Introduction to Chemical Engineering Analysis Using Mathematica: for Chemists, Biotechnologists and Materials Scientists

948 Pages·2021·31.841 MB·English

by  Henry C. Foley

For Karin
Introduction to Chemical Engineering
Analysis Using Mathematica
Introduction to
Chemical Engineering Analysis
Using Mathematica
For Chemists, Biotechnologists and
Materials Scientists
Second Edition
Henry C. Foley
New York Institute of Technology
New York, NY, United States
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Contents
Introduction ...................................................................... ix
Abitofanexplanationofthisbook .................................................. ix
Chaptersubjectsinbrief .............................................................. xi
Conclusion............................................................................. xx
Chapter 1:AprimerofMathematica ............................................. 1
GettingstartedinMathematica ....................................................... 1
Basics .................................................................................. 1
Equals(=),equalequals(==),andcolonequals(:=) ................................ 2
Simplecommands ..................................................................... 12
Table.................................................................................... 14
Do ...................................................................................... 23
Plot,Plot3D,andContourPlot ........................................................ 26
Module................................................................................. 33
ListPlot,Fit,andShow ................................................................ 49
DSolve ................................................................................. 81
NDSolve ............................................................................... 93
NonlinearModelFit .................................................................... 98
Point:anotherversatilegraphicsmethod............................................. 107
Conclusion............................................................................. 129
Chapter 2:Elementary singlecomponentsystems ................................. 131
Theconservationofmassprinciple,theconceptofacontrolvolume .............. 131
Fillingavesselwithapelletedsolid:conservationofmass..................... 136
Pressurizinganinitiallyevacuatedtankwithanidealgas....................... 153
Fillingacylindricaltank .......................................................... 158
Timedependentflows ............................................................. 162
Geometryandtheleft-handsideofthemassbalanceequation ..................... 167
Thetriangulartrough.............................................................. 167
Theconicaltank ................................................................... 175
Thesemi-cylindricaltrough....................................................... 179
Thesphericaltank ................................................................. 191
Depositingapolymercoatingonadisk .......................................... 192
v
Contents
Conclusion............................................................................. 200
Chapter 3:The draining tank and related systems ................................ 201
Theright-handsideofthemassbalanceequation ................................... 201
Mechanismofwaterflowfromatank:Torricelli’slaw-aconstitutive
relationship.................................................................. 202
Experimentandtheconstitutiveequation ........................................ 203
Solvingforlevelasafunctionoftime............................................ 212
Massinput,output,andcontrol................................................... 214
Control ............................................................................. 223
Conclusion............................................................................. 232
Chapter 4:Multiple componentsystems .......................................... 233
Theconceptofthecomponentbalance............................................... 233
Concentrationversusdensity.......................................................... 234
Thewell-mixedsystem................................................................ 235
Multicomponentsystems.............................................................. 236
Liquidandaninsolublesolid ..................................................... 236
Liquidandsolublesolid........................................................... 247
Densityasafunctionofconcentration ........................................... 261
Washingasaltsolutionfromavessel............................................. 271
Thepulseinputtracerexperimentandanalysis.................................. 277
Mixing.............................................................................. 285
Conclusion............................................................................. 292
Chapter 5:Multiple phases-masstransfer ....................................... 295
Saltdissolution ........................................................................ 296
BatchDissolution.................................................................. 298
Fittothebatchdata................................................................ 304
Semi-continuous:pseudo-steadystate............................................ 308
Fullsolution........................................................................ 310
Liquid-liquidsystem .................................................................. 318
Fullycontinuous................................................................... 318
Conclusion............................................................................. 355
Chapter 6:Adsorptionand permeation ........................................... 357
Adsorption ............................................................................. 357
Semi-continuousadsorption....................................................... 381
Continuousadsorption............................................................. 404
Plugflowandasimpleratemodel................................................ 425
Langmuirandplugflowanumericalapproach .................................. 439
Permeation............................................................................. 454
vi
Contents
Permeationasadsorptionanddiffusion .......................................... 455
Expandingcell..................................................................... 473
Conclusion............................................................................. 482
Chapter 7:Reacting species-kinetics and batchreactors.......................... 483
Howchemicalreactionstakeplace ................................................... 484
No-flow/batchsystem ................................................................. 488
Simpleirreversiblereactions-firsttoNth order ..................................... 489
Firstorderkinetics................................................................. 489
Secondorderkineticsoverall ..................................................... 499
Nth order........................................................................... 506
Reversiblereactions-chemicalequilibrium ......................................... 509
Complexreactions..................................................................... 525
Series............................................................................... 525
Series-parallelreactions........................................................... 539
Highdilution....................................................................... 544
Langmuir-Hinshelwood-Hougen-Watsonkinetics(LHHW).................... 551
Microbialpopulationdynamics................................................... 569
Temperaturedependenceofreactionrates ....................................... 575
Conversionandselectivity ............................................................ 600
Timerequiredforaspecifiedconversion............................................. 605
Effectofstoichiometry................................................................ 609
Complexreactionsandthesteadystateapproximation.............................. 612
Lindemann......................................................................... 612
Rice-Herzfeld...................................................................... 620
Conclusion............................................................................. 632
Chapter 8:Flowreactors ......................................................... 633
Introductiontoflowreactors .......................................................... 633
Semi-continuoussystems,fed-batchreactors .................................... 633
Secondorderkineticsandnegligiblevolumechange............................ 651
Pseudo-steadystateanalysisinFBR.............................................. 675
Numericalanalysisofthefed-batchreactor...................................... 678
Constantvolumebatchreactor(CVBR)versusthefed-batchreactor(FBR)... 681
Accountingforlargervolumechange ............................................ 693
Economicpotential................................................................ 697
Continuousflowreactors.............................................................. 712
Continuousflowstirredtankreactor.............................................. 713
SteadystateCSTRwithhigherorder,reversiblekinetics ....................... 718
Timedependence-thetransientapproachtosteadystateandsaturation
kinetics...................................................................... 724
vii
Contents
Plugflowreactors...................................................................... 734
SolutionofthesteadystatePFR.................................................. 738
Mixingeffectsonselectivities:seriesandseries-parallelwithCSTRandPFR 746
PFRasaseriesofCSTRs ......................................................... 755
Residencetimedistribution ....................................................... 770
TimedependentPFR-completeandnumericalsolutions........................... 788
Introduction........................................................................ 788
TransientPFR...................................................................... 789
Equations,initialconditions,andboundaryconditions.......................... 789
Conclusion............................................................................. 806
Chapter 9:Additional examples .................................................. 807
Anotherlookatthelevel-controlledtank............................................. 807
Perturbationoftheinletflowrate&control ......................................... 807
Integrationthroughandbeyondthedisturbance ..................................... 809
Proportional,integral,anddifferentialcontrol ................................... 815
Generalmodelfortitrationofastrongacidwithastrongbase ..................... 824
ThepHofaweakacid................................................................. 840
Thepartialmolalvolumeofsolution................................................. 846
ThedesignofanoptimalCSTR ...................................................... 859
Alinearoptimization.................................................................. 865
Linearornon-linear? .............................................................. 870
Differentialequationswithimpulsefunctions ................................... 875
Perceptrons:primitiveAI ......................................................... 879
Thetransferfunction .................................................................. 880
Theartificialneuron(AN)............................................................. 885
TruthTablesforlogicgates ....................................................... 894
MapsandgraphicalinterpretationofANDandOR ............................. 896
Agraphicalaside .................................................................. 897
TheNOTgateorinverter.......................................................... 902
Combinationsofgates............................................................. 905
TheNANDandNORgates ....................................................... 909
Summaryoftwoinputlogicgates................................................ 918
Conclusion............................................................................. 921
Index ............................................................................. 923
viii
Introduction
A bit of an explanation of this book
Welcometo“AnIntroductiontoChemicalEngineeringAnalysisUsingMathematica.”This
bookisaguideforanyonewhoisinterestedinmathematicalmodeling,andespeciallyofsys-
temsthatinvolvechemistry.Whileaimedatchemicalengineeringstudentsandprofessionals,
itmaybeevenmoreusefultochemists,biochemists,biotechnologists,materialsscientists,
biologists,andanyoneelsewhowantstobuildmodelsusingbasicconceptsofanalysisand
Wolfram’sComputinglanguage,Mathematica.
Modelingisbasedoncomputationalthinkingtheskillofanalysiscombinedwiththeuseof
computationalmethods,bothsymbolicandnumerical,andwithgraphicalinformationdis-
plays.Thiscombinationmakesbuildingmodelsandusingthemtoconveythebehaviorofa
systemfasterandeasiertodothaniteverhasbeen.Theprocessofimprovingamodelisa
cycleofcomparisonofthemodel’sbehaviortomeasurementsmadeoftherealsystem.Suc-
cessiveimprovementsbringthemodelclosertorealitywitheachcycleofcomparisonand
subsequentchange.Amodelcanbeginatarelativelyprimitivestatewithananalysisthatac-
countsforonlythegrossestfeaturesofthesystem,andthenitcanberefinedaswelearnmore
aboutthesystemandincorporatethatlearningintotheanalysis.Thatthefirstmodeldevel-
opedisoftena“learning”modelisfine,becausethelearningmodelisthestartingpointfor
theconstructionofmoresophisticatedmodelthatmayeventuallybringtogetherasetofsub-
modelsthatareintegratedintooneoverallmodel.Ultimately,amodelapprehendsthatwhich
weknow,andneedtoknow,aboutthesystem.
Thereasonthelearningmodelisimportantisthatitletsusbeginthethoughtprocessesof
analysis.Modeling,issomewhatlikewriting-bothhavetostartbyputtingideasdownonpa-
per.Gettingstarted,isthemostimportantstepsinthewholeprocess.Beingabletogetstarted
becomeseasier,ifwebeginwithalearningmodel.Thisbookteachesyouhowtobuildsimple
learningmodelsbydoingstraightforwardanalysisandcomputing.Ifyoucangetthespiritof
doingmodelsatthelevelofthisbook,thenitiscertainthatyouwillhaveanimportantand
usefulskillandyouwillbereadilyabletotransitiontomorecomplexandsophisticatedanal-
ysesandmodelsasyourknowledgegrowsandastheproblemdemands.
ix