Chemical Complexity via Simple Models

375 Pages·2018·96.158 MB·English

by  Gregory Bykov, Valeriy I. / Tsybenova, Svetlana B. / Yablonsky

Bykov,Tsybenova,Yablonsky
ChemicalComplexityviaSimpleModels
DeGruyterGraduate
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Valeriy I. Bykov, Svetlana B. Tsybenova,
Gregory Yablonsky
Chemical
Complexity via
Simple Models
|
MODELICS
Authors
Prof.ValeriyI.Bykov
RussianAcademyofSciences
EmanuelInstituteofBiochemicalPhysics
KosyginStreet4/11
119334Moscow
RussianFederation
Dr.SvetlanaB.Tsybenova
RussianAcademyofSciences
EmanuelInstituteofBiochemicalPhysics
KosyginStreet4/11
119334Moscow
RussianFederation
Prof.GregoryYablonsky
SaintLouisUniversity
DepartmentofChemistry
3450LindellBlvd
St.LouisMO63103
UnitedStatesofAmerica
ISBN978-3-11-046491-7
e-ISBN(PDF)978-3-11-046494-8
e-ISBN(EPUB)978-3-11-046514-3
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Preface
Theideaofwritingthisbookwasbornin2015duringtheInternationalConference
“Mathematics in (Bio)Chemical Kinetics and Engineering” (MACKiE-2015), held in
Ghent (Belgium). Professors Valeriy Bykov and Grigoriy (Gregory) Yablonsky were
colleagues who worked closely at the Boreskov Institute of Catalysis (Novosibirsk,
Russia)formorethanadecadeinthe1970sto1980s.TheyestablishedtheSiberian
chemico-mathematicalteam–togetherwithAlexanderGorbanandVladimirElokhin.
They co-authored many books and articles related to the area of the mathematical
modeling ofchemicalprocesses. Dr Svetlana Tsybenovajoined thisactivitylater in
the1990s,enhancingitscomputationalandappliedaspects.
AftergraduatingfromNovosibirskStateUniversityin1968,ValeriyBykovstarted
hisscientificcareerintheDepartmentofMathematicalModelingattheBoreskovIn-
stituteofCatalysis.ProfessorMikhailSlin’koandDrAlbertFedotovwerehisscientific
supervisors.In1985,ValeriyBykovreceivedhisdegreeofDoctorofPhysicsandMathe-
matics(PhysicalChemistry)fromtheInstituteofChemicalPhysicsinChernogolovka.
GregoryYablonskyalsoworkedinthesameDepartmentofMathematicalModel-
ingattheBoreskovInstituteofCatalysis(Novosibirsk),firstasapost-graduatestudent
andthenasaresearcher.ProfessorMikhailSlin’kowasalsohissupervisor.In1989,
GregoryYablonskyreceivedhisdegreeofDoctorofScience(PhysicalChemistry)from
theBoreskovInstitute.
Svetlana Tsybenova graduated from Krasnoyarsk State Technical University in
1996andreceivedherPhDinTechnicalSciencesfromthesameuniversityin1999.In
2011,shereceivedthedegreeofDoctorofPhysicsandMathematics(PhysicalChem-
istry)fromBashkirStateUniversity,Ufa;herbeingadviserwasProfessorSemyonSpi-
vak.
In1978,therewasaremarkablemomentinthisstorywhenascientificdelegation
from the USA, the three prominent professors Rutherford Aris, Dan Luss, and Har-
monRay,visitedtheBoreskovInstituteinNovosibirsk.Thiswasastartingpointfor
Soviet–Americancooperationinmathematicalchemistry.Unfortunately,thiscooper-
ationmetmanypoliticalobstacles.Nonetheless,itbecameasignificantstimulusfor
afruitfulexchangeofinformationandideas.
Overthelast50years,themaindirectionsandapproacheshavebeendetermined
inmathematicalchemistry,boththeoreticalandapplied.Discoveriesofnewexperi-
mentalfacts,i.e.,therateofhysteresis,chemicaloscillations,chaos,etc,creatednew
challengesindecodingthecomplexityofchemicalreactions.Batteriesofmathemat-
icalmodelsdistinguishedbythelevelofcomplexityandassumedfactorshavebeen
developedforimitatingcomplexchemicalbehavior.
“Battery of models”, “zoo of models”, or “marketof models” – different meta-
phorscanbeused.Nevertheless,therealalternativeincontemporarymodelingisbe-
tweenthemodeltakenfromthe“market”andthatproducedbytheindividual“tailor”.
https://doi.org/10.1515/9783110464948-201
VI | Preface
Certainly,asuitfromthetailorismoreelegant;however,itismuchcheaperandfaster
tobuyasuitinasupermarketandadaptitifnecessary.
Anoptimalstrategyofmodelingcanbeformulatedasfollows:
1. todeveloptypical(“simple”)modelsfordescribingthephenomenaofourinter-
est;
2. toadaptthemtoconcretephenomenaorprocesses.
Aspecialquestionarose:whatisthesimplestmodeltodescribenewlydiscoveredcrit-
icalphenomena?Thisbookisdevotedtobasicmodels,whichcanbeusedasbuilding
blocksforconstructingthemathematicalmodelsofcomplexchemicalprocesses.We
callthemethodologyofselectingandanalyzingthesemodels“modelics”.Ourbookis
focusedonsimplenonlinearmodels.
Generally,theconceptsof“simplicity”andthe“simplemodel”arecomplex.Ein-
stein’sadvicewas:“Makeeverythingassimpleaspossiblebutnotsimple.”Onthe
otherhand,LeonardodaVincisaid:“Simplicityistheultimatesophistication.”So,
whenworkingwithsimplicity,wemovethroughthe“grayzone”betweenscience,art,
andphilosophy,andtheinscriptiononthegatesis:“Lessismore!”
The authors express their gratitude to the colleagues who provided them with
help at various times and in different situations: Professors Sergey Varfolomeev,
Bair Bal’zhinimaev, Alexander Gorban’, Semyon Spivak, Aizek Volpert, Konstantin
Shkadinskii,SergeyReshetnikov,GeorgijMalinetskii,andZulhairMansurov.
Finally,wewouldliketothankourbelovedonesfortheirsupportandunderstand-
ing.
ValeriyBykov,Moscow,2017
SvetlanaTsybenova,Moscow,2017
GregoryYablonsky,St.Louis,2017
Contents
Preface|V
PartI: Generalpart
1 Introduction.Howtodescribecomplexprocessesusingsimplemodels:
Modelics|3
1.1 Model...modeling... |3
1.2 Top-downandbottom-up|4
2 Categorizationofmodels|6
2.1 Physicalframeworkofmodeldesign|6
2.1.1 Modelsoftransport|7
2.1.2 Thebatchreactor|8
2.1.3 Thecontinuousstirred-tankreactor|8
2.1.4 Theplug-flowreactor|9
2.1.5 Thepulsereactor|10
2.2 Howtosimplifycomplexmodels?Principlesofsimplification|10
2.2.1 Physicochemicalassumptionsofsimplificationof
chemico-mathematicalmodels|11
2.3 Mathematicalconceptsofsimplificationinchemicalkinetics|15
2.3.1 Mathematicalstatusofthequasi-steady-state(QSS)
approximation|15
2.3.2 Limitsofsimplification:optimalmodel|17
PartII: Chemicalmodelics
3 Basicmodelsofchemicalkinetics|21
3.1 Equationsofchemicalkineticsandaschemeofparametric
analysis|21
3.1.1 Experimentalbackground|21
3.1.2 Equationsofchemicalkinetics|23
3.1.3 Schemeofparametricanalysis|25
3.2 Autocatalyticmodels|32
3.2.1 Autocatalytictrigger|32
3.2.2 Autocatalyticoscillators|34
3.2.3 Associationreaction|59
3.3 Catalyticschemesoftransformations|63
VIII | Contents
3.3.1 Catalytictriggers|63
3.3.2 Catalyticoscillators|72
3.4 Catalyticcontinuousstirred-tankreactor(CSTR)|84
3.4.1 Flowreactorwithanautocatalytictrigger|86
3.4.2 Flowreactorwithacatalytictrigger|89
3.4.3 Flowreactorwithanautocatalyticoscillator|93
3.4.4 Flowreactorwithacatalyticoscillator|93
3.4.5 Kinetic“chaos”inducedbynoise|94
3.5 Two-centermechanisms|96
3.5.1 Oscillator–triggermodel|96
3.5.2 Oscillator–oscillatormodel|99
3.5.3 ModelwithastepofinteractionofcentersZ1 󴀘󴀯Z2|101
3.5.4 Modelwithadiffusionchangeofinteractioncenters|102
3.6 SimplestmodelsofCOoxidationonplatinum|106
3.7 Nonidealkinetics|113
3.8 Savchenko’smodel|124
3.9 ModeloftheBelousov–Zhabotinskyreaction|130
4 Thermokineticmodels|142
4.1 Continuousstirred-tankreactors(CSTR)|142
4.2 Zel’dovich–Semenovmodel|143
4.2.1 ReactionA→P|144
4.2.2 TheoxidationreactionA+O2 →P|152
4.2.3 ReactionnA→P|157
4.2.4 ReactionA→Pwitharbitrarykinetics|162
4.2.5 Semenovdiagramasastabilitycriterion|164
4.3 Aris–Amundsonmodel|168
4.3.1 ReactionA→P|168
4.3.2 Reactionofthen-thorder|181
4.3.3 Theoxidationreaction|183
4.3.4 Reactionwitharbitrarykinetics|186
4.3.5 Andronov–Hopfbifurcations|189
4.3.6 Safeandunsafeboundariesofregionsofcriticalphenomena|194
4.4 Volter–Salnikovmodel|197
4.5 Modelsofacontinuousstirredtankreactorandatubereactor|205
4.5.1 Parametricanalysisofadimensionalmodel|206
4.5.2 Relationbetweendimensionlessanddimensionalmodels|214
4.5.3 Determinationofignitionboundaries|215
4.5.4 Continuoustubereactor|216
4.6 Combustionmodelofhydrocarbonmixture|218
4.7 Thermocatalytictriggersandoscillators|228
4.7.1 TheEley–Ridealmonomolecularmechanism|231
Contents | IX
4.7.2 TheEley–Ridealbimolecularmechanism|233
4.7.3 Thelinearcatalyticcycle|235
4.7.4 TheLangmuir–HinshelwoodMechanism|235
4.7.5 Autocatalyticschemesoftransformations|237
4.7.6 Autocatalyticoscillator|245
4.8 Parallelscheme|248
4.9 Consistentscheme|252
4.10 Onereversiblereaction|255
4.11 Modelofspontaneouscombustionofbrown-coaldust|259
4.12 ModelingofthenitrationofamylinaCSTRandatubereactor|266
4.12.1 ParametricanalysisofthemathematicalmodelofaCSTR|267
4.12.2 Modelofatubereactor|272
5 Modelsofmacrokinetics|281
5.1 Homogeneous–heterogeneousreaction|282
5.2 Modelofanimperfectlystirredcontinuousreactor|287
5.3 Dissipativestructuresontheactivesurface|291
5.4 Themodelofsorption–reaction–diffusion |299
5.5 Macrokineticsofcatalyticreactionsonsurfaces
ofvariousgeometries|307
5.6 Nonlinearinteractionbetweentheactivesurfaceandbulk
ofasolid|311
5.7 Modelsofwavepropagationreactions|315
5.8 MacroclustersonthecatalystsurfaceattheCOoxidationonPt|319
5.9 Modelofcokingthefeedchannelsofthefuel|322
PartIII: Modelicseverywhere
6 Modelsofpopulationdynamics:“prey–predator”models|335
6.1 “Prey–predator”model|335
6.1.1 Nonlinearityofreproduction|336
6.1.2 Competitioninthepreypopulation|337
6.1.3 Saturationofthepredator|337
6.1.4 Competitionforthepredator|338
6.1.5 Competitionofthepreyandsaturationofthepredator|338
6.1.6 Nonlinearityofeatingofthepreybythepredatorandsaturation
ofthepredator|339
6.1.7 Competitionofthepredatorforthepreyandsaturation
ofthepredator|340
6.1.8 Nonlinearityofreproductionofpredatorandcompetition
ofprey|340