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:
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 a line drawn through
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
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.