3566
Ind. Eng. Chem. Res. 2004, 43, 3566-3576
Visualization of High-Dimensional Liquid-Liquid Equilibrium Phase Diagrams Benny Harjo and Ka M. Ng* Department of Chemical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
Christianto Wibowo ClearWaterBay Technology, Inc., 20311 Valley Boulevard, Suite C, Walnut, California 91789
Liquid-liquid extraction is usually used along with other separation processes for the recovery of pure components. It is desirable that the liquid-liquid equilibrium (LLE) phase behavior, which is the thermodynamic basis for liquid-liquid extraction, be represented in a phase diagram. This is because the visualization of process limitations has a crucial role in the construction of feasible separation schemes for achieving the overall separation objective. However, because most applications involve multicomponent mixtures, visualization of the LLE phase diagram in its entirety becomes difficult or even impossible. Therefore, a visualization approach to represent high-dimensional LLE phase diagrams based on projections and cuts to reduce dimensionality is proposed. In such an approach, the liquid-liquid immiscibility regions are represented as a collection of projected tie lines. By superimposing the resulting diagram with any other map of process boundaries in composition space, such as a solid-liquid equilibrium phase diagram, one can clearly observe the possible use of liquid-liquid extraction in crossing the boundaries, an option that is not apparent when only numerical data are presented. Two common separation scenarios are used to demonstrate the applicability and advantages of this approach, particularly in illustrating the close interactions of liquid-liquid extraction with distillation and crystallization. Introduction Liquid-liquid extraction or solvent extraction is widely used for the separation, recovery, purification, or concentration of pharmaceuticals, natural products, and bioproducts, as well as other high-value-added products. It is particularly suited for separating closeboiling materials and heat-sensitive materials and for recovering compounds from dilute aqueous solution. Some examples of its applications are listed in Table 1. Unfortunately, the liquid-liquid phase split seldom results in a pure product. For this reason, liquid-liquid extraction is normally combined with other techniques such as distillation and crystallization to form a hybrid process, wherein different separation driving forces are used in different parts of the process such that the overall separation objective can be achieved.1 For example, antibiotics are often recovered from fermentation broths using liquid-liquid extraction followed by crystallization to obtain pure products.2 Another example is the purification of diethoxymethane from a mixture with ethanol and water, where the presence of azeotropes prevents the recovery of the pure component using only distillation.3 Liquid-liquid extraction can be used to bypass the limitations imposed by the azeotropes, thus allowing recovery of pure components.4 A method for synthesizing a hybrid process by identifying the process limitations or boundaries in composition space has been proposed.5 Such process boundaries can be visualized on phase diagrams. Examples include * To whom correspondence should be addressed. Tel.: +8522358-7238. Fax: +852-2358-0054. E-mail:
[email protected].
residue curve maps (RCMs), in which various regions corresponding to different feasible products that can be obtained by distillation can be identified, and solidliquid equilibrium (SLE) phase diagrams, which show regions where different crystallization products can be obtained. Visualization of process limitations makes the construction of feasible separation schemes for achieving the overall separation objective more convenient. Liquid-liquid equilibrium (LLE) phase behavior, which is the thermodynamic basis for liquid-liquid extraction, has routinely been represented in composition space using phase diagrams.6 For binary systems, the phase diagram consists of a collection of tie lines forming one or more immiscibility regions in a twodimensional temperature-composition (T-x) space. An LLE phase diagram for a ternary system normally takes the shape of a triangle and shows the immiscibility regions at a given temperature and pressure. As the number of components in the system increases further, visualization of the phase diagram in its entirety becomes difficult or even impossible. For example, it is quite challenging to view the three-dimensional immiscibility region in an isobaric-isothermal quaternarysystem phase diagram. Unfortunately, dealing with high-dimensional (high-D) phase diagrams is unavoidable given that most real applications involve multicomponent mixtures, as is apparent from Table 1. One way of visualizing high-D phase diagram is by taking projections. Cruickshank et al.7 proposed a graphical projection method to represent a quaternary LLE phase diagram with one partially miscible pair. This projection has been used in the design of liquidliquid extraction processes.8,9 Frameworks for the rep-
10.1021/ie034186x CCC: $27.50 © 2004 American Chemical Society Published on Web 05/13/2004
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3567 Table 1. Selected Examples of Applications of Liquid-Liquid Extraction feeda water, canola oil, free fatty acids water, citric acid water, nicotine, water-soluble components fermentation broth, vanillin fermentation broth, antibiotic AL072 D-phenylglycine, D-(p-hydroxy)-phenylglycine, amoxicillin, ampicillin, 6-aminopenicillanic acid ginkgo extract, terpene trilactones cell extract, human growth hormone water, acetic acid a
extraction solvent(s)
ref
methanol/ethanol butanol + tricaprylin toluene methyl tert-butyl ether isopropyl alcohol 1-butanol + water
26 27 28 29 30 31
ethyl acetate poly(ethylene glycol) + sodium chloride phosphine oxides + ketones
32 33 34
Desired component is in italics.
resentation of high-D SLE phase diagrams have been developed for nonreactive molecular systems,10 electrolyte mixtures,11 and systems involving polymorphs.12 In these frameworks, a sequence of cuts and projections of the high-D phase diagram is considered, to provide a mental picture of the system in its entirety. However, the application of similar ideas for visualizing high-D LLE phase diagrams in general is not trivial because the LLE regions are highly nonlinear, making it difficult or impossible to reconstruct the original LLE region in hyperspace just by looking at their projections. This article proposes a visualization approach to represent the LLE phase behavior of multicomponent systems. It focuses on systems with two coexisting liquid phases, in which case the immiscibility region consists of tie lines connecting the compositions of two phases in equilibrium. For such systems, it is convenient to visualize the LLE phase behavior by plotting a set of representative tie lines. If the phase diagram is highdimensional, the dimensionality is reduced by taking projections and/or cuts. Such an approach is useful in aiding the synthesis of separation processes involving liquid-liquid extraction. Visualization of LLE Phase Behavior LLE phase behavior can be represented on phase diagrams by identifying regions where two liquid phases coexist in equilibrium. By superimposing the resulting diagram with an RCM, SLE phase diagram, or any other map of process boundaries in composition space, one can clearly observe the potential use of liquid-liquid extraction in crossing the boundaries, an option that is not apparent when only numerical data are presented. Consequently, a hybrid process that meets the overall separation objective can be synthesized with less effort. LLE Phase Diagrams. Knowledge of typical phase behaviors is useful in mapping out the LLE region for a specific system at hand. In particular, variations of LLE phase behavior with temperature and composition need to be considered, whereas the effect of pressure is usually negligible except at high pressures or near the critical region. Figure 1 shows common binary LLE phase diagrams at a given pressure.6,13 A point f inside the LLE region (Figure 1a) would split into two liquid phases, the equilibrium compositions of which are connected by a tie line (denoted by dashed line) passing through f. Because the two phases must have the same temperature and pressure, all tie lines are parallel to the x axis. The relative amounts of the two phases can be determined by the lever rule. Generally, liquidliquid phase splits occur only over a certain temperature range. Figure 1a shows the upper critical solution temperature (UCST), which is the highest temperature
Figure 1. Common types of binary LLE phase behavior in isobaric T-x diagrams.
at which two liquid phases can still exist in equilibrium. A UCST will not be observed if it is above the bubble point of the mixture such that the LLE region intersects the vapor-liquid equilibrium (VLE) region, as shown in Figure 1b. Similarly, the lower critical solution temperature (LCST) forms the lower bound of the LLE region (Figure 1c) and will not be observed if the LLE region intersects the SLE region (Figure 1d). Because systems with UCSTs are more common than those with LCSTs,14 the size of the LLE region typically decreases (tie lines become shorter) with increasing temperature. An example of an isobaric T-x diagram for a ternary system is depicted in Figure 2a. If any binary pair is immiscible or partially miscible, there must exist an immiscibility or LLE region extending from that edge into the interior of the triangle. Such a region must either end at a plait point (denoted by p) or extend to another edge representing an immiscible or partially miscible pair. Therefore, the LLE region appears as a miscibility gap inside the prism. Figure 2b shows two isothermal cuts at temperatures T1 and T2, superimposed onto a single triangular diagram. The T-x phase diagram of a quaternary system cannot be seen in its entirety, but its isothermal cut can be represented in a three-dimensional tetrahedron
3568 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004
Figure 2. Example of a ternary LLE phase diagram: (a) isobaric cut in the form of a T-x prism diagram, (b) isothermal cuts at T1 and T2.
Figure 4. Reducing dimensionality by projection: (a) isothermal cut of a quaternary T-x diagram with one partially miscible pair, (b) Ja¨necke projection from B of Figure 4a, (c) CD lumping projection, (d) Cruickshank projection from AB.
Figure 3. Some examples of various isothermal cuts of a quaternary T-x diagram.
diagram (Figure 3). It is clear that an immiscibility region on a triangular face must extend into the interior of the tetrahedron. A single immiscibility region can connect two or more partially miscible pairs (Figure 3b and c), but it is also possible to have more than one immiscibility region (Figure 3d). Projections and Cuts. To visualize high-D systems, the dimensionality has to be reduced by performing projections and cuts. In doing so, a set of such projections and/or cuts has to be selected in such a way that the LLE phase behavior can still be clearly observed. There are different types of projections and cuts, but only a few that are both practical and meaningful are discussed here. These are all for reducing the dimensionality by 1. To reduce the dimensionality by more than 1, the same type of projection can be repeated, or different types of projections can be performed sequentially in any combination. Also, because the loss of some information is unavoidable with a single projection, one
might need to examine more than one projection to understand the LLE phase behavior of a high-D system. Ja¨ necke or normalization projection is defined by selecting a reference component from which the projection rays emanate. The overall effect is normalization of the composition with respect to the reference component. This projection is suitable for eliminating components that are not expected to affect the LLE, such as minor impurities and inerts, or for obtaining a solvent-free projection. For example, a Ja¨necke projection from B of the quaternary system in Figure 4a results in a B-free projection (Figure 4b). The curve (dotted line) represents the outer edges of the projection of the liquid-liquid immiscibility gap. Points E and R on the selected tie line ER represent A-lean and A-rich phases, respectively. The projection of the tie line is denoted by E′R′ in Figure 4b. Despite the absence of component B after the projection, it can still be observed that points E′ and R′ are A-lean and A-rich, respectively, which reflects the system behavior represented by the original tie line ER. Also, it can clearly be observed that the relative amount of D in E′ is greater than that in R′. In parallel or lumping projection, the projection rays are parallel to an edge connecting two reference components, which appear lumped together in the projection. This projection is useful to lump two or more components, all of which need to be represented in the projection although their individual compositions are not so important. Figure 4c depicts the projection of tie line ER after a parallel projection along CD, which lumps C and D together. Such a projection shows the total composition of C and D, but not their individual compositions. The envelope (dotted line) represents the outer edges of the projection of the liquid-liquid immiscibility gap. Other projections can be taken by choosing the direction of the projection rays according to special needs. For example, in Cruickshank projection, the tetrahedron is projected onto a plane parallel to two nonintersecting edges (AB and CD in Figure 4a).15 The
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3569
Figure 5. Reducing dimensionality by isoplethal cut: (a) isothermal cut of a quaternary T-x diagram showing two selected tie lines, (b) isoplethal cut at 50% A.
envelope (dotted line) again represents the outer edges of the projection of the liquid-liquid immiscibility gap. The projection appears as a square with AB and CD as diagonals (Figure 4d). Cruickshank projection is useful for visualizing the LLE phase behavior of a quaternary system with one partially miscible pair, because the immiscibility region can be easily identified in the projection. However, it might not be suitable for a different type of system, such as that with two partially miscible pairs (Figure 3b), in which case identifying the immiscibility region in the projection would be more difficult. The use of cuts in the visualization of LLE phase behavior is limited to isobaric and isothermal cuts discussed earlier. Isoplethal cuts are not useful because the cutting plane does not show the compositions of the liquid phases in equilibrium. For example, upon taking an isoplethal cut at 50% A (Figure 5a), only intersection points with the tie lines appear in the picture (Figure 5b). Clearly, such a cut is not useful for visualizing LLE behavior. Application in Conceptual Design The visualization method is particularly useful for aiding the synthesis of separation processes involving liquid-liquid extraction.The typical separation objective is to obtain a certain product with given specifications such as purity or maximum impurity content. To achieve this objective, other separation processes such as distillation and crystallization are often used in conjunction with liquid-liquid extraction. A representative generic flowsheet of such a hybrid process is shown in Figure 6. The feed to the extraction unit generally consists of the feed solvent and solutes, some of which are desirable and others of which are byproducts or impurities to be removed. An extraction solvent, which can consist of a single or multiple components, is added to isolate the target component(s). The extract is further processed in other separation units to obtain the desired products. Because of the presence of separation boundaries, such a process would meet the separation objective only if the feed to the distillation or crystallization unit were located in the correct region of feasible product(s). Visual Approach to Liquid-Liquid Extraction Design. Visualization can provide useful guidance for selecting extraction conditions such as temperature, pH, and amount and composition of the extraction solvent, so that the separation objective can be met. The basic idea is to locate representative tie lines that show the compositions after a phase split under various conditions and to superimpose the resulting diagram on other maps of process boundaries in composition space. By
Figure 6. Representative generic flowsheet of hybrid processes involving liquid-liquid extraction.
taking appropriate projections, the tie line(s) that would produce a stream located inside a certain region can be identified. For example, the amount of extraction solvent can be selected such that the extract lies inside the SLE compartment of a target component, which can then be recovered in high purity using crystallization. The visualization approach relies on the availability of some LLE data. Data for various binary and ternary systems can be found in references such as the DECHEMA handbook.16 It is a common practice to select extraction conditions to be 25 °C and 1 atm for a basecase design, as LLE data are often available at these conditions. However, because the optimum operating conditions depend on the phase behavior, data at other temperatures might be required. Furthermore, data involving natural products, pharmaceuticals, and other high-value-added compounds are normally not available in the literature and have to be obtained experimentally. Common experimental methods and description of apparatuses used in determining the LLE data have been discussed in detail.17 A fully automated workstation, which allows more measurements to be performed per day, has been developed for LLE measurements.18 Generating a large amount of experimental data to map out the whole LLE region is usually infeasible because of limited time and resources. There are two better ways to approach the problem. The first is to perform experiments for generating representative tie lines in a certain order, such as by gradually increasing or decreasing the extraction solvent-to-feed molar ratio (S/F), temperature, or composition of the extraction solvent. Each time, the tie line is plotted on selected projections to see whether the separation objective can be met. Insights from typical LLE behavior, such as shorter tie lines at higher temperature or greater distances from an edge representing a partially miscible pair, can be used to determine the conditions at which the next experimental data should be collected. In other words, visualization guides the direction of experimental work. This approach is practical only when the range of operating conditions to be studied is narrow. The second approach is to fit some experimental data (tie lines) to a thermodynamic model, which can then be used to calculate other tie lines either inside or, to a limited extent, outside the experimental range. To minimize the calculation effort, tie lines are generated in a certain order as in the first approach.
3570 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004
LLE Modeling. An LLE model is obtained by equating the fugacity of each component in the two liquid phases.19 Using the activity coefficient approach, the fugacity of component i in the liquid phase, ˆf Li , is given by
ˆf Li ) xiγif oi
(1)
where xi is the mole fraction, γi is the activity coefficient, and f oi is the standard-state fugacity of component i. Using the same standard-state fugacity for both liquid phases, the equality of fugacity for a system with c components can be written as
(xiγi)(1) ) (xiγi)(2)
i ) 1, 2, ..., c
(2)
(2) where x(1) i and xi are the mole fractions of component i at equilibrium in the first and second liquid phases, respectively. Mathematical methods are available for solving this equation. For example, a reliable and robust method that combines the flash calculation and stability algorithm has been developed.20 Among the available activity coefficient models, some are better than others for different purposes, and some demand more data for parameter regression than others.14 Often, parameter adjustment by performing selected experiments is necessary to improve model accuracy. The procedure for parameter fitting and adjustment has been discussed elsewhere.21 As an alternative, the data can also be empirically correlated using a suitable model based on statistics.8 However, the range of available experimental data often limits the use of such methods for interpolation. Once the equilibrium compositions have been obtained, projections can easily be generated by plotting the points using a set of canonical coordinates.22 The canonical coordinates for plotting a Ja¨necke projection from a reference component are obtained by ignoring the mole fraction of that component and then normalizing the mole fractions of the other components. For example, for a Ja¨necke projection from B of the quaternary system in Figure 4a, the coordinate representing the relative amount of D, x′D, is given by
x′D )
xD xA + xC + xD
(3)
The canonical coordinates for a lumping projection are obtained by lumping the mole fractions of the two reference components. The mole fractions of other components remain unchanged. For example, the coordinates used to plot the projection along CD of the quaternary system in Figure 4a are given by
x′B ) xB
(4)
x′CD ) xC + xD
(5)
Similarly, other projections can be generated in three simple steps. First, the projection rays are defined. Second, the canonical coordinates are identified following the general formula of Wibowo and Ng.22 Finally, points on the phase diagram are plotted using the coordinates. Examples The approach is illustrated using two common separation scenarios to demonstrate its applicability and
advantages, particularly in synthesizing hybrid processes involving distillation and crystallization. In the first example, the feed contains a relatively volatile mixture, and distillation is used for product recovery after liquid-liquid extraction. In the second example, liquid-liquid extraction is followed by crystallization for product recovery. Example 1: Separation of a Four-Component System Involving Distillation. This example demonstrates how visualization helps determine the operating conditions of liquid-liquid extraction such that a target component can be obtained in relatively high purity using distillation. Such extraction and distillation hybrid processes can be found in the recovery of acetic acid from aqueous solution, and the separation of canola oil from free fatty acids, among others (Table 1). The feed mixture is a homogeneous solution containing feed solvent A and two solutes: B (desired component) and C (impurity). Distillation alone is not a feasible option because the presence of multiple azeotropes creates a separation boundary that prevents separation of pure B. In addition, the feed is relatively dilute with a large amount of solvent A, which has a high heat of vaporization. Therefore, it is decided to add an extraction solvent S, which is partially miscible with A, to obtain a B-rich extract, which is then fed to a distillation system to obtain pure B (Figure 7a). S can be recovered from this distillation system and recycled to the extraction process. The raffinate can be sent to other separation units for further processing, partly recycled, or simply sent to waste processing. It is assumed that the operating pressure in the extractor is above the bubble-point pressure such that no vapor phase exists. There is also no liquid-liquid phase split in the distillation columns. The objective is to determine extraction conditions (S/F and temperature) that would put the extract in the correct distillation region such that B can be recovered in high purity using distillation. The information regarding the feed and the boiling points of the pure components and azeotropes are summarized in Table 2. From this information, a sketch of the RCM (Figure 7b) can be constructed.23 The residue curves (not drawn) would start from the unstable node (AS) and end at the stable nodes (A and B). From the RCM, it is clear that there are two distillation regions. The boundaries are assumed to be linear (not curved). B can be recovered as a high-purity distillation product only when the feed composition is located in region I. To visualize the phase diagram in two dimensions, an appropriate projection needs to be selected. Ja¨necke projection from C (Figure 7c) is chosen first because it eliminates the minor impurity C, which is not expected to play a major role in the LLE behavior. The projection clearly shows that the feed (point F) is located in region II, which confirms that it is not possible to recover B from this feed using only distillation, so that another unit is needed to cross the distillation boundary.Unfortunately, the projection shows an overlapping region rather than a distinct area for region I. In other words, if a point lies in the overlapping region, it is not possible to visually determine whether it is in region I or II. Note that such an overlapping region appears only in the projection and not in the original high-D diagram. The LLE behavior is calculated using the UNIQUAC parameters listed in Table 2. Calculations were performed using ICAS software provided by the Technical University of Denmark. Representative tie lines for
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3571
Figure 7. Process flowsheet and phase diagrams for example 1: (a) sketch of the process flowsheet, (b) sketch of the RCM in threedimensional diagram showing two distillation regions, (c) Ja¨necke projection from C after the superimposition of the RCM and LLE phase diagram, (d) AC lumping projection.
various values of S/F and T were calculated and are shown in the projection. Note that, because pure S is mixed with the feed, the mixing point through which the tie line passes always lies on the straight line connecting F and S. Because of the lever rule, as more S is added (higher S/F), the mixing point moves closer toward S, resulting in a shift of the tie line toward edge AS. As the extraction temperature increases, the size of LLE region is reduced, which is typical for a system with a UCST, as indicated by the shorter tie lines. This trend suggests that there should be no immiscibility gap within region I at high temperatures, at which the distillation column can be operated. From Figure 7c, it can be observed that, for S/F ) 0.25, operation at the three different extractor temperatures would always produce an extract located in region II, which implies that this S/F is infeasible. With more solvent (S/F g 0.5), some of the extracts appear to be inside the overlapping region, which means they can be in either region I or region II. To verify the location of these points, other projections need to be
generated. Note that projections that would lump the extraction solvent and major component in the feed, such as an AS lumping projection, should not be chosen because such a projection cannot be expected to clearly show the LLE phase split behavior with the variation of S/F. Figure 7d shows the AC lumping projection, which lumps the minor impurity C into the feed solvent A. This projection turns out to be useful because the two distillation regions can be identified, although it is inevitable that it has an overlapping region. It now becomes clear that, at S/F ) 2, operation at the three temperatures would always produce an extract in region I. The same is true for operation at 10 °C with S/F ) 1. It has been demonstrated that visualization provides the advantage of being able to quickly screen possible operating conditions to determine whether an extract can be produced in the desired region. This approach also provides physical insights that would otherwise be difficult to see. For instance, the use of a lower S/F value needs to be compensated by operating at a lower temperature to produce an extract in the desired region.
3572 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 Table 2. Input Information for Example 1 Feed Information component
mole fraction
A B C
0.8 0.1 0.1 Operating Conditions
P
1 atm LLE Information: UNIQUAC Parameters35 pure-component parameters
binary interaction parameters, aij (K) A B C S
A
B
C
S
r
q
0.0 453.7 366.0 1366.0
-164.3 0.0 -495.6 -226.2
-151.1 926.1 0.0 312.8
440.1 -44.0 -75.1 0.0
0.816 2.574 2.195 2.868
0.904 2.336 2.072 2.412
VLE Information component
Tb (°C)
azeotrope (binary)
Tb (°C)
composition
A B C S
100 88 65 58
AB AS BC CS
72 56 62 54
63 mol % B 85 mol % S 52 mol % B 80 mol % S
However, relying on these projections might not always provide a conclusive answer regarding the exact location of a process point. For example, it is not clear whether the points close to the boundary (S/F ) 0.5 at 10 °C, S/F ) 1 at 25 and 40 °C) are located in region I or II, because they appear in the overlapping region in both projections. In fact, these points appear in the overlapping region in all other Ja¨necke and lumping projections as well, so no conclusion can be drawn even after more projections are plotted. Although it is possible to visually verify the exact location of these points, such as by taking a special projection in which the projection ray is parallel to the distillation boundary such that the overlapping region disappears, taking such a projection is not practical because the distillation boundary is often nonlinear. In this case, further confirmation is needed, such as by calculating the residue curve that passes through the particular point. Nonetheless, visualization has helped to narrow down the range of feasible operating conditions, so that the effort for performing such calculations is kept at a minimum. Depending on the selection of solvent S, the phase behavior might indicate that the liquid immiscibility region does not extend into the desired region, even at very low temperatures. In that case, the extract would always lie in region II regardless of the value of S/F. Such a situation would have indicated that S is not a good choice for this separation process, and another extraction solvent would have had to be selected. The method of visualizing the process points discussed here can also be applied to processes with recycle streams. For example, part of the raffinate stream (Figure 7a) can be recycled to the feed to minimize the loss of the desired component. To take into account such a recycle, material balances need to be performed simultaneously to evaluate the new location of the feed point to the extractor after the feed has been mixed with the recycle stream. This would be an iterative process as the new feed would give a different composition of the recycle stream. Example 2: Separation of a Five-Component System Involving Crystallization. This example
illustrates the role of visualization in designing a liquid-liquid extraction process such that a target component can be recovered in a pure form in a subsequent crystallizer. Such extraction and crystallization hybrid processes can be found in the recovery of citric acid and antibiotic amoxicillin from aqueous solution using a two-component extraction solvent, among others (Table 1). The feed to the system is a solidfree fermentation broth, containing feed solvent A, desired product B, and some impurities. An extraction solvent consisting of two components, S1 and S2, has been selected to extract B from the broth. Most of the impurities would not be extracted, because they have negligible solubility in the extraction solvent. However, impurity C is known to have a relatively high solubility in the solvent, so it is expected to be present in the extract. To recover product B in a pure form, the extract mixture is then fed to a crystallization system. A sketch of the process flowsheet is shown in Figure 8a. Because the extract contains both B and C, it is important to ensure that pure B can be obtained in the subsequent crystallization unit. The objective in this example is to determine S/F and extraction solvent composition in the extractor such that the extract lies in the correct region for pure B to crystallize out. It is assumed that LLE experimental data for two different values of S/F and various compositions of the extraction solvent are available (Table 3). Because the impurities other than C are not expected to play a role in the LLE, their presence in the feed has been neglected. Therefore, there are five components to be considered: A, B, C, S1, and S2. As an attempt to reduce the dimensionality of the phase diagram, isobaric and isothermal cuts are considered. However, because the resulting four-dimensional cut still cannot be visualized, further reduction of the dimensionality is necessary. Figure 8b sketches part of an isobaric-isothermal cut of the SLE phase diagram, that is, the quaternary subsystem A-B-CS1. In other words, it is a constant-composition cut for which the S2 concentration is zero. The unsaturated region, B-saturation region (below the B-saturation surface), C-saturation region (below the C-saturation surface), and BC-cosaturation region (below the two other regions) can be identified from the diagram. The BC-cosaturation region is the region inside which three phases coexist (solid B, solid C, and liquid). It can be expected that other constant-composition cuts at various ratios of S1 to S2 would feature similar regions. A sequence of such cuts can provide a mental picture of the four-dimensional diagram. An alternative approach is to take a Ja¨necke projection from S1 followed by another Ja¨necke projection from S2 (Figure 8c). This sequence of projections, which reduces the dimensionality of the original four-dimensional diagram by 2, is expected to be a suitable choice for visualization, because the extraction solvent is not expected to crystallize out in the temperature range of the crystallization. Note that such a dimensionality reduction cannot be visually demonstrated in the same way as in Figure 4 (from three- to two-dimensional). The isothermal cut at 25 °C, calculated on the basis of simple eutectic and ideal behavior assumptions, outlines the boundaries of the B- and C-saturation regions. The BCcosaturation region (bounded by the dotted line) lies below the two regions. Several LLE tie lines are plotted on the projection. The projection clearly shows that, as S/F increases, the relative amount of C in the extract
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3573
Figure 8. Process flowsheet and phase diagrams for example 2: (a) sketch of the process flowsheet; (b) sketch of the isothermal cuts of the SLE phase diagram of A-B-C-S1; (c) Ja¨necke projection from S1, followed by Ja¨necke projection from S2, superimposed on the LLE phase diagram, at 25 °C; (d) Ja¨necke projection from S1, followed by Ja¨necke projection from S2, at 40 °C; (e) S1S2 lumping projection, followed by Ja¨necke projection from A.
3574 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 Table 3. Input Information for Example 2 Feed Information
Operating Conditions
component
mole fraction
A B C others
0.79 0.1 0.08 0.03
Textr P
25 °C 1 atm
LLE Information liquid phase I (extract)
liquid phase II (raffinate)
S/F
% S2
xA
xB
xC
xS1
xS2
xOthers
xA
xB
xC
xS1
xS2
xOthers
0.25 2 0.25 2 0.25 2
20 20 40 40 60 60
0.168 0.065 0.133 0.040 0.104 0.026
0.201 0.043 0.213 0.044 0.225 0.045
0.124 0.039 0.113 0.038 0.100 0.036
0.406 0.683 0.324 0.527 0.228 0.358
0.102 0.171 0.216 0.351 0.342 0.536
0.000 0.000 0.000 0.000 0.000 0.000
0.946 0.985 0.937 0.979 0.928 0.973
0.002 0.000 0.002 0.000 0.002 0.000
0.052 0.014 0.060 0.019 0.069 0.025
0.001 0.000 0.001 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.001 0.000
0.000 0.001 0.000 0.001 0.000 0.001
SLE Information component
Tm (°C)
∆Hfus (J/mol)
A B C S1 S2
0 97 83 -115 5
6002 16 500 25 600 5971 9866
increases. At S/F ) 2, the extract is even located in the C-saturation region. This indicates the need to use less extraction solvent (e.g., S/F ) 0.25) such that the extract is located in the B-saturation region as desired. Changing the extraction solvent composition controls the relative amounts of A and C in the extract. A higher concentration of S2 would give an extract that contains less A, which translates into a lower separation load in the downstream units. The extract would also contain less C, which means more pure B can be recovered in the crystallizer without cocrystallization of C. For the extract represented by point P, crystallization of B must stop before reaching point Q, beyond which C starts to cocrystallize. By the lever rule, the maximum solid recovery in the crystallizer is given by PQ/BQ, which is about 17% for this case. This value would certainly be lower for other extracts shown in Figure 8c. Figure 8d shows the same projection of an isothermal cut at 40 °C. It can be seen that the B-saturation region is now wider, and the maximum solid recovery for extract P is now about 24%, as given by PQ′/BQ′. In other words, the recovery is higher if the crystallizer is operated at 40 °C rather than 25 °C. This seemingly anomalous behavior is due to the fact that, within this temperature range, the maximum recovery is actually controlled by the cocrystallization of C rather than by the solubility of B. Clearly, visualization of the phase diagram makes identifying such behavior easier. Because the projections in Figure 8c and d do not show the amounts of S1 and S2, it is not clear whether point P and other extracts at S/F ) 0.25 are actually located in the unsaturated region, the B-saturation region, or even the BC-cosaturation region. This information can easily be obtained by plotting another projection, that is, the S1S2 lumping projection (lumping the two components in the extraction solvent) followed by a Ja¨necke projection from A (eliminating the feed solvent), as shown in Figure 8e. Two isothermal projections at 25 and 40 °C are shown. This projection clearly shows that all of the extracts are in the unsaturated region at both temperatures. However, upon removal of solvent in the crystallizer, P would move into the
B-saturation region, as indicated by the dashed arrow. It can also be seen that, after solvent removal, extracts obtained from operation at S/F ) 2 would move into the C-saturation region, which is consistent with the observations from Figure 8c and d. As demonstrated in the examples, modeling goes hand-in-hand with visualization in producing the desired picture. One can easily calculate hypersurfaces in high-dimensional space that are impossible to visualize, as well as the lower-dimensional pictures generated after the application of suitable projections and/or cuts.22 Such pictures are then plotted and used to assist decision making in process synthesis. Therefore, the selection of appropriate projections and cuts is a key element in this approach. Conclusions A visualization approach to the conceptual design of hybrid processes involving liquid-liquid extraction has been presented. The approach is applicable for designing both continuous and batch extractors, which are often encountered in pharmaceutical and natural product applications. It relies on the availability of phase equilibrium data, which can be generated by either calculations or experiments. Visualization can guide the decision making at the early conceptual design stage, especially in selecting the extraction conditions such as temperature, pH, and amount and composition of the extraction solvent so as to achieve the overall separation objective. This approach provides useful insights that are hard to see when only numerical data are present. Visualization of high-D LLE phase diagrams serves as a key element in a workflow for the development of liquid-liquid extraction processes, which is summarized in Figure 9. Such a workflow allows the development of the process to be done in a more systematic way, in a shorter time, and with less effort as compared to trialand-error. On the basis of the separation objectives, the key components in the feed are identified, and the extraction solvent is selected. This is followed by the selection of a suitable thermodynamic model to repre-
Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 3575
it is important to reduce the number of components first, for example, by ignoring minor impurities. Furthermore, as discussed in the first example, it is possible to visually determine the exact location of a process point using a certain specific projection, although such a projection is usually not practical. Therefore, the proposed approach is complementary to experimental studies and more detailed simulation methods developed by others.24,25 Acknowledgment We gratefully acknowledge Prof. Rafiqul Gani of CAPEC-TU Denmark for providing the ICAS (Integrated Computer Aided System) software used for the LLE calculations. The financial support of UGC Grant HKUST 6018/02P for support of this work is also gratefully acknowledged. Notation aij ) UNIQUAC binary interaction parameters, K c ) number of components E ) extract or extraction-solvent-rich phase E′ ) extract in a projected representation f oi ) standard-state fugacity, atm ˆf Li ) fugacity of component i in the liquid phase, atm F ) amount of feed, mol P ) pressure, atm r, q ) UNIQUAC volume and area parameters, respectively R ) raffinate or extraction-solvent-lean phase R′ ) raffinate in a projected representation S ) amount of extraction solvent, mol S/F ) extraction solvent-to-feed molar ratio T ) temperature, °C Tb ) boiling point, °C Tm ) melting point, °C xi ) mole fraction of component i (2) x(1) i , xi ) equilibrium mole fractions of component i in the first and second liquid phases, respectively x′i ) mole fraction of component i in a projected representation Figure 9. Workflow for the development of liquid-liquid extraction processes.
sent the system, depending on the molecular nature of the components involved in the mixture. Next, the corresponding parameter values in the model must be collected from the literature, extracted from experimental data through parameter fitting, or estimated when they are not available. These parameter values are then used to perform LLE calculations, the results of which are plotted on selected projections of the high-D phase diagram. If necessary for improving accuracy, the model parameters can be adjusted by incorporating additional experimental data focused on selected regions of the phase diagram, such as near a separation boundary. Clearly, visualization plays a key role in identifying such regions. In cases in which the separation objectives cannot be satisfied, another iteration with a different extraction solvent or inclusion of more components will be necessary. Once a configuration that meets the objectives is found, the development is continued to the next level, which might include a more detailed design of the extractor and extraction solvent recovery system and subsequent scale-up. The visualization approach might be impractical when too many components are considered. Therefore,
Greek Letters γi ) activity coefficient of component i ∆Hfus ) heat of fusion, J/mol Subscripts cry ) crystallizer extr ) extractor
Literature Cited (1) O’Young, L.; Natori, Y.; Pressly, T. G.; Ng, K. M. A Physical Limitation Based Framework for Separations Synthesis. Comput. Chem. Eng. 1997, 21, S223. (2) Schugerl, K. Solvent Extraction in Biotechnology: Recovery of Primary and Secondary Metabolites; Springer-Verlag: Berlin, 1994. (3) Martin, D. L.; Raynolds, P W. Process for the Purification of Diethoxymethane from a Mixture with Ethanol and Water. U.S. Patent 4,740,273, 1988. (4) Biegler, L. T.; Grossmann, I. E.; Westerberg, A. W. Systematic Methods of Chemical Process Design; Prentice Hall: Upper Saddle River, NJ, 1997. (5) Pressly, T. G.; Ng, K. M. Process Boundary Approach to Separations Synthesis. AIChE J. 1999, 45, 1939. (6) Francis, A. W. Liquid-Liquid Equilibriums; Wiley: New York, 1963. (7) Cruickshank, A. J. B.; Haertsch, N.; Hunter, T. G. LiquidLiquid Equilibria of Four-Component Systems. Ind. Eng. Chem. 1950, 42, 2154.
3576 Ind. Eng. Chem. Res., Vol. 43, No. 14, 2004 (8) Ruiz, F.; Marcilla, A.; Gomis, V. Method for EquilibriumStage Calculations in Liquid-Liquid Extraction: Application to Countercurrent Cascade Design for a Quaternary System. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 631. (9) Marcilla, A.; Gomez, A.; Reyes, J. A.; Olaya, M. M. New Method for Quaternary Systems Liquid-Liquid Extraction Tray to Tray Design. Ind. Eng. Chem. Res. 1999, 38, 3083. (10) Samant, K. D.; Berry, D. A.; Ng, K. M. Representation of High-Dimensional, Molecular Solid-Liquid Phase Diagrams. AIChE J. 2000, 46, 2435. (11) Wibowo, C.; Ng, K. M. Visualization of High-Dimensional Phase Diagrams of Molecular and Ionic Mixtures. AIChE J. 2002, 48, 991. (12) Wibowo, C.; Samant, K. D.; Ng, K. M. Visualization of High-Dimensional Solid-Liquid Phase Diagrams Involving Compounds and Polymorphs. AIChE J. 2002, 48, 2179. (13) Ricci, J. E. The Phase Rule and Heterogeneous Equilibrium; van Nostrand: New York, 1951. (14) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; McGraw-Hill: New York, 2001. (15) Olaya, M. M.; Garcia, A. N.; Marcilla, A. Liquid-LiquidSolid Equilibria for the Quaternary System Water + Acetone + 1-Butanol + Sodium Chloride at 25 °C. J. Chem. Eng. Data 1996, 41, 910. (16) Sorenson, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1979; Vol. 5, Parts 2 and 3. (17) Novak, J. P.; Matous, J.; Pick, J. Studies in Modern Thermodynamics: Liquid-Liquid Equilibria; Elsevier Science: New York, 1987. (18) Kuzmanovic, B.; van Delden, M. L.; Kuipers, N. J. M.; de Haan, A. B. Fully Automated Workstation for Liquid-Liquid Equilibrium Measurements. J. Chem. Eng. Data 2003, 48, 1237. (19) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1999. (20) Wasylkiewicz, S. K.; Sridhar, L. N.; Doherty, M. F.; Malone, M. F. Global Stability Analysis and Calculation of Liquid-Liquid Equilibrium in Multicomponent Mixtures. Ind. Eng. Chem. Res. 1996, 35, 1395. (21) Urlic, L.; Campana, H.; Gani, R. Adapting Thermodynamic Models for Design and Simulation of Separation Processes. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1110. (22) Wibowo, C.; Ng, K. M. Visualization of High-Dimensional Systems via Geometric Modeling with Homogeneous Coordinates. Ind. Eng. Chem. Res. 2002, 41, 2213.
(23) Doherty, M. F.; Malone, M. F. Conceptual Design of Distillation Systems; McGraw-Hill: New York, 2001. (24) Minotti, M.; Doherty, M. F.; Malone, M. F. A Geometric Method for the Design of Liquid Extractors. Ind. Eng. Chem. Res. 1996, 35, 2672. (25) Labarta, J. A. R.; Grossmann, I. E. Disjunctive Optimization Design Models for Complex Liquid-Liquid Multistage Extractors. AIChE J. 2001, 47, 2243. (26) Batista, E.; Monnerat, S.; Kato, K.; Stragevitch, L.; Meirelles, A. J. A. Liquid-Liquid Equilibrium for Systems of Canola Oil, Oleic Acid, and Short Chain Alcohols. J. Chem. Eng. Data 1999, 44, 1360. (27) Lintomen, L.; Pinto, R. T. P.; Batista, E.; Meirelles, A. J. A.; Maciel, M. R. W. Liquid-Liquid Equilibrium of the Water + Citric Acid + Short Chain Alcohol + Tricaprylin System at 298.15 K. J. Chem. Eng. Data 2001, 46, 546. (28) Garcia, M. A.; de Lucas, A.; Valverde, J. L.; Rodriguez, J. F. Liquid-Liquid Equilibria of Nicotine + Water + Toluene at Various Temperatures. J. Chem. Eng. Data 2000, 45, 540. (29) Muheim, A.; Muller, B.; Munch, T.; Wetli, M. Microbiological Process for Producing Vanillin. U.S. Patent 6,235,507, 2001. (30) Lee, Y. W.; Lee, Y. S.; Yon, C. S.; Suh, J. W.; Lee, C. H.; Lim, Y. H.; Yoo, I. D. A Process for Producing Legionella Specific Antibiotic Using Streptomyces sp. AL91. U.S. Patent 5,503,997, 1996. (31) Rudolph, E. S. J.; Zomerdijk, M.; Ottens, M.; van der Wielen, L. A. M. Solubilities and Partition Coefficients of SemiSynthetic Antibiotics in Water + 1-Butanol Systems. Ind. Eng. Chem. Res. 2001, 40, 398. (32) Lichtblau, D.; Berova, N.; Berger, J.; Nakanishi, K. Method for Isolating Terpene Trilactones (Ginkgolides, Bilobalide) from Leaves and Pharmaceutical Powders of Ginkgo biloba. U.S. Patent 6,590,109, 2003. (33) Hayenga, K. J.; Valex, P. P. Methods for Protein Purification Using Aqueous Two-Phase Extraction. U.S. Patent 6,437,101, 2002. (34) van Brunt, V. Process for Recovering Acetic Acid from Aqueous Acetic Acid Solutions. U.S. Patent 5,175,357, 1992. (35) Ruiz, F.; Gomis, V. Correlation of Quaternary LiquidLiquid Equilibrium Data Using UNIQUAC. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 216.
Received for review October 15, 2003 Revised manuscript received April 2, 2004 Accepted April 7, 2004 IE034186X
