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]
5.465637762966823e-05 [6.25109760e-02 9.15982178e-01 3.13902325e-04 2.08314810e-02
1.20487455e-04 2.40974910e-04]
6.355289861933646e-05 [6.25096500e-02 9.15983962e-01 3.13891371e-04 2.08310392e-02
1.20485806e-04 2.40971613e-04]
7.244941960900468e-05 [6.25083241e-02 9.15985746e-01 3.13880417e-04 2.08305973e-02
1.20484158e-04 2.40968316e-04]
8.134594059867291e-05 [6.25069982e-02 9.15987529e-01 3.13869464e-04 2.08301554e-02
1.20482509e-04 2.40965019e-04]
9.024246158834114e-05 [6.25056723e-02 9.15989313e-01 3.13858512e-04 2.08297136e-02
1.20480861e-04 2.40961722e-04]
0.0001080355035676776 [6.25030205e-02 9.15992880e-01 3.13836609e-04 2.08288299e-02
1.20477565e-04 2.40955129e-04]
0.00012582854554701406 [6.25003689e-02 9.15996447e-01 3.13814708e-04 2.08279463e-02
1.20474268e-04 2.40948537e-04]
0.00014362158752635051 [6.24977174e-02 9.16000014e-01 3.13792809e-04 2.08270627e-02
1.20470973e-04 2.40941945e-04]
0.00016141462950568697 [6.24950659e-02 9.16003581e-01 3.13770911e-04 2.08261791e-02
1.20467677e-04 2.40935354e-04]
0.00017920767148502342 [6.24924146e-02 9.16007148e-01 3.13749016e-04 2.08252955e-02
1.20464382e-04 2.40928764e-04]
0.00019700071346435988 [6.24897633e-02 9.16010714e-01 3.13727123e-04 2.08244120e-02
1.20461087e-04 2.40922174e-04]
0.00023258679742303278 [6.24844611e-02 9.16017847e-01 3.13683343e-04 2.08226451e-02
1.20454498e-04 2.40908996e-04]
0.00025757629800287604 [6.24807380e-02 9.16022855e-01 3.13652605e-04 2.08214044e-02
1.20449872e-04 2.40899744e-04]
0.0002825657985827193 [6.24770151e-02 9.16027864e-01 3.13621870e-04 2.08201637e-02
1.20445247e-04 2.40890493e-04]
0.00030755529916256255 [6.24732923e-02 9.16032872e-01 3.13591140e-04 2.08189231e-02
1.20440622e-04 2.40881244e-04]
0.0003325447997424058 [6.24695698e-02 9.16037879e-01 3.13560413e-04 2.08176826e-02
1.20435998e-04 2.40871995e-04]
0.00035753430032224907 [6.24658474e-02 9.16042887e-01 3.13529691e-04 2.08164421e-02
1.20431374e-04 2.40862748e-04]
0.0003825238009020923 [6.24621252e-02 9.16047894e-01 3.13498973e-04 2.08152017e-02
1.20426751e-04 2.40853503e-04]
0.0004075133014819356 [6.24584032e-02 9.16052901e-01 3.13468258e-04 2.08139614e-02
1.20422129e-04 2.40844258e-04]
0.00043250280206177884 [6.24546814e-02 9.16057907e-01 3.13437548e-04 2.08127211e-02
1.20417507e-04 2.40835015e-04]
0.0004574923026416221 [6.24509598e-02 9.16062914e-01 3.13406841e-04 2.08114809e-02
1.20412886e-04 2.40825773e-04]
0.00048248180322146535 [6.24472384e-02 9.16067920e-01 3.13376139e-04 2.08102408e-02
1.20408266e-04 2.40816532e-04]
0.0005074713038013086 [6.24435171e-02 9.16072926e-01 3.13345441e-04 2.08090007e-02
1.20403646e-04 2.40807292e-04]
0.0005324608043811518 [6.24397961e-02 9.16077931e-01 3.13314747e-04 2.08077607e-02
1.20399027e-04 2.40798054e-04]
0.000557450304960995 [6.24360752e-02 9.16082937e-01 3.13284056e-04 2.08065207e-02
1.20394409e-04 2.40788817e-04]
0.0005824398055408382 [6.24323545e-02 9.16087942e-01 3.13253370e-04 2.08052808e-02
1.20389791e-04 2.40779581e-04]
0.0006074293061206814 [6.24286340e-02 9.16092947e-01 3.13222688e-04 2.08040410e-02
1.20385173e-04 2.40770347e-04]
0.0006324188067005246 [6.24249137e-02 9.16097951e-01 3.13192010e-04 2.08028012e-02
1.20380557e-04 2.40761114e-04]
0.0006574083072803678 [6.24211936e-02 9.16102956e-01 3.13161335e-04 2.08015615e-02
1.20375941e-04 2.40751882e-04]
0.000682397807860211 [6.24174737e-02 9.16107960e-01 3.13130665e-04 2.08003218e-02
1.20371326e-04 2.40742651e-04]
0.0007073873084400542 [6.24137539e-02 9.16112964e-01 3.13099999e-04 2.07990822e-02
1.20366711e-04 2.40733422e-04]
0.0007323768090198974 [6.24100344e-02 9.16117967e-01 3.13069337e-04 2.07978427e-02
1.20362097e-04 2.40724194e-04]
0.0007573663095997406 [6.24063150e-02 9.16122971e-01 3.13038679e-04 2.07966033e-02
1.20357483e-04 2.40714967e-04]
0.0007823558101795838 [6.24025958e-02 9.16127974e-01 3.13008025e-04 2.07953638e-02
1.20352871e-04 2.40705741e-04]
0.000807345310759427 [6.23988768e-02 9.16132977e-01 3.12977374e-04 2.07941245e-02
1.20348258e-04 2.40696517e-04]
0.0008323348113392702 [6.23951580e-02 9.16137979e-01 3.12946728e-04 2.07928852e-02
1.20343647e-04 2.40687294e-04]
0.0008573243119191134 [6.23914393e-02 9.16142981e-01 3.12916086e-04 2.07916460e-02
1.20339036e-04 2.40678072e-04]
0.0008823138124989566 [6.23877209e-02 9.16147984e-01 3.12885448e-04 2.07904069e-02
1.20334426e-04 2.40668852e-04]
0.0009073033130787998 [6.23840027e-02 9.16152985e-01 3.12854814e-04 2.07891678e-02
1.20329816e-04 2.40659632e-04]
0.000932292813658643 [6.23802846e-02 9.16157987e-01 3.12824184e-04 2.07879287e-02
1.20325207e-04 2.40650414e-04]
0.0009572823142384862 [6.23765667e-02 9.16162988e-01 3.12793558e-04 2.07866898e-02
1.20320599e-04 2.40641198e-04]
0.0009822718148183294 [6.23728490e-02 9.16167989e-01 3.12762936e-04 2.07854509e-02
1.20315991e-04 2.40631982e-04]
0.0010072613153981726 [6.23691315e-02 9.16172990e-01 3.12732318e-04 2.07842120e-02
1.20311384e-04 2.40622768e-04]
0.0010322508159780158 [6.23654141e-02 9.16177991e-01 3.12701704e-04 2.07829732e-02
1.20306778e-04 2.40613555e-04]
0.001057240316557859 [6.23616970e-02 9.16182991e-01 3.12671094e-04 2.07817345e-02
1.20302172e-04 2.40604343e-04]
0.0010822298171377022 [6.23579801e-02 9.16187991e-01 3.12640488e-04 2.07804959e-02
1.20297566e-04 2.40595133e-04]
0.0011072193177175454 [6.23542633e-02 9.16192991e-01 3.12609886e-04 2.07792573e-02
1.20292962e-04 2.40585924e-04]
0.0011322088182973886 [6.23505467e-02 9.16197990e-01 3.12579287e-04 2.07780187e-02
1.20288358e-04 2.40576716e-04]
0.0011571983188772318 [6.23468304e-02 9.16202989e-01 3.12548694e-04 2.07767803e-02
1.20283755e-04 2.40567509e-04]
0.001182187819457075 [6.23431141e-02 9.16207988e-01 3.12518103e-04 2.07755419e-02
1.20279152e-04 2.40558304e-04]
0.0012071773200369182 [6.23393981e-02 9.16212987e-01 3.12487517e-04 2.07743035e-02
1.20274550e-04 2.40549100e-04]
0.0012296678705587772 [6.23360539e-02 9.16217486e-01 3.12459993e-04 2.07731891e-02
1.20270409e-04 2.40540817e-04]
0.0012521584210806362 [6.23327098e-02 9.16221984e-01 3.12432473e-04 2.07720747e-02
1.20266268e-04 2.40532536e-04]
0.0012746489716024953 [6.23293657e-02 9.16226483e-01 3.12404955e-04 2.07709603e-02
1.20262128e-04 2.40524255e-04]
0.0012971395221243543 [6.23260220e-02 9.16230981e-01 3.12377441e-04 2.07698460e-02
1.20257988e-04 2.40515976e-04]
0.0013196300726462133 [6.23226783e-02 9.16235478e-01 3.12349930e-04 2.07687317e-02
1.20253848e-04 2.40507697e-04]
0.0013398715681158862 [6.23196691e-02 9.16239526e-01 3.12325172e-04 2.07677289e-02
1.20250124e-04 2.40500247e-04]
0.0013601130635855592 [6.23166601e-02 9.16243574e-01 3.12300418e-04 2.07667262e-02
1.20246399e-04 2.40492798e-04]
0.001380354559055232 [6.23136512e-02 9.16247622e-01 3.12275666e-04 2.07657235e-02
1.20242675e-04 2.40485350e-04]
0.001400596054524905 [6.23106424e-02 9.16251669e-01 3.12250917e-04 2.07647208e-02
1.20238951e-04 2.40477903e-04]
0.001420837549994578 [6.23076337e-02 9.16255716e-01 3.12226170e-04 2.07637182e-02
1.20235228e-04 2.40470456e-04]
0.001441079045464251 [6.23046252e-02 9.16259763e-01 3.12201426e-04 2.07627156e-02
1.20231505e-04 2.40463011e-04]
0.001481562036403597 [6.22986084e-02 9.16267857e-01 3.12151945e-04 2.07607106e-02
1.20224061e-04 2.40448122e-04]
0.001522045027342943 [6.22925921e-02 9.16275950e-01 3.12102476e-04 2.07587057e-02
1.20216618e-04 2.40433236e-04]
0.0015625280182822892 [6.22865764e-02 9.16284042e-01 3.12053016e-04 2.07567009e-02
1.20209177e-04 2.40418354e-04]
0.0016030110092216353 [6.22805611e-02 9.16292134e-01 3.12003567e-04 2.07546964e-02
1.20201738e-04 2.40403475e-04]
0.0016434940001609814 [6.22745463e-02 9.16300225e-01 3.11954129e-04 2.07526920e-02
1.20194300e-04 2.40388600e-04]
0.0016839769911003275 [6.22685320e-02 9.16308315e-01 3.11904701e-04 2.07506877e-02
1.20186864e-04 2.40373728e-04]
0.0017244599820396736 [6.22625182e-02 9.16316405e-01 3.11855283e-04 2.07486836e-02
1.20179429e-04 2.40358859e-04]
0.0017649429729790196 [6.22565048e-02 9.16324494e-01 3.11805876e-04 2.07466797e-02
1.20171996e-04 2.40343993e-04]
0.0018054259639183657 [6.22504920e-02 9.16332582e-01 3.11756480e-04 2.07446760e-02
1.20164565e-04 2.40329131e-04]
0.0018459089548577118 [6.22444796e-02 9.16340670e-01 3.11707093e-04 2.07426724e-02
1.20157136e-04 2.40314272e-04]
0.001926874936736404 [6.22324563e-02 9.16356843e-01 3.11608352e-04 2.07386657e-02
1.20142282e-04 2.40284563e-04]
0.002007840918615096 [6.22204350e-02 9.16373013e-01 3.11509653e-04 2.07346596e-02
1.20127434e-04 2.40254868e-04]
0.0020888069004937884 [6.22084156e-02 9.16389181e-01 3.11410995e-04 2.07306542e-02
1.20112593e-04 2.40225187e-04]
0.0021697728823724806 [6.21963982e-02 9.16405347e-01 3.11312379e-04 2.07266495e-02
1.20097759e-04 2.40195518e-04]
0.0022507388642511728 [6.21843827e-02 9.16421509e-01 3.11213805e-04 2.07226454e-02
1.20082931e-04 2.40165863e-04]
0.002331704846129865 [6.21723692e-02 9.16437669e-01 3.11115273e-04 2.07186419e-02
1.20068110e-04 2.40136220e-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 1.389 seconds)