The feed flow rate, solvent flow rate and feed composition are given. The desired raffinate composition is specified, and the extract composition and the number of stages to obtain the desired raffinate composition are determined by mass balances. First, the mixing point composition is calculated and located on the ternary phase diagram. The mixing point corresponds to the composition that would be obtained if the feed and solvent flows were mixed together. The mass balance is:

overall:

solute

:

solvent

:

carrier

:

where

is the feed flow rate (kg/h);

is the solvent flow rate (kg/h);

is the combined feed and solvent flow rate (kg/h);

,

and

refer to the mass fractions of the solute, solvent and carrier in

, where the superscripts

,

and

refer to the three kinds of stream: feed, solvent and mixed. The coordinates of the mixing point

on the ternary diagram are (

).

The mixing point can also be located on the phase diagram using the lever rule:

where

is the length of the line segment from the mixing point to the feed composition

, and

is the length of the line segment from the mixing point

to the solvent composition S.

A line is drawn from the desired raffinate composition

through the mixing point until it intersects the phase boundary, giving the extract composition leaving stage 1,

.

The operating point

is located at the intersection of a line drawn through points

and

and a line drawn through points

and

, because the overall mass balance for the system is:

This equation is rearranged to define the operating point:

A tie line from

to the right side of the phase boundary yields the raffinate composition leaving stage 1,

; this line represents the first equilibrium stage.

A mass balance on stage 1 is:

Thus, the extract composition leaving stage 2,

, is found by drawing a straight line from

to

(because

from the previous equation). Where this line intersects the left side of the phase boundary is the composition

.

This procedure is repeated for additional stages until the raffinate composition is nearly equal to the desired raffinate composition

. The number of orange lines drawn is the number of equilibrium stages.

See [1–4] for screencasts that describe the Hunter–Nash method and present examples.

This Demonstration is a Mathematica version of a browser-based simulation [5].