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PETE 310 Lectures # 6 & # 7 Phase Behavior – Pure Substances (Lecture # 5) Two Component Mixtures Three & Multicomponent Mixtures

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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

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Phase Diagrams Types of phase diagrams for a single component (pure substance) (PT) (PV) or (P ) (TV) or (T

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Phase Diagrams Single Component Phase Diagram

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Phase Diagrams Vapor Pressure Curve Pressure Temperature Vapor Liquid Critical Point l v P c T c

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Hydrocarbon Families Physical Properties One point in the Vapor Pressure Curve

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Pressure vs Specific Volume Pure Substance TcTc 2-phase T Specific Volume (ft 3 / lbm) Pressure ( psia ) V v V L CP

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Tabulated critical properties (McCain) Pure Component Properties

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Heat Effects Accompanying Phase Changes of Pure Substances Heat Effects Accompanying Phase Changes of Pure Substances Lv = T V dP v dT With V = V Mg -V Ml Btu/lb-mol Clapeyron equation

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Heat Effects Accompanying Phase Changes of Pure Substances Heat Effects Accompanying Phase Changes of Pure Substances Lv = T V dP v dT = Approximate relation (Clausius - Clapeyron Equation) dP v dT RT 2 P v Lv

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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 o F 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 o F

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COX - Vapor Pressure Charts (normal paraffins) Pressure Temperature heavier Non-linear scale Log scale

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Determination of Fluid Properties Temperature of Test Constant V t1 V t2 V t3 = V b V t5 V t4 liquid gas Hg P 1 >> P s P 2 > P s P 3 = P s P 4 = P s P 5 =P s Ps =saturation pressure

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Vapor Pressure Determination Pressure P S Volume V L T2T2T2T2 T1T1T1T1

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

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

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

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Our Systems of Concern Gas system Oil system open

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A separator z i (T 1,P 1 ) x i (T 1,P 2 ) y i (T 1,P 2 ) P 1 > P 2 T 1,P 2

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with In general Mathematical Relationships

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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

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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 P at a fixed P (PV) zi or (P ) zi

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Pressure vs Temperature Diagram (PT) zi CB CT CP Bubble Curve Dew Curve Pressure Temperature Liquid Gas 2 Phases Zi = fixed

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Pressure Composition Diagrams - Binary Systems

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Temperature vs. Composition Diagrams – Binary Systems Temperature Pressure Bubble Curve Dew Curve 2-phases x 1, y 1 PaPa PaPa CP 1 CP 2 T1sT1s T2sT2s T2sT2s T1sT1s 0 1

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Gas-Liquid Relations z 1 =overall mole fraction of [1],y 1 =vapor mole fraction of [1],x 1 =liquid mole fraction of [1]

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Supercritical Conditions Binary Mixture

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Quantitative Phase Equilibrium Exercise

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Ternary Diagrams: Review

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Pressure Effect C3C3 C3C3 nC 5 C3C3 C1C1 Gas p=14.7 psia C1C1 nC 5 Gas 2-phase Liquid p=380 psia C3C3 nC 5 C1C1 C3C3 Gas 2-phase Liquid p=500 psia C1C1 Gas 2-phase Liquid nC 5 p=1500 psia 2-phase Liquid C1C1 nC 5 Gas p=2000 psia C1C1 nC 5 C3C3 Liquid p=2350 psia

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Dilution Lines Ternary Diagrams: Review

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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.

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Ternary Diagrams: Review Quantitative Representation of Phase Equilibria - Tie (or equilibrium) lines All mixtures whose overall composition (z i ) is along a tie line have the SAME equilibrium gas (y i ) and liquid composition (x i ), but the relative amounts on a molar basis of gas and liquid (f v and f l ) change linearly (0 – vapor at B.P., 1 – liquid at B.P.).

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Illustration of Phase Envelope and Tie Lines

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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 (C 7 + ) intermediate (C 2 -C 6 ) light (C 1, CO 2, N 2 - C 1, CO 2 -C 2,...)

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Uses of Ternary Diagrams Miscible Recovery Processes Solvent1 oil Solvent2

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

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Practice Ternary Diagrams Pressure Effect T=180F P=14.7 psia Pressure 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

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Practice Ternary Diagrams Pressure 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

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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

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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

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Pressure-Temperature Diagram for Multicomponent Systems

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Changes During Production and Injection Temperature t 1 Pressure t 3 t 2 Gas Injection Production t t 3 2 Gas Injection Production

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Homework See Syllabus please

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