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Design of solvent extraction circuit schemes
Hydrometallurgy 74 (2004) 19 – 38 www.elsevier.com/locate/hydromet
Design of solvent extraction circuit schemes Edelmira D. Ga´lvez a,*, Carlos A. Vega a, Ross E. Swaney b, Luis A. Cisternas c a
Departamento de Ingenierı´a Metalu´rgica, Universidad Cato´lica del Norte, Casilla 1280-Antofagasta, Chile b Department of Chemical Engineering, University of Wisconsin, USA c Departamento de Ingenierı´a Quı´mica, Universidad de Antofagasta, Casilla 170-Antofagasta, Chile Received 10 September 2002; received in revised form 23 September 2003; accepted 27 October 2003
Abstract The technology of solvent extraction in the hydrometallurgical industry typically consists of two circuits, an extraction circuit and a stripping circuit, coupled by a common solvent. Process flow patterns regularly range from single-solvent circulation loops to schemes employing solvent and aqueous bypass or intermediate solvent recycle. The design of these processes using graphical methods runs into a series of complications produced by the coupling of the flow loops. In this paper, a graphical method is developed for the preliminary analysis of different flow structures for these coupled circuits. The method is simple and can be performed by hand. Several examples are presented to illustrate the utility of the proposed method. D 2003 Elsevier B.V. All rights reserved.
1. Introduction Solvent extraction is one of the most frequently used technologies in modern hydrometallurgy, as well as in some water recycling processes. The technology has been applied to the extraction of numerous metallic elements (Gupta and Mukherjee, 1990; Habashi, 1993), and many advances in the application of this technology have been developed (Rydberg et al., 1992). Solvent extraction essentially is a separation process based on apparent equilibrium steps. In a majority of hydrometallurgical applications, it consists of two circuits of apparent equilibrium stages coupled by a common solvent. In the first step, the metal is extracted from an aqueous solution by an organic solvent. In the second step, the metal is recovered
* Corresponding author. 0304-386X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.hydromet.2003.10.005
from the organic solvent, providing recovery of the solvent and producing a more concentrated and more pure aqueous solution. The fact that these operations represent two coupled circuits introduces characteristics into their design procedure that do not arise in systems having only a single circuit of equilibrium states. El-Rifai and Ettouney (1999) studied the design of two countercurrent cascades coupled by a single solvent between the cascades with constant slopes of the operating and equilibrium lines. In their work, a method is developed for obtaining optimum recirculation of the solvent and an optimal number of stages in each cascade. More recently, the same authors (ElRifai and Ettouney, 2002) extended their work to include two independent solvent circulation loops. In various operations encountered in hydrometallurgy, however, linear equilibrium relationships are atypical, and countercurrent cascades are not used. Instead,
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circuits are used that employ other flow configurations such as aqueous and solvent bypass or intermediate solvent recycle. Moreover, optimum operation depends not only on the extraction and stripping steps but also on the costs of the upstream steps, such as leaching, and the downstream steps, such as electrowinning. Furthermore, the extraction percentage may not be the most important factor but rather the total production capacity, given that material not extracted is recycled to the circuits. Design of these circuits using standard McCabe– Thiele diagrams has some drawbacks including: (a) each circuit will have different operating lines; (b) the concentration ranges of the extraction and stripping steps may differ very widely to present them in a single diagram; and (c) iterations will normally be required to determine the various concentrations. Cisternas and Ga´lvez (2000) developed a representation of the problem by means of superstructures, with one superstructure for the aqueous streams and another for the organic streams, in which all types of configurations are permitted. However, the mathematical representation of the problem contains numerous bilinearities that make it difficult to solve. More recently, in a similar study (Alonso et
al., 2001), linearizations of the bilinear terms were used, employing formulations with binary variables. Although this formulation is simpler to solve than the previous one, it imposes limitations in the model, and the mathematical programming problem requires algorithms which are not commercially available. The present study presents a simple graphical representation that provides a way to develop preliminary designs of solvent extraction circuits for hydrometallurgy. Here, the graphical representation is developed, several examples of circuits are presented, and its use in determining the various stage compositions is illustrated.
2. Development of the graphical representation In overview, hydrometallurgical solvent extraction circuits (Fig. 1) are comprised as follows: A leaching step extracts the metal from the mineral, producing the electrolytic leachate solution [generally known as the pregnant leach solution (PLS)]. This is fed into the solvent extraction steps where the metal is extracted by the stripped organic. The discharged aqueous
Fig. 1. Typical hydrometallurgical solvent extraction circuit.
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solution, known as raffinate, is recirculated to the leaching step. Elsewhere, the loaded organic is fed into the stripping steps where the metal is extracted by the spent electrolyte. The resulting strong electrolyte is sent to the metal recuperation step which could be an electrowinning operation or another operation such as crystallization. The solvent extraction and stripping steps are frequently carried out at industrial scale with mixer – settlers. As the name suggests, this equipment includes a mixer to disperse one phase into the other to provide interfacial contact for mass transfer, followed by a decanter to allow the phases to coalesce and separate. The extraction and stripping steps depend on the kinetics of mass transfer, and, typically, the extraction efficiency is accounted for by the use of apparent equilibrium curves. These curves must be experimentally determined. Fig. 2 shows typical equilibrium curves for the hydrometallurgical process of copper extraction. It may be observed from these that while the aqueous copper concentrations in the extraction range below 8 g/L, in the stripping steps, they would range up to 50 g/L. This magnitude difference makes the graphical representation of the steps awkward. Consider as an example the circuit of the lower diagram of Fig. 3 for the extraction of copper, formed
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by one extraction step and one stripping step. The PLS concentration is 5.9 g/L (x0 = 5.9), while the desired concentration of the strong electrolyte is 45 g/L (z1 = 45). The material balance in the extraction step is given by Eq. (1), while the stripping step balance is given by Eq. (2). Both balances assume that the densities of the solutions are constant. Oðy1 y¯ 1 Þ ¼ Aðx0 x1 Þ
ð1Þ
Oðy1 y¯ 1 Þ ¼ Qðz1 z0 Þ
ð2Þ
In these equations, O is the volumetric flow of organic solvent; A is the aqueous volumetric flow in the extraction step; and Q is the aqueous volumetric flow in the stripping step. The mass concentrations of solute are given by x for the aqueous phase in the extraction step, y and y¯ for the organic phase in the extraction and stripping steps, respectively, and z for the aqueous stripping phase. The representation of this process in Fig. 2 is difficult due to the range of concentrations that must be included in the diagram. The extraction and stripping steps will also have differing ratios of aqueous/organic flow, complicating the execution of the iterative design procedure. These difficulties are improved by employing a new concentration coordinate zˇ for the aqueous strip-
Fig. 2. Extraction and stripping apparent equilibrium curves. Metal concentration in g Cu/L of solution. Data was taken from Aguirre and Gonza´lez (1998).
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Fig. 3. 1E – 1E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
ping phase, such that, on the one hand, the operating lines of both the extraction and stripping steps will have the same slope, that is, ð3Þ
and employing the previous decision, the following relation is obtained: Q Q z 1 x0 zˇ 0 ¼ z0 ð4Þ A A
and, on the other hand, the concentration ranges will be of the same magnitude. One option, used in this study, is to make the two maximum concentrations equivalent, that is, zˇ1 = x0. Matching Eqs. (2) and (3),
A generalization of Eq. (4) allows any coordinate zi to be transformed into the new coordinate zˇi. The values x0 (the highest concentration in the aqueous phase of the extraction stages) and zm (the highest concentra-
Oðy1 y¯ 1 Þ ¼ Aðˇz1 zˇ 0 Þ
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tion in the aqueous phase of the stripping stages) are selected as references and become coincident. These concentrations represent the concentration of the solution obtained from leaching, and the concentration desired for the recuperation step (see Fig. 1). The coordinate transformation equation is: Q Q z m x0 zˇ i ¼ zi ð5Þ A A Fig. 4 shows the same apparent equilibrium curves as in Fig. 2, with the extraction apparent equilibrium
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curve modified according to Eq. (5) with x0 = 5.9 and zm = 45. Various Q/A ratios have been included. The upper diagram of Fig. 4 may be used to design coupled extraction and stripping circuits using equations similar to Eqs. (1) and (3). The lower diagram of Fig. 4 allows rapid conversion from coordinate zˇ to coordinate z. The upper part of Fig. 3 shows the representation of the circuit of the lower part of Fig. 3 in the diagram of ( y,y¯) versus (x,zˇ). The stage operating lines of the extraction and stripping stages are
Fig. 4. Apparent equilibrium curves with new coordinate.
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represented by line AB. Ratios A/O = Q/A = 1 were used. In this representation, the aqueous PLS is fed to the extraction stage at concentration x0, and the aqueous raffinate has concentration x1. The aqueous -spent electrolyte enters the stripping stage at transformed concentration zˇ0 (which is equal to x1) and leaves the plant at transformed concentration zˇ1 (which is equal to x0). The organic phase is fed into the extraction stage at concentration y2 (which is equal to y¯1) and is withdrawn at concentration y1 (which is equal to y¯2). Because of the new coordinate, the operating lines for both the stripping and the extraction stages coincide, with a slope equal to the aqueous extraction flow rate divided by the organic flow rate. The coordinate transformation [Eq. (5)] confers another important and very convenient property. When more than one stage is employed in either of the extraction or stripping circuits, a general countercurrent flow pattern will exist between the aqueous and organic flows between the stages. A mass balance may be constructed around any envelope containing a group of consecutive stages in one of the circuits. With the stages depicted horizontally (see Fig. 10 for example), the streams in the mass balance are exactly those aqueous and organic streams that pass through the left- and right-hand sides of the envelope. Let the extraction stages be numbered from 1 to n, where the PLS feed at x0 enters stage 1, and let the stripping stages be numbered from 1 to m, where the richest organic stream enters stage m at concentration y¯m + 1 and the spent electrolyte enters stage 1 at zˇ0. If the left-hand side of the envelope is chosen to cross the left-end aqueous and organic streams at highest concentrations (x0,y1) or (zˇm,y¯m + 1), then these mass balances are of the form Oðyiþ1 y1 Þ ¼ Aðxi x0 Þ
ð6Þ
Oð¯yi y¯ mþ1 Þ ¼ Aðˇzi1 zˇ m Þ
ð7Þ
Because y¯m + 1 = y1 and zˇm = x0, the two lines described by Eqs. (6) and (7) coincide. The resulting countercurrent operating line can be used in the manner of the McCabe –Thiele method to construct
a representation of the extraction and stripping stages. The unified operating line conveniently manages the interdependence of the two groups of stages. Countercurrent cascades are easily ‘‘steppedoff’’, and circuits with more general flow patterns may be constructed using the procedures described below.
3. Circuit representation In order to develop multistage circuits, some iteration may be necessary to determine the concentrations and flows required to carry out a given metal extraction. The concentration, x0, obtainable from leaching is considered as known, along with the concentration, z m , desired from the metal recovery step. Assume at this point that the ratio Q/A is also known. Using these parameters, a diagram can be constructed of ( y,y¯) versus (x,zˇ), in which the extraction and stripping circuits can be represented. Again, consider the scheme presented in Fig. 1. There are n solvent extraction stages and m stripping circuit stages. It is important to remember that the values of zˇm and x0 are equal, as a consequence of Eq. (5). The amount of metal M extracted in the leaching stage is equal to the quantity of metal recovered in the recovery stage, that is: M ¼ Aðx0 xn Þ ¼ Qðzm z0 Þ
ð8Þ
If the values for z are replaced by equivalent values zˇ via Eq. (5), then Eq. (8) produces: M ¼ Aðˇzm zˇ 0 Þ
ð9Þ
By comparing Eqs. (8) and (9) and considering that zˇm = x0, it is then clear also that zˇ0 = xn. Consequently, the endpoints of the unified operating line are given by (xn = zˇ0, yn + 1 = y¯1) and (x0 = zˇm, y1 = y¯m + 1). Circuits are represented in the diagram by determining for each extraction and stripping stage the positions of its equilibrium point and its two feed points. The equilibrium point (xi, yi) or (zˇi, y¯i) lies on the appropriate apparent equilibrium curve and corresponds to the compositions of the pair of
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streams exiting the stage (e.g., point 1 in Fig. 5). The feed points are located on the countercurrent operating line (6,7) which has a slope of A/O at the composition values xi 1 and yi + 1, or zˇi 1 and y¯i + 1. Horizontal and vertical lines connect each stage feed point with two equilibrium points, the feed point’s source stage and the stage being fed (see Fig. 5). The operating line is fixed by the selection of three more degrees of freedom. These are in addition to x0 and zm which are specified in order to use the coordinate transformation [Eq. (5)]. Therefore, for a specified xn, fixing the numbers of stages, n and m, determines the operating line, and the required flowrate, O, of the organic stream is obtained from its resulting slope. Alternatively, the values of A/O, n and m can be specified, and then a resulting value for xn (and z0) is determined. The diagram offers an immediate indication of the range of organic flowrates which are feasible for a given x0 and xn. The two lines constructed as shown in Fig. 6 correspond to the limiting cases for n ! l and m ! l. The slopes of these
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two lines give bounds (A/O)min,(A/O)max on the feasible flowrates. In general, there can be both a maximum and a minimum limit for the organic flow. For countercurrent flow patterns, the familiar cascade ‘‘staircase’’ pattern is traversed on each side of the operating line. However, other general flow patterns are represented as easily by locating the stage feed points accordingly. In cases where a feed is to be mixed from two source streams, the feed point can be located on a mixing tie line between the source streams. With selected values for n and m, the endpoints of the operating line are located by iteration. In order to use the coordinate transformation, x0, zm and Q/A must be specified. The process for constructing the diagram in the basic case is as follows: 3.1. Basic procedure (xn given): (see Fig. 5) 1. Estimates are made of y¯1 and y1, and the operating line is drawn through these values.
Fig. 5. Unified operating line with extraction and stripping stages.
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Fig. 6. Feasible range for flow ratio A/O.
2. The n extraction stages are ‘‘stepped-off’’ beginning at (xn, yn) and working back to x0. A new estimate of y¯1 is obtained. 3. The m stripping stages are ‘‘stepped-off’’ beginning at (zˇm,y¯m) and working back to zˇ0. A new estimate of y¯1 is obtained. 4. 1, 2 and 3 are repeated as needed to convergence. 3.2. Basic procedure (A/O given): (see Fig. 5) 1. An estimate is made of y1 = y¯m + 1, and the operating line is drawn through this endpoint with slope A/O. 2. The m stripping stages are ‘‘stepped-off’’ beginning at (zˇm, y¯m) and working back to zˇ0. An estimate of xn is obtained. 3. The n extraction stages are ‘‘stepped-off’’ beginning at (xn, yn) and working back to x0. A new estimate of y1 is obtained. 4. 1, 2 and 3 are repeated as needed to convergence.
3.3. Procedure for bypass cases Sometimes it can be advantageous to bypass some of the total aqueous or organic flow around one or more of the stages. The object is usually to reduce the mass load in the stage(s). When the two equilibrium lines have significantly differing slopes, this technique can sometimes be employed without requiring an increase in the total number of stages. The graphical representation of bypass cases is accomplished by constructing an additional operating line segment for the stages that are bypassed. Fig. 7a –d illustrate schematically the four cases of aqueous/organic bypassing for extraction/stripping stages. The operating line segment for the bypassed stages intersects the main operating line at the point ‘‘A’’ where the bypassing flow branches away from the stage flow. Relative to the main operating line, the slope of the segment is increased by organic
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Fig. 7. (a) Extraction organic bypass. (b) Extraction aqueous bypass. (c) Stripping organic bypass. (d) Stripping aqueous bypass.
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bypassing and reduced by aqueous bypassing and is given accordingly by the value of (A/O)i selected for the bypassed stages. The line segment ends at the composition of the stage outlet flow (‘‘B’’) that will be recombined with the bypassed flow (‘‘C’’). For organic bypassing, the recombination of the two flows is given by a vertical mixing line constructed between the segment endpoint and a point located at the bypass flow composition. For aqueous bypassing, the mixing line is horizontal. The intersection ‘‘D’’ of the mixing line with the main operating line gives the recombination point from which further stages may be continued.
3.4. Procedure for intermediate recycles In a number of situations, it is advantageous to recycle the organic from an intermediate stripping stage to an intermediate extraction stage and vice versa. For example, this may enable reduction of the number of stages needed in the circuit, or may provide more flexibility of plant operation (White, 1988). Furthermore, when the two equilibrium lines have significantly differing slopes, this technique may again allow a decrease in stage mass loads without increasing the total number of stages.
Fig. 8. Extraction intermediate recycle. (a) From an intermediate stripping stage to an intermediate extraction stage, (b) from an intermediate extraction stage to an intermediate stripping stage.
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Intermediate recycles are represented in the diagram by dividing the main operating line into connected segments of different slopes. The slope of each segment is given by the value of A/Oi determined by the organic flowrate through the extraction and stripping stages of the segment. Fig. 8a illustrates recycle from an intermediate stripping stage to an intermediate extraction stage. The operating line is formed by two segments joined at point ‘‘A’’. Fig. 8b represents the case when the recycle is from extraction stages to stripping stages.
4. Examples The following series of examples serve to demonstrate the application of the ( y,y¯) versus (x,zˇ) diagram. For the examples, zm = 45 g/L, x0 = 5.9 g/L, Q/A = 1, and A/O = 1.
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4.3. 2E –2S circuit This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2. The circuit is presented in Fig. 10. In this case, the iterative procedure is similar to the previous example, but now the determination of zˇ0 (which is equal to x2) is accomplished after stepping-off two stages. 4.4. 2E –2S dual circuit This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2, but using a dual configuration (two independent solvent loops). The circuit is presented in Fig. 11. In this case, the iterative procedure is similar to 1E –1S system, but now estimation of y1 and y2 is required because there are two coupled cascades in series which can be solved sequentially.
4.1. 2E – 1S circuit 4.5. 1E –2S circuit This example was studied in Fig. 3. The circuit is composed of one extraction stage and one stripping stage, that is, n = 1 and m = 1. The iterative procedure is easy to do because y¯1 (and y2) is known because z1 is in apparent equilibrium with y¯1. If x2 were known, then there would be no need to iterate because it is in apparent equilibrium with y1.
This example demonstrates a circuit composed of one extraction stage and two stripping stages, n = 1 and m = 2. The circuit is presented in Fig. 12. In this case, the iterative procedure is similar to the previous examples. 4.6. 1E –3S circuit
4.2. 2E – 1S circuit This example demonstrates a circuit composed of two extraction stages and one stripping stage, n = 2 and m = 1. The circuit is presented in Fig. 9. In this case, A/O is given, so the iterative procedure is as follows: An estimate is made of y1 (which is equal to y¯2), and, as x0 (and zˇ1) is known, we can plot point ( y1, x0). Then, an operating line is drawn through this endpoint with slope A/O. The stripping stage is drawn easily because zˇ1 is in apparent equilibrium with y¯1, whose intersection with the operating line allows the determination of zˇ0 (which is equal to x2). Then, the two extraction stages are ‘‘stepped-off’’ beginning at (x2, y2) and working back to x0. A new estimate of y1 is obtained. These steps are repeated until convergence.
This example demonstrates a circuit composed of one extraction and three stripping stages, n = 1 and m = 3. The circuit is presented in Fig. 13. In this case, the iterative procedure is similar to the previous examples, but three stages must be stepped-off in the stripping cascade. 4.7. 2E –2S circuit with intermediate recycle This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2, but with an intermediate recycle of the organic solvent between the extraction and stripping cascades. The circuit is presented in Fig. 14. In this case, A/O values are given, and they change such that the ratio is higher in the second
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Fig. 9. 2E – 1E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
extraction/first stripping stages than in the first extraction/second stripping stages. Furthermore, the A/O ratio is equal in the second extraction/first stripping stages and in the first extraction/second stripping stages. The iterative procedure is as fol-
lows: An estimate is made of y1 (which is equal to y¯3), and, as x0 (and zˇ2) is known, we can plot point ( y1, x0). Then, an operating line is drawn through this endpoint with slope (A/O)V—the ratio in the first extraction/second stripping stages. The
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Fig. 10. 2E – 2E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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Fig. 11. 2E – 2E dual circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
second stripping stage is drawn easily is in apparent equilibrium with y¯2; this determination of zˇ 1. Next, the first stage is drawn from y1 to determine
because zˇ2 allows the extraction the values
of point ( y2, x1). Then, the second operating line is drawn through this endpoint with slope (A/O)U— the ratio in the second extraction/first stripping stages. The first stripping stage is drawn from
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Fig. 12. 1E – 2E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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z3
Fig. 13. 1E – 3E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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Fig. 14. 2E – 2E circuit with intermediate recycle (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
zˇ1 on the second operating line to determine zˇ0 which provides a value for x2. Then, the two extraction stages are stepped off beginning at x2
and working back to x0. A new estimate of y1 is obtained. The procedure is repeated as needed to convergence.
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4.8. 2E – 1S circuit with cascade This example demonstrates a circuit composed of two extraction stages and two stripping stage, n = 2 and
m = 1, but this case has a cascade configuration for the aqueous flows associated with the extraction steps. The circuit is presented in Fig. 15. In this example, it is unnecessary to iterate to determine the various com-
Fig. 15. 2E – 1E circuit with cascade (bottom) and representation in a ( y, y¯) versus (x, zˇ) diagram (above).
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positions. Fig. 15 is constructed for the case where the aqueous flows A in each extraction step are made equal.
5. Remarks and conclusions The ratios between aqueous and organic flows generally limited by the requirements to maintain continuity of the desired phase during operation, characteristics of dispersion and coalescence,
are the the the
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level of purity of the desired product, and the capacity and percentage of extraction desired. However, it is possible to use the graphical representation presented to carry out the analysis of the effect of these ratios on the percentage of metal extracted and the capacity of the circuits. For example, Fig. 16 shows the 1E –1S circuit for different ratios of A/O and Q/A. It can be observed that a decrease in the A/ O ratio produces an increase in the percentage of metal extracted but at the same time increases the size of the equipment for the same flow rate of A.
Fig. 16. Effect of A/O and Q/A ratios on 1E – 1E circuit.
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On the other hand, a decline in the Q/A ratio produces a reduction in the concentration of spent electrolyte, as shown in Fig. 16, for the case where A/O = 2. In the examples studied, it can be seen that the number of extraction stages has a greater influence on the percentage of metal extraction (%E) than does the number of stripping stages. For example, the 1E –1S circuit has a %E of 87%, compared to the %E of 97% for the 2E– 1S circuit. This latter value is maintained practically constant when a stripping stage is added (2E –2S circuit). On the other hand, the 1E – 2S and 1E –3S circuits show values for %E of 90% and 91%, respectively, which confirms the preceding statement. By observing the 2E –2S, dual 2E – 2S, and 2E –2S with bypass circuits, similar values for %E can be observed. The dual circuit, however, permits the flexibility of using different A/O ratios in each stage, through which it is possible to raise the %E. Finally, the 2E – 1S circuit (%E = 97%) can be compared with the 2E – 1S circuit with cascade (%E = 58%). The latter, although having a significantly lower percentage extraction, has a greater capacity for the extraction of copper (6.8 g/L of aqueous solution fed to the solvent extraction stages compared with 5.2 g/L for the case without the cascade). The graphical representation shown can be utilized for the study of different configurations of solvent extraction and stripping circuits, coupled by a common solvent. It provides a rapid and simple way of determining the various stage compositions and thereby of obtaining material balances. Analysis of the effects of using different ratios between the aqueous and organic phases can also be performed. List of symbols A M O Q x
Aqueous volumetric flow in extraction stages Amount of metal extracted in the leaching step and recovered in the recovery step Organic volumetric flow. Aqueous volumetric flow in stripping stages Metal concentration in the aqueous phase in extraction stages (x0: PLS concentration; xn: raffinate concentration)
Y
y¯
z
zˇ
Metal concentration in the organic phase in extraction stages ( y1 loaded organic concentration; yn + 1 stripped organic concentration) Metal concentration in the organic phase in stripping stages ( y¯m + 1: loaded organic concentration; y¯1: stripped organic concentration) Metal concentration in the aqueous phase in stripping stages (z0: spent electrolyte concentration; zm: strong electrolyte concentration) Transformed metal concentration coordinate in the aqueous phase in stripping stages (zˇ0: spent electrolyte concentration coordinate; zˇm: strong electrolyte concentration coordinate)
Acknowledgements The authors wish to thank CONICYT for financing of FONDECYT PROJECT # 1990956 of which the present study is a part.
References Alonso, A.I., Lassahn, A., Gruhn, G., 2001. Optimal design of nondispersive solvent extraction processes. Comput. Chem. Eng. 25, 267 – 285. Aguirre, M.G., Gonza´lez, M.W., 1998. Evaluacio´n y control de la planta semi industrial de extraccio´n por solvente de Minera Escondida. Bs thesis, Universidad Cato´lica del Norte. Cisternas, L.A., Ga´lvez, E.D., 2000. Synthesis of solvent extraction separation schemes in hydrometallurgy. In: Pierucci, S. (Ed.), ESCAPE-10. Elsevier. El-Rifai, M.A., Ettouney, R.S., 1999. Integrated analysis of coupled separation operations. Chem. Eng. Sci. 54, 1891 – 1902. El-Rifai, M.A., Ettouney, R.S., 2002. Integrated design of coupled separation processes with independent solvent circulation loops. Chem. Eng. Sci. 57, 651 – 661. Gupta, C.K., Mukherjee, T.K., 1990. Hydrometallurgy in Extraction Processes CRC Press. Habashi, F., 1993. A Textbook of Hydrometallurgy Me`tallurgie Extractive Que`bec, Enr. Rydberg, J., Musikas, C., Choppin, G.R., 1992. Principles and Practices of Solvent Extraction Marcel Dekker. White, D.A., 1988. Solvent extraction for metal recovery incorporating organic and aqueous phase bypass. Hydrometallurgy 21, 145 – 154.
Design of solvent extraction circuit schemes Edelmira D. Ga´lvez a,*, Carlos A. Vega a, Ross E. Swaney b, Luis A. Cisternas c a
Departamento de Ingenierı´a Metalu´rgica, Universidad Cato´lica del Norte, Casilla 1280-Antofagasta, Chile b Department of Chemical Engineering, University of Wisconsin, USA c Departamento de Ingenierı´a Quı´mica, Universidad de Antofagasta, Casilla 170-Antofagasta, Chile Received 10 September 2002; received in revised form 23 September 2003; accepted 27 October 2003
Abstract The technology of solvent extraction in the hydrometallurgical industry typically consists of two circuits, an extraction circuit and a stripping circuit, coupled by a common solvent. Process flow patterns regularly range from single-solvent circulation loops to schemes employing solvent and aqueous bypass or intermediate solvent recycle. The design of these processes using graphical methods runs into a series of complications produced by the coupling of the flow loops. In this paper, a graphical method is developed for the preliminary analysis of different flow structures for these coupled circuits. The method is simple and can be performed by hand. Several examples are presented to illustrate the utility of the proposed method. D 2003 Elsevier B.V. All rights reserved.
1. Introduction Solvent extraction is one of the most frequently used technologies in modern hydrometallurgy, as well as in some water recycling processes. The technology has been applied to the extraction of numerous metallic elements (Gupta and Mukherjee, 1990; Habashi, 1993), and many advances in the application of this technology have been developed (Rydberg et al., 1992). Solvent extraction essentially is a separation process based on apparent equilibrium steps. In a majority of hydrometallurgical applications, it consists of two circuits of apparent equilibrium stages coupled by a common solvent. In the first step, the metal is extracted from an aqueous solution by an organic solvent. In the second step, the metal is recovered
* Corresponding author. 0304-386X/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.hydromet.2003.10.005
from the organic solvent, providing recovery of the solvent and producing a more concentrated and more pure aqueous solution. The fact that these operations represent two coupled circuits introduces characteristics into their design procedure that do not arise in systems having only a single circuit of equilibrium states. El-Rifai and Ettouney (1999) studied the design of two countercurrent cascades coupled by a single solvent between the cascades with constant slopes of the operating and equilibrium lines. In their work, a method is developed for obtaining optimum recirculation of the solvent and an optimal number of stages in each cascade. More recently, the same authors (ElRifai and Ettouney, 2002) extended their work to include two independent solvent circulation loops. In various operations encountered in hydrometallurgy, however, linear equilibrium relationships are atypical, and countercurrent cascades are not used. Instead,
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circuits are used that employ other flow configurations such as aqueous and solvent bypass or intermediate solvent recycle. Moreover, optimum operation depends not only on the extraction and stripping steps but also on the costs of the upstream steps, such as leaching, and the downstream steps, such as electrowinning. Furthermore, the extraction percentage may not be the most important factor but rather the total production capacity, given that material not extracted is recycled to the circuits. Design of these circuits using standard McCabe– Thiele diagrams has some drawbacks including: (a) each circuit will have different operating lines; (b) the concentration ranges of the extraction and stripping steps may differ very widely to present them in a single diagram; and (c) iterations will normally be required to determine the various concentrations. Cisternas and Ga´lvez (2000) developed a representation of the problem by means of superstructures, with one superstructure for the aqueous streams and another for the organic streams, in which all types of configurations are permitted. However, the mathematical representation of the problem contains numerous bilinearities that make it difficult to solve. More recently, in a similar study (Alonso et
al., 2001), linearizations of the bilinear terms were used, employing formulations with binary variables. Although this formulation is simpler to solve than the previous one, it imposes limitations in the model, and the mathematical programming problem requires algorithms which are not commercially available. The present study presents a simple graphical representation that provides a way to develop preliminary designs of solvent extraction circuits for hydrometallurgy. Here, the graphical representation is developed, several examples of circuits are presented, and its use in determining the various stage compositions is illustrated.
2. Development of the graphical representation In overview, hydrometallurgical solvent extraction circuits (Fig. 1) are comprised as follows: A leaching step extracts the metal from the mineral, producing the electrolytic leachate solution [generally known as the pregnant leach solution (PLS)]. This is fed into the solvent extraction steps where the metal is extracted by the stripped organic. The discharged aqueous
Fig. 1. Typical hydrometallurgical solvent extraction circuit.
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solution, known as raffinate, is recirculated to the leaching step. Elsewhere, the loaded organic is fed into the stripping steps where the metal is extracted by the spent electrolyte. The resulting strong electrolyte is sent to the metal recuperation step which could be an electrowinning operation or another operation such as crystallization. The solvent extraction and stripping steps are frequently carried out at industrial scale with mixer – settlers. As the name suggests, this equipment includes a mixer to disperse one phase into the other to provide interfacial contact for mass transfer, followed by a decanter to allow the phases to coalesce and separate. The extraction and stripping steps depend on the kinetics of mass transfer, and, typically, the extraction efficiency is accounted for by the use of apparent equilibrium curves. These curves must be experimentally determined. Fig. 2 shows typical equilibrium curves for the hydrometallurgical process of copper extraction. It may be observed from these that while the aqueous copper concentrations in the extraction range below 8 g/L, in the stripping steps, they would range up to 50 g/L. This magnitude difference makes the graphical representation of the steps awkward. Consider as an example the circuit of the lower diagram of Fig. 3 for the extraction of copper, formed
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by one extraction step and one stripping step. The PLS concentration is 5.9 g/L (x0 = 5.9), while the desired concentration of the strong electrolyte is 45 g/L (z1 = 45). The material balance in the extraction step is given by Eq. (1), while the stripping step balance is given by Eq. (2). Both balances assume that the densities of the solutions are constant. Oðy1 y¯ 1 Þ ¼ Aðx0 x1 Þ
ð1Þ
Oðy1 y¯ 1 Þ ¼ Qðz1 z0 Þ
ð2Þ
In these equations, O is the volumetric flow of organic solvent; A is the aqueous volumetric flow in the extraction step; and Q is the aqueous volumetric flow in the stripping step. The mass concentrations of solute are given by x for the aqueous phase in the extraction step, y and y¯ for the organic phase in the extraction and stripping steps, respectively, and z for the aqueous stripping phase. The representation of this process in Fig. 2 is difficult due to the range of concentrations that must be included in the diagram. The extraction and stripping steps will also have differing ratios of aqueous/organic flow, complicating the execution of the iterative design procedure. These difficulties are improved by employing a new concentration coordinate zˇ for the aqueous strip-
Fig. 2. Extraction and stripping apparent equilibrium curves. Metal concentration in g Cu/L of solution. Data was taken from Aguirre and Gonza´lez (1998).
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Fig. 3. 1E – 1E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
ping phase, such that, on the one hand, the operating lines of both the extraction and stripping steps will have the same slope, that is, ð3Þ
and employing the previous decision, the following relation is obtained: Q Q z 1 x0 zˇ 0 ¼ z0 ð4Þ A A
and, on the other hand, the concentration ranges will be of the same magnitude. One option, used in this study, is to make the two maximum concentrations equivalent, that is, zˇ1 = x0. Matching Eqs. (2) and (3),
A generalization of Eq. (4) allows any coordinate zi to be transformed into the new coordinate zˇi. The values x0 (the highest concentration in the aqueous phase of the extraction stages) and zm (the highest concentra-
Oðy1 y¯ 1 Þ ¼ Aðˇz1 zˇ 0 Þ
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tion in the aqueous phase of the stripping stages) are selected as references and become coincident. These concentrations represent the concentration of the solution obtained from leaching, and the concentration desired for the recuperation step (see Fig. 1). The coordinate transformation equation is: Q Q z m x0 zˇ i ¼ zi ð5Þ A A Fig. 4 shows the same apparent equilibrium curves as in Fig. 2, with the extraction apparent equilibrium
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curve modified according to Eq. (5) with x0 = 5.9 and zm = 45. Various Q/A ratios have been included. The upper diagram of Fig. 4 may be used to design coupled extraction and stripping circuits using equations similar to Eqs. (1) and (3). The lower diagram of Fig. 4 allows rapid conversion from coordinate zˇ to coordinate z. The upper part of Fig. 3 shows the representation of the circuit of the lower part of Fig. 3 in the diagram of ( y,y¯) versus (x,zˇ). The stage operating lines of the extraction and stripping stages are
Fig. 4. Apparent equilibrium curves with new coordinate.
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represented by line AB. Ratios A/O = Q/A = 1 were used. In this representation, the aqueous PLS is fed to the extraction stage at concentration x0, and the aqueous raffinate has concentration x1. The aqueous -spent electrolyte enters the stripping stage at transformed concentration zˇ0 (which is equal to x1) and leaves the plant at transformed concentration zˇ1 (which is equal to x0). The organic phase is fed into the extraction stage at concentration y2 (which is equal to y¯1) and is withdrawn at concentration y1 (which is equal to y¯2). Because of the new coordinate, the operating lines for both the stripping and the extraction stages coincide, with a slope equal to the aqueous extraction flow rate divided by the organic flow rate. The coordinate transformation [Eq. (5)] confers another important and very convenient property. When more than one stage is employed in either of the extraction or stripping circuits, a general countercurrent flow pattern will exist between the aqueous and organic flows between the stages. A mass balance may be constructed around any envelope containing a group of consecutive stages in one of the circuits. With the stages depicted horizontally (see Fig. 10 for example), the streams in the mass balance are exactly those aqueous and organic streams that pass through the left- and right-hand sides of the envelope. Let the extraction stages be numbered from 1 to n, where the PLS feed at x0 enters stage 1, and let the stripping stages be numbered from 1 to m, where the richest organic stream enters stage m at concentration y¯m + 1 and the spent electrolyte enters stage 1 at zˇ0. If the left-hand side of the envelope is chosen to cross the left-end aqueous and organic streams at highest concentrations (x0,y1) or (zˇm,y¯m + 1), then these mass balances are of the form Oðyiþ1 y1 Þ ¼ Aðxi x0 Þ
ð6Þ
Oð¯yi y¯ mþ1 Þ ¼ Aðˇzi1 zˇ m Þ
ð7Þ
Because y¯m + 1 = y1 and zˇm = x0, the two lines described by Eqs. (6) and (7) coincide. The resulting countercurrent operating line can be used in the manner of the McCabe –Thiele method to construct
a representation of the extraction and stripping stages. The unified operating line conveniently manages the interdependence of the two groups of stages. Countercurrent cascades are easily ‘‘steppedoff’’, and circuits with more general flow patterns may be constructed using the procedures described below.
3. Circuit representation In order to develop multistage circuits, some iteration may be necessary to determine the concentrations and flows required to carry out a given metal extraction. The concentration, x0, obtainable from leaching is considered as known, along with the concentration, z m , desired from the metal recovery step. Assume at this point that the ratio Q/A is also known. Using these parameters, a diagram can be constructed of ( y,y¯) versus (x,zˇ), in which the extraction and stripping circuits can be represented. Again, consider the scheme presented in Fig. 1. There are n solvent extraction stages and m stripping circuit stages. It is important to remember that the values of zˇm and x0 are equal, as a consequence of Eq. (5). The amount of metal M extracted in the leaching stage is equal to the quantity of metal recovered in the recovery stage, that is: M ¼ Aðx0 xn Þ ¼ Qðzm z0 Þ
ð8Þ
If the values for z are replaced by equivalent values zˇ via Eq. (5), then Eq. (8) produces: M ¼ Aðˇzm zˇ 0 Þ
ð9Þ
By comparing Eqs. (8) and (9) and considering that zˇm = x0, it is then clear also that zˇ0 = xn. Consequently, the endpoints of the unified operating line are given by (xn = zˇ0, yn + 1 = y¯1) and (x0 = zˇm, y1 = y¯m + 1). Circuits are represented in the diagram by determining for each extraction and stripping stage the positions of its equilibrium point and its two feed points. The equilibrium point (xi, yi) or (zˇi, y¯i) lies on the appropriate apparent equilibrium curve and corresponds to the compositions of the pair of
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streams exiting the stage (e.g., point 1 in Fig. 5). The feed points are located on the countercurrent operating line (6,7) which has a slope of A/O at the composition values xi 1 and yi + 1, or zˇi 1 and y¯i + 1. Horizontal and vertical lines connect each stage feed point with two equilibrium points, the feed point’s source stage and the stage being fed (see Fig. 5). The operating line is fixed by the selection of three more degrees of freedom. These are in addition to x0 and zm which are specified in order to use the coordinate transformation [Eq. (5)]. Therefore, for a specified xn, fixing the numbers of stages, n and m, determines the operating line, and the required flowrate, O, of the organic stream is obtained from its resulting slope. Alternatively, the values of A/O, n and m can be specified, and then a resulting value for xn (and z0) is determined. The diagram offers an immediate indication of the range of organic flowrates which are feasible for a given x0 and xn. The two lines constructed as shown in Fig. 6 correspond to the limiting cases for n ! l and m ! l. The slopes of these
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two lines give bounds (A/O)min,(A/O)max on the feasible flowrates. In general, there can be both a maximum and a minimum limit for the organic flow. For countercurrent flow patterns, the familiar cascade ‘‘staircase’’ pattern is traversed on each side of the operating line. However, other general flow patterns are represented as easily by locating the stage feed points accordingly. In cases where a feed is to be mixed from two source streams, the feed point can be located on a mixing tie line between the source streams. With selected values for n and m, the endpoints of the operating line are located by iteration. In order to use the coordinate transformation, x0, zm and Q/A must be specified. The process for constructing the diagram in the basic case is as follows: 3.1. Basic procedure (xn given): (see Fig. 5) 1. Estimates are made of y¯1 and y1, and the operating line is drawn through these values.
Fig. 5. Unified operating line with extraction and stripping stages.
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Fig. 6. Feasible range for flow ratio A/O.
2. The n extraction stages are ‘‘stepped-off’’ beginning at (xn, yn) and working back to x0. A new estimate of y¯1 is obtained. 3. The m stripping stages are ‘‘stepped-off’’ beginning at (zˇm,y¯m) and working back to zˇ0. A new estimate of y¯1 is obtained. 4. 1, 2 and 3 are repeated as needed to convergence. 3.2. Basic procedure (A/O given): (see Fig. 5) 1. An estimate is made of y1 = y¯m + 1, and the operating line is drawn through this endpoint with slope A/O. 2. The m stripping stages are ‘‘stepped-off’’ beginning at (zˇm, y¯m) and working back to zˇ0. An estimate of xn is obtained. 3. The n extraction stages are ‘‘stepped-off’’ beginning at (xn, yn) and working back to x0. A new estimate of y1 is obtained. 4. 1, 2 and 3 are repeated as needed to convergence.
3.3. Procedure for bypass cases Sometimes it can be advantageous to bypass some of the total aqueous or organic flow around one or more of the stages. The object is usually to reduce the mass load in the stage(s). When the two equilibrium lines have significantly differing slopes, this technique can sometimes be employed without requiring an increase in the total number of stages. The graphical representation of bypass cases is accomplished by constructing an additional operating line segment for the stages that are bypassed. Fig. 7a –d illustrate schematically the four cases of aqueous/organic bypassing for extraction/stripping stages. The operating line segment for the bypassed stages intersects the main operating line at the point ‘‘A’’ where the bypassing flow branches away from the stage flow. Relative to the main operating line, the slope of the segment is increased by organic
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Fig. 7. (a) Extraction organic bypass. (b) Extraction aqueous bypass. (c) Stripping organic bypass. (d) Stripping aqueous bypass.
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bypassing and reduced by aqueous bypassing and is given accordingly by the value of (A/O)i selected for the bypassed stages. The line segment ends at the composition of the stage outlet flow (‘‘B’’) that will be recombined with the bypassed flow (‘‘C’’). For organic bypassing, the recombination of the two flows is given by a vertical mixing line constructed between the segment endpoint and a point located at the bypass flow composition. For aqueous bypassing, the mixing line is horizontal. The intersection ‘‘D’’ of the mixing line with the main operating line gives the recombination point from which further stages may be continued.
3.4. Procedure for intermediate recycles In a number of situations, it is advantageous to recycle the organic from an intermediate stripping stage to an intermediate extraction stage and vice versa. For example, this may enable reduction of the number of stages needed in the circuit, or may provide more flexibility of plant operation (White, 1988). Furthermore, when the two equilibrium lines have significantly differing slopes, this technique may again allow a decrease in stage mass loads without increasing the total number of stages.
Fig. 8. Extraction intermediate recycle. (a) From an intermediate stripping stage to an intermediate extraction stage, (b) from an intermediate extraction stage to an intermediate stripping stage.
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Intermediate recycles are represented in the diagram by dividing the main operating line into connected segments of different slopes. The slope of each segment is given by the value of A/Oi determined by the organic flowrate through the extraction and stripping stages of the segment. Fig. 8a illustrates recycle from an intermediate stripping stage to an intermediate extraction stage. The operating line is formed by two segments joined at point ‘‘A’’. Fig. 8b represents the case when the recycle is from extraction stages to stripping stages.
4. Examples The following series of examples serve to demonstrate the application of the ( y,y¯) versus (x,zˇ) diagram. For the examples, zm = 45 g/L, x0 = 5.9 g/L, Q/A = 1, and A/O = 1.
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4.3. 2E –2S circuit This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2. The circuit is presented in Fig. 10. In this case, the iterative procedure is similar to the previous example, but now the determination of zˇ0 (which is equal to x2) is accomplished after stepping-off two stages. 4.4. 2E –2S dual circuit This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2, but using a dual configuration (two independent solvent loops). The circuit is presented in Fig. 11. In this case, the iterative procedure is similar to 1E –1S system, but now estimation of y1 and y2 is required because there are two coupled cascades in series which can be solved sequentially.
4.1. 2E – 1S circuit 4.5. 1E –2S circuit This example was studied in Fig. 3. The circuit is composed of one extraction stage and one stripping stage, that is, n = 1 and m = 1. The iterative procedure is easy to do because y¯1 (and y2) is known because z1 is in apparent equilibrium with y¯1. If x2 were known, then there would be no need to iterate because it is in apparent equilibrium with y1.
This example demonstrates a circuit composed of one extraction stage and two stripping stages, n = 1 and m = 2. The circuit is presented in Fig. 12. In this case, the iterative procedure is similar to the previous examples. 4.6. 1E –3S circuit
4.2. 2E – 1S circuit This example demonstrates a circuit composed of two extraction stages and one stripping stage, n = 2 and m = 1. The circuit is presented in Fig. 9. In this case, A/O is given, so the iterative procedure is as follows: An estimate is made of y1 (which is equal to y¯2), and, as x0 (and zˇ1) is known, we can plot point ( y1, x0). Then, an operating line is drawn through this endpoint with slope A/O. The stripping stage is drawn easily because zˇ1 is in apparent equilibrium with y¯1, whose intersection with the operating line allows the determination of zˇ0 (which is equal to x2). Then, the two extraction stages are ‘‘stepped-off’’ beginning at (x2, y2) and working back to x0. A new estimate of y1 is obtained. These steps are repeated until convergence.
This example demonstrates a circuit composed of one extraction and three stripping stages, n = 1 and m = 3. The circuit is presented in Fig. 13. In this case, the iterative procedure is similar to the previous examples, but three stages must be stepped-off in the stripping cascade. 4.7. 2E –2S circuit with intermediate recycle This example demonstrates a circuit composed of two extraction stages and two stripping stages, n = 2 and m = 2, but with an intermediate recycle of the organic solvent between the extraction and stripping cascades. The circuit is presented in Fig. 14. In this case, A/O values are given, and they change such that the ratio is higher in the second
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Fig. 9. 2E – 1E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
extraction/first stripping stages than in the first extraction/second stripping stages. Furthermore, the A/O ratio is equal in the second extraction/first stripping stages and in the first extraction/second stripping stages. The iterative procedure is as fol-
lows: An estimate is made of y1 (which is equal to y¯3), and, as x0 (and zˇ2) is known, we can plot point ( y1, x0). Then, an operating line is drawn through this endpoint with slope (A/O)V—the ratio in the first extraction/second stripping stages. The
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Fig. 10. 2E – 2E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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Fig. 11. 2E – 2E dual circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
second stripping stage is drawn easily is in apparent equilibrium with y¯2; this determination of zˇ 1. Next, the first stage is drawn from y1 to determine
because zˇ2 allows the extraction the values
of point ( y2, x1). Then, the second operating line is drawn through this endpoint with slope (A/O)U— the ratio in the second extraction/first stripping stages. The first stripping stage is drawn from
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Fig. 12. 1E – 2E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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34
z3
Fig. 13. 1E – 3E circuit (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
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Fig. 14. 2E – 2E circuit with intermediate recycle (bottom) and representation in ( y, y¯) versus (x, zˇ) diagram (above).
zˇ1 on the second operating line to determine zˇ0 which provides a value for x2. Then, the two extraction stages are stepped off beginning at x2
and working back to x0. A new estimate of y1 is obtained. The procedure is repeated as needed to convergence.
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4.8. 2E – 1S circuit with cascade This example demonstrates a circuit composed of two extraction stages and two stripping stage, n = 2 and
m = 1, but this case has a cascade configuration for the aqueous flows associated with the extraction steps. The circuit is presented in Fig. 15. In this example, it is unnecessary to iterate to determine the various com-
Fig. 15. 2E – 1E circuit with cascade (bottom) and representation in a ( y, y¯) versus (x, zˇ) diagram (above).
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positions. Fig. 15 is constructed for the case where the aqueous flows A in each extraction step are made equal.
5. Remarks and conclusions The ratios between aqueous and organic flows generally limited by the requirements to maintain continuity of the desired phase during operation, characteristics of dispersion and coalescence,
are the the the
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level of purity of the desired product, and the capacity and percentage of extraction desired. However, it is possible to use the graphical representation presented to carry out the analysis of the effect of these ratios on the percentage of metal extracted and the capacity of the circuits. For example, Fig. 16 shows the 1E –1S circuit for different ratios of A/O and Q/A. It can be observed that a decrease in the A/ O ratio produces an increase in the percentage of metal extracted but at the same time increases the size of the equipment for the same flow rate of A.
Fig. 16. Effect of A/O and Q/A ratios on 1E – 1E circuit.
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On the other hand, a decline in the Q/A ratio produces a reduction in the concentration of spent electrolyte, as shown in Fig. 16, for the case where A/O = 2. In the examples studied, it can be seen that the number of extraction stages has a greater influence on the percentage of metal extraction (%E) than does the number of stripping stages. For example, the 1E –1S circuit has a %E of 87%, compared to the %E of 97% for the 2E– 1S circuit. This latter value is maintained practically constant when a stripping stage is added (2E –2S circuit). On the other hand, the 1E – 2S and 1E –3S circuits show values for %E of 90% and 91%, respectively, which confirms the preceding statement. By observing the 2E –2S, dual 2E – 2S, and 2E –2S with bypass circuits, similar values for %E can be observed. The dual circuit, however, permits the flexibility of using different A/O ratios in each stage, through which it is possible to raise the %E. Finally, the 2E – 1S circuit (%E = 97%) can be compared with the 2E – 1S circuit with cascade (%E = 58%). The latter, although having a significantly lower percentage extraction, has a greater capacity for the extraction of copper (6.8 g/L of aqueous solution fed to the solvent extraction stages compared with 5.2 g/L for the case without the cascade). The graphical representation shown can be utilized for the study of different configurations of solvent extraction and stripping circuits, coupled by a common solvent. It provides a rapid and simple way of determining the various stage compositions and thereby of obtaining material balances. Analysis of the effects of using different ratios between the aqueous and organic phases can also be performed. List of symbols A M O Q x
Aqueous volumetric flow in extraction stages Amount of metal extracted in the leaching step and recovered in the recovery step Organic volumetric flow. Aqueous volumetric flow in stripping stages Metal concentration in the aqueous phase in extraction stages (x0: PLS concentration; xn: raffinate concentration)
Y
y¯
z
zˇ
Metal concentration in the organic phase in extraction stages ( y1 loaded organic concentration; yn + 1 stripped organic concentration) Metal concentration in the organic phase in stripping stages ( y¯m + 1: loaded organic concentration; y¯1: stripped organic concentration) Metal concentration in the aqueous phase in stripping stages (z0: spent electrolyte concentration; zm: strong electrolyte concentration) Transformed metal concentration coordinate in the aqueous phase in stripping stages (zˇ0: spent electrolyte concentration coordinate; zˇm: strong electrolyte concentration coordinate)
Acknowledgements The authors wish to thank CONICYT for financing of FONDECYT PROJECT # 1990956 of which the present study is a part.
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