PETE 310PETE 310

Lectures # 6 & # 7Lectures # 6 & # 7

Phase Behavior – Phase Behavior – Pure Pure Substances (Lecture # 5)Substances (Lecture # 5)

Two Component MixturesTwo Component Mixtures

Three & Multicomponent Three & Multicomponent MixturesMixtures

Learning ObjectivesLearning Objectives

After completing this chapter After completing this chapter you will be able to:you will be able to:

Understand pure component phase Understand pure component phase behavior as a function of pressure, behavior as a function of pressure, temperature, and molecular size.temperature, and molecular size.

Understand the behavior of binary Understand the behavior of binary and multicomponent mixturesand multicomponent mixtures

Behavior understood through Behavior understood through properproper interpretation of phase diagramsinterpretation of phase diagrams

Phase DiagramsPhase Diagrams

Types of phase diagrams for a Types of phase diagrams for a single component (pure single component (pure substance)substance)

(PT)(PT) (PV) or (P(PV) or (P)) (TV) or (T(TV) or (T

Phase DiagramsPhase Diagrams

Single Component Phase DiagramSingle Component Phase DiagramP

ress

ure

P c

TemperatureT c

Liquid (1 phase)

Vapor (1 phase)

Solid

(1 phase)

Sublimation Curve (2 phases)

Triple Point

(3 phases)

Vapor Pressure

Curve (2 phases)

Critical

Point

Fusion Curve2 phases

Phase DiagramsPhase DiagramsVapor Pressure CurveVapor Pressure Curve

Pre

ssu

re

Temperature

Vapor

Liquid

Critical Point

l

v

Pc

T c

Hydrocarbon Families Hydrocarbon Families Physical Properties Physical Properties

One point in theOne point in theVapor Pressure CurveVapor Pressure Curve

Pressure vs Specific Pressure vs Specific Volume Pure SubstanceVolume Pure Substance

Tc

2-phase

T

Specific Volume (ft3 / lbm)

Pre

ssu

re (

psi

a)

Vv

VL

CP

Tabulated critical properties Tabulated critical properties (McCain)(McCain)

Pure Component Pure Component PropertiesProperties

Heat Effects Accompanying Heat Effects Accompanying Phase Changes of Pure Phase Changes of Pure

SubstancesSubstances  

Lv = TV dPv

dTWith

V = VMg-VMl

Btu/lb-mol

Clapeyron equation

Heat Effects Heat Effects Accompanying Phase Accompanying Phase

Changes of Pure Changes of Pure SubstancesSubstances

  Lv = TV dPv

dT

=

Approximate relation (Clausius - Clapeyron Equation)

dPv

dT

RT2 Pv

Lv

Example of Heat Effects Example of Heat Effects Accompanying Phase Accompanying Phase

Changes Changes Steam flooding Problem:Steam flooding Problem:

Calculate how many BTU/day Calculate how many BTU/day (just from the latent heat of (just from the latent heat of steam) are provided to a steam) are provided to a reservoir by injecting 6000 reservoir by injecting 6000 bbl/day of steam at 80% quality bbl/day of steam at 80% quality and at a T=462 and at a T=462 ooF F

COX - Vapor Pressure COX - Vapor Pressure ChartsCharts

(normal paraffins)(normal paraffins)

Pre

ssu

reP

ress

ure

Temperature Temperature

heavier heavier

Non-linear scaleNon-linear scale

Log scaleLog scale

Determination of Fluid Determination of Fluid PropertiesProperties

Temperature of Test Constant

Vt1

Vt2

Vt3

=V

b

Vt5

Vt4

liquid liquid liquidliquid

liquid

gas gas

Hg Hg HgHg

Hg

P1 >> P

sP

2 > P

sP

3 = P

sP

4 = P

sP

5 =P

s

1 2 3 4 5Ps =saturation pressurePs =saturation pressure

Vapor Pressure Vapor Pressure DeterminationDetermination

Pre

ssur

e

PS

Volume

VL

TT22

TT11

Binary MixturesBinary Mixtures

Relationships to analyze: P, T, Relationships to analyze: P, T, molar or specific volume or (molar molar or specific volume or (molar or mass density) - as for a pure or mass density) - as for a pure component – component –

++COMPOSITION – Molar CompositionCOMPOSITION – Molar Composition

Hydrocarbon CompositionHydrocarbon Composition

The hydrocarbon composition The hydrocarbon composition may be expressed on a weight may be expressed on a weight basis or on a basis or on a molar basismolar basis (most (most common)common)

Recall Recall

""

""

iofweightmolecular

iofmass

Mw

Mn

i

ii

Hydrocarbon CompositionHydrocarbon Composition

By convention liquid compositions By convention liquid compositions (mole fractions) are indicated with an (mole fractions) are indicated with an xx and gas compositions with a and gas compositions with a yy..

liquidnn

nx

21

11

gasnn

ny

21

11

Our Systems of ConcernOur Systems of Concern

VaporPv

Tv

niv

LiquidPl

Tl

nil

VaporPv

Tv

niv

LiquidPl

Tl

nil

Gas systemGas system

Oil systemOil system

openopen

A separatorA separator

zi(T1,P1)

xi(T1,P2)

yi(T1,P2)

P1 > P2T1,P2

withwith

In generalIn general

Mathematical Mathematical RelationshipsRelationships

vl fyfxz 111 vv fyfxz 111 1 )(

lv

vv nnnn

nnf

2121

21

)(

11

1 1

xy

xzfv

ii

iiv xy

xzf

Key ConceptsKey Concepts

Fraction of vapor (fv)Fraction of vapor (fv)Mole fractions in vapor (or Mole fractions in vapor (or

gas) phase gas) phase yi yiMole fractions in liquid (or oil) Mole fractions in liquid (or oil)

phase phase xi xiOverall mole fractions (zi) Overall mole fractions (zi)

combining gas & liquid combining gas & liquid

Phase Diagrams forPhase Diagrams forBinary MixturesBinary Mixtures

Types of phase diagrams for a Types of phase diagrams for a two- component mixturetwo- component mixture

Most commonMost common (PT) (PT) zizi at a fixed composition at a fixed composition

(Pzi) (Pzi) TT at a fixed T at a fixed T

(Tzi(TziPPat a fixed Pat a fixed P

(PV) (PV) zizi or (P or (P) ) zizi

Pressure vsPressure vsTemperature Diagram (PT)Temperature Diagram (PT)zizi

CB

CT

CP

Bubble Curve

Dew Curve

Pre

ssu

re

Temperature

Liquid

Gas

2 Phases

Zi = fixed

Pressure Composition Pressure Composition Diagrams - Binary Diagrams - Binary

SystemsSystems

Temperature x1, y1

Pre

ssu

re

P2v

TaCP1

Bubble Curve

Dew C

urve

2-phases

Liquid

Vapor

P1v P1

v

CP2

P2v

Ta0 1

Temperature vs. Temperature vs. Composition Diagrams – Composition Diagrams –

Binary SystemsBinary Systems

Temperature

Pre

ssu

re

Bubble Curve

Dew Curve

2-phases

x1, y1

Pa

Pa

CP1

CP2

T1s T2

s

T2s

T1s

0 1

Gas-Liquid RelationsGas-Liquid Relations

Temperature

Pre

ssu

re

PD

PB

T = Ta

Ta

CPM

z1 = fix ed

z1y1x1

10

A

B

C

z1=overall mole fraction of [1], y1=vapor mole fraction of [1], x1=liquid mole fraction of [1]

Supercritical ConditionsSupercritical Conditions Binary MixtureBinary Mixture

Ta Tb Tg

Temperature x1, y1

Ta

Tb

Tg

[1]

[2]

P1

P2v

Quantitative Phase Quantitative Phase Equilibrium ExerciseEquilibrium Exercise

P-xy Diagram

0

400

800

1200

1600

2000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Composition (%C1)

Pre

ssu

re (

psi

a)

T=160F

Quantitative Phase Quantitative Phase Equilibrium ExerciseEquilibrium Exercise

P-xy Diagram

0

400

800

1200

1600

2000

2400

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Composition (%C1)

Pre

ssu

re (

psi

a)

T=100F

T=160F

T=220F

Ternary Diagrams: ReviewTernary Diagrams: Review

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.1

.1

.2

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1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

L

H I

Ternary Diagrams: ReviewTernary Diagrams: Review

Pressure EffectPressure Effect

C3C3

nC5 C3

C1

Gas

p=14.7 psia

C1

nC5

Gas

2-phase

Liquid

p=380 psiaC3 nC5

C1

C3

Gas

2-phase

Liquid

p=500 psia

C1

Gas

2-phase

Liquid

nC5 p=1500 psia

2-phase

Liquid

C1

nC5

Gas

p=2000 psia

C1

nC5 C3

Liquid

p=2350 psia

Dilution LinesDilution LinesTernary Diagrams: ReviewTernary Diagrams: Review

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.1

.2

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1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C10 n-C4

x

Ternary Diagrams: ReviewTernary Diagrams: Review

Quantitative Representation of Quantitative Representation of Phase Equilibria - Tie (or Phase Equilibria - Tie (or equilibrium) linesequilibrium) lines

Tie lines join equilibrium conditions of Tie lines join equilibrium conditions of the gas and liquid at a given pressure the gas and liquid at a given pressure and temperature.and temperature.

Dew point curve gives the gas Dew point curve gives the gas composition.composition.

Bubble point curve gives the liquid Bubble point curve gives the liquid composition.composition.

Ternary Diagrams: ReviewTernary Diagrams: Review

Quantitative Representation of Quantitative Representation of Phase Equilibria - Tie (or Phase Equilibria - Tie (or equilibrium) linesequilibrium) lines

All mixtures whose overall composition All mixtures whose overall composition (z(zii) is along a tie line have the SAME ) is along a tie line have the SAME equilibrium gas (yequilibrium gas (yii) and liquid ) and liquid composition (xcomposition (xii), but the relative ), but the relative amounts on a molar basis of gas and amounts on a molar basis of gas and liquid (fliquid (fvv and f and fll) change linearly (0 – ) change linearly (0 – vapor at B.P., 1 – liquid at B.P.).vapor at B.P., 1 – liquid at B.P.).

Illustration of Phase Illustration of Phase Envelope and Tie LinesEnvelope and Tie Lines

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.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C10 n-C4

CP

Uses of Ternary DiagramsUses of Ternary Diagrams

Representation of Multi-Component Representation of Multi-Component Phase Behavior with a Phase Behavior with a Pseudoternary DiagramPseudoternary Diagram

Ternary diagrams may approximate Ternary diagrams may approximate phase behavior of multi-component phase behavior of multi-component mixtures by grouping them into 3 mixtures by grouping them into 3 pseudocomponentspseudocomponents

heavy (Cheavy (C77++))

intermediate (Cintermediate (C22-C-C66))light (Clight (C11, CO, CO2 , 2 , NN22- C- C1, 1, COCO22-C-C22, ...), ...)

Uses of Ternary DiagramsUses of Ternary Diagrams

Miscible Recovery ProcessesMiscible Recovery Processes

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.1

.1

.2

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1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C2-C6C7+

A

O

Solvent1Solvent1

oiloil

Solvent2Solvent2

ExerciseExercise

Find overall composition of mixture Find overall composition of mixture made with 100 moles oil "O" + 10 made with 100 moles oil "O" + 10 moles of mixture "A".moles of mixture "A".____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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.1

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1.1 .2 .3 .4 .5 .6 .7 .8 .90

01

C1

C2-C6C7+

A

O

Practice Ternary Practice Ternary DiagramsDiagrams

Pressure EffectPressure Effect

T=180FP=14.7 psia

Pressure Effect

O

T=180FP=200 psia

C1-C3-C10

Pressure Effect

O

T=180FP=400 psia

Pressure Effect

O

T=180FP=600 psia

Pressure Effect

O

Practice Ternary DiagramsPractice Ternary DiagramsPressure EffectPressure Effect

T=180FP=1000 psia

Pressure Effect

O

T=180FP=1500 psia

Pressure Effect

O

T=180FP=2000 psia

O

T=180FP=3000 psia

O

T=180FP=4000 psia

O

Practice Ternary DiagramsPractice Ternary Diagrams

Temperature EffectTemperature Effect

T=100FP=2000 psia

Temperature Effect

O

T=150FP=2000 psia

Temperature Effect

O

T=200FP=2000 psia

Temperature Effect

O

T=300FP=2000 psia

Temperature Effect

O

Practice Ternary DiagramsPractice Ternary Diagrams

Temperature EffectTemperature Effect

T=350FP=2000 psia

Temperature Effect

O

T=400FP=2000 psia

Temperature Effect

O

T=450FP=2000 psia

Temperature Effect

O

Pressure-Temperature Pressure-Temperature Diagram for Diagram for

Multicomponent SystemsMulticomponent SystemsR

eser

voir

Pre

ssu

re

Reservoir Temperature

Bubble-Curve

Dew-Curve

60%

20%0%

2-Phase

1-Phase 1-PhaseCP

Changes During Changes During Production and InjectionProduction and Injection

Temperature

t1

Pre

ssu

re

t3

t2

Gas

Injection

Productiont

t3

2

Gas

Injection

Production

HomeworkHomework

See Syllabus pleaseSee Syllabus please