VLE with a bulk liquid phase

If the two liquid phases exist in the molar ratio b:(1-b), then we can calculate the bulk average liquid composition according to the following equation:

We can then define a "pseudo K-value" between the vapor composition and this bulk composition:

If we substitute for the xi terms by using the general relationship xi = yi/Ki, we have the following equation:

This simplifies to the following equation, which relates the pseudo K-value to the true K-values:

We can further simplify this equation by replacing the K-values with their definitions:

or

This pseudo K-value for the bulk liquid phase is useful when setting up the equations for the flash solution, but it has the disadvantage that it depends on the phase fractions as well as the phase properties.