101.9 Vle

ChE 101 Fundamentals of Chemical Engineering

Material Balances in Multiphase Systems

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Outline ¤ Vapor-Liquid Equilibrium – Phase diagrams – Raoult’s Law

¤ Gas-Liquid Equilibrium – Henry’s Law – Psychrometric charts

¤ Liquid-Liquid Equilibrium ¤ Solid-Liquid Equilibrium

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Recall: Separation Processes

How do we determine these compositions?

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Phase Diagrams

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Phase Diagrams

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Phase Diagrams

𝑃 𝑠𝑎𝑡 𝑇

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Phase Diagrams ¤ Equations for vapour/saturation pressure – Clapeyron equation – Antoine equation ln 𝑃 𝑠𝑎𝑡

𝐵 =𝐴− 𝑇+𝐶

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Phase Diagrams ¤ Graphs for vapour/saturation pressure (Cox chart)

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Phase Diagrams

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Phase Diagrams

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Gibbs Phase Rule ¤ Applicable to systems at equilibrium with no reaction – F: degrees of freedom, number of independent intensive variables needed to fix all other intensive variables – P: number of phases – C: number of independent components 𝐹 =2−𝑃+𝐶

¤ Ex. How many number of phases in: – A solution of salt in water – Saturated salt solution with salt crystals settling – A system of CaCO3 decomposing to CaO and CO2 – Oil and water 11

Vapor-Liquid Equilibrium ¤ Ex. Alcohol solution – NBP of water: 100oC – NBP of ethanol: 78.4oC – How many degrees of freedom? – Composition in vapour: 𝑦𝑖 – Composition in liquid: 𝑥𝑖 – Recall: partial pressure 𝑃𝑖 = 𝑦𝑖 𝑃

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Vapor-Liquid Equilibrium ¤ Raoult’s Law: 𝑃𝑖 ∝ 𝑥𝑖

𝑦𝑖 𝑃 = 𝑥𝑖 𝑃𝑖𝑠𝑎𝑡 𝑇 13

Vapor-Liquid Equilibrium ¤ Non-ideal solutions

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Vapor-Liquid Equilibrium ¤ P-xy Diagram Tie line

Total Total

Liquid region Vapor region

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Vapor-Liquid Equilibrium ¤ T-xy diagram Liquid region

Vapor region

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Vapor-Liquid Equilibrium ¤ Recall: ILAR

V L

F

𝐹 =𝐿+𝑉 𝑧𝑖 𝐹 = 𝑥𝑖 𝐿 + 𝑦𝑖 𝑉

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Vapor-Liquid Equilibrium Ex. Based on the T-xy diagram for toluene and benzene (x-axis is for benzene), • Which is the more volatile component? • What are the vapor pressures of each component at 100oC? • What are the normal boiling points of each component? • Equal amounts of toluene at 85oC and benzene at 110oC are mixed at atmospheric conditions • What it the final temperature? • What are the final compositions?

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Vapor-Liquid Equilibrium Ex. A 70% toluene mixture in a closed isothermal piston cylinder at 100oC and 1000 mmHg is depressurized to 600 mmHg • What is the initial state of the system? • At what P will the first bubble form? What is its composition? • At what P will the last drop of liquid evaporate? What is its composition? • What are the liquid and vapor compositions at 750 mmHg? What is the vapor-liquid ratio at this point?

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Vapor-Liquid Equilibrium

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Vapor-Liquid Equilibrium ¤ Bubble-P calculation – Given: T, 𝑥𝑖 𝑖

𝑦𝑖 𝑃 =

𝑖

¤ Dew-P calculation – Given: T, 𝑦𝑖

𝑦𝑖 𝑠𝑎𝑡 𝑃 𝑖 𝑖

𝑇

𝑠𝑎𝑡 𝑥𝑖 𝑃𝑖

=

𝑇 =𝑃

𝑥𝑖 1 = 𝑃 𝑖𝑃

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Vapor-Liquid Equilibrium Ex. A 70% toluene mixture in a closed isothermal piston cylinder at 100oC and 1000 mmHg is depressurized to 600 mmHg • What is the initial state of the system? • At what P will the first bubble form? What is its composition? • At what P will the last drop of liquid evaporate? What is its composition? • What are the liquid and vapor compositions at 750 mmHg? What is the vapor-liquid ratio at this point?

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Vapor-Liquid Equilibrium ¤ Bubble-T calculation – Given: P, 𝑥𝑖

𝑃− 𝑖

𝑦𝑖 𝑃 = 𝑃 −

𝑖

𝑥𝑖 𝑃𝑖𝑠𝑎𝑡 𝑇 = 0

– For binary solutions, 𝑃 = 𝑥1 𝑃1𝑠𝑎𝑡 + 𝑥2 𝑃2𝑠𝑎𝑡 – Let 𝛼 =

𝑃1𝑠𝑎𝑡 𝑃2𝑠𝑎𝑡

𝐵1 𝑇+𝐶1

= exp 𝐴1 − 𝐴2 − 𝑃 𝑠𝑎𝑡 𝑃2 = 𝑥1 𝛼 + 𝑥2 𝐵2 𝑇= 𝑠𝑎𝑡 − 𝐶2 𝐴2 − ln 𝑃2

−

𝐵2 𝑇+𝐶2

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Vapor-Liquid Equilibrium ¤ Bubble-T calculation – Given: P, 𝑥𝑖

Guess T

Calc 𝛼

Calc 𝑃2𝑠𝑎𝑡

Converge

Calc new T 24

Vapor-Liquid Equilibrium ¤ Dew-T calculation – Given: P, 𝑦𝑖

𝑦𝑖 𝑠𝑎𝑡 𝑃 𝑖 𝑖

𝑇

=

𝑥𝑖 1 = 𝑃 𝑖𝑃

– For binary solutions, 1 𝑦1 𝑦2 = 𝑠𝑎𝑡 + 𝑠𝑎𝑡 → 𝑃1𝑠𝑎𝑡 = 𝑃 𝑦1 + 𝑦2 𝛼 𝑃 𝑃1 𝑃2 𝐵1 𝑇= 𝑠𝑎𝑡 − 𝐶1 𝐴1 − ln 𝑃1

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Vapor-Liquid Equilibrium ¤ Dew-T calculation – Given: P, 𝑦𝑖

Guess T

Calc 𝛼

Calc 𝑃1𝑠𝑎𝑡

Converge

Calc new T 26