Liquid extraction produces separation of the constituents of a liquid solution by contact with another insoluble liquid. If the components of the original solution distribute differently between the two liquids, separation will result. The component balances will be essentially identical to those for leaching, but there are two major differences that complicate the calculations:
Common applications of liquid extraction include: the separation and purification of lube oils, separation of penicillin from fermentation broth, etc.
Extraction is driven by chemical differences, not by vapor pressure differences, and so can be used in situations when distillation is impractical. For instance, it can be used to separate materials with similar boiling points (so that distillation is impractical) or mixtures containing temperature sensitive compounds.
Distillation and evaporation produce finished products; liquid extraction generally does not. The products are still mixtures, although with new compositions, and these must be separated to obtain final products. Secondary separation often requires distillation or evaporation. The overall process cost thus must be considered when choosing extraction.
Extraction may become economical for dilute aqueous solutions when evaporation would require vaporization of very large amounts of water.
Certain terms are commonly used when describing extraction processes. The solution to be extracted is called the feed, the liquid used in contacting is the solvent. The enriched solvent product is the extract and the depleted feed is called the raffinate.
Extraction processes may be be single stage, multistage crosscurrent, or countercurrent. Cocurrent extraction offers no advantages over a single stage (convince yourself of this!). This class will primarily be concerned with countercurrent systems.
Extraction calculations require an understanding of ternary equilibrium. You probably should refresh your memory on how ternary diagrams are read and used. I would anticipate that you learned this in your material balance course.
One new term that may not be familiar is the plait point. This point is located near the top of the two-phase envelope, at the inflection point. It represents a condition where the 3-component mixture separates into two phases, but the phases have identical compositions. (Compare this with an azeotropic mixture of liquid and vapor.)
There are two main classes of liquid-liquid equilibrium that occur in extraction. A Class I system is the one I expect you are familiar with; it has one immiscible pair of compounds and produces the familiar envelope. Class II mixtures have two pair of immiscible compounds, and so the two-phase envelope crosses the triangular diagram like a bridge. Class I mixtures are the most common and are preferable -- so if you can pick a solvent to get a Class I, you usually want to do so. Classes can change with temperature, so that is also a concern.
One of the key decisions when designing an extraction process is the choice of the solvent to be used. Issues include:
As with the other separations we discuss, there are two primary calculations:
Since LL equilibrium is seldom available in algebraic form, the calculations tend to be iterative or graphical. You have a choice of graphical approaches depending on the type of equilibrium diagram you have available (or choose to construct):
For a given feed mixture, required degree of extraction, operating pressure and temperature, and choice of solvent, there is a minimum solvent-to-feed ratio which corresponds to an infinite number of contact stages.
As with the other separations we have studied, this corresponds to a "pinch" between the equilibrium and operating curves at the feed composition. Algebraically, this corresponds to an extract phase in equilibrium with the entering feed. The pinch can also be found graphically -- on a McCabe-Thiele type construction, minimum solvent ratio corresponds to a pinch (curves intersecting) at the feed composition. During a triangular construction, a feed pinch is represented by the operating line overlapping a tie-line and running through the feed point.
A theoretical upper limit or maximum solvent-to-feed ratio also can be determined. If you visualize the ternary diagrams, you notice that if enough solvent is added, the equilibrium curve is crossed and the single phase region is entered. Once this happens, it is impossible to divide the mixture into different phases, hence no separation is achieved. The maximum solvent-to-feed ratio is thus that which puts the mixture on the phase boundary.
A modified McCabe-Thiele approach is probably the most straightforward graphical technique for solving extraction problems. As always, the main constraint is the equilibrium data. When the data is given in a tabular form, it isn't difficult to construct the needed y (solute in the extract phase) vs. x (solute in the raffinate phase) diagram; however, it is a bit of a chore to pull the points off of a ternary diagram. In the latter case, it may may sense to construct directly on the triangle.
Once you have the y vs. x plot, the component and material balances can be used to set the endpoints of the operating curve. Interior points can be found by selecting an intermediate value of x, and calculating the appropriate y (this typically is an iterative calculation). You want to find enough interior points to be sure of the shape of the curve, but shouldn't have to calculate too many of these points. The operating curve that results will typically be curved. For extraction calculations, both the equilibrium and the operating equations will be typically be curved.
Once the curves are available, they can be "stepped off" into triangles, just as one would expect from McCabe-Thiele.
Construction on a ternary diagram is a little messier. The diagrams are typically much more crowded and so counting stages is more complicated. You also typically need substantial extra space on the side of the diagram; often you want to tape a spare sheet of paper in place to get the workspace. Pocket rulers end up being too short, so make sure you have a longer (~ 2 ft) straightedge around.
The first step is to locate the known endpoints.
The fundamental idea of all constructions is that a single line connects points made from "mixing" two streams. The endpoints are thus connected two different ways.
First, a segment is drawn connecting the "entering" streams (La, Vb) and one between the "leaving" streams (Lb, Va). These will intersect in the middle of the diagram at a "mixing point", M. Since the two streams leaving an ideal stage, are in equilibrium, this point is related to the equilibrium curve. Lever arm principles apply, so that the M point splits the line segments proportionately to the solvent/feed ratio, so that
An "operating" point, P, is located by connecting the "sides" of the cascade: La to Va and Lb to Vb. The P point can lie on either side of the triangle, depending on the slope of the tie lines. (This is where that extra piece of paper comes in handy!) All possible operating points must pass through the P point.
With the endpoints and the P point, the stages can be stepped off. Begin at the Va (extract product) point. Trace down a tie- line to the raffinate side of the envelope; the intersection will be at the composition of the stream leaving stage one, so this is the L1 point. Next, construct a line connecting L1 with P and extend the line back across to the extract side of the diagram. This is an operating line, and the intersection is the V2 point. The triangle that has been formed represents one ideal equilibrium stage.
This procedure -- down a tie line, up an operating line -- is repeated until the feed point is reached/passed. The total number of triangles created is the number of stages. Often the construction gets crowded and may be hard to read.
Problems can be varied by changing the given information. You then will need to think through the relationships (solvent/feed ratio, equilibrium tie-lines, operating lines, etc.) and adapt the procedure.
Minimum solvent-to-feed is determined by extending the tie-line that runs through the feed point until it intersects the segment connecting Vb and Lb. This intersection is the point Pmin, an operating point at minimum S/F. The line is then extended back across the envelope to the extract side. The intersection is the point Vmin, corresponding to the extract product at minimum S/F. (Remember that a "pinch" on this type of diagram means that the operating and equilibrium (tie-lines) overlap.) A mixing point "Mmin" can be determined using the feed point, Vb, Lb, and Vmin, and the lever-arm rule will provide a value for the S/F ratio.
Maximum solvent-to-feed is found by locating a point "Mmax" on the line connecting the fresh solvent and the feed, at the point where it intersects the extract side of the envelope. S/F is then calculated by lever arm.
Rarely do you have all the equilibrium tie lines you want. It is thus good to know that there is a fairly easy way of generating additional lines.
To do this, you construct a "conjugate curve" from the existing tie lines. Take each endpoint and draw a line from it downward, perpendicular to base of the triangle. The extensions from the raffinate side will intersect those from the extract side, and each pair forms a point on the conjugate curve. The final point is the plait point. When a new tie line is needed, one composition is chosen, a line is traced down to the conjugate curve, and then back up to the envelope on the other side. This is the other end of the tie line.
Graphical solution can be readily done on rectangular equilibrium diagrams, but this method will not be discussed here. This method is usually the first choice only if the equilibrium data is already plotted in rectangular form.
Original: 9 April 1997; 26 Mar 1999
Revised: 29 Mar 1999; 26 Oct 2002; 3 Mar 2003
Copyright 1997, 1999, 2002, 2003 by R.M. Price -- All Rights Reserved