The feed composition is selected within a narrow range of compositions, but the solvent composition and the desired raffinate composition are specified. The extract composition and the number of stages to obtain the desired raffinate composition are determined by mass balances. First, the composition of the mixing point is calculated and located on the ternary phase diagram. The mixing point corresponds to the composition that would be obtained if the feed and the solvent flows were mixed together.

The mixing point

is located on the phase diagram between the feed and solvent points:

,

where

and

are the feed and solvent compositions.

A line is drawn from the desired raffinate composition

through the mixing point until it intersects the phase boundary; this gives 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

and

because the overall mass balance for the system is:

.

This equation is rearranged to determine 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 (orange).

A mass balance in stage 1 (total feed in = total feed out) 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 of

.

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

without being less than

. The number of orange equilibrium lines drawn is the number of equilibrium stages needed to obtain

.

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