# Apply the Hunter-Nash Method to Liquid-Liquid Extraction

In this Demonstration, you can construct a ternary phase diagram step by step using the Hunter–Nash method to determine the number of equilibrium stages needed to achieve a certain separation. Press the "new problem" button to generate a new set of conditions; pressing this button takes you back to the beginning of the Demonstration. Check "solution" to see the answer. Once you check "solution", you cannot change your answers. Click "next" to move onto the next step, but once you press "next", you cannot go backward.

### DETAILS

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:
which can be written as:
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].
References
[1] Hunter–Nash Method: Liquid-Liquid Extraction [Video]. (Apr 13, 2018) www.youtube.com/watch?v=e0Yt5RMkyj4.
[2] Hunter–Nash Method: Liquid-Liquid Extraction Example [Video]. (Apr 13, 2018) www.youtube.com/watch?v=FaKIZU3XPR8.
[3] Hunter–Nash Method 1: Mixing and Operating Points [Video]. (Apr 13, 2018) www.youtube.com/watch?v=-yW0jIcH0_E.
[4] Hunter–Nash Method 2: Number of Stages [Video]. (Apr 13, 2018) www.youtube.com/watch?v=JZuavrt8ksQ.
[5] T. Bánsági and T. L. Rodgers, Liquid-Liquid Extraction: Hunter-Nash Method. (Apr 13, 2018) chem.co.nf/LLE/ternary_hn.html.

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