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PETE 310

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PETE 310

Lectures # 6 & # 7

Phase Behavior – Pure Substances (Lecture # 5)

Two Component Mixtures

Three & Multicomponent Mixtures

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

- Types of phase diagrams for a single component (pure substance)
- (PT)
- (PV) or (Pr)
- (TV) or (Tr)

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

Single Component Phase Diagram

Critical Point

r

P

l

c

Pressure

Liquid

r

v

Vapor

T

c

Temperature

Vapor Pressure Curve

One point in the

Vapor Pressure Curve

T

)

psia

CP

Tc

Pressure (

2-phase

V

V

L

v

Specific Volume (ft3 / lbm)

- Tabulated critical properties (McCain)

d

P

v

Lv

=

T

D

V

dT

Clapeyron equation

Btu/lb-mol

With

DV = VMg-VMl

d

P

v

Lv

V

dT

Lv

d

P

v

P

v

dT

2

R

T

=

T

D

Approximate relation (Clausius - Clapeyron Equation)

=

- 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

Log scale

heavier

Pressure

Temperature

Non-linear scale

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

Ps =saturation pressure

Temperature of Test Constant

T2

Pressure

P

S

T1

V

L

Volume

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

- COMPOSITION – Molar Composition

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

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

Gas system

open

Oil system

yi(T1,P2)

P1 > P2

zi(T1,P1)

T1,P2

xi(T1,P2)

with

In general

- 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 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

Zi = fixed

CB

CP

Liquid

CT

Bubble Curve

Pressure

2 Phases

Gas

Dew Curve

Temperature

CP1

Ta

Liquid

P1v

P1v

Bubble Curve

Pressure

2-phases

CP2

Dew Curve

P2v

Vapor

P2v

1

Ta

0

Temperature

x1, y1

Pa

T2s

CP1

Dew Curve

Pressure

2-phases

CP2

Pa

Bubble Curve

T1s

T2s

Temperature

1

T1s

x1, y1

0

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

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

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

Pressure Effect

C3

C3

Dilution Lines

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.

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.).

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, ...)

Miscible Recovery Processes

Solvent2

Solvent1

oil

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

__________________________

________________________

_______________________

_____________________

___________________

_________________

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

Pressure Effect

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

Pressure Effect

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

Temperature Effect

Temperature Effect

Temperature Effect

Temperature Effect

T=400F

P=2000 psia

T=450F

P=2000 psia

T=350F

P=2000 psia

O

O

O

Temperature Effect

1-Phase

1-Phase

CP

Bubble-Curve

60%

0%

Reservoir Pressure

20%

2-Phase

Dew-Curve

Reservoir Temperature

t

t

1

Production

Production

t

2

2

Gas

Gas

Pressure

Injection

Injection

t

t

3

3

Temperature

- See Syllabus please