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 proper interpretation of phase diagrams
Pressure vs Specific Volume Pure Substance
psia )
T
CP
Pressure (
Tc
2-phase
V
L
V
v
Specific Volume (ft3 / lbm)
A Problem Pressure ( psia )
T CP
Tc
2-phase
VL
Vv Specific Volume (ft3 / lbm)
Pure Component Properties Tabulated critical properties (McCain)
Pure Component Data in Excel Should link to a downloadable Excel file…
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
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 Mw i molecular weight of " i"
Our Systems of Concern
Gas system open
Oil system
Hydrocarbon Composition By convention liquid compositions (mole fractions) are indicated with an x and gas compositions with a y.
n1 x 1 n1 n2 liquid
n1 y 1 n1 n2 gas
A separator yi(T1,P2)
zi(T1,P1)
T1,P2
P1 > P2
xi(T1,P2)
Mathematical Relationships z1 x 1fl 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 twocomponent 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 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
3-D Phase Diagram
(T,x)P
(P,x)T
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
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
Typical Black-Oil System Phase Equilibria Methane/n-Decane 6000 BP (200) Pressure (psia)
5000
DP (200) Gas cap composition
4000 3000 2000 1000 0 0.00
0.20
Black Oil Composition
0.40
0.60
x1, y1, z 1, (1 = Methane)
0.80
1.00
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 C
C1
C1
1
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
nC5
p=1500 psia C3
nC5
p=2000 psia
C3
p=2350 psia
C3
Ternary Diagrams: Review C1
Dilution Lines .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 .8
.2
.7
.3
Solvent2 .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
Phase Diagrams Types of phase diagrams for a single component (pure substance) (PT) (PV) or (Pr) (TV) or (Tr
