OpenSpecEngineering

Splits a two-component feed into vapor and liquid at a fixed temperature and pressure. From the feed composition and the two K-values, it finds the fraction of the feed that vaporizes and the composition of each phase. Process engineers use it to size the split in a flash drum, a partial condenser or a separator, and as a check on simulator results.

Equations

Σ z_i·(K_i − 1) / (1 + ψ·(K_i − 1)) = 0

x_i = z_i / (1 + ψ·(K_i − 1))     y_i = K_i·x_i

The first line is the Rachford–Rice equation [1], [2]. ψ = V/F is the molar vapor fraction: the moles of vapor leaving per mole of feed. z_i is the feed mole fraction of component i, x_i its mole fraction in the liquid and y_i in the vapor. K_i = y_i/x_i is its equilibrium ratio at the drum’s temperature and pressure. For two components the equation is linear in ψ, so the page solves it exactly:

ψ = −(z₁·a + z₂·b) / (a·b),   a = K₁ − 1,   b = K₂ − 1

When ψ comes out at or below 0, the feed is at or below its bubble point and stays liquid. At or above 1 it is at or above its dew point and is all vapor. The page reports these cases instead of compositions.

Inputs

• K-values depend on temperature and pressure, and in real mixtures on composition too. For an ideal mixture, K_i = P_i^sat/P from Raoult’s law. Otherwise take them from a correlation, a chart or a simulator.
• One K must be above 1 and the other below 1. Otherwise there is no two-phase split.

Limits and common mistakes

• Mole fractions and molar flows only. Convert mass flows and mass fractions first.
• The page assumes the K-values you enter hold at the drum’s conditions. It doesn’t find the temperature of an adiabatic flash, which needs an energy balance.
• Only two components. A multicomponent feed needs the full sum solved by iteration.

Worked example

A feed of 30 mol% benzene in toluene enters a drum held at 100 °C and 101.325 kPa. At 100 °C the vapor pressures are 180.4 and 74.23 kPa, so Raoult’s law gives K = 1.78 for benzene and 0.733 for toluene. How much of the feed flashes, and what are the two products?

1. Enter Feed Mole Fraction — Light Component 0.3.
2. Enter K-value — Light Component 1.78 and K-value — Heavy Component 0.733, and press Solve. The Solution shows: Vapour fraction V/F: 0.22616
   Liquid fraction L/F: 0.77384
   Liquid composition x1 (light): 0.255014
   Vapour composition y1 (light): 0.453926
   Liquid composition x2 (heavy): 0.744986
   Vapour composition y2 (heavy): 0.546074

Check the benzene balance: 0.77384 × 0.255014 + 0.22616 × 0.453926 = 0.1973 + 0.1027 = 0.3000, the feed. Also y₁/x₁ = 0.453926/0.255014 = 1.78 = K₁.