Process modeling and simulation for chemical engineers : theory and practice

356 Pages·2017·6.415 MB·English

by  Upreti, Simant Ranjan

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PROCESS MODELING
AND SIMULATION FOR
CHEMICAL ENGINEERS
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PROCESS MODELING
AND SIMULATION FOR
CHEMICAL ENGINEERS
THEORY AND PRACTICE
SimantRanjanUpreti
DepartmentofChemicalEngineering,
RyersonUniversity,
Toronto,Canada
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Thiseditionfirstpublished2017
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LibraryofCongressCataloging-in-PublicationData
Names:Upreti,SimantRanjan,author.
Title:Processmodelingandsimulationforchemicalengineers:theoryand
practice/SimantRanjanUpreti.
Description:Chichester,UK;Hoboken,NJ:JohnWiley&Sons,2017.|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016053339|ISBN9781118914687(cloth)|ISBN9781118914663
(epub)
Subjects:LCSH:Chemicalprocesses–Mathematicalmodels.|Chemical
processes–Dataprocessing.
Classification:LCCTP155.7.U672017|DDC660/.284401–dc23
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CONTENTS
Preface xiii
Notation xv
1 Introduction 1
1.1 System 1
1.1.1 UniformSystem 2
1.1.2 PropertiesofSystem 2
1.1.3 ClassificationofSystem 3
1.1.4 Model 3
1.2 Process 3
1.2.1 ClassificationofProcesses 4
1.2.2 ProcessModel 5
1.3 ProcessModeling 6
1.3.1 Relations 7
1.3.2 Assumptions 7
1.3.3 VariablesandParameters 8
1.4 ProcessSimulation 9
1.4.1 Utility 9
1.4.2 SimulationMethods 10
1.5 DevelopmentofProcessModel 11
1.6 LearningaboutProcess 13
1.7 SystemSpecification 14
Bibliography 16
Exercises 16
2 FundamentalRelations 17
2.1 BasicForm 17
2.1.1 Application 19
2.2 MassBalance 21
viii
2.2.1 MicroscopicBalances 21
2.2.2 EquationofChangeforMassFraction 23
2.3 MoleBalance 24
2.3.1 MicroscopicBalances 24
2.3.2 EquationofChangeforMoleFraction 25
2.4 MomentumBalance 26
2.4.1 ConvectiveMomentumFlux 27
2.4.2 TotalMomentumFlux 28
2.4.3 MacroscopicBalance 29
2.4.4 MicroscopicBalance 31
2.5 EnergyBalance 33
2.5.1 MicroscopicBalance 33
2.5.2 MacroscopicBalance 35
2.6 EquationofChangeforKineticandPotentialEnergy 38
2.6.1 MicroscopicEquation 38
2.6.2 MacroscopicEquation 40
2.7 EquationofChangeforTemperature 41
2.7.1 MicroscopicEquation 41
2.7.2 MacroscopicEquation 42
2.A EnthalpyChangefromThermodynamics 44
2.B DivergenceTheorem 48
2.C GeneralTransportTheorem 50
2.D EquationsinCartesian,CylindricalandSphericalCoordinateSystems 53
2.D.1 EquationsofContinuity 54
2.D.2 EquationsofContinuityforIndividualSpecies 54
2.D.3 EquationsofMotion 55
2.D.4 EquationsofChangeforTemperature 56
Bibliography 57
Exercises 57
3 ConstitutiveRelations 59
3.1 Diffusion 59
3.1.1 MulticomponentMixtures 60
3.2 ViscousMotion 60
3.2.1 NewtonianFluids 61
3.2.2 Non-NewtonianFluids 62
3.3 ThermalConduction 63
3.4 ChemicalReaction 63
3.5 RateofReaction 65
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3.5.1 EquationsofChangeforMoles 66
3.5.2 EquationsofChangeforTemperature 67
3.5.3 MacroscopicEquationofChangeforTemperature 69
3.6 InterphaseTransfer 71
3.7 ThermodynamicRelations 72
3.A EquationsinCartesian,CylindricalandSphericalCoordinateSystems 74
3.A.1 EquationsofContinuityforBinarySystems 74
3.A.2 EquationsofMotionforNewtonianFluids 75
3.A.3 EquationsofChangeforTemperature 76
References 77
Bibliography 77
Exercises 78
4 ModelFormulation 79
4.1 Lumped-ParameterSystems 80
4.1.1 IsothermalCSTR 80
4.1.2 FlowthroughEccentricReducer 83
4.1.3 LiquidPreheater 84
4.1.4 Non-IsothermalCSTR 87
4.2 Distributed-ParameterSystems 90
4.2.1 NicotinePatch 90
4.2.2 FluidFlowbetweenInclinedParallelPlates 93
4.2.3 TaperedFin 96
4.2.4 ContinuousMicrochannelReactor 99
4.2.5 OxygenTransporttoTissues 103
4.2.6 DermalHeatTransferinCylindricalLimb 106
4.2.7 SolventInducedHeavyOilRecovery 108
4.2.8 HydrogelTablet 112
4.2.9 NeutronDiffusion 117
4.2.10 HortonSphere 119
4.2.11 ReactionsaroundSolidReactant 122
4.3 FluxesalongNon-LinearDirections 127
4.3.1 SaccadicMovementofanEye 128
4.A InitialandBoundaryConditions 131
4.A.1 InitialCondition 131
4.A.2 BoundaryCondition 131
4.A.3 PeriodicCondition 132
4.B ZeroDerivativeatthePointofSymmetry 133
4.C EquationofMotionalongtheRadialDirectioninCylindricalCoordinates 134
References 137
x
Exercises 137
5 ModelTransformation 139
5.1 TransformationbetweenOrthogonalCoordinateSystems 139
5.1.1 ScaleFactors 139
5.1.2 DifferentialElements 142
5.1.3 VectorRepresentation 143
5.1.4 DerivativesofUnitVectors 144
5.1.5 DifferentialOperators 146
5.2 TransformationbetweenArbitraryCoordinateSystems 155
5.2.1 TransformationofVelocity 155
5.2.2 TransformationofSpatialDerivatives 156
5.2.3 CorrectnessofTransformationMatrices 156
5.3 LaplaceTransformation 161
5.3.1 Examples 162
5.3.2 PropertiesofLaplaceTransforms 164
5.3.3 SolutionofLinearDifferentialEquations 168
5.4 MiscellaneousTransformations 178
5.4.1 HigherOrderDerivatives 178
5.4.2 Scaling 178
5.4.3 ChangeofIndependentVariable 179
5.4.4 Semi-InfiniteDomain 179
5.4.5 Non-AutonomoustoAutonomousDifferentialEquation 180
5.A DifferentialOperatorsinanOrthogonalCoordinateSystem 180
5.A.1 GradientofaScalar 180
5.A.2 DivergenceofaVector 181
5.A.3 LaplacianofaScalar 184
5.A.4 CurlofaVector 184
References 186
Bibliography 186
Exercises 186
6 ModelSimplificationandApproximation 189
6.1 ModelSimplification 189
6.1.1 ScalingandOrderingAnalysis 190
6.1.2 Linearization 193
6.2 ModelApproximation 200
6.2.1 DimensionalAnalysis 201
6.2.2 ModelFitting 204
6.A LinearFunction 220
6.B ProofofBuckinghamPiTheorem 221
xi
6.C Newton’sOptimizationMethod 223
References 224
Bibliography 224
Exercises 225
7 ProcessSimulation 227
7.1 AlgebraicEquations 227
7.1.1 LinearAlgebraicEquations 227
7.1.2 Non-LinearAlgebraicEquations 236
7.2 DifferentialEquations 241
7.2.1 OrdinaryDifferentialEquations 242
7.2.2 ExplicitRunge–KuttaMethods 242
7.2.3 Step-SizeControl 246
7.2.4 StiffEquations 247
7.3 PartialDifferentialEquations 253
7.3.1 FiniteDifferenceMethod 255
7.4 DifferentialEquationswithSplitBoundaries 263
7.4.1 ShootingNewton–RaphsonMethod 264
7.5 PeriodicDifferentialEquations 268
7.5.1 ShootingNewton–RaphsonMethod 268
7.6 ProgrammingofDerivatives 271
7.7 Miscellanea 274
7.7.1 IntegrationofDiscreteData 274
7.7.2 RootsofaSingleAlgebraicEquation 276
7.7.3 CubicEquations 278
7.A PartialPivotingforMatrixInverse 281
7.B DerivationofNewton–RaphsonMethod 281
7.B.1 QuadraticConvergence 282
7.C GeneralDerivationofFiniteDifferenceFormulas 284
7.C.1 FirstDerivative,CenteredSecondOrderFormula 285
7.C.2 SecondDerivative,ForwardSecondOrderFormula 286
7.C.3 ThirdDerivative,MixedFourthOrderFormula 287
7.C.4 CommonFiniteDifferenceFormulas 289
References 291
Bibliography 291
Exercises 291
8 MathematicalReview 295
8.1 OrderofMagnitude 295
xii
8.2 Big-ONotation 295
8.3 AnalyticalFunction 295
8.4 Vectors 296
8.4.1 VectorOperations 297
8.4.2 Cauchy–SchwarzInequality 302
8.5 Matrices 302
8.5.1 Terminology 303
8.5.2 MatrixOperations 304
8.5.3 OperatorInequality 305
8.6 Tensors 306
8.6.1 Multilinearity 306
8.6.2 Coordinate-Independence 306
8.6.3 RepresentationofSecondOrderTensor 307
8.6.4 EinsteinorIndexNotation 308
8.6.5 KroneckerDelta 310
8.6.6 OperationsInvolvingVectorsandSecondOrderTensors 310
8.7 Differential 318
8.7.1 Derivative 318
8.7.2 PartialDerivativeandDifferential 318
8.7.3 ChainRuleofDifferentiation 319
8.7.4 MaterialandTotalDerivatives 321
8.8 TaylorSeries 322
8.8.1 MultivariableTaylorSeries 323
8.8.2 FirstOrderTaylorExpansion 323
8.9 L’Hoˆpital’sRule 326
8.10 Leibniz’sRule 326
8.11 IntegrationbyParts 327
8.12 Euler’sFormulas 327
8.13 SolutionofLinearOrdinaryDifferentialEquations 327
8.13.1 SingleFirstOrderEquation 327
8.13.2 SimultaneousFirstOrderEquations 328
Bibliography 332
Index 333