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PETE 310. Lectures # 6 & # 7 Phase Behavior – Pure Substances (Lecture # 5) Two Component Mixtures Three & Multicomponent Mixtures. Learning Objectives. After completing this chapter you will be able to:

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Pete 310

PETE 310

Lectures # 6 & # 7

Phase Behavior – Pure Substances (Lecture # 5)

Two Component Mixtures

Three & Multicomponent Mixtures


Learning objectives

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 proper interpretation of phase diagrams


Phase diagrams

Phase Diagrams

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

    • (PT)

    • (PV) or (Pr)

    • (TV) or (Tr)


Phase diagrams1

Fusion Curve

Critical

2

phases

Point

P

c

Solid

Liquid

(1 phase)

(1 phase)

Pressure

Vapor Pressure

Curve (2 phases)

Vapor (1 phase)

Triple Point

(3 phases)

Sublimation Curve (2 phases)

T

Temperature

c

Phase Diagrams

Single Component Phase Diagram


Phase diagrams2

Critical Point

r

P

l

c

Pressure

Liquid

r

v

Vapor

T

c

Temperature

Phase Diagrams

Vapor Pressure Curve


Hydrocarbon families physical properties

Hydrocarbon Families Physical Properties

One point in the

Vapor Pressure Curve


Pressure vs specific volume pure substance

T

)

psia

CP

Tc

Pressure (

2-phase

V

V

L

v

Specific Volume (ft3 / lbm)

Pressure vs Specific Volume Pure Substance


Pure component properties

Pure Component Properties

  • Tabulated critical properties (McCain)


Heat effects accompanying phase changes of pure substances

d

P

v

Lv

=

T

D

V

dT

Heat Effects Accompanying Phase Changes of Pure Substances

Clapeyron equation

Btu/lb-mol

With

DV = VMg-VMl


Heat effects accompanying phase changes of pure substances1

d

P

v

Lv

V

dT

Lv

d

P

v

P

v

dT

2

R

T

Heat Effects Accompanying Phase Changes of Pure Substances

=

T

D

Approximate relation (Clausius - Clapeyron Equation)

=


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

COX - Vapor Pressure Charts(normal paraffins)

Log scale

heavier

Pressure

Temperature

Non-linear scale


Determination of fluid properties

1

2

3

4

5

gas

gas

b

V

V

V

=

V

t1

t2

V

t3

t4

t5

V

liquid

liquid

liquid

liquid

liquid

Hg

Hg

Hg

Hg

Hg

>>

P

P

>

P

P

=

P

P

=

P

P

=P

P

1

s

2

s

3

s

4

s

5

s

Determination of Fluid Properties

Ps =saturation pressure

Temperature of Test Constant


Vapor pressure determination

Vapor Pressure Determination

T2

Pressure

P

S

T1

V

L

Volume


Binary mixtures

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

Hydrocarbon Composition

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

    • Recall


Hydrocarbon composition1

Hydrocarbon Composition

  • By convention liquid compositions (mole fractions) are indicated with an x and gas compositions with a y.


Our systems of concern

Our Systems of Concern

Gas system

open

Oil system


A separator

yi(T1,P2)

P1 > P2

zi(T1,P1)

T1,P2

xi(T1,P2)

A separator


Mathematical relationships

Mathematical Relationships

with

In general


Key concepts

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


Pete 310

Phase Diagrams for

Binary 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) Pat a fixed P

    • (PV) zi or (Pr) zi


Pressure vs temperature diagram pt zi

Zi = fixed

CB

CP

Liquid

CT

Bubble Curve

Pressure

2 Phases

Gas

Dew Curve

Temperature

Pressure vsTemperature Diagram (PT)zi


Pressure composition diagrams binary systems

CP1

Ta

Liquid

P1v

P1v

Bubble Curve

Pressure

2-phases

CP2

Dew Curve

P2v

Vapor

P2v

1

Ta

0

Temperature

x1, y1

Pressure Composition Diagrams - Binary Systems


Temperature vs composition diagrams binary systems

Temperature vs. Composition Diagrams – Binary Systems

Pa

T2s

CP1

Dew Curve

Pressure

2-phases

CP2

Pa

Bubble Curve

T1s

T2s

Temperature

1

T1s

x1, y1

0


Gas liquid relations

A

z

= fix

ed

1

T

= T

CP

a

B

M

P

B

C

Pressure

P

D

y

1

T

0

x

z

1

a

1

1

Temperature

Gas-Liquid Relations

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


Supercritical conditions binary mixture

Supercritical Conditions Binary Mixture


Quantitative phase equilibrium exercise

Quantitative Phase Equilibrium Exercise


Quantitative phase equilibrium exercise1

Quantitative Phase Equilibrium Exercise


Ternary diagrams review

Ternary Diagrams: Review


Ternary diagrams review1

C1

C1

C1

Gas

Gas

Gas

2-phase

2-phase

Liquid

Liquid

nC5

C3

nC5

C3

nC5

C3

p=500 psia

p=14.7 psia

p=380 psia

C1

C1

C1

Gas

Gas

2-phase

2-phase

Liquid

Liquid

Liquid

nC5

C3

nC5

nC5

p=2000 psia

p=2350 psia

p=1500 psia

Ternary Diagrams: Review

Pressure Effect

C3

C3


Ternary diagrams review2

Ternary Diagrams: Review

Dilution Lines


Ternary diagrams review3

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 review4

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 (fv and fl) change linearly (0 – vapor at B.P., 1 – liquid at B.P.).


Illustration of phase envelope and tie lines

Illustration of Phase Envelope and Tie Lines


Uses of ternary diagrams

Uses of Ternary Diagrams

Representation of Multi-Component Phase Behavior with a Pseudoternary Diagram

  • Ternary 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 diagrams1

Uses of Ternary Diagrams

Miscible Recovery Processes

Solvent2

Solvent1

oil


Exercise

Exercise

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

__________________________

________________________

_______________________

_____________________

___________________

_________________


Practice ternary diagrams

T=180F

P=200 psia

T=180F

P=14.7 psia

T=180F

P=600 psia

Pressure Effect

Pressure Effect

Pressure Effect

Pressure Effect

T=180F

P=400 psia

C1-C3-C10

O

O

O

O

Practice Ternary Diagrams

Pressure Effect


Practice ternary diagrams1

Pressure Effect

Pressure Effect

T=180F

P=4000 psia

T=180F

P=1000 psia

T=180F

P=2000 psia

T=180F

P=3000 psia

T=180F

P=1500 psia

O

O

O

O

O

Practice Ternary Diagrams

Pressure Effect


Practice ternary diagrams2

Temperature Effect

Temperature Effect

Temperature Effect

Temperature Effect

T=100F

P=2000 psia

T=200F

P=2000 psia

T=150F

P=2000 psia

T=300F

P=2000 psia

O

O

O

O

Practice Ternary Diagrams

Temperature Effect


Practice ternary diagrams3

Temperature Effect

Temperature Effect

Temperature Effect

T=400F

P=2000 psia

T=450F

P=2000 psia

T=350F

P=2000 psia

O

O

O

Practice Ternary Diagrams

Temperature Effect


Pressure temperature diagram for multicomponent systems

1-Phase

1-Phase

CP

Bubble-Curve

60%

0%

Reservoir Pressure

20%

2-Phase

Dew-Curve

Reservoir Temperature

Pressure-Temperature Diagram for Multicomponent Systems


Changes during production and injection

t

t

1

Production

Production

t

2

2

Gas

Gas

Pressure

Injection

Injection

t

t

3

3

Temperature

Changes During Production and Injection


Homework

Homework

  • See Syllabus please


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