Show Some Flash and Dew the Dew with a Little Bubbly!

DOFPro Team

Introduction

  • The five most common vapor-liquid phase equilibrium calculations
  • Performed on binary Txy and Pxy phase diagrams
    • Bubble P (BUBL P)
    • Dew P (DEW P)
    • Bubble T (BUBL T)
    • Dew T (DEW T)
    • Flash (FLASH)

Txy and Pxy Binary Phase Diagrams

\(\mathrm{vapor}\)

\(2\text{–}\phi\)

\(\mathrm{liquid}\)

\(\mathrm{vapor}\)

\(2\text{–}\phi\)

\(\mathrm{liquid}\)

The Lever Rule for Phase Diagrams

\(\text{Phase }\alpha\)

\(\text{Phase }\beta\)

\(2\text{–}\phi\)

\(x_\mathrm{O}\)

\(x_\alpha\)

\(x_\beta\)

\(l_1 = x_\mathrm{O} - x_\alpha\)

\(l_2 = x_\beta - x_\mathrm{O}\)

\(l_3 = x_\beta - x_\alpha\)

If
\(\ \ \ \ n_\mathrm{total} = n_\alpha + n_\beta\)

Then
\(\ \ \ \ n_\alpha l_1 = n_\beta l_2\)

\(\ \ \ \ \dfrac{n_\alpha}{n_\mathrm{total}} = \dfrac{l_2}{l_3}\)

\(\ \ \ \ \dfrac{n_\beta}{n_\mathrm{total}} = \dfrac{l_1}{l_3}\)

If \(\alpha\) is a liquid and \(\beta\) is a vapor, then
\(\mathcal{V} \equiv \dfrac{n_\beta}{n_\mathrm{total}} = \dfrac{l_1}{l_3}\) and \(\mathcal{L} \equiv \dfrac{n_\alpha}{n_\mathrm{total}} = \dfrac{l_2}{l_3}\)

BUBL P, BUBL T, DEW P, DEW T, and FLASH

For binary VLE mixtures, five types of calculations are usually performed:

  1. BUBL P – Given all \(x_i\)’s and \(T\), calculate \(P\) at which the first bubble forms, and \(y_i\)’s of the bubble.
  2. BUBL T – Given all \(x_i\)’s and \(P\), calculate \(T\) at which the first bubble forms, and \(y_i\)’s of the bubble.
  3. DEW P – Given all \(y_i\)’s and \(T\), calculate \(P\) at which the first droplet condenses, and \(x_i\)’s of the droplet.
  4. DEW T – Given all \(y_i\)’s and \(P\), calculate \(T\) at which the first droplet condenses, and \(x_i\)’s of the droplet.
  5. FLASH – Given overall composition (\(z_i\)’s) and \(T\) and \(P\), calculate \(x_i\)’s and \(y_i\)’s, and relative amounts of vapor, \(\mathcal{V}\), and liquid, \(\mathcal{L}\).

Graphical BUBL P, DEW P

Overall
Composition

Subcooled
Liquid

Superheated
Vapor

\(2\text{–}\phi\)

Bubble
Pressure

Bubble
Composition

Dew
Pressure

Dew
Composition

Low Boiling
Azeotrope

Graphical FLASH on Pxy

Overall
Composition

Subcooled
Liquid

Superheated
Vapor

\(2\text{–}\phi\)

Flash Temperature

Flash
Pressure

Liquid
Composition

Vapor
Composition

\(a\)

\(a \approx 0.20 - 0.12 = 0.08\)

\(b\)

\(b \approx 0.37-0.20 = 0.17\)

\(\mathcal{V} = \dfrac{a}{a+b} \approx 32\%\)

\(\mathcal{L} = 1-\mathcal{V} = \dfrac{b}{a+b} \approx 68\%\)

Graphical FLASH on Txy

Overall
Composition

Subcooled
Liquid

Superheated
Vapor

\(2\text{–}\phi\)

Flash Pressure

Flash
Temperature

Liquid
Composition

Vapor
Composition

\(a\)

\(a \approx 0.20 - 0.12 = 0.08\)

\(b\)

\(b \approx 0.37-0.20 = 0.17\)

\(\mathcal{V} = \dfrac{a}{a+b} \approx 32\%\)

\(\mathcal{L} = 1-\mathcal{V} = \dfrac{b}{a+b} \approx 68\%\)

Graphical BUBL T, DEW T

Overall
Composition

Subcooled
Liquid

Superheated
Vapor

\(2\text{–}\phi\)

Dew
Temperature

Dew
Composition

Bubble
Temperature

Bubble
Composition

Low Boiling
Azeotrope

The Takeaways

  1. A \(Pxy\) binary phase diagram can be used for Bubble P and Dew P graphical calculations.
  2. A \(Txy\) binary phase diagram can be used for Bubble T and Dew T graphical calculations.
  3. Either a \(Pxy\) or \(Txy\) binary phase diagram can be used for a Flash calculation, and when using the same \(T\) and \(P\) they should agree with each other.
  4. It is not easy to automate using graphical binary phase diagrams, and they don’t work for more than two species.






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