PVT and phase behavior of petroleum reservior fluids

202 Pages·1998·47.65 MB·English

by  Ali Danesh

Pill’
MID
Volumes1-5, 7, 10,11, 13.14. 16, 17,21,22.23-27, 29.31 areout01print.
6 FundamentalsofNumerical ReservoirSimulation PHASE BEHAVIOUR OF
8 FundamentalsofReservoirEngineering
9 Compactionand FluidMigration
PE:1RO
12 FundamentalsofFracturedReservoirEngineering LEOlvi RESERVOIR FLUIDS
iSa FundamentalsofWell-logInterpretation,1.The acquisitionofloggingdata
15b FundamentalsofWell-logInterpretation,2.Tire interpretationofloggingdata
18a ProductionandTransportofOilandGas,A. Flowmechanicsandproduction
18b Production andTransportofOilandGas,8.GatheringandTransport
t9a SurfaceOperationsinPetroleumProduction, I
19b SurfaceOperationsinPetroleumProduction, II
20 Geo/ogyinPetroleumProduction All DANESH
28 WellCementing
Department ofPetroleum Engineering
30 Carbonate ReservoirCharacterization:AGeologic-EngineeringAnalysis, PartI Heriot Watt University
32 FluidMechanicsforPetroleumEngineers
Edinburgh, Scotland
33 PetroleumRelatedRockMechanics
34 APracticalCompaniontoReservoirStimulation
35 HydrocarbonMigrationSystemsAnalysis
36 ThePracticeofReservoirEngineering
37 ThermalPropertiesandTemperalurerelatedBehaviorofRock/fluid Syslems
38 StudiesinAbnormalPressures
39 MicrobialEnhancementofOilRecovery—Re~enAldvances
Proceedingsofthe1992lOternationalConferenceonMicrobialEnhanced OilRecovery
—
40. AsphaltenesandAsphalts,I
41 SubsidenceduetoFluidWithdrawal
42 CasingDesign— TheoryandPractice
43 Tracers intheOilField -
44 CarbonateReservoirCharacterization:A Geologic-EngineeringAnalysis, Part II
45 ThermalModelingofPetroleumGeneration: TheoryandApplications I
46 HydrocarbonExplorationandProduction -
47 PVTandPhaseBehaviour ofPetroleum ReservoirFluids
______
1998
ELSEVIER
~--
Amsterdam Lausanne NewYork Oxford Shannon Singapore Tokyo
— -~ — — — —
CONTENTS
PREFACE
NOMENCLA1’URE
PHASEBEHAVIOUR FUNDAMENTALS
l:l RESERVOIR FLUIDCOMPOSITION
1.2 PhASEBEhAVIOUR 3
I’urc (‘onipound 4
(‘orrcspondirig Stales It)
MulticoniponentMi’xture IS
LibraryofCongressCataloginginPublicationData 22
Acatalogrecordfrom theLibraryofCongresshasbeenappliedfor. 1.3 (‘LASSIFICATIONOF RESERVOIRFLUIDS
l)ryGas 24
WetGas 25
25
Gas Condensate
VolatileOil 27
BlackOil 28
1.4 REFERENCES 29
30
1.5 EXERCISES
2. PVTTESTS ANDCORRELATIONS 33
34
2.1 FLUII) SAMPLING
WellPreparation 34
36
Sample Collection
2.2 PVT‘l’ESTS38
40
2.2.1 DryGas
41
2.2.2 WetGas
42
2.2.3 Black Oil
52
2.2.4 GasConclensate
2.2.5 VolatileOil 65
66
2.3 EMPIRICAL CORRELATIONS
ISBN:0444821961 2.3.1 BlackOil 67
RubblePointPressure 68
© 1998 ElsevierScience By. Allrightsreserved. GasinSolution 70
OilFormationVolume Factor 70
Nopartofthis publicationmaybereproduced, stored ina retrievalsystemortransmitted inanyformor TotalFarinalion Vo/unre Factor 71
byany means, electronic, mechanical, photocopying, recording orotherwise, without the priorwritten OilDensity 73
permissionofthepublisher, ElsevierScience By., Copyright &Permissions Department,P.O. Box 521, Oil Viscosity 77
1000AMAmsterdam,TheNetherlands. 2.3.2 NaturalGas 79
VolumetricData 80
Special regulations forreaders in the U.S.A. —This publication has beenregistered with the Copyriglil 83
ClearanceCenter Inc. (CCC. 222 Rosewood Drive, Danvers, MA, 01923. Information can be obtained (;~Viscosity
86
fromtheCCCaboutconditionsunderwhich photocopiesofparts ofthispublication maybemadein the 2.3.3 FormationWater
U.S.A. Allothercopyrightquestions,including photocopyingoutsideofthe U.S.A., should bereferred to WaterCr,ntentofhydrocarbonPhase 87
thepublisher. ll’ drocarbonsoluinlityin Water 90
5 92
WalerFormation VolumeFactor
92
Noresponsibilityisassumed bythe publisherfor anyinjuryand/ordamageto personsorproperty asa CompressibilityofWater
matter of products liability, negligence or otherwise, orfrom any use or operation of any methods, WalerDensity 93
products,instructionsorideascontainedinthematerialherein. WalerViscosity 93
2.4 REFERENCES 95
®Thepaperused inthispublicationmeetstherequirementsofANSI/NISOZ39.48 1992 2.5 EXERCISES 99
(PermanenceofPaper).
PrintedinTheNetherlands.
DirectApplication 241
3. PHASEEQUILIBRIA 105 6.4 REFERENCES 247
3.1 CRITERIAFOREQUILIBRIUM I05 6.5 EXERCISES 249
Chemical Potential 107
Fugacity 108 7. GASINJECTION 253
Activity Ill 7.1 MISCIBILITYCONCEPTS 254
3.2 EQUILIBRIUM RATIO III Miscibility inReal Reservoir Fluids 258
Raoult’sLaw 112
Henry’sLaw 114 7.2 EXPERIMENTAL STUDIES 260
EmpiricalCorrelations 116 SlimTube 260
3.3 REFERENCES 125 Rising BubbleApparatus 265
3.4 EXERCISES 127 ContactExperiments 266
270 7.3 PREI)IC1’IONOFMISCIBILITYCONI)ITIONS
4. EQUATIONS OFSTATE 129 FirstContact Miscibility 270
4.1 VIRIALEOS ANDITS MODIFICATIONS 130 Vaporising GasDrive 270
273
Starling-Benedict-Webb-Rubin EOS 131 Condensing-VaporisingGasDrive 277
4.2 CUBICEQUATIONS OFSTATE 132 7.4 REFERENCES 279
4.2.1 Two-ParameterEOS 138 7.5 EXERCISES
Soave-Redlich-Kwong EOS 140 281
Peng-Robinson EOS 141 8. INTERFACIALTENSION 282
VolumeSh~fl 141 8.1 MEASUREMENTMETHODS 285
4.2.2 Three-ParameterEOS 45 8.2 PREDICTIONOFINTERFACIALTENSION 285
Schmidt-WenzelEOS 146 ParachorMethod 288
Patel-Teja EOS 147 CorrespondingStatesCorrelation 289
4.2.3 Attraction TermTemperature Dependency 149 Comparison ofPredictiveMethods 292
4.3 MIXINGRULES 153 8.3 WATER-UYDROCARBON INTERFACIALTENSION 295
4.3.1 RandomMixingRules 154 8.4 REFERENCES 297
4.3.2 Non-RandomMixingRules 158 8.5 EXERCISES
4.4 REFERENCES 162 301
9. APPLICATIONIN RESERVOIRSIMULATION
4.5 EXERCISES 165 302
9.1 GROUPING
302
5. PHASEBEHAVIOURCALCULATIONS 167 GroupSelection 308
5.1 VAPOUR-LIQUID EQUILIBRIUMCALCULATIONS 168 Group Properties 310
RootSelection 175 Composition Retrieval 314
RapidFlashCalculations 179 9.2 COMPARiSON OFFOS 316
5.2 STABILITY ANALYSIS 183 PhaseComposition 318
StabilityLimit 189 Saturation I’ressure 319
5.3 CRITICALPOINTCALCULATIONS 192 Density 320
5.4 COMPOSITIONALGRADING 195 GasandLiquid Volumes 322
EquilibriumAssumption 197 Robustness 323
Non-Equilibrium Fluids 198 9.3 TUNINGOFEOS 324
HeatofTransport 2(X) FluidCharacterisation 325
Significance 201 SelectionofEOS 325
5.5 REFERENCES 203 ExperimentalData 327
5.6 EXERCISES 206 SelectionofRegressionVariables 330
LimitsofTunedParameters 330
6. FLUIDCHARACTERISATION 209 Methodology 331
6.1 EXPERIMENTAL METHODS 210 9.4 DYNAMIC VALIDATION OFMODEL 333
Distillation 210 RelativePermeabilityFunction 334
GasChromatography 215 ViscosityPrediction 338
6.2 CRITICALPROPERTIES 221 Implementation 340
Lee-KeslerCorrelations 221 9.5 EVALUA’rIONOFRESERVOIRFLUIDSAMPLES 345
Riazi-DauhertCorrelations 222 9.6 REFERENCES 349
PerturbationExpansionCorrelations 223 9.7. EXERCISES
6.3 DESCRII9’IONOFFLUIDIIEAVY END 227 353
SingleCarbonNumberFunction 228 APPENDICES
ContinuousDescription 234 385
INDEX
vi vii
NOMENCLATURE
a attractiveterni parameterof equationofstate
PREFACE
A dimensionlessattractive termparameterofequation ofstate
b repulsive tcrm(co-volume) parameterofequationofstate
B clinrensiontcss repulsiveterm parameterofequation ofstate
lI~ gas formation volumire f~itcor
Reliablemeasurement and predictionofphasebehaviourandpropertiesofpetrolciini
It, oil Iurinaliiiirvolt:lire factor
reservoirfluidsareessential indesigning optimum recovery processesandenhancing
B total formation volume factor
hydrocarbon production. This book explains relevant fundamentals and presents
C~ gasisothermalcompressibilitycoefficient
practicalmethods ofdetermining requiredproperties forengineering applications by
C, oil isothermalcompressibilitycoefficient
judiciousreviewofestablishedpracticesandrecent advances.
f fugacity
G Gibbs energy
Although the emphasis is on the application ofPVT and phasebehaviour data to
h height
engineering problems,experimental methods are reviewed and their limitations are
identified. Thisshouldprovidethe readerwith a morethoroughunderstanding ofthe Ii molarentha!py
subjectandarealisticevaluation ofmeasuredandpredictedresults. H totalenthalpy
I1~ Flenry’sconstant
The book is based on the material developed over many years as lecture notes in h partial molarentlIi~PlY
1
courses presented to staff in gas and oil industry, and postgraduate students of k peruieahility
petroleumengineering. Itcovers variousaspectsofthesubject, hencecan he tailored k, binaryinteraction parameter
for different audience. The first two chapters along with selected sections from k,~ gasrelative permeability
chapters 3 and5 can serve as thesubject matterofan introductorycourse, whereas k,, oil relativepermeability
the restwould be ofmore interest topractising engineers andpostgraduate students. K equilibriumratio
Ampleexamples areincluded toillustrate thesubject, andfurtherexercises aregiven K~ Watsoncharacterisationfactor
in each chapter. Graphical methods and simple correlations amenable to hand m slopein ~scorrelation withtemperature
calculations are still used in the industry, hencethey are included in this hook. The M molecularweight(molarmass)
emphasis, however, is on the more advanced compositional approaches which are n moleorcarbonnumber
attaining wider application in industry as high computational capabilities are N numberofcomponents
becomingreadilyavailable. N~ numberofpseudo-components
P presstire
I would like to thank Professor DII Tehrani for reviewing the manuscript and P, bubblepoint pressure
valuable suggestions stemming from his vast industrial experience - Also, I urn P1 convergence pressure
grateful to Professors M. Michelsen and C. Whitson for their helpful commentson P5 parachor
sectionsofthe book. Much ofthe material in this book is based on the author’s 0
P~ vapour pressure
experience gainedthroughconductingresearchsponsoredby the petroleum industry,
R universalgasconslant
atHeriot-WattUniversity. I amindebted tothesponsors, mystudentsandcolleagues
R, gasinsolution
for their contributions that made this book possible. In particular, I would
S specificgravity,relativedensity at 288 K(60“F)
acknowledgevaluablecontributionsofProfessorACTodd, MrFGoozalpour,DrDII ‘l temperature
Xu, Mr K Movaghar Nezhad and Dr DAvolonitis. My son Amircheerfully helped
I~ irorrirathoihiigpointtemperature
meinpreparingthehook graphics.
ii iriiitar:nlcini.r! encigy
V imiolarvotunie
~ velocity
V volume
x, mimicfraction
y, molefraction invapourphase
7., mole fraction
Z compressibility factor
Z Rackettcompressibility factor
55
GREEKLETI’ERS StJPERSCRIPt’S
a temperaturedependency coefficient ofattractiveterm F Iced, imrixliile
h hydrocarbon phase
meanvalueparameterofrdistributionfunction
liquidphase
Cj activity
o referencestate
~ fugacitycoeffricient 5 saltmration
~y parameterof distributionfunction V vapour l)hase
s~ calculatedcriticalcompressibility factor W waterphase
K totalnumberofphases
j.t chemical potential
p massdensity
Pu molardensity SUBSCRIP’I’S
~ interfacialtension
t lowest molecularweightin Fdistribution functiomi I) baseorbubblepoint
(i) acentric factor C critical point
(I differential liberation process
LI EOSparametercoefficient
e activity coefficient It gas
It hydiocarbirmi
~ anyphase 0 oil
r reduced property=value/valtmc atcritical point
s salt
w w,mter
ACRONYMS
hbl barrel
BIP binaryinteraction parameter
CCE constantcompositionexpansion
CGR condensatetogasvolumetricratio
CVD constantvolume depletion
DL differential liberation
EOS equation(s)ofstate
GOR gastooil volumetricratio (Sc)
GLR gastoliquidvolumetricratio(Sc)
GPA GasProcessors Association
GPM gallonofliquidperthousandcubic feetofgas(sc)
IFT interfacial tension
MMP minimum miscibility pressure
MME minimum miscibility enrichment
PNA paraffins-naphthenes-aromatics
PR Peng-RobinsonEOS
PT Patel-TejaEOS
Sc standardconditions
SCF standardcubic feet
SRK Soave-Redlich-Kwong EOS
STB stocktankbarrel
SW Schmidt-Wenzel EOS
TBP trueboilingpointtemperature
VPT Valderrama-Patel-Teja FOS
7JRK Zudkevitch-Joffe-Redlich-Kwong EOS
xi
1
PHASE BEHAVIOUR
FUNDAMENTALS
Petroletimreservoir fluids arecomposed mainly of hydrocarbon constituents. Water is atso
present in gas and oil reservoirsin an interstitialfonrr. The influenceof water on tIre phase
hchavioumrandpropertiesofhydrocarbon fluidsin mostcasesisofa minorconsideration. The
phasebehaviourofoilandgas, therefore, isgenerally treatedindependent oftire water plrase,
unlesswater-hydrocarbonsolid structures,knownas hydrates, areformed.
The behaviourof a hydrocarbon mixture at reservoirand surfaceconditions isdetermined by
itschemical composition and the prevailing temperature and pressure. This behaviour isof a
primeconsideration intiredevelopment arid management of reservoirs, affecting all aspects of
petroleumexplorationandproduction.
Altirotmgh a reservoir litmiut may he composed of many thousands of compounds. tire phase
behaviour fundamentalscan be explained by exami0ing the behaviour of pure and simple
mrrulticonrponentmriixiurcs. Thebehaviourolall realreservoirfluiulsbasically follows the saline
principle,buttohicilitate tIreapplicationoftiretechnologyin theindustry,reservoir fluids have
heemrclassified intovarious groups such as the (try gas, wet gas, gas condensate, volatile oil
and blackoil.
I RESERVOIR FLUII) COMPOSITION
‘lucre are various hypotheses reg~ridiirgthe fornratiorr of petroleum fromorganic materials.
Ihese views suggest thattIre coisrpositmon of a reservoir fluid depends on the depositionai
environmentoftheformation,itsgeologicalmaturity, andthemigrationpathfromthesourceto
trap rocksIi. Reservoir gassesaremainlycomposed of hydrocarbon molecules ofsmall and
mediumni size,s and sonic light non-hydrocarbon compormnd.s such as nitrogen and carbon
dioxide, whereasoilsarepredominantlycomposedofheaviercompounds.
Fluids advancing into a trapping reservoir may be of different compositions due to being
generated at different times and environments. thence, lateral and vertical compositional
variations within areservoir will he expected dumring the early reservoir life. Reservoir fluids
2 1. t’lraseHelun’,ourFiinukun:e,,i~i!.c I.1. ReservoirFluidO~nrposit:on 3
are generallyconsideredtohaveattainedequilibrium atmaturityduetomolecular diffusion and can affect the properties of reservoir fluids, particularly the rock-fluid behaviotmr,
mixing over geological times. However, there are airrple evidences of reservoirs still disproportionally higherthantlreirconcentrations7. Theseheavycompounds maybe present
maintaining significantcompositiomial variations, particularly tatcially as tIre dillusiye rrixing in colloidal suspension in the reservoir oil and precipitate out of solution by changes in the
may require many tens of million years to eliminate coiripositmonal hmclcmogeiiuitcs I2I ~ tcmrrpcratumreorcomnpos!tiomrs occurringdurimigproduction.
Furthermore, the pressure and the temperature increirse with depth for a tluid column iir a
reservoir. Thiscan alsoresult incompositionalgrading with depth. Foroperatiomial puposes.
this behaviour is of considerable interest for near critical lluids, and oils containing bight H
concentrationsofasphaltic material. Thecompositional gradingand its estimiration based on
thermodynamic conceptswill bediscussedinSection 5.3. H—C—H
It H II H It II H H H H
The crude oil composition is of major consideration in petroleum refining. A number of I I I I I I I I I I
comprehensive research projects sponsored by the American Petroleuni Institute have II— C—C—C—C—C—C—li H—C—C—C—C—C—H ALKANES
investigated crude oil constituents and identified petroleum compounds. API6 studied the I I I I I I I I I I I (PARAFFINS)
composition of a single crude oil for 40 years. ihe sulphur, nitrogen and orgtrmiomricttrlhic II II U H It II II II It II It
compremndsofcrude oil strniptcs were investigated in projects API-48. API 52 ;inrd API-Sti
respectively. API-60sttmdied petroleum heavyends. Nelson 31 givesa review of petrolcumni Norinnat Icx;ine iso-lieranc
chemistry andtestmethods usedin therefiningindustry. II
liighlydetailedinformationontheconstituentscomposingareservoirfluid isnotofvery muchr It—C~—H
use inexplorationandproductionprocesses. Reservoir fluids arecommonly idcmrtilmcdby their
H tt It It II HH H
constituentsindividuallytopentanes.andheaviercompoundsarereportedas groupsconsrposed I I I I I I
mostly of components with equal numberof carbons such as C6’s, C7’s. Cg’s. All the It—C—C—C—C—C C’ II—C—C—C—C=C ALKENES
compounds formingeach single carbon number group do not necessarily possess the same I I I I I I I
number of carbons as will he discussed in Section 6. I. Tire most common method of Ii It II II It It H H II II H
describingtheheavyfractionistolumpall theconipoundsheaviertitanC and meport itasC +.
6 7
I-Itexenc 3-Meltryt-IPentene
hydrocarbon compounds can be expressed by the general formula ofCi1II2Irf~with some
sulphur, nitrogen, oxygen and minor metallic elements mostly present in heavy fractions.
Hydrocarboncompoundsareclassifiedaccording totheirstructures,which determinethe value / H
oTfhe~,.pTarhaeffniniasjoerricelsasasreescoarmeppoasreadffionfss(aatlukraanteesd).hoyldertoincasrb(aolnkesnterasi)g,hntacphhathinesnews,itahnd~=a2ro.maLtiicgsh.t H\ ,,,,,~ -~ c/\1t1t C~ H
paraffins in reservoir fluids are sometimes identified and reported as those with a single
hydrocarbonchain, as normal, and others with branched chain hydrocarbons, as iso. The I1\~ I/It I II
olefinseries(~=0)haveunsaturatedstraight chainsandarenotusually foundinreservoirfluids
H~~
due to their unstable nature. The naphthenes arecyclic compounds composed of saturated H/NC ~C\
/\
ring(s)with ~=0. The aromalics (~,=-6)are unsaturated cyclic cotripounds. N~rphthrenes~mmr(h
It It
aromatics formamajorpartofC6-Ctt groupsandsomeofthem suchitSmethyl-cycio-pcntanc. 11
bcnzene, tohuene and xylene are often individually identified in the extended analysis of
reservoirfluids. For example, the structural formulasof tire above groups of hydrocarbons C’yclotrcxanc Benzcne
withsixcarbonsareshownin Figure 1.1. NAI’IIrIIENLs AROMATICS
As reservoir hydrocarbon liquids may be composed of many thousand components, they
cannot all be identified and measured. However, the concentration of hydrocarbon Figure 1.1. Structural formulaofvariousgroupsofhydrocarbonswithsixcarbons.
componentsbelonging tothe same structuralclass are occasionallymeasured and reported as
groups. particularly for gas condensate fluids. The test to measure the concentration of
paraffrns,naphthenes,andaromatics as groups is commonly referred toas the PNA test 141-
1.2 PIIASE BEHAVIOUR
Furtherinformationonthestructure ofreservoirfluidcomnpoundsand their labelling according
totheIUPAC systemcanhefound in SJ. The compositional analysis of reservoir fluids anh
Reservoir hydrocarbonsexistasvapour, liquidorsolid phases. A phaseisdefinedasa partof
theircharacterisationwillbediscussedinChapter6. asystemli whtciris physicallydistinct from otherparts by definiteboundaries. Areservoir oil
(liquid phase) may form gas (vapour phrase) during depletion. The evolved gas initially
Nitrogen,oxygenandsulphurare foundin light and heavy fractions ofreservoir fluids. Gas remaIns dispersed iii the oil phase before forming large mobile clusters, but the mixture is
reservoirscontainingpredominantlyN2,H2S.orc02havealsobeendiscovered. Polycychic consideredas atwo-phrase system in botlr cases. The formationor disappearanceofa phase,
hydrocarbonswithfusedrings which aremoreabundantinheavier fractionsmaycontainN, S,
orvariationsinpropertiesofaphraseinamulti-phasesystemare ratephenomena. The subject
and0. Thesecompoundssuchascarboids, carbenes, asphaltenesand resinsare identified by ofphasebehaviotmr, however.focitses onlyontheState ofequilibrium, wherenochanges will
their solubihity,or lack ofit, indifferentsolvents 6. The polarnature of these compounds
occur withtime iftIre system is heft at tire prevailing constant pressure and temperature. A
4 1. PhaseBehan’iour Fu,rdamelrta/.l 1.2. !‘ha.ce liehaeu~ur S
systemreaches equilibrium when itattains its minimum energy level, as will be disctmssed in critical temperature. Ilence tIre vapour pressure values at temperatures above the critical
Chapter3. The assumptionofequilibrium between fluid phases in contact in a reservoir, in temperatures,shtowrrby ® in Frgurrc1.3,arenot real,butsimply extrapolated values.
mostcases, is valid in engineering applications. Fluids atequihihriumm are also referred to as
saturatedfluids.
Critical Poini
The state of a phase is fully defined when its conrposrtion, temperature arid prcssurre are
specified. Allthe intensive properties for such aphase at tire prevailing conditions are tmxed
and identifiable. The intensive properties are those which do not depend oil tire amount of
material (contrary totheextensive properties), such as the density andtIre specific heat. The 8
termpropertythroughout thishook referstointensiveproperties.
A
At equilibrium, a system may form of a nunrber of co-exiting phases, wimlr all tIre fluid
constituents present in all theequilibrated phases. The number of independent variables to Solid
definesuch asystemisdeterminedbytheGibbsp/roserule descrihetasfollows.
A phase composed of N components is fully defined by its number of irrolcs plus two A Vapour
ii. I)
thermodynamic functions, commonly tenrperatumre anul pressure, that is, by N÷2variables. triplePonni
Theintensivepropertiesare,however, determined by only N+I variables a~tire concentration
ofcomponentsarenotallindependent, butconstrainedby,
tennperatnnrc
(II)
Figure I.2. Pressure-temperaturedragrrrmrrofpure suibstairce.
where, x isthe mole fraction ofcomponent i. Thums, for a systersi with K phrases, tire total
1
numberofvariables areequal to rc(N-fI). However, the temperature, presstrr’e. and chenrical
potential ofeachcomponentthroughout all phasesshouldbe unifornrratequilrhriunrconditions, The lineAR on Figure 1.2 is the solid-liquid equilibrium line, which is also krtown as tire
aswillbedescribedin Chapter3. This inrpuses (N÷2)(ic-I) constraints. lterrce. the nunrber mrrclting pointcurve. l’hre intersectionof the vapour_liqummd and liquid-solid lines ts the triple
of independent variables, or so-called the degrees of freedom, F, necessary to (lefirre a point. Itisthreonlypoirrtwherethethree phasescartcoexistforapuresystem.
multiphasesystemisgivenby,:
Tire lureAD is the solid-vapour equnihihriunr line orthe suhlitrratmon curve. The solid carbon
F= K(N+l)-(N+2)(K-l) =N - K+2 (1.2) uphhiroaxsieulebe(hdaryvioicuer)dviaagproarmis.ing into itsgaseous form is acommon exampleof thisregion of the
For a single-component (pure) system, the degrees of freedom is equal to three nrinus thc
numberof phases. Thestate of the equihibriurm of a vapour-liquiuh mixture of a pure lluid, lire variation of saturated fluid ulensity with teirrperature for a pure compound is shown in
therefore,can bedeterminedby identifyingeitheritspressureorits tcnrperalume. Figure 1.5. Thedensities of vapour and liquidphases approach eachother as tire temperature
iiru-reases. Ihey hcconie equal at conuhitions kmiowiras tire Criticalpoint. AlltIre differences
Pure Compound between tire phrasesarere(Iuced as thesystem approaciresthecritical point. Indeed, thep/maces
i,eu’onre t/iC .Sa?tiCuiiid iF,(IiStiprh’i415/i(1ble at tire(‘riticalpoint.
The phasebehaviour of apure compound is strowir by tire prcssurc-teiriperutrrre di:rgrurnrr it
Figure1.2. Alltheconditionsat winchtire vapourand umquidphases can coexist at cqtrrlmtamrrrir gome I.4 showsIIre variationof saturatedIiuidchensrIywith temperature foranurmrrbcr ofprime
are shown by the line AC. Any fluid at any otlrer pressure-tenrperatui’e conditions, is Irydroearbomrs All tIre conmporrrrds slrow a sirmnilar tremid, that is, tIre vapour and liquid
-
unsaturatedsinglephase asrequired bythe phraserule. Thefluid above and totire leftof the rlemrsiries bccorrre equal at tIrecnrtrcat point. OtIrerproperties also show tire same tiend. ‘Ilre
lineisreferredtoasacompressedorundersaturated liquid,wlrereas thatheiowandtotheright en mciii tenrrperatrire. I~.,arid tIre critical pressure, P,. are tire niaxilriuni terriperature arid
oftIre lineiscalledasuperhreatedvapourrorgas.
meat which iiproe conrpororilcirur fomnmr coexisting ilrascs.
1
The line AC is commonly known as the vapour pressure curve, as it shows tire pressure The ternrs vapour and liquid are ret’erred to the less and the more dense phases of a fluid at
exerted by the vapour coexisting with its liquid at any temperature. The temperature equilihriunr, Ileirce.a purecorripound atatemperature aboveits critical valuecanirotbe called
corresponding tothe atmospheric pressure is calleut tire normal boiling point or simply tire eitlrerliqumidorvapour, lire continuity of vapour and liquidis scherrraticahhy strown in Figure
boilingpointofthecompound. Theboilingpoint,Tb, ofsome compotrnds foundtin reservoir 1.6. TIredensity at e~rclrpoint is sirown by the shauhing intensity, where tIre ularker shadmrrg
fluids aregiven in Table A.I in Appendix A. Figure 1.3 shows tIre logarithm of vapour correspondstoairiglrerdensity. Tirediscontirruity across the vapour-pressurecurve becomes
pressureplottedagainstanarbitrarytemperature scaleforsome compouinuls. The scale,which less significant as tire temperatui’e increases arid vanishes above tIre cmitical poirrl. Tire
is an adjusted reciprocal of the absolute temperature, has been selected so that the vapour superheated vapour F can he chranged gradumally to tIre compressed liqumid F, thiough an
pressures of water and most hydrocarbons can be exhibited by straight lines. This plot is arbitrarypatlrEGF, Witiroutany abrupt phrasecirange.
known as tireCoxchart. A pure substance cannot existas liquid at a temperaturre above its
6 1, PhaseBelrannon,rFwrda,,re,m,url.s 1.2. Phase Behaviour 7
t-i--~ ~ L- 1000
j~.-~J
-IL
-
~ 2
moo
!L~i~ LE~L mOO
no
~ H~ ~ no
V :i~_~:‘-,~—-~
2
“I ~
0U,~ IL. -~ - 7Z L 7 U2U,,
.‘O
~ ~ ~ ~
0
~
~4
~
~
no.’
00 iso 200 250 300 350 400 450 500 350600 700 ~ ~00 000
Temperature,°F
Temperature,°F
K=(°F+459.67)/l.8 MPa=O.006895psia
K=(°F-f459.67)/1.8 MPa=Q.006895 psia
Fhoimgeurr1e811w.3iih. pVerampiossuiornp.ressure ofnormal paraffins. McGraw-tlitt CompaniesCnnpyrigtrn. Rcpnnxiuccd Figtmre 1.3 (Coin). Vapour pressure of normal paraffins. McGraw.Hitt Companies Copyright.
Rcprnstucedfioi~nI~!s~iitrpermnnicsionn
8 I. Pha.meRehannonrrFnondamnre,rtat.r 1.2.PhaseBehaviour 9
Temperature,K
200 250 300 350 400 450 S00 550 600 650 SanurmuedI_rquiul
I...., . A
C C
I)
ilHifliItIU
Saunnr~niedVapour
‘tennnpr’rarure
I1f~ITU uigure 1.5. Vamiatiomrsofsaturated tluiddensitywith tennperature.
fI I~‘&II
~ 10-44151 41401
‘!•iUIU
A
~tiIi~iJllhI!~
U
•1 a
________ Ill~-
ftI~FI~IIt1 C,
fttiWH-ft1t-tt ~1f~U-~~’II-U~-tf~f~UIt
H II
II~~B~~Iit~LAflI
fH+HIfH P-H-I-/ ~Yt-1~4kY
ftt±1-i’H±H+~f+H1-I-H+H-fl
1enrnpermninrre
ll~llt~iill~
rLIFHU Irginr’e I.6. (‘ontinltrity oh’vapour anul hmquid. Mc(Ir~nw-Ititt(‘onnipannies Cnipyrngtii Reprnstnncent trim
—100 0 tOO 200 - 30C 400 500 600 700 IS!with pernnnnssionn.
TIne pressure—volunre diagram of a pure substance is shown in Figure 1.7. (‘onsider tire
Temperature,oF corrrpresseulhiquniul. Point A, ata tercrperature below tire critical temperature. lbe reductiomn of
fluid pm’cssure at constant teirnperature increases its volume. As tine liquniul is relatively
incomrrpressiblc tine finnuI expansiomn issmall until tire vapour prcssnrre is reaclred, at Point 13
where tire firstbubble evolves. Furtherexparrsioinof tire systeirn results unchi~rmiginigtire liquid
Figure 1.4. Saturated fluiddensityofpure compoumnds (curves iderrtilred by lettersare related
iran tirevapour phn:ise. Fora pure substance Ilie pressure remlraius constant mmd equnal to tIre
tobinaryandmulticomponent fluidsdescribed in Reference8).McCraw-ttiltConinpanies Copynigtnn
vmrpourr pressure, aconsequmence oftire phase rurle, until the last dropoftire liquid virponises,
Reproduced from 81wiihpermission.
Point I). ~h’lnipsoint,where tIrevapourisin equnilihrnumrr with an imnfinitesimnral anrnount of hiqtnid
iscalledtIre utewpoinn.