Vapor-liquid-liquid equilibrium calculations

We use the simplified equilibrium expression to calculate the equilibrium when there are two liquid phases present. For vapor-liquid equilibrium (VLE), the simplified equilibrium expression is:

The following figure shows a typical vapor-liquid-liquid (VLLE) equilibrium system.

The following equation is the equilibrium between phases V and LI:

Similarly, the following equation is the equilibrium between phases V and LII:

We can write the following equilibrium K-values for each phase pair:

We divide the two K-values to form the following equation.

Therefore, we can write the following three equilibrium equations between the three pairs of phases:

Only two out of these three equations are independent. We can choose any two of the equilibrium equations for the equation set, and any choice from the three available pairs should lead to the identical solution.

In principle, the activity coefficients are a function of only the phase where the component is found. For example:

We assure consistency between the three-phase equilibrium equations by using a single, unique g() function for each liquid phase.