{"id":35,"date":"2019-12-13T21:59:43","date_gmt":"2019-12-13T21:59:43","guid":{"rendered":"https:\/\/libraryresources.nse.org.ng\/chemicalengineeringseparations\/chapter\/liquid-liquid-extraction-2\/"},"modified":"2026-03-16T01:12:53","modified_gmt":"2026-03-16T01:12:53","slug":"liquid-liquid-extraction-2","status":"publish","type":"chapter","link":"https:\/\/libraryresources.nse.org.ng\/chemicalengineeringseparations\/chapter\/liquid-liquid-extraction-2\/","title":{"raw":"Liquid-liquid Extraction","rendered":"Liquid-liquid Extraction"},"content":{"raw":"

Staged Liquid-Liquid Extraction and Hunter Nash Method<\/h2>\n$E_n$\u00a0= extract leaving stage $n$. This could refer to the mass of the stream or the composition of the stream.\n\n$F$ = solvent entering extractor stage 1. This could refer to the mass of the stream or the composition of the stream.\n\n$n$ = generic stage number\n\n$N$ = Final stage. This is where the fresh solvent S enters the system and the final raffinate $R_N$\u00a0leaves the system.\n\n$M$ = Composition of the mixture representing the overall system. Points ($F$ and $S$) and ($E_1$ and $R_N$) must be connected by a straight line that passes through point $M$. $M$ will be located within the ternary phase diagram.\n\n$P$ = Operating point. $P$ is determined by the intersection of the straight line connecting points ($F$, $E_1$) and the straight line connecting points ($S$, $R_N$). Every pair of passing streams must be connected by a straight line that passes through point $P$. $P$ is expected to be located outside of the ternary phase diagram.\n\n$R_n$ = raffinate leaving stage $n$. This could refer to the mass of the stream or the composition of the stream.\n\n$S$ = solvent entering extractor stage $N$. This could refer to the mass of the stream or the composition of the stream.\n\n$S\/F$ = mass ratio of solvent to feed\n\n$(x_i)_n$ = Mass fraction of species $i$ in the raffinate leaving stage $n$\n\n$(y_i)_n$\u00a0= Mass fraction of species $i$ in the extract leaving stage $n$\n\n[caption id=\"attachment_600\" align=\"aligncenter\" width=\"1024\"]\"Schematic Process schematic for multistage liquid-liquid extraction.[\/caption]\n\n \n\nDetermining number of stages $N$ when (1) feed rate; (2) feed composition; (3) incoming solvent rate; (4) incoming solvent composition; and (5) outgoing raffinate composition have been specified\/selected.\n
    \n \t
  1. Locate points $F$ and $S$ on the ternary phase diagram. Connect with a straight line.<\/li>\n \t
  2. Do a material balance to find the composition of one species in the overall mixture. Use this composition to locate point $M$ along the straight line connection points $F$ and $S$. Note the position of point $M$.<\/li>\n \t
  3. Locate point $R_N$ on the ternary phase diagram. It will be on the equilibrium curve. Draw a straight line from $R_N$ to $M$ and extend to find the location of $E_1$\u00a0on the equilibrium curve.<\/li>\n \t
  4. On a fresh copy of the graph, with plenty of blank space on each side of the diagram, note the location of points $F$, $S$, and $R_N$ (specified\/selected) and $E_1$\u00a0(determined in step 3).<\/li>\n \t
  5. Draw a straight line between $F$ and $E_1$. Extend to both sides of the diagram. Draw a second straight line between $S$ and $R_N$. Note the intersection of these two lines and label as \u201c$P$\u201d.<\/li>\n \t
  6. Determine the number of equilibrium stages required to achieve the desired separation with the selected solvent mass.<\/li>\n<\/ol>\n- Stream $R_N$ is in equilibrium with stream $E_N$. Follow the tie-lines from point $R_N$ to $E_N$.\n\n- Stream $E_N$ passes stream $R_{N-1}$. Connect point $E_N$ to operating point $P$ with a straight line, mark the location of $R_{N-1}$.\n\n- Stream $R_{N-1}$ is in equilibrium with stream $E_{N-1}$. Follow the tie-lines from stream $R_{N-1}$ to $E_{N-1}$.\n\n- Stream $E_{N-1}$ passes stream $R_{N-2}$. Connect $E_{N-1}$ to operating point $P$ with a straight line, mark the location of $R_{N-2}$.\n\n- Continue in this manner until the extract composition has reached or passed $E_{1}$. Count the number of equilibrium stages.\n\n \n\nWatch this two-part series of videos from LearnChemE<\/a> that shows how to use the Hunter Nash method to find the number of equilibrium stages required for a liquid-liquid extraction process.\n