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 4.82047306e-04]
5.704253439999999e-06 [6.24960842e-02 9.15640475e-01 3.13852556e-04 2.08265184e-02
2.41023156e-04 4.82046311e-04]
8.388608e-06 [6.24958844e-02 9.15640745e-01 3.13850905e-04 2.08264518e-02
2.41022658e-04 4.82045316e-04]
1.107296256e-05 [6.24956846e-02 9.15641014e-01 3.13849253e-04 2.08263852e-02
2.41022161e-04 4.82044321e-04]
1.375731712e-05 [6.24954847e-02 9.15641284e-01 3.13847602e-04 2.08263186e-02
2.41021663e-04 4.82043326e-04]
1.912602624e-05 [6.24950850e-02 9.15641823e-01 3.13844299e-04 2.08261854e-02
2.41020668e-04 4.82041336e-04]
2.449473536e-05 [6.24946853e-02 9.15642362e-01 3.13840996e-04 2.08260522e-02
2.41019673e-04 4.82039346e-04]
2.986344448e-05 [6.24942857e-02 9.15642902e-01 3.13837693e-04 2.08259191e-02
2.41018678e-04 4.82037356e-04]
3.52321536e-05 [6.24938860e-02 9.15643441e-01 3.13834391e-04 2.08257859e-02
2.41017683e-04 4.82035366e-04]
4.596957184e-05 [6.24930866e-02 9.15644519e-01 3.13827785e-04 2.08255195e-02
2.41015693e-04 4.82031386e-04]
5.4870728526960826e-05 [6.24924240e-02 9.15645413e-01 3.13822310e-04 2.08252987e-02
2.41014043e-04 4.82028087e-04]
6.377188521392165e-05 [6.24917614e-02 9.15646307e-01 3.13816834e-04 2.08250778e-02
2.41012394e-04 4.82024788e-04]
7.267304190088248e-05 [6.24910987e-02 9.15647201e-01 3.13811359e-04 2.08248570e-02
2.41010744e-04 4.82021489e-04]
8.15741985878433e-05 [6.24904361e-02 9.15648094e-01 3.13805884e-04 2.08246362e-02
2.41009095e-04 4.82018190e-04]
9.047535527480413e-05 [6.24897735e-02 9.15648988e-01 3.13800409e-04 2.08244154e-02
2.41007445e-04 4.82014891e-04]
0.00010827766864872576 [6.24884483e-02 9.15650776e-01 3.13789459e-04 2.08239738e-02
2.41004147e-04 4.82008293e-04]
0.00012607998202264741 [6.24871232e-02 9.15652564e-01 3.13778510e-04 2.08235322e-02
2.41000848e-04 4.82001696e-04]
0.00014388229539656907 [6.24857980e-02 9.15654351e-01 3.13767562e-04 2.08230906e-02
2.40997550e-04 4.81995099e-04]
0.00016168460877049072 [6.24844729e-02 9.15656139e-01 3.13756614e-04 2.08226490e-02
2.40994251e-04 4.81988503e-04]
0.00017948692214441237 [6.24831479e-02 9.15657926e-01 3.13745666e-04 2.08222074e-02
2.40990953e-04 4.81981907e-04]
0.00019728923551833402 [6.24818228e-02 9.15659714e-01 3.13734719e-04 2.08217659e-02
2.40987655e-04 4.81975311e-04]
0.00023289386226617732 [6.24791728e-02 9.15663288e-01 3.13712827e-04 2.08208828e-02
2.40981060e-04 4.81962120e-04]
0.0002578948426625719 [6.24773121e-02 9.15665798e-01 3.13697456e-04 2.08202627e-02
2.40976429e-04 4.81952859e-04]
0.00028289582305896643 [6.24754514e-02 9.15668308e-01 3.13682086e-04 2.08196426e-02
2.40971799e-04 4.81943598e-04]
0.000307896803455361 [6.24735909e-02 9.15670818e-01 3.13666718e-04 2.08190226e-02
2.40967169e-04 4.81934338e-04]
0.00033289778385175555 [6.24717303e-02 9.15673328e-01 3.13651350e-04 2.08184026e-02
2.40962539e-04 4.81925078e-04]
0.0003578987642481501 [6.24698698e-02 9.15675838e-01 3.13635983e-04 2.08177826e-02
2.40957910e-04 4.81915819e-04]
0.00038289974464454467 [6.24680094e-02 9.15678348e-01 3.13620618e-04 2.08171626e-02
2.40953281e-04 4.81906561e-04]
0.00040790072504093923 [6.24661490e-02 9.15680857e-01 3.13605253e-04 2.08165427e-02
2.40948652e-04 4.81897304e-04]
0.0004329017054373338 [6.24642887e-02 9.15683367e-01 3.13589890e-04 2.08159227e-02
2.40944023e-04 4.81888047e-04]
0.00045790268583372834 [6.24624285e-02 9.15685876e-01 3.13574527e-04 2.08153028e-02
2.40939395e-04 4.81878791e-04]
0.0004829036662301229 [6.24605683e-02 9.15688385e-01 3.13559166e-04 2.08146829e-02
2.40934768e-04 4.81869535e-04]
0.0005079046466265175 [6.24587082e-02 9.15690895e-01 3.13543806e-04 2.08140630e-02
2.40930140e-04 4.81860280e-04]
0.0005329056270229121 [6.24568481e-02 9.15693404e-01 3.13528447e-04 2.08134432e-02
2.40925513e-04 4.81851026e-04]
0.0005579066074193066 [6.24549881e-02 9.15695913e-01 3.13513089e-04 2.08128233e-02
2.40920886e-04 4.81841773e-04]
0.0005829075878157012 [6.24531281e-02 9.15698422e-01 3.13497732e-04 2.08122035e-02
2.40916260e-04 4.81832520e-04]
0.0006079085682120958 [6.24512682e-02 9.15700931e-01 3.13482376e-04 2.08115837e-02
2.40911634e-04 4.81823268e-04]
0.0006329095486084903 [6.24494083e-02 9.15703440e-01 3.13467021e-04 2.08109639e-02
2.40907008e-04 4.81814016e-04]
0.0006579105290048849 [6.24475485e-02 9.15705949e-01 3.13451668e-04 2.08103441e-02
2.40902383e-04 4.81804765e-04]
0.0006829115094012794 [6.24456888e-02 9.15708457e-01 3.13436315e-04 2.08097244e-02
2.40897758e-04 4.81795515e-04]
0.000707912489797674 [6.24438291e-02 9.15710966e-01 3.13420964e-04 2.08091047e-02
2.40893133e-04 4.81786266e-04]
0.0007329134701940685 [6.24419695e-02 9.15713474e-01 3.13405613e-04 2.08084849e-02
2.40888508e-04 4.81777017e-04]
0.0007579144505904631 [6.24401099e-02 9.15715983e-01 3.13390264e-04 2.08078652e-02
2.40883884e-04 4.81767769e-04]
0.0007829154309868577 [6.24382504e-02 9.15718491e-01 3.13374915e-04 2.08072456e-02
2.40879261e-04 4.81758521e-04]
0.0008079164113832522 [6.24363909e-02 9.15721000e-01 3.13359568e-04 2.08066259e-02
2.40874637e-04 4.81749275e-04]
0.0008329173917796468 [6.24345316e-02 9.15723508e-01 3.13344222e-04 2.08060063e-02
2.40870014e-04 4.81740028e-04]
0.0008579183721760413 [6.24326722e-02 9.15726016e-01 3.13328877e-04 2.08053867e-02
2.40865391e-04 4.81730783e-04]
0.0008829193525724359 [6.24308129e-02 9.15728524e-01 3.13313533e-04 2.08047671e-02
2.40860769e-04 4.81721538e-04]
0.000905420234929191 [6.24291396e-02 9.15730781e-01 3.13299724e-04 2.08042094e-02
2.40856609e-04 4.81713219e-04]
0.0009279211172859461 [6.24274663e-02 9.15733039e-01 3.13285917e-04 2.08036518e-02
2.40852450e-04 4.81704899e-04]
0.0009504219996427012 [6.24257931e-02 9.15735296e-01 3.13272110e-04 2.08030942e-02
2.40848290e-04 4.81696581e-04]
0.0009729228819994563 [6.24241199e-02 9.15737553e-01 3.13258304e-04 2.08025367e-02
2.40844131e-04 4.81688263e-04]
0.0009954237643562114 [6.24224468e-02 9.15739810e-01 3.13244499e-04 2.08019791e-02
2.40839973e-04 4.81679945e-04]
0.0010179246467129665 [6.24207737e-02 9.15742067e-01 3.13230694e-04 2.08014216e-02
2.40835814e-04 4.81671628e-04]
0.0010404255290697216 [6.24191007e-02 9.15744323e-01 3.13216891e-04 2.08008640e-02
2.40831656e-04 4.81663312e-04]
0.0010629264114264767 [6.24174277e-02 9.15746580e-01 3.13203088e-04 2.08003065e-02
2.40827498e-04 4.81654996e-04]
0.0010854272937832318 [6.24157547e-02 9.15748837e-01 3.13189287e-04 2.07997490e-02
2.40823340e-04 4.81646681e-04]
0.001107928176139987 [6.24140818e-02 9.15751094e-01 3.13175486e-04 2.07991915e-02
2.40819183e-04 4.81638366e-04]
0.001130429058496742 [6.24124090e-02 9.15753350e-01 3.13161686e-04 2.07986340e-02
2.40815026e-04 4.81630052e-04]
0.0011529299408534971 [6.24107362e-02 9.15755607e-01 3.13147887e-04 2.07980766e-02
2.40810869e-04 4.81621738e-04]
0.0011754308232102522 [6.24090634e-02 9.15757863e-01 3.13134089e-04 2.07975191e-02
2.40806712e-04 4.81613425e-04]
0.0011979317055670073 [6.24073907e-02 9.15760120e-01 3.13120291e-04 2.07969617e-02
2.40802556e-04 4.81605112e-04]
0.0012204325879237624 [6.24057180e-02 9.15762376e-01 3.13106495e-04 2.07964043e-02
2.40798400e-04 4.81596800e-04]
0.0012429334702805175 [6.24040454e-02 9.15764632e-01 3.13092699e-04 2.07958469e-02
2.40794244e-04 4.81588489e-04]
0.0012654343526372726 [6.24023728e-02 9.15766889e-01 3.13078905e-04 2.07952895e-02
2.40790089e-04 4.81580178e-04]
0.0012879352349940277 [6.24007002e-02 9.15769145e-01 3.13065111e-04 2.07947322e-02
2.40785934e-04 4.81571867e-04]
0.0013104361173507828 [6.23990277e-02 9.15771401e-01 3.13051318e-04 2.07941748e-02
2.40781779e-04 4.81563558e-04]
0.001332936999707538 [6.23973553e-02 9.15773657e-01 3.13037526e-04 2.07936175e-02
2.40777624e-04 4.81555248e-04]
0.001355437882064293 [6.23956829e-02 9.15775913e-01 3.13023735e-04 2.07930601e-02
2.40773470e-04 4.81546940e-04]
0.0013779387644210482 [6.23940105e-02 9.15778169e-01 3.13009944e-04 2.07925028e-02
2.40769316e-04 4.81538631e-04]
0.0014004396467778033 [6.23923382e-02 9.15780425e-01 3.12996155e-04 2.07919455e-02
2.40765162e-04 4.81530324e-04]
0.0014229405291345584 [6.23906659e-02 9.15782680e-01 3.12982366e-04 2.07913883e-02
2.40761008e-04 4.81522017e-04]
0.0014454414114913135 [6.23889937e-02 9.15784936e-01 3.12968579e-04 2.07908310e-02
2.40756855e-04 4.81513710e-04]
0.0014679422938480686 [6.23873215e-02 9.15787192e-01 3.12954792e-04 2.07902738e-02
2.40752702e-04 4.81505404e-04]
0.0014904431762048237 [6.23856494e-02 9.15789448e-01 3.12941006e-04 2.07897165e-02
2.40748549e-04 4.81497099e-04]
0.0015129440585615788 [6.23839773e-02 9.15791703e-01 3.12927221e-04 2.07891593e-02
2.40744397e-04 4.81488794e-04]
0.0015354449409183339 [6.23823052e-02 9.15793959e-01 3.12913436e-04 2.07886021e-02
2.40740245e-04 4.81480489e-04]
0.001557945823275089 [6.23806332e-02 9.15796214e-01 3.12899653e-04 2.07880449e-02
2.40736093e-04 4.81472186e-04]
0.001580446705631844 [6.23789613e-02 9.15798469e-01 3.12885871e-04 2.07874878e-02
2.40731941e-04 4.81463882e-04]
0.0016029475879885992 [6.23772893e-02 9.15800724e-01 3.12872089e-04 2.07869306e-02
2.40727790e-04 4.81455580e-04]
0.0016254484703453543 [6.23756175e-02 9.15802980e-01 3.12858308e-04 2.07863735e-02
2.40723639e-04 4.81447277e-04]
0.0016479493527021094 [6.23739456e-02 9.15805235e-01 3.12844528e-04 2.07858163e-02
2.40719488e-04 4.81438976e-04]
0.0016704502350588645 [6.23722739e-02 9.15807490e-01 3.12830749e-04 2.07852592e-02
2.40715337e-04 4.81430675e-04]
0.0016929511174156196 [6.23706021e-02 9.15809745e-01 3.12816971e-04 2.07847021e-02
2.40711187e-04 4.81422375e-04]
0.0017132019115366991 [6.23690976e-02 9.15811775e-01 3.12804572e-04 2.07842007e-02
2.40707452e-04 4.81414904e-04]
0.0017334527056577786 [6.23675931e-02 9.15813804e-01 3.12792173e-04 2.07836994e-02
2.40703718e-04 4.81407435e-04]
0.0017537034997788582 [6.23660887e-02 9.15815834e-01 3.12779775e-04 2.07831980e-02
2.40699983e-04 4.81399966e-04]
0.0017739542938999377 [6.23645842e-02 9.15817863e-01 3.12767377e-04 2.07826967e-02
2.40696249e-04 4.81392497e-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, clone=True)
reactor.area = Ac
reactor.mass_flow_rate = gas.density * u0 * Ac
reactor.energy_enabled = False
rsurf = ct.ReactorSurface(gas_si_n_interface, reactor, clone=True)
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 1.341 seconds)