PETE 310

Lectures # 6 & # 7

Two Component Mixtures

Three & Multicomponent Mixtures

(and review Lecture#5)

Learning Objectives

After completing this chapter you will be able to:

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

Understand the behavior of binary and multicomponent mixtures

Behavior understood through properinterpretation of phase diagrams

Pressure vs Specific Volume Pure Substance

Tc

2-phase

T

Specific Volume (ft3 / lbm)

Pre

ssu

re (

psia

)

Vv

VL

CP

A Problem

Tc

2-phase

T

Specific Volume (ft3 / lbm)

Pre

ssu

re (

psia

)

VvVL

CP

Tabulated critical properties (McCain)

Pure Component Properties

Pure Component Data in Excel

Should link to a downloadable Excel file…

Heat Effects Accompanying Phase Changes of Pure Substances

Lv = TDV dPv

dTWith

DV = VMg-VMl

Btu/lb-mol

Clapeyron equation

Heat Effects Accompanying Phase Changes of Pure

Substances

Lv = TDV dPv

dT

=

Approximate relation (Clausius - Clapeyron Equation)

dPv

dT RT 2Pv

Lv

Example of Heat Effects Accompanying Phase Changes

Example of Heat Effects Accompanying Phase Changes

Steam flooding Problem:

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

COX - Vapor Pressure Charts(normal paraffins)

Pre

ss

ure

Temperature

heavier

Non-linear scale

Log scale

Determination of Fluid Properties

Temperature of Test Constant

Vt1

Vt2

Vt3

=V

b

Vt5

Vt4

liquid liquid liquidliquid

liquid

gas gas

Hg Hg HgHg

Hg

P1

>> Ps

P2

> Ps

P3

= Ps

P4

= Ps

P5

=Ps

1 2 3 4 5

Ps =saturation pressure

Vapor Pressure DeterminationP

ress

ure

PS

Volume

V L

T2

T1

Binary Mixtures

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

+COMPOSITION – Molar Composition

Hydrocarbon Composition

The hydrocarbon composition may beexpressed on a weight basis or on a molarbasis (most common)

Recall

""

""

iofweightmolecular

iofmass

Mw

Mn

i

ii

Our Systems of Concern

Gas system

Oil system

open

Hydrocarbon Composition

By convention liquid compositions (molefractions) are indicated with an x and gascompositions with a y.

liquidnn

nx

21

11

gasnn

ny

21

11

A separator

zi(T1,P1)

xi(T1,P2)

yi(T1,P2)

P1 > P2T1,P2

with

In general

Mathematical Relationships

vl fyfxz 111 vv fyfxz 111 1 )(

lv

vv

nnnn

nnf

2121

21

)(

11

1 1

xy

xzfv

ii

iiv

xy

xzf

Key Concepts

Fraction of vapor (fv)

Mole fractions in vapor (or gas) phase yi

Mole fractions in liquid (or oil) phase xi

Overall mole fractions (zi) combining gas & liquid

Phase Diagrams forBinary Mixtures

Types of phase diagrams for a two-component mixture

Most common

(PT) zi at a fixed composition

(Pzi) T at a fixed T

(Tzi) P at a fixed P

(PV) zi or (Pr) zi

Pressure vsTemperature Diagram (PT)zi

CB

CT

CP

Bubble Curve

Dew Curve

Press

ure

Temperature

Liquid

Gas

2 Phases

Zi = fixed

Pressure Composition Diagrams - Binary Systems

Temperature x1, y1

Pre

ssu

re

P2v

TaCP1

2-phases

Liquid

Vapor

P1v P1

v

CP2

P2v

Ta0 1

Temperature vs. Composition Diagrams – Binary Systems

Temperature

Pre

ss

ure

2-phases

x1, y1

Pa

Pa

CP1

CP2

T1s T2

s

T2s

T1s

0 1

3-D Phase

Diagram

(P,x)T

(T,x)P

Gas-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 Conditions Binary Mixture

Ta Tb Tg

Temperature x1, y1

Ta

Tb

Tg

[1]

[2]

P1

P2v

Quantitative Phase Equilibrium 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 0.8

Composition (%C1)

Pre

ss

ure

(p

sia

) T=160F

Quantitative Phase Equilibrium 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 (

psia

)

T=100F

T=160F

T=220F

Quantitative Phase Equilibrium ExerciseP-xy Diagram

0

400

800

1200

1600

2000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Composition (%C1)

Pre

ss

ure

(p

sia

) T=160F

Phase Equilibria Methane/n-Decane

0

1000

2000

3000

4000

5000

6000

0.00 0.20 0.40 0.60 0.80 1.00

x1, y1, z1, (1 = Methane)

Pre

ss

ure

(p

sia

)

BP (200)

DP (200)

Gas cap

composition

Black Oil Composition

Typical Black-Oil System

Ternary Diagrams: Review

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

.1 .2 .3 .4 .5 .6 .7 .8 .90

0

1

L

H I

Ternary Diagrams: Review

Pressure Effect

C3C3

nC5 C3

C1

Gas

p=14.7 psia

C1

nC5

2-phase

Liquid

p=380 psiaC3 nC5

C1

C3

2-phase

Liquid

p=500 psia

C1

2-phase

Liquid

nC5p=1500 psia

2-phase

Liquid

C1

nC5p=2000 psia

C1

nC5 C3

Liquid

p=2350 psia

Dilution Lines

Ternary Diagrams: Review

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

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

0

1

C1

C10 n-C4

x

Ternary Diagrams: Review

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

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

Dew point curve gives the gas composition.

Bubble point curve gives the liquid composition.

Ternary Diagrams: Review

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

All mixtures whose overall composition (zi) is along a tie line have the SAME equilibrium gas (yi) and liquid composition (xi), but the relative amounts on a molar basis of gas and liquid (fvand fl) change linearly (0 – vapor at B.P., 1 –liquid at B.P.).

Illustration of Phase Envelope and Tie Lines

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

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

0

1

C1

C10 n-C4

CP

Uses of Ternary Diagrams

Representation of Multi-Component Phase Behavior with a Pseudoternary DiagramTernary diagrams may approximate phase behavior of multi-component mixtures by grouping them into 3 pseudocomponents

heavy (C7+)

intermediate (C2-C6)

light (C1, CO2 , N2- C1, CO2-C2, ...)

Uses of Ternary Diagrams

Miscible Recovery Processes

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

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

0

1

C1

C2-C6C7+

A

O

Solvent1

oil

Solvent2

Exercise

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

__________________________

________________________

_______________________

_____________________

___________________

_________________

.9

.8

.7

.6

.5

.4

.3

.2

.1

.1

.2

.3

.4

.5

.6

.7

.8

.9

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

0

1

C1

C2-C6C7+

A

O

Practice Ternary DiagramsPressure Effect

T=180F

P=14.7 psiaPressure Effect

O

T=180F

P=200 psia

C1-C3-C10

Pressure Effect

O

T=180F

P=400 psia

Pressure Effect

O

T=180F

P=600 psia

Pressure Effect

O

Practice Ternary DiagramsPressure Effect

T=180F

P=1000 psia

Pressure Effect

O

T=180F

P=1500 psia

Pressure Effect

O

T=180F

P=2000 psia

O

T=180F

P=3000 psia

O

T=180F

P=4000 psia

O

Practice Ternary Diagrams

Temperature Effect

T=100F

P=2000 psia

Temperature Effect

O

T=150F

P=2000 psia

Temperature Effect

O

T=200F

P=2000 psia

Temperature Effect

O

T=300F

P=2000 psia

Temperature Effect

O

Practice Ternary Diagrams

Temperature Effect

T=350F

P=2000 psia

Temperature Effect

O

T=400F

P=2000 psia

Temperature Effect

O

T=450F

P=2000 psia

Temperature Effect

O

Pressure-Temperature Diagram for Multicomponent Systems

Reserv

oir

Pre

ssu

re

Reservoir Temperature

60%

20%0%

2-Phase

1-Phase 1-Phase

CP

Changes During Production and Injection

Temperature

t1

Pre

ssure

t3

t2

Gas

Injection

Production

t

t3

2

Gas

Injection

Production

Homework

See Syllabus please

Phase Diagrams

Types of phase diagrams for a singlecomponent (pure substance)

(PT)

(PV) or (Pr)

(TV) or (Tr