Flash Evaporation - Equilibrium Flash of A Multi-component Liquid

Equilibrium Flash of A Multi-component Liquid

The equilibrium flash of a multi-component liquid may be visualized as a simple distillation process using a single equilibrium stage. It is very different and more complex than the flash evaporation of single-component liquid. For a multi-component liquid, calculating the amounts of flashed vapor and residual liquid in equilibrium with each other at a given temperature and pressure requires a trial-and-error iterative solution. Such a calculation is commonly referred to as an equilibrium flash calculation. It involves solving the Rachford-Rice equation:

where:

• z_i is the mole fraction of component i in the feed liquid (assumed to be known);
• β is the fraction of feed that is vaporised;
• K_i is the equilibrium constant of component i.

The equilibrium constants K_i are in general functions of many parameters, though the most important is arguably temperature; they are defined as:

where:

• x_i is the mole fraction of component i in liquid phase;
• y_i is the mole fraction of component i in gas phase.

Once the Rachford-Rice equation has been solved for β, the compositions x_i and y_i can be immediately calculated as:

The Rachford-Rice equation can have multiple solutions for β, at most one of which guarantees that all x_i and y_i will be positive. In particular, if there is only one β for which:

then that β is the solution; if there are multiple such β's, it means that either K_max<1 or K_min>1, indicating respectively that no gas phase can be sustained (and therefore β=0) or conversely that no liquid phase can exist (and therefore β=1).

It is possible to use Newton's method for solving the above water equation, but there is a risk of converging to the wrong value of β; it is important to initialise the solver to a sensible initial value, such as (β_max+β_min)/2 (which is however not sufficient: Newton's method makes no guarantees on stability), or, alternatively, use a bracketing solver such as the bisection method or the Brent method, which are guaranteed to converge but can be slower.

The equilibrium flash of multi-component liquids is very widely utilized in petroleum refineries, petrochemical and chemical plants and natural gas processing plants.