A McCabe-Thiele graphically constructed solution for a liquid-liquid extraction mass-transfer problem requires the corresponding liquid-liquid equilibrium solubility data to be available for the considered ternary system, while such data should be presented in a compatible type of diagram. It also requires some other assumptions to be fulfilled, because it is based on the analogy toward the corresponding method when applied to liquid-vapour equilibrium, where comparable assumptions should hold. Namely, both the liquid solvents are considered immiscible and a single solute is considered dissolved and distributed between both liquid phases. Moreover, for each (ideal) stage, equilibrium should be achieved, while counter-current extraction is adopted for multistage extraction.

Dear Jovana Djokic

A distribution isotherm is a plot of the equilibrium concentration of the extracted species in the extracted phase against its concentration in the raffinate layer at a given temperature. Distribution isotherm can be prepared for either the extraction process (and in this case it is called extraction isotherm) or the stripping process (which called stripping isotherm).

Data for the extraction isotherm could be easily obtained from either "phase ratio variation" single contact of a fixed volume of  aqueous feed ( input leach liquor) with different volumes of organic solvent or else by "saturation process" repeated contact of one and the same aliquot of the organic solvent with several aliquots of fresh input leach liquor.

Mc-Cabe Thiele diagram is a composite plot of the distribution isotherm and the operating line. The operating line could be established by only one point, which corresponds to the final raffinate composition and the ratios of the aqueous to organic phases that determines the slope of the line, as it is a straight line.

The diagram can be used to evaluate the extraction results and to approximate the number of theoretical stages required for the extraction process.

Dear Jovana Djokic

In a LLE process, theoretical steps of extraction can be estimated using Distribution Isotherm and Mc. Cabe Tail diagram. In order to obtain Distribution Isotherm, various organic to aqueous ratio are mixed in a constant temperature. After reaching equilibrium, two phases (aqueous and organic) are separated and metal concentration are measured in them. 

Distribution Isotherm and an operating line are used in order to draw and analysis of Mc. Cabe Tail diagram. As the mentioned operating line is a straight line, it can be drawn by any 2 points of the line. Also, it can be drawn by a point and the line slope. Slope of this line is aqueous to organic ratio and the one point which are needed to draw the line (X0) is the concentration of copper at the starting time of process. With having these all, Y1 will be reached by the following equation.

Y1=A/O(x0-xn) + yn+1                                                (1)

Jovana

A McCabe-Thiele diagram can be used for LLE with a ternary system (two solvents, one solute). The usual assumption is the extract and raffinate phase flow rates are constant, which is reasonable for dilute systems and near total immiscibility. This assumption leads to a straight operating line, and is sufficiently accurate in many cases. Deviation from these conditions results in a curved operating line, but the curvature can be estimated for improved accuracy. For more detail and an example, see McCabe, Smith and Harriott (Unit Operations of Chemical Engineering, 7th ed., McGraw-Hill, New York, 2005, Ch. 23).

You mentioned you know your feed and raffinate concentrations. If you don't also know the extract concentration, you can calculate it by mass balance. I assume the starting solvent concentration is zero. If you adopt the constant flow rate assumption, you have enough data to plot the operating line, whose terminal points are (xR, 0) and (xF, yE) where x and y are the raffinate and extract phase concentrations (usually mole fractions are used), and R, E and F are raffinate, extract and feed, respectively. You also need equilibrium data, which may be available in handbooks or online, or you can generate it yourself, either experimentally, or with a theoretical model using either a process simulator or hand calculations (simulator is better).

Speaking of simulators, LLE can be simulated using ChemCAD, Aspen Plus, and probably others.

Hope this helps!

Alan

Thank you for answers. Informations you gave me are very helpful.

Sincerely, Jovana Djokic