Multiphase Equilibria of Complex Reservoir Fluids: An Equation of State Modeling Approach

220 Pages·2021·3.15 MB·English

by  Huazhou Li

Petroleum Engineering
Huazhou Li
Multiphase
Equilibria
of Complex
Reservoir Fluids
An Equation of State Modeling
Approach
Petroleum Engineering
Editor-in-Chief
GbengaOluyemi,RobertGordonUniversity,Aberdeen,Aberdeenshire,UK
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AmirmasoudKalantari-Dahaghi,DepartmentofPetroleumEngineering,West
VirginiaUniversity,Morgantown,WV,USA
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PA,USA
MartinFernø,DepartmentofPhysicsandTechnology,UniversityofBergen,
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Huazhou Li
Multiphase Equilibria
of Complex Reservoir Fluids
An Equation of State Modeling Approach
HuazhouLi
DepartmentofCivilandEnvironmental
Engineering,SchoolofMining
andPetroleumEngineering
UniversityofAlberta
Edmonton,AB,Canada
ISSN2366-2646 ISSN2366-2654 (electronic)
PetroleumEngineering
ISBN978-3-030-87439-1 ISBN978-3-030-87440-7 (eBook)
https://doi.org/10.1007/978-3-030-87440-7
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Stillnessiseasytomaintain.
Whathasnotyetemergediseasytoprevent.
Thebrittleiseasytoshatter.
Thesmalliseasytoscatter.
Solveitbeforeithappens.
Orderitbeforechaosemerges.
Atreeaswideasaman’sembracegrowsfromatinyshoot.
Atowerofninestoriesstartswithapileofdirt.
Aclimbofeighthundredfeetstartswherethefootstands.
Thosewhoactwillfail.
Thosewhoseizewilllose.
So,thesagedoesnotactandthereforedoesnotfail,doesnotseize
andthereforedoesnotlose.
Peoplefailatthethresholdofsuccess.
Beascautiousattheendasatthebeginning.
Thentherewillbenofailure.
Therefore,thesagedesiresnodesire,
doesnotvalueraretreasures,
learnswithoutlearning,
recoverswhatpeoplehaveleftbehind.
Hewantsallthingstofollowtheirownnaturebutdaresnotact.
—LaoTzu
TranslatedbyStefanStenudd
Preface
Ourearthiscomposedofmattersthatappearasdistinctphasestates.Theapparent
onesincludevaporphase,liquidphase,andsolidphase.Inatypicalsummerwalk
inasouthwestcommunityintheCityofEdmonton,onecouldeasilyspotastorm
pondthatisfilledwithwater,surroundedbybanks,andoverlaidbyair.Allthethree
phasescanbeidentifiedeasilywithnakedeyes.Thewaterappearsasaliquidphase,
thebanksappearasasolidphase,andtheairappearsasavaporphase.
If we drill a well that goes to the deeper part of the earth to tap oil and gas
resourcesfromahydrocarbon reservoir,wecanstillencounter theco-existence of
three-phasestatesinatinyporespacetherein,albeitbeingunobservablewithnaked
eyes.Thethreephaseswouldbeavaporhydrocarbonphase,aliquidhydrocarbon
phase, and a solid rock phase. However, the pressure and temperature condition
in the tiny pore space would be much more elevated than that in the storm pond.
Todescribetheaforementionedvapor-liquid-solidthree-phaseequilibriaunderboth
atmospheric and elevated conditions, we resort to thermodynamic models. Some
thermodynamic models are capable of modeling such multiphase equilibria over
extended pressure/temperature conditions. It is noted, nonetheless, that the solid
phaseintheabovetwoscenarioswouldbenormallyexcludedinthethermodynamic
modelsasitspresencehasatrivialeffectontheoverallphaseequilibria.
Butasolidphasemaybeofrelevancetopetroleumreservoirfluids.Complexfluid
mixtures, which do not only exhibit vapor-liquid phase equilibria, but also vapor-
liquid-solidphaseequilibria,havebeenincreasinglydiscoveredintheunderground
petroleumreservoirs.Thesolidphasesmaybeintheformofasphaltenes,waxes,and
hydrates.Itishighlyimportanttoproperlycharacterizethestaticphasebehavioras
wellasthedynamicflowbehaviorofthesecomplexfluidsoverawiderangeofcondi-
tionsbecausetheycanexertalargeimpactontheproductivityofpetroleumreservoirs.
Forexample,waxprecipitationinaparaffinicreservoirfluid,duetothechangeof
temperature/pressureconditionsalongtheproductiontubing,maychokethenormal
oilproductionorevenrenderthewellunproductive.Tounderstandwhenandwhere
waxprecipitationoccurs,onehastobuildathermodynamicmodelthatcanreliably
predictthephasebehaviorofsuchparaffinicreservoirfluidundervariedconditions.
vii
viii Preface
This monograph will cover the fundamental thermodynamic frameworks
governing the multiphase equilibria of complex reservoir fluids. An emphasis will
begiventotheuseofCubicEquationofState(CEOS)modelstodescribethephase
equilibriaofcomplexreservoirfluidsaswellasthecorrespondingalgorithmimple-
mentations.Thismonographprovidesdetailedcoverageofthetwoessentialmodules
ofatypicalmultiphaseequilibriumcalculationalgorithm,i.e.,stabilitytestandmulti-
phaseflash.Complementarytootherbookswithsimilartitles,thismonographgives
astate-of-the-artoverviewofthemostrobustandefficientversionsofthemultiphase
equilibriumcalculationalgorithmswhicharedevelopedintheveryrecentyears.
Themonographiscomprisedoffivechapters.Chapter1givesabriefintroduction
tothefundamentaltheoriesrelatedtothephasebehaviormodelingofreservoirfluids.
Chapter2reviewsthepopularCEOSs.Chapter3focusesonthetheoreticaltreatise
andnumericalimplementationofphasestabilitytest.InChap.4,themathematical
modelsandnumericalalgorithmsrelatedtotwo-phaseequilibriumcalculationsare
presented.ThemonographendswithChap.5whichcoversthemathematicalmodels
andnumericalalgorithmsdedicatedtomultiphaseequilibriumcalculations.Atthe
end of each chapter, example questions are provided to exemplify the important
conceptsandproceduresintroducedintheprecedingsections.Ihopethissuccinct
monographwillbeofvaluetoacademicsandengineersworkingintherelatedarea.
IwouldliketosincerelythankmyformerPh.D.advisor,Dr.DaoyongYangatthe
UniversityofRegina,whointroducedmetotheinterestingfieldofphasebehavior
ofreservoirfluidsin2009.IwouldalsoliketothankmyPh.D.studentMr.Lingfei
XuforcalculatingthephaseenvelopeshowninQuestion4ofChap.2.Lastbutnot
least, I am grateful for the financial support provided by the University of Alberta
andtheNaturalSciencesandEngineeringResearchCouncilofCanada(NSERC).
Edmonton,Canada HuazhouLi
Contents
1 Introduction ................................................... 1
1.1 FirstandSecondLawsofThermodynamics .................... 1
1.2 FundamentalThermodynamicRelations ....................... 2
1.3 PhaseStabilityandPhaseEquilibriumConditions ............... 4
1.4 FugacityandFugacityCoefficients ............................ 5
1.5 GibbsPhaseRule ........................................... 7
1.6 PhaseBehaviorofPureFluids ................................ 7
1.7 PhaseBehaviorofBinaryMixtures ........................... 9
1.8 GeneralPhaseBehaviorofComplexReservoirFluids ........... 12
1.9 ExampleQuestions ......................................... 18
References ..................................................... 23
2 CubicEquationofState ......................................... 25
2.1 BriefOverviewofMostPopularEOSs ........................ 25
2.2 vdWEOS ................................................. 27
2.3 RKEOS .................................................. 29
2.4 SRKEOS ................................................. 30
2.5 PREOS ................................................... 36
2.6 VolumeTranslationModelsinCEOS .......................... 41
2.6.1 HistoricalDevelopment ............................... 41
2.6.2 Impact of Using Volume Translation on Phase
EquilibriumCalculations .............................. 45
2.6.3 Distance-Function-BasedVolumeTranslationModel
forPREOSandSRKEOS ............................ 47
2.6.4 Pressure–Volume Crossover Issue Caused
by Temperature-Dependent Volume Translation
Models ............................................. 54
2.7 Huron-VidalMixingRule ................................... 57
2.8 FurtherReadings ........................................... 60
2.9 ExampleQuestions ......................................... 60
References ..................................................... 78
ix
x Contents
3 PhaseStabilityTest ............................................. 83
3.1 GibbsFreeEnergyAnalysisofPhaseEquilibria ................ 83
3.2 DerivationoftheTPDFunction .............................. 88
3.3 SolutionMethods ........................................... 92
3.3.1 EquationSolvingApproach ........................... 92
3.3.2 Trust-Region-BasedMinimizationApproach ............. 110
3.4 ExampleQuestions ......................................... 122
References ..................................................... 137
4 Two-PhaseEquilibriumCalculations ............................. 139
4.1 EqualFugacityCondition .................................... 139
4.2 DerivationofRREquation ................................... 139
4.3 OtherFormsofRREquation ................................. 143
4.4 NumericalAlgorithmofTwo-PhaseEquilibriumCalculations .... 144
4.5 ExampleQuestions ......................................... 151
References ..................................................... 160
5 MultiphaseEquilibriumCalculations ............................ 163
5.1 MultiphaseFlashCalculationTheories ........................ 163
5.1.1 RREquationforMultiphaseFlash ...................... 163
5.1.2 MultiphaseFlashApproachProposedbyMichelsen
(1994) .............................................. 165
5.1.3 MultiphaseFlashApproachProposedbyLeibovici
andNichita(2008) ................................... 166
5.1.4 MultiphaseFlashApproachProposedbyOkunoetal.
(2010) .............................................. 167
5.1.5 MultiphaseFlashApproachProposedbyPetitfrere
andNichita(2014)andPanetal.(2021) ................. 169
5.2 General Trust-Region-Based Three-Phase Equilibrium
CalculationAlgorithm ...................................... 170
5.3 Vapor–Liquid-LiquidThree-PhaseEquilibriumCalculation
Algorithms ................................................ 172
5.4 Vapor–Liquid-AqueousThree-PhaseEquilibriumCalculation
Algorithms ................................................ 188
5.5 Free-Water and Augmented Free-Water Three-Phase
EquilibriumCalculationAlgorithms ........................... 190
5.6 Vapor–Liquid-Asphaltene Three-Phase Equilibrium
CalculationAlgorithms ...................................... 190
5.7 FurtherDiscussion .......................................... 198
5.8 FurtherReadings ........................................... 202
5.9 ExampleQuestions ......................................... 202
References ..................................................... 208