## Flash Calculation (Raoult’s Law)

This article shows step by step procedure to do Bubble Point, Dew Point and Flash Calculation based on Raoult’s Law.

### Bubble Point Calculation

Bubble point of a system is the temperature at which liquid mixture begins to vaporize.

**Obtain process parameters**

Get liquid mixture molar composition ( Xi ) and Pressure (P) of the system. Obtain equilibrium ratios ( Ki ) for the components. Ki can be calculated from Antoine equation.

`Yi = Ki.Xi`

`Ki(T) = (e`

^{A - B / (T + C) })/ P

where Yi is vapor phase molar composition in equilibrium with liquid and A,B,C are Antoine equation constants.

**Calculate Bubble Point**

At Bubble Point temperature summation of vapor phase molar fraction should be 1.

`Σ Ki(T).Xi = 1`

Above equation can be solved iteratively using Newton Raphson method. An initial temperature T is assumed. Function F(T) is calculated as following.

`F(T) = Σ Ki(T).Xi - 1`

Derivative of F(T) is calculated as following.

`F'(T) = Σ (B.Ki(T)/(T+C)² ).Xi`

New estimate of temperature is calculated as following.

`T`_{New} = T - F(T)/F'(T)

Function F(T) and F'(T) are calculated based on new temperature and this process is repeated till there is negligible difference in between T and T_{New}. Bubble point temperature thus obtained is then used to calculate vapor phase composition based on above equations.

### Dew Point Calculation

Dew point is the temperature at which liquid begins to condense out of the vapor.

**Obtain process parameters**

Get vapor mixture molar composition ( Yi ) and Pressure (P) of the system. Obtain equilibrium ratios ( Ki ) for the components.

`Yi = Ki.Xi`

`Ki(T) = (e`

^{A - B / (T + C) })/ P

**Calculate Dew Point**

At Dew Point temperature summation of liquid phase molar fraction should be 1.

`Σ Yi / Ki(T) = 1`

Above equation can be solved iteratively using Newton Raphson method. An initial temperature T is assumed. Function F(T) is calculated as following.

`F(T) = Σ Yi / Ki(T) - 1`

Derivative of F(T) is calculated as following.

`F'(T) = Σ -Yi.( B/(Ki.(T+C)² ))`

New estimate of temperature is calculated as following.

`T`_{New} = T - F(T)/F'(T)

Function F(T) and F'(T) are calculated based on new temperature and this process is repeated till there is negligible difference in between T and T_{New}. Dew point temperature thus obtained is then used to calculate liquid phase composition based on above equations.

### Flash Calculation

A mixture when flashed to conditions between bubble and dew point separates in vapor and liquid phases. Flash calculation is done to determine vapor fraction and composition of liquid, vapor formed when a mixture is flashed at a given pressure and temperature.

**Obtain process parameters**

Get molar composition ( Zi )of the mixture and flash conditions mainly pressure (P) and temperature (T) of the system. Obtain equilibrium ratios ( Ki ) for the components.

`Yi = Ki.Xi`

**Solve Flash Equations**

Based on material balance on the system

`1 = V + L`

`Zi = V.Yi + L.Xi`

where V & L are vapor and liquid fractions. Solving above equations for Xi gives

`Xi = Zi / ( V.( Ki - 1) + 1 )`

At Flash conditions

`0 = Σ Yi - Σ Xi`

Above equation can be solved iteratively using Newton Raphson method. An initial vapor fraction V is assumed. Function F(V) is calculated as following.

`F(V) = Σ Yi - Σ Xi`

`= Σ [Zi.(Ki - 1)/(V.(Ki - 1) + 1)]`

Derivative of F(V) is calculated as following.

`F'(V) = Σ -[Zi.(Ki - 1)² /( V.(Ki - 1) + 1)²]`

New estimate of vapor fraction is calculated as following.

`V`_{New} = V - F(V)/F'(V)

Function F(V) and F'(V) are calculated based on new vapor fraction and this process is repeated till there is negligible difference in between V and V_{New}. Vapor fraction thus obtained is then used to estimate vapor and liquid molar composition based on above equations.