Post on 21-Jul-2018
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
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