Lurie Modeling of Oil Product and Gas Pipeline Transportation

230 Pages·2008·1.783 MB·English

by  Mikhail V. Lurie, Emmanuil Sinaiski

MichaelV.Lurie
ModelingofOilProductand
GasPipelineTransportation
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Michael V. Lurie
Modeling of Oil Product and
Gas Pipeline Transportation
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carefullyproduced.Nevertheless,authors,
Prof.Dr.MichaelV.Lurie editors,andpublisherdonotwarrantthe
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ofOilandGas includingthisbook,tobefreeoferrors.
Moscow,RussianFederation Readersareadvisedtokeepinmindthat
statements,data,illustrations,procedural
Translation detailsorotheritemsmayinadvertentlybe
EmmanuilG.Sinaiski inaccurate.
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2008WILEY-VCHVerlagGmbH&Co.
KGaA,Weinheim
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ISBN: 978-3-527-40833-7
V
InmemoryoftheTeacher–academicianLeonidI.Sedov
ModelingofOilProductandGasPipelineTransportation.MichaelV.Lurie
Copyright2008WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40833-7
VII
Foreword
Thisbookisdedicatedfirstandforemosttoholdersofamaster’sdegreeand
postgraduatestudentsofoilandgasinstituteswhohavedecidedtospecialize
inthefieldoftheoreticalproblemsinthetransportationofoil,oilproductsand
gas. It contains methods of mathematical modeling of the processes taking
placeinpipelineswhentransportingthesemedia.
By the term mathematical model is understood a system of mathematical
equationsinwhichframeworkaclassofsomeprocessescouldbestudied.The
solutionoftheseequationsprovidesvaluesofparameterswithoutcarryingout
modeland,especially,fullscaleexperiments.
Physical laws determining the dynamics of fluids and gases in pipes are
presented.Itisthenshownhowtheselawsaretransformedintomathematical
equations that are at the heart of one or another mathematical model. In
the framework of each model, are formulated problems with the aim of
investigating concrete situations. In doing so there are given methods of its
solution.
Thebookisself-sufficientforstudyingthesubjectbutthetextisoutlinedin
suchawaythatitimpelsthereadertoaddressoneselftocloseracquaintance
ofconsideredproblemcontaininginspecialtechnicalliterature.
ProfessorMichaelV.Lurie
Moscow
ModelingofOilProductandGasPipelineTransportation.MichaelV.Lurie
Copyright2008WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40833-7
IX
Contents
DedicationPage V
Foreword VII
Preface XIII
ListofSymbols XV
1 FundamentalsofMathematicalModelingofOne-Dimensional
FlowsofFluidandGasinPipelines 1
1.1 MathematicalModelsandMathematicalModeling 1
1.1.1 GoverningFactors 3
1.1.2 SchematizationofOne-DimensionalFlowsofFluidsandGases
inPipelines 4
1.2 IntegralCharacteristicsofFluidVolume 5
1.3 TheLawofConservationofTransportedMediumMass.
TheContinuityEquation 7
1.4 TheLawofChangeinMomentum.TheEquationofFluidMotion 9
1.5 TheEquationofMechanicalEnergyBalance 11
1.5.1 BernoulliEquation 15
1.5.2 InputofExternalEnergy 16
1.6 EquationofChangeinInternalMotionKineticEnergy 17
1.6.1 HydraulicLosses(ofMechanicalEnergy) 18
1.6.2 FormulasforCalculationoftheFactorλ(Re,ε) 20
1.7 TotalEnergyBalanceEquation 22
1.8 CompleteSystemofEquationsforMathematicalModeling
ofOne-DimensionalFlowsinPipelines 29
2 ModelsofTransportedMedia 31
2.1 ModelofaFluid 31
2.2 ModelsofIdealandViscousFluids 32
2.3 ModelofanIncompressibleFluid 34
2.4 ModelofElastic(SlightlyCompressible)Fluid 34
ModelingofOilProductandGasPipelineTransportation.MichaelV.Lurie
Copyright2008WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40833-7
X Contents
2.5 ModelofaFluidwithHeatExpansion 34
2.6 ModelsofNon-NewtonianFluids 36
2.7 ModelsofaGaseousContinuum 38
2.7.1 ModelofaPerfectGas 39
2.7.2 ModelofaRealGas 39
2.8 ModelofanElasticDeformablePipeline 42
3 StructureofLaminarandTurbulentFlowsinaCircularPipe 45
3.1 LaminarFlowofaViscousFluidinaCircularPipe 45
3.2 LaminarFlowofaNon-NewtonianPowerFluidinaCircularPipe 47
3.3 LaminarFlowofaViscous-PlasticFluidinaCircularPipe 49
3.4 TransitionofLaminarFlowofaViscousFluidtoTurbulentFlow 51
3.5 TurbulentFluidFlowinaCircularPipe 52
3.6 AMethodtoControlHydraulicResistancebyInjectionof
Anti-TurbulentAdditiveintotheFlow 62
3.7 GravityFluidFlowinaPipe 65
4 ModelingandCalculationofStationaryOperatingRegimesofOil
andGasPipelines 73
4.1 ASystemofBasicEquationsforStationaryFlowofan
IncompressibleFluidinaPipeline 73
4.2 BoundaryConditions.ModelingoftheOperationofPumpsand
Oil-PumpingStations 75
4.2.1 Pumps 75
4.2.2 Oil-PumpingStation 78
4.3 CombinedOperationofLinearPipelineSectionandPumping
Station 81
4.4 CalculationsontheOperationofaPipelinewithIntermediate
Oil-PumpingStations 84
4.5 CalculationsonPipelineStationaryOperatingRegimesin
FluidPumpingwithHeating 87
4.6 ModelingofStationaryOperatingRegimesofGas-PipelineSections 92
4.6.1 DistributionofPressureinStationaryGasFlowinaGas-Pipeline 94
4.6.2 PressureDistributioninaGas-PipelinewithGreatDifference
inElevations 96
4.6.3 CalculationofStationaryOperatingRegimes
ofaGas-Pipeline(GeneralCase) 97
4.6.4 InvestigationofThermalRegimesofaGas-PipelineSection 98
4.7 ModelingofBlowerOperation 100
5 ClosedMathematicalModelsofOne-DimensionalNon-Stationary
FlowsofFluidandGasinaPipeline 109
5.1 AModelofNon-StationaryIsothermalFlowofaSlightlyCompressible
FluidinaPipeline 109
5.2 AModelofNon-StationaryGasFlowinaPipeline 112
Contents XI
5.3 Non-StationaryFlowofaSlightlyCompressibleFluid
inaPipeline 113
5.3.1 WaveEquation 113
5.3.2 PropagationofWavesinanInfinitePipeline 115
5.3.3 PropagationofWavesinaSemi-InfinitePipeline 117
5.3.4 PropagationofWavesinaBoundedPipelineSection 119
5.3.5 MethodofCharacteristics 121
5.3.6 Initial,BoundaryandConjugationConditions 124
5.3.7 HydraulicShockinPipes 127
5.3.8 AccountingforVirtualMass 134
5.3.9 HydraulicShockinanIndustrialPipelineCausedbyInstantaneous
ClosingoftheGateValve 135
5.4 Non-IsothermalGasFlowinGas-Pipelines 138
5.5 GasOutflowfromaPipelineintheCaseofaCompleteBreak
ofthePipeline 146
5.6 MathematicalModelofNon-StationaryGravityFluidFlow 149
5.7 Non-StationaryFluidFlowwithFlowDiscontinuities
inaPipeline 152
6 DimensionalTheory 157
6.1 DimensionalandDimensionlessQuantities 157
6.2 Primary(Basic)andSecondary(Derived)MeasurementUnits 158
6.3 DimensionalityofQuantities.DimensionalFormula 159
6.4 ProofofDimensionalFormula 161
6.5 CentralTheoremofDimensionalTheory 163
6.6 Dimensionally-DependentandDimensionally-Independent
Quantities 164
6.7 Buckingham(cid:1)-Theorem 168
7 PhysicalModelingofPhenomena 173
7.1 SimilarityofPhenomenaandthePrincipleofModeling 173
7.2 SimilarityCriteria 174
7.3 ModelingofViscousFluidFlowinaPipe 175
7.4 ModelingGravityFluidFlow 176
7.5 ModelingtheFluidOutflowfromaTank 178
7.6 SimilarityCriteriafortheOperationofCentrifugalPumps 179
8 DimensionalityandSimilarityinMathematicalModeling
ofProcesses 183
8.1 OriginationofSimilarityCriteriaintheEquationsofa
MathematicalModel 183
8.2 One-DimensionalNon-StationaryFlowofaSlightlyCompressible
FluidinaPipeline 184
8.3 GravityFluidFlowinaPipeline 186
8.4 PipelineTransportationofOilProducts.Batching 187