795518e-04]
0.000707956193506318 [6.24438222e-02 9.15710975e-01 3.13420931e-04 2.08091024e-02
2.40893134e-04 4.81786268e-04]
0.0007329587059852632 [6.24419622e-02 9.15713484e-01 3.13405578e-04 2.08084825e-02
2.40888509e-04 4.81777019e-04]
0.0007579612184642085 [6.24401023e-02 9.15715993e-01 3.13390226e-04 2.08078627e-02
2.40883885e-04 4.81767770e-04]
0.0007829637309431537 [6.24382424e-02 9.15718502e-01 3.13374875e-04 2.08072429e-02
2.40879261e-04 4.81758522e-04]
0.0008079662434220989 [6.24363825e-02 9.15721011e-01 3.13359526e-04 2.08066231e-02
2.40874637e-04 4.81749274e-04]
0.0008329687559010441 [6.24345227e-02 9.15723520e-01 3.13344177e-04 2.08060033e-02
2.40870014e-04 4.81740027e-04]
0.0008579712683799894 [6.24326630e-02 9.15726028e-01 3.13328829e-04 2.08053836e-02
2.40865391e-04 4.81730781e-04]
0.0008829737808589346 [6.24308032e-02 9.15728537e-01 3.13313483e-04 2.08047638e-02
2.40860768e-04 4.81721535e-04]
0.0009079762933378798 [6.24289435e-02 9.15731046e-01 3.13298137e-04 2.08041441e-02
2.40856145e-04 4.81712291e-04]
0.0009304785545689306 [6.24272699e-02 9.15733303e-01 3.13284327e-04 2.08035864e-02
2.40851985e-04 4.81703971e-04]
0.0009529808157999814 [6.24255963e-02 9.15735561e-01 3.13270517e-04 2.08030286e-02
2.40847826e-04 4.81695651e-04]
0.0009754830770310321 [6.24239227e-02 9.15737819e-01 3.13256709e-04 2.08024709e-02
2.40843666e-04 4.81687332e-04]
0.000997985338262083 [6.24222491e-02 9.15740076e-01 3.13242901e-04 2.08019132e-02
2.40839507e-04 4.81679014e-04]
0.0010204875994931336 [6.24205756e-02 9.15742334e-01 3.13229094e-04 2.08013555e-02
2.40835348e-04 4.81670696e-04]
0.0010429898607241842 [6.24189021e-02 9.15744591e-01 3.13215288e-04 2.08007978e-02
2.40831189e-04 4.81662379e-04]
0.0010654921219552349 [6.24172287e-02 9.15746849e-01 3.13201482e-04 2.08002402e-02
2.40827031e-04 4.81654062e-04]
0.0010879943831862856 [6.24155553e-02 9.15749106e-01 3.13187678e-04 2.07996825e-02
2.40822873e-04 4.81645745e-04]
0.0011104966444173362 [6.24138819e-02 9.15751363e-01 3.13173874e-04 2.07991249e-02
2.40818715e-04 4.81637430e-04]
0.0011329989056483869 [6.24122086e-02 9.15753620e-01 3.13160071e-04 2.07985673e-02
2.40814557e-04 4.81629114e-04]
0.0011532509407563326 [6.24107027e-02 9.15755652e-01 3.13147649e-04 2.07980654e-02
2.40810815e-04 4.81621631e-04]
0.0011735029758642784 [6.24091967e-02 9.15757683e-01 3.13135228e-04 2.07975636e-02
2.40807074e-04 4.81614148e-04]
0.0011937550109722241 [6.24076908e-02 9.15759715e-01 3.13122807e-04 2.07970617e-02
2.40803333e-04 4.81606665e-04]
0.0012342590811881154 [6.24046791e-02 9.15763777e-01 3.13097968e-04 2.07960581e-02
2.40795851e-04 4.81591702e-04]
0.0012747631514040067 [6.24016676e-02 9.15767840e-01 3.13073131e-04 2.07950545e-02
2.40788370e-04 4.81576740e-04]
0.001315267221619898 [6.23986561e-02 9.15771902e-01 3.13048297e-04 2.07940510e-02
2.40780890e-04 4.81561779e-04]
0.0013557712918357892 [6.23956448e-02 9.15775964e-01 3.13023466e-04 2.07930474e-02
2.40773410e-04 4.81546820e-04]
0.0013962753620516805 [6.23926336e-02 9.15780026e-01 3.12998637e-04 2.07920440e-02
2.40765932e-04 4.81531863e-04]
0.0014367794322675718 [6.23896225e-02 9.15784088e-01 3.12973811e-04 2.07910405e-02
2.40758454e-04 4.81516908e-04]
0.001477283502483463 [6.23866115e-02 9.15788149e-01 3.12948988e-04 2.07900372e-02
2.40750977e-04 4.81501954e-04]
0.0015177875726993543 [6.23836007e-02 9.15792211e-01 3.12924167e-04 2.07890338e-02
2.40743501e-04 4.81487002e-04]
0.0015582916429152456 [6.23805899e-02 9.15796272e-01 3.12899349e-04 2.07880305e-02
2.40736026e-04 4.81472051e-04]
0.001598795713131137 [6.23775793e-02 9.15800333e-01 3.12874533e-04 2.07870272e-02
2.40728551e-04 4.81457102e-04]
0.0016392997833470282 [6.23745688e-02 9.15804394e-01 3.12849720e-04 2.07860240e-02
2.40721078e-04 4.81442155e-04]
0.001720307923778811 [6.23685483e-02 9.15812516e-01 3.12800102e-04 2.07840177e-02
2.40706133e-04 4.81412266e-04]
0.0018013160642105937 [6.23625281e-02 9.15820636e-01 3.12750494e-04 2.07820115e-02
2.40691191e-04 4.81382383e-04]
0.0018823242046423765 [6.23565085e-02 9.15828756e-01 3.12700897e-04 2.07800055e-02
2.40676253e-04 4.81352507e-04]
0.0019633323450741593 [6.23504894e-02 9.15836876e-01 3.12651311e-04 2.07779996e-02
2.40661319e-04 4.81322637e-04]
0.002044340485505942 [6.23444707e-02 9.15844994e-01 3.12601735e-04 2.07759940e-02
2.40646387e-04 4.81292775e-04]
0.0021253486259377244 [6.23384526e-02 9.15853112e-01 3.12552169e-04 2.07739884e-02
2.40631459e-04 4.81262919e-04]
0.002206356766369507 [6.23324349e-02 9.15861230e-01 3.12502614e-04 2.07719831e-02
2.40616535e-04 4.81233069e-04]
0.0022873649068012895 [6.23264177e-02 9.15869347e-01 3.12453070e-04 2.07699779e-02
2.40601613e-04 4.81203226e-04]
0.002368373047233072 [6.23204010e-02 9.15877463e-01 3.12403536e-04 2.07679728e-02
2.40586695e-04 4.81173390e-04]
0.0024493811876648546 [6.23143848e-02 9.15885578e-01 3.12354012e-04 2.07659680e-02
2.40571780e-04 4.81143560e-04]
0.002530389328096637 [6.23083691e-02 9.15893693e-01 3.12304499e-04 2.07639632e-02
2.40556869e-04 4.81113738e-04]
0.0026113974685284197 [6.23023538e-02 9.15901807e-01 3.12254997e-04 2.07619587e-02
2.40541961e-04 4.81083921e-04]
0.0026924056089602023 [6.22963391e-02 9.15909920e-01 3.12205505e-04 2.07599543e-02
2.40527056e-04 4.81054112e-04]
0.002773413749391985 [6.22903248e-02 9.15918033e-01 3.12156023e-04 2.07579501e-02
2.40512154e-04 4.81024309e-04]
0.0028544218898237674 [6.22843110e-02 9.15926145e-01 3.12106552e-04 2.07559460e-02
2.40497256e-04 4.80994512e-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.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()
Total running time of the script: (0 minutes 1.446 seconds)