Transcript PETE 310 Lectures 6 & 7 - Two Component Mixtures and Three

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:
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
Types of phase diagrams for a
single component (pure substance)
 (PT)
 (PV) or (Pr)
 (TV) or (Tr)
Phase Diagrams
Single Component Phase Diagram
Fusion Curve
2 phases
Critical
Point
Pressure
Pc
Solid
(1 phase)
Liquid
(1 phase)
Vapor Pressure
Curve (2 phases)
Triple Point
(3 phases)
Vapor (1 phase)
Sublimation Curve (2 phases)
Temperature
Tc
Phase Diagrams
Vapor Pressure Curve
Critical Point
r
l
Pressure
Pc
Liquid
r
v
Vapor
Tc
Temperature
Hydrocarbon Families
Physical Properties
One point in the
Vapor Pressure Curve
Pressure vs Specific Volume
Pure Substance
psia )
T
CP
Pressure (
Tc
2-phase
V
L
V
v
Specific Volume (ft3 / lbm)
Pure Component Properties
Tabulated critical properties (McCain)
Heat Effects Accompanying Phase
Changes of Pure Substances
Clapeyron equation
Lv
v
dP
= TD V
dT
With
DV = VMg-VMl
Btu/lb-mol
Heat Effects Accompanying
Phase Changes of Pure
Substances
Lv
v
dP
= TD V
dT
Approximate relation (Clausius - Clapeyron Equation)
dP v
dT
=
Lv
RT
2
Pv
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)
Pressure
Log scale
heavier
Temperature
Non-linear scale
Determination of Fluid
Properties
Ps =saturation pressure
V
2
V
t1
liquid
3
V t3 = V b
1
t2
liquid
4
5
gas
V
gas
V
t4
liquid
t5
liquid
liquid
Hg
Hg
Hg
Hg
Hg
P 1 >> P
s
P2 > P
s
P3 = P
s
Temperature of Test Constant
P4 = P
s
P 5 =P
s
Vapor Pressure Determination
Pressure
T2
PS
T1
VL
Volume
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
be expressed on a weight basis or
on a molar basis (most common)
Recall
Mi
mass of " i"
ni 

Mwi molecular weight of " i"
Hydrocarbon Composition
By convention liquid compositions (mole
fractions) are indicated with an x and gas
compositions with a y.
 n1 

x1  
 n1  n2  liquid
 n1 

y 1  
 n1  n2  gas
Our Systems of Concern
Gas system
open
Oil system
A separator
yi(T1,P2)
zi(T1,P1)
T1,P2
P1 > P2
xi(T1,P2)
Mathematical Relationships
z1  x1fl  y 1fv
with
fv 
z1  x 1
y 1  x1
In general
z1  x1(1  fv )  y 1fv
(n1  n2 )v
fv 
n1  n2 )v  n1  n2 )l
zi  x i
fv 
y i  xi
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 for
Binary Mixtures
Types of phase diagrams for a
two- component mixture
Most common
 (PT)
 (Pzi)
T
at a fixed composition
at a fixed T
zi
or (Pr)
zi
 (Tzi) P at a fixed P
 (PV)
zi
Pressure vs
Temperature Diagram (PT)zi
Zi = fixed
CB
CP
Pressure
Liquid
CT
Bubble Curve
2 Phases
Gas
Dew Curve
Temperature
Pressure Composition Diagrams
- Binary Systems
CP1
Ta
Liquid
P1v
Pressure
P1v
P2
2-phases
CP2
P2v
v
Ta
Temperature
0
Vapor
x1, y1
1
Temperature vs. Composition
Diagrams – Binary Systems
Pa
T2s
Pressure
CP1
2-phases
CP2
T1s
Pa
T1s Temperature T2s
0
x1, y1
1
Gas-Liquid Relations
z1 = fix ed
CP
PB
T = Ta
M
A
B
Pressure
C
PD
Ta
Temperature
z1=overall mole fraction of [1],
0
x1
y1=vapor mole fraction of [1],
z1
y1
1
x1=liquid mole fraction of [1]
Supercritical Conditions Binary
Mixture
Ta
Tb
Tg
Tg
Tb
P1
[1]
Ta
[2]
P2v
Temperature
x1, y 1
Quantitative Phase Equilibrium
Exercise
P-xy Diagram
2000
Pressure (psia)
1600
T=160F
1200
800
400
0
0.0
0.1
0.2
0.3
0.4
0.5
Composition (%C1)
0.6
0.7
0.8
Quantitative Phase Equilibrium
Exercise
P-xy Diagram
2400
T=100F
T=160F
T=220F
Pressure (psia)
2000
1600
1200
800
400
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Composition (%C1)
0.7
0.8
0.9
1.0
Ternary Diagrams: Review
L
.1
.9
.8
.2
.7
.3
.6
.4
.5
.5
.4
.6
.3
.7
.8
.2
.9
.1
0
1
H0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1
I
Ternary Diagrams: Review
Pressure Effect
C1
C1
C1
Gas
2-phase
2-phase
nC5
p=14.7 psia
C3
Liquid
nC5
p=380 psia
C3
Liquid
nC5
p=500 psia
C1
C1
Liquid
Liquid
C1
C3
2-phase
2-phase
Liquid
nC5
p=1500 psia
nC5
C3
p=2000 psia
C3
nC5
p=2350 psia
C3
Ternary Diagrams: Review
Dilution Lines
C1
.1
.9
.8
.2
.7
.3
.6
.4
.5
.5
.6
.4
.7
.3
.8
.2
x
.9
C10
.1
1
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
0
1 n-C4
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 (fv and fl) change
linearly (0 – vapor at B.P., 1 – liquid at
B.P.).
Illustration of Phase Envelope
and Tie Lines
C1
.1
.9
.8
.2
.7
.3
.6
.4
.5
.5
CP
.6
.4
.7
.3
.8
.2
.9
C10
.1
1
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
0
1 n-C4
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 Diagrams
Miscible Recovery Processes
C1
.1
.9
Solvent2
.8
.2
.7
.3
.6
.4
.5
.5
.6
.4
A
.3
.7
.8
.2
O
.9
C7+
1
0
.1
Solvent1
.2
.3
.4
oil
.5
.6
.1
.7
.8
.9
0
1 C2-C6
Exercise
Find overall composition of mixture made with
100 moles oil "O" + 10 moles of mixture "A".
__________________________
C1
________________________
_______________________
_____________________
___________________
_________________
.1
.9
.8
.2
.7
.3
.6
.4
.5
.5
.6
.4
A
.3
.7
.8
.2
O
.9
C7+
.1
1
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
0
1 C2-C6
Practice Ternary Diagrams
Pressure Effect
T=180F
P=14.7 psia
Pressure Effect
T=180F
P=200 psia
Pressure Effect
C1-C3-C10
O
T=180F
P=400 psia
O
O
Pressure Effect
T=180F
P=600 psia
O
Pressure Effect
Practice Ternary Diagrams
Pressure Effect
T=180F
P=1000 psia
Pressure Effect
O
T=180F
P=2000 psia
O
T=180F
P=1500 psia
Pressure Effect
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=200F
P=2000 psia
O
T=150F
P=2000 psia
Temperature Effect
O
Temperature Effect
T=300F
P=2000 psia
O
Temperature Effect
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
O
Temperature Effect
Pressure-Temperature Diagram
for Multicomponent Systems
1-Phase
1-Phase
Reservoir Pressure
CP
60%
20%
2-Phase
Reservoir Temperature
0%
Changes During Production and
Injection
t
1
Production
Pressure
t
2
Gas
Injection
t
Temperature
3
Homework
See Syllabus please