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: :\sum_i\frac{z_i \, ( K_i -1)}{1 + \beta \, (K_i - 1)}=0 where: •
zi is the mole fraction of component
i in the feed liquid (assumed to be known); •
β is the fraction of feed that is vaporised; •
Ki is the equilibrium constant of component
i. The equilibrium constants
Ki are in general functions of many parameters, though the most important is arguably temperature; they are defined as: :y_i = K_i \, x_i where: •
xi is the mole fraction of component
i in liquid phase; •
yi is the mole fraction of component
i in gas phase. Once the Rachford-Rice equation has been solved for
β, the compositions
xi and
yi can be immediately calculated as: :\begin{align} x_i &= \frac{z_i}{1+\beta(K_i-1)}\\ y_i &= K_i\,x_i. \end{align} The Rachford-Rice equation can have multiple solutions for
β, at most one of which guarantees that all
xi and
yi will be positive. In particular, if there is only one
β for which: :\frac{1}{1-K_\text{max}} = \beta_\text{min} then that
β is the solution; if there are multiple such
β's, it means that either
Kmaxmin>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 (
βmax+
βmin)/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. ==Contrast with spray drying==