Simultaneous Mass Transfer and Chemical Reactions in Engineering Science

666 Pages·2023·6.025 MB·English

by  Bertram K. C. Chan

SimultaneousMassTransferandChemicalReactionsinEngineering
Science
Simultaneous Mass Transfer and Chemical
Reactions in Engineering Science
Bertram K. C. Chan
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PrintISBN:978-3-527-34665-3
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Typesetting Straive,Chennai,India
Dedicatedto
● thegloryofGod,
● mybetterhalfMarieNashedYacoubChan,and
● the fond memories of my high school physical science teacher, the Rev. Brother
Vincent Cotter, BSc, at the De La Salle Catholic College, Cronulla, Sydney, New
SouthWales,Australia,aswellasmyformerprofessorsinChemicalEngineeringin
Australia,including:
– attheUniversityofNewSouthWales:
Professor Geoffrey Harold Roper and Visiting Professor Thomas Hamilton
Chilton,fromtheUniversityofDelaware,USA
– andattheUniversityofSydney:
ProfessorThomasGirvanHunterandProfessorRudolfGeorgeHermanPrince.
vii
Contents
Preface xiii
AuthorBiography xv
1 IntroductiontoSimultaneousMassTransferandChemical
ReactionsinEngineeringScience 1
1.1 Gas–LiquidReactions 1
1.1.1 SimultaneousBiomolecularReactionsandMassTransfer 2
1.1.1.1 TheBiomedicalEnvironment 2
1.1.1.2 TheIndustrialChemistryandChemicalEngineeringEnvironment 3
1.1.2 Conclusions 6
1.1.3 Summary 6
1.2 TheModelingofGas–LiquidReactions 7
1.2.1 FilmTheoryofMassTransfer 7
1.2.2 SurfaceRenewalTheoryofMassTransfer 9
1.2.3 AbsorptionintoaQuiescentLiquid 11
1.2.3.1 AbsorptionAccompaniedbyChemicalReactions 13
1.2.3.2 IrreversibleReactions 13
1.2.4 AbsorptionintoAgitatedLiquids 17
1.2.4.1 AnExampleofaFirst-OrderReaction 19
1.2.4.2 TheFilmModel 20
1.3 TheMathematicalTheoryofSimultaneousMassTransferandChemical
Reactions 20
1.3.1 PhysicalAbsorption 21
1.3.2 ChemicalAbsorption 21
1.3.2.1 PreliminaryRemarksonSimultaneousMassTransfer(Absorption)with
ChemicalReactions 21
1.3.2.2 SomeSolutionstotheMathematicalModelsoftheTheoryof
SimultaneousMassTransferandChemicalReactions 22
1.3.2.3 ApproximateClosedFormSolutions 23
1.3.3 NumericalSolutions 29
1.4 DiffusiveModelsofEnvironmentalTransport 30
FurtherReading 30
viii Contents
2 DataAnalysisUsingRProgramming 31
2.1 DataandDataProcessing 32
2.1.1 Introduction 32
2.1.2 DataCoding 33
2.1.2.1 AutomatedCodingSystems 34
2.1.3 DataCapture 34
2.1.4 DataEditing 35
2.1.5 Imputations 35
2.1.6 DataQuality 36
2.1.7 QualityAssurance 36
2.1.8 QualityControl 36
2.1.9 QualityManagementinStatisticalAgencies 36
2.1.10 ProducingResults 37
2.2 BeginningR 38
2.2.1 RandStatistics 38
2.2.2 AFirstSessionUsingR 40
2.2.3 TheREnvironment(ThisisImportant!) 52
2.3 RasaCalculator 54
2.3.1 MathematicalOperationsUsingR 54
2.3.2 AssignmentofValuesinR,andComputationsUsingVectorsand
Matrices 56
2.3.3 ComputationsinVectorsandSimpleGraphics 57
2.3.4 UseofFactorsinRProgramming 57
2.3.4.1 BodyMassIndex 59
2.3.5 SimpleGraphics 59
2.3.6 xasVectorsandMatricesinStatistics 62
2.3.7 SomeSpecialFunctionsthatCreateVectors 64
2.3.8 ArraysandMatrices 65
2.3.9 UseoftheDimensionFunctiondim()inR 65
2.3.10 UseoftheMatrixFunctionmatrix()inR 66
2.3.11 SomeUsefulFunctionsOperatingonMatricesinR:colnames,
rownames,andt(fortranspose) 66
2.3.12 NA“NotAvailable”forMissingValuesinDatasets 67
2.3.13 SpecialFunctionsthatCreateVectors 68
2.4 UsingRinDataAnalysisinHumanGeneticEpidemiology 73
2.4.1 EnteringDataattheRCommandPrompt 73
2.4.1.1 CreatingaData-FrameforRComputationUsingtheEXCEL
Spreadsheet(onaWindowsPlatform) 73
2.4.1.2 ObtainingaDataFramefromaTextFile 75
2.4.1.3 DataEntryandAnalysisUsingtheFunctiondata.entry() 77
2.4.1.4 DataEntryUsingSeveralAvailableRFunctions 77
2.4.1.5 DataEntryandAnalysisUsingtheFunctionscan() 79
2.4.1.6 DataEntryandAnalysisUsingtheFunctionSource() 81
2.4.1.7 DataEntryandAnalysisUsingtheSpreadsheetInterfaceinR 82
Contents ix
2.4.1.8 HumanGeneticEpidemiologyUsingR:TheCRANPackage
Genetics 83
2.4.2 TheFunctionlist()andtheConstructionofdata.frame()inR 84
2.4.3 StockMarketRiskAnalysis 87
2.4.3.1 Univariate,Bivariate,andMultivariateDataAnalysis 87
2.A Appendix.DocumentationforthePlotFunction 109
2.A.1 Description 109
2.A.2 Usage 109
2.A.3 Arguments 109
2.A.4 Details 109
2.A.5 SeeAlso 110
FurtherReading 110
3 ATheoryofSimultaneousMassTransferandChemical
ReactionswithNumericalSolutions 111
3.1 Introduction 111
3.1.1 AClassicalExperimentalStudyofSimultaneousAbsorptionofCarbon
DioxideandAmmoniainWater 111
3.1.2 PhysicalAbsorption 112
3.1.2.1 Results 113
3.2 BiomolecularReactions 114
3.2.1 OccurrencesofSimultaneousBiomolecularReactionsandMassTransfer
AreCommoninManyBiomedicalEnvironments 114
3.3 SomeExamplesinChemicalEngineeringSciences 115
3.3.1 SimultaneousChemicalReactionsandMassTransfer 115
3.4 SomeModelsintheDiffusionalOperationsofEnvironmentalTransport
UnaccompaniedbyChemicalReactions 116
3.4.1 DiffusionModelsofEnvironmentalTransport 116
3.4.2 Advection–DiffusionModelsofEnvironmentalTransport 116
3.5 TheConceptofDiffusion 116
3.5.1 Publishers’Remarks 116
3.5.2 Fick’sLawsofDiffusion 117
3.5.2.1 Fick’sFirstLawofDiffusion(Steady-StateLaw) 117
3.5.2.2 Fick’sSecondLawofDiffusion 119
3.5.3 DerivationofFick’sLawsofDiffusion 120
3.5.3.1 Remarks:AdditionalRemarksonFick’sLawsofDiffusion 120
3.5.3.2 ExampleSolutioninOneDimension:DiffusionLength 122
3.6 TheConceptoftheMassTransferCoefficient 122
3.7 TheoreticalModelsofMassTransfer 123
3.7.1 NernstOne-FilmTheoryModelandtheLewis–WhitmanTwo-Film
Model 123
3.7.1.1 GasTransferRates 123
3.7.1.2 TheNernstOne-FilmModel 123
3.7.1.3 MassTransferCoefficients 123
3.7.1.4 TheLewis–WhitmanTwo-FilmModel 124
x Contents
3.7.1.5 TheTwo-FilmModel 124
3.7.1.6 Single-FilmControl 126
3.7.1.7 Applications 126
3.7.2 Higbie’sPenetrationTheoryModel 127
3.7.3 Danckwerts’SurfaceRenewalTheoryModel 129
3.7.4 BoundaryLayerTheoryModel 131
3.7.4.1 Fluid–FluidInterfaces 131
3.7.4.2 Fluid–SolidInterfaces 131
3.7.4.3 Example:Prandtl’sExperimentalMassTransferfromaFlatPlate 131
3.7.5 MassTransferUnderLaminarFlowConditions 132
3.7.6 MassTransferPastSolidsUnderTurbulentFlow 132
3.7.7 SomeInterestingSpecialConditionsofMassTransfer 132
3.7.7.1 EquimolarCounter-DiffusionofAandB(N = −N ) 132
A B
3.7.7.2 ForLiquid-PhaseDiffusion 133
3.7.7.3 ConversionsFormulasforMassTransferCoefficientsinDifferent
Forms 134
3.7.8 ApplicationstoChemicalEngineeringDesign 134
3.7.8.1 DesigningaPackedColumnfortheAbsorptionofGaseousCO bya
2
LiquidSolutionofNaOH,UsingtheMathematicalModelof
SimultaneousGasAbsorptionwithChemicalReactions 134
3.7.8.2 CalculationofPackedHeightRequirementforReducingtheChlorine
ConcentrationinaChlorine–AirMixture 141
3.8 TheoryofSimultaneousBimolecularReactionsandMassTransferin
TwoDimensions 144
3.8.1 NumericalSolutionsofaModelinTermsofSimultaneousSemi-linear
ParabolicDifferentialEquations 144
3.8.1.1 TheoryofSimultaneousBimolecularReactionsandMassTransferin
TwoDimensions 144
3.8.2 ExistenceandUniquenessTheoremsofFirst-OrderLinearOrdinary
DifferentialEquations 174
3.8.2.1 DifferentialEquations 174
3.8.2.2 ContractionMappingsonaBanachSpace 174
3.8.2.3 ApplicationtoDifferentialEquations 177
3.8.3 AnExistenceTheoremoftheGoverningSimultaneousSemi-linear
ParabolicPartialDifferentialEquations 183
3.8.4 AUniquenessTheoremoftheGoverningSimultaneousSemi-linear
ParabolicPartialDifferentialEquations 188
3.9 TheoryofSimultaneousBimolecularReactionsandMassTransferin
TwoDimensions:FurtherCasesofPracticalInterests 192
3.9.1 CaseofStagnantFilmofFiniteThickness–Second-OrderIrreversible
Reactions 192
3.9.2 CaseofUnsteady-StateAbsorptionintheStagnantLiquid–Slow
First-OrderReaction(S&P325,328) 196
3.9.3 SimultaneousAbsorptionofTwoGasesinaLiquidinWhichEachThen
ReactsWithaThirdComponentintheLiquid 198
Contents xi
3.9.3.1 MathematicalModeling 199
3.9.3.2 AnalysisoftheModel:A+B→ 201
3.9.3.3 Discussions 201
3.9.3.4 FurtherTheoreticalAnalysis 202
3.9.4 SimultaneousAbsorptionofTwoGasesinaLiquidinWhichEachThen
ReactswithaThirdComponentintheLiquid 210
3.9.4.1 TheMathematicalModel 210
3.9.4.2 AnalysisoftheModel 210
3.9.4.3 BoundaryConditions 212
3.9.4.4 MassTransferCoefficients 212
3.9.5 CasesofSlowFirst-OrderReactions 213
3.9.5.1 CaseofUnsteady-StateAbsorptionintheStagnantLiquid 213
3.9.5.2 CaseofUnsteady-StateAbsorptionintheStagnantLiquid–Slow
First-OrderReactions 216
3.10 FurtherTheoreticalAnalysis 218
FurtherReading 219
4 NumericalWorkedExamplesUsingRforSimultaneousMass
TransferandChemicalReactions 221
4.1 AdvectionandConvection 221
4.1.1 Advection 221
4.1.2 Advectionvs.Convection 222
4.1.2.1 Meteorology 222
4.1.2.2 TheMathematicsofAdvection 222
4.1.2.3 TheAdvectionEquation 223
4.1.2.4 TheAdvectionOperatorintheIncompressibleNavier–Stokes
Equations 224
4.2 WorkedExamples 224
4.3 PartialDifferentialEquations 386
4.4 AParabolicPDE 387
4.4.1 Steady-StateSolution 388
4.4.2 TheMethodofLines 389
FurtherReading 390
5 MoreNumericalWorkedExamplesUsingRforSimultaneous
MassTransferandChemicalReactions 391
5.1 Introduction 391
5.2 Advection 391
5.2.1 Advectionvs.Convection 392
5.2.1.1 Meteorology 392
5.2.1.2 TheMathematicsofAdvection 392
5.2.1.3 TheAdvectionEquation 393
5.2.1.4 SolvingtheAdvectionEquation 393
5.2.1.5 TheAdvectionOperatorintheIncompressibleNavier–Stokes
Equations 394