Flash calculations

Flash calculations are used to determine the equilibrium distribution of components between the vapour and liquid phases when a multi-component mixture undergoes a phase change, such as in distillation, evaporation, or condensation processes. The calculations involve combining equations for Vapour Liquid Equilibrium (VLE) with the component mass balances, and in some cases the energy balance.

WARNING

The calculations below primarily assume that VLE is based on Raoult’s Law for ideal mixtures which states that the vapour pressure of each component is proportional to its mole fraction in the liquid phase.

The K-value for a component  is expressed using Raoult’s Law as:

Nomenclature

Symbol	Description	Unit
	Mole fraction of component in the liquid phase
	Mole fraction of component in the vapour phase
	Mole fraction of component in the feed
	Raoult’s Law K-value or Equilibrium Constant for component	-
	Total pressure of the system
	Partial pressure of component
	Vapour pressure of component  at the system temperature
F	Total molar feed flow to flash vessel
V	Molar vapour flow from flash vessel
L	Molar liquid flow from flash vessel
	Feed stream molar enthalpy
	Vapour stream molar enthalpy
	Liquid stream molar enthalpy

Bubble point calculation

To find the point at which liquid just starts to boil at a given temperature we compute where the sum of the vapour fractions reaches 1.

Where Raoult’s Law applies this gives:

is a function of temperature (one method to estimate vapour pressure is the Antoine Equation), so for a given liquid mixture composition at a given temperature we can directly calculate the bubble point pressure.

The vapour composition of each component can then be calculated:

Dew point calculation

To find the point at which vapour just starts to condense at a given temperature we compute where the sum of the liquid fractions reaches 1.

Where Raoult’s Law (substitute ) applies this gives:

is a function of temperature (one method to estimate vapour pressure is the Antoine Equation), so for a given vapour mixture composition at a given temperature we can directly calculate the dew point pressure.

NOTE

When calculating dew point with non-condensable component far above its critical point we can assume , and so goes to zero.

Flash to determine liquid and vapour streams

Flash on a stream that splits to a vapour and liquid stream.

The initial material balance on component :

We add a further specification by assuming that the vapour and liquid are at equilibrium and follow Raoult’s Law:

Pressure-Temperature flash

By substituting equation into and solving to find the liquid mole fraction:

Substituting total molar balance :

The vapour split is not known so cannot be directly calculated. Considering that , this results in the Rachford-Rice equation:

which is easy enough to solve for the vapour split .

Pressure-Enthalpy flash

For an adiabatic flash we must consider the energy balance of the system by maintaining a constant enthalpy:

Approach as per Pressure-Temperature flash above and iterate on until enthalpy requirement is met.