New Graphical Method for Representing Characteristic Features of

The abscissa and ordinate of MUD are a flow rate and a logarithm of concentration, respectively. Their scales are properly set to have a common scale ...
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Ind. Eng. Chem. Res. 2002, 41, 277-284

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New Graphical Method for Representing Characteristic Features of Extraction Masashi Yamamoto and Masaru Ishida* Chemical Resources Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Japan 226-8503

The effect of solvent species (i.e., cyclohexanol, nitromethane, and R-furan aldehyde) on the extraction of acetic acid from its aqueous solution is analyzed with a new graphical method using a material-utilization diagram (or MUD) for each individual component. The abscissa and ordinate of MUD are a flow rate and a logarithm of concentration, respectively. Their scales are properly set to have a common scale of area on MUDs. This new method graphically and precisely provides important properties such as changes in concentration of each component in two phases, the distribution coefficient, selectivity, and exergy loss. MUDs for both water and acetic acid reflect the effect of the solvent species. They depict a factor of selectivity attained in the system. Changes in the concentration of a solvent give rise to a large exergy loss, indicating the importance of the solvent selection. The small exergy loss is accomplished by cyclohexanol in a countercurrent multistage scheme. This relates to a small amount of solvent supplied and to the selectivity in the system. MUD for every component exhibits characteristic features of extraction depending on the solvent species. 1. Introduction The design of a chemical process system is a very creative work. We have to consider various factors (e.g., material balance, energy balance, reaction path with its kinetics, separation task, waste disposal, etc.). It is important to grasp the essential features of each constituent process. A graphical method is effective to represent features of a complex process. For energy features, the examination of supply and the removal of heat or power is necessary. The temperature of heat may be a crucial parameter. An energy flow diagram (or Sankey diagram), an exergy flow diagram1 (or the Grassmann diagram), and an energy-utilization diagram2,3 (or EUD) have been applied. However, there are some processes, such as the bioprocess, which proceed at a nearly constant temperature. For the process, the flow rate and concentration of each component have important information. Extraction is one of such processes. Recently, extraction has been used in the recovery of carboxylic acid,4,5 rare earths,6,7 novel metals,8,9 and so forth. A target solute in the feed mixture is selectively extracted, giving rise to separation. A specific solvent has to be added to the mixture for the accomplishment of high selectivity. Although distribution of the solute into two phases takes place, the solute, diluent, and solvent undergo mixing by addition of the solvent. Hence, we need to examine changes in both the concentration and the flow rate of each component in each phase for designing a high-performance extraction system. We have proposed a material-utilization diagram10,11 (or MUD) for analyzing the behavior of each component in a chemical process, in which concentration plays an important role. In MUD, we can trace the changes in concentration and flow rate of each component simultaneously. In addition, exergy loss or exergy gain for * Corresponding author. Phone: +81-45-924-5254. Fax: +81-45-924-5253. E-mail: [email protected].

the change in concentration is graphically represented by the specific area. In this paper, we examine the effect of three different solvents (i.e., cyclohexanol, nitromethane, and R-furan aldehyde) on the extraction of acetic acid from its aqueous solution with a new graphical method using MUD. By comparison of MUDs for different solvent systems, the effectiveness and drawbacks of the solvent species are demonstrated graphically. 2. Graphical Representation of Characteristic Features of Extraction 2.1. Triangular Diagram. Let us suppose that 90% of acetic acid in a 15 wt % acetic acid aqueous solution is extracted until equilibrium by a pure solvent. The equilibrium relation12 in the ternary extraction system (i.e., acetic acid/water/solvent) is usually represented on a triangular diagram as shown in Figure 1. In Figure 1a, a mutual solubility curve at 300 K for the system using cyclohexanol (system I) as a solvent is given. The dot on the curve with a capital P stands for the plait point of the system. The dash-dotted line represents a tie line in a single-stage extraction. The solid ones are tie lines for the countercurrent six-stage extraction. The solvent-rich phase at stage i is termed as an extract phase (Ei), whereas the solvent-lean phase is referred to as a raffinate phase (Ri). The curves at 300 K using R-furan aldehyde (system II) and nitromethane (system III) are drawn in parts b and c of Figure 1, respectively. The convenience of the triangular diagram is obvious. Because an equilibrium relation of the ternary mixture over the whole concentration region is shown, we can graphically obtain an operating condition on this diagram. The points, where the curve intersects the abscissa, show equilibrium concentrations for a binary mixture of solvent and water in both solvent-rich and solvent-lean phases. By comparison of three diagrams, we may recognize that water is easy to dissolve in cyclohexanol but difficult to dissolve in nitromethane in the solvent-rich phase. Moreover, concentrations of

10.1021/ie010484n CCC: $22.00 © 2002 American Chemical Society Published on Web 12/18/2001

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Figure 1. Mutual solubility curve with tie lines for an acetic acid/water/solvent system at 300 K on a triangular diagram.

Figure 2. MUD for an acetic acid/water/cyclohexanol system in single-stage extraction (system I).

acetic acid show that the largest distribution coefficient and the highest concentration of acetic acid in extract are achieved in system I. However, it is hard to estimate the concentration and distribution coefficient of diluent and then the selectivity of the solute. Quantitative information about the flow rate is not shown. Features of the multicomponent system involving more than three components are not represented. 2.2. Application of MUD to Extraction. (a) Tracing Changes in Concentration and Flow Rate. Because it is essential to grasp a concentration and a flow rate of each component for examining characteristic features of extraction, application of MUD to extraction may be appropriate. Figure 2 shows MUD for singlestage extraction of system I. The basis for drawing MUD in this paper is on the feed rate of 100 g/s, meaning 0.250 mol/s (nAR1,in) of acetic acid and 4.718 mol/s (nWR1,in) of water, giving rise to concentrations of xAR1,in ) 0.050 and xWR1,in ) 0.950. We have assumed that the extraction reaches equilibrium. The ordinate of MUD represents a logarithm of the mole fraction of each constituent component j, whereas the abscissa shows a flow rate nj (mol) at the bottom or its energy dimension njRT0 (kJ) at the top. T0 is an environmental temperature, say 300 K. The changes in concentration and flow rate of component j in the raffinate phase are drawn at the left-hand side on MUD, and those in the extract phase are represented at the right-hand side. First, let us follow the change in concentration and flow rate of acetic acid on MUD shown in Figure 2a.

Acetic acid in a feed is represented by line ab at xAR1,in. The width of line ab shows the flow rate of acetic acid in the feed, nAR1,in. Because the flow rate of acetic acid is quite small as compared with that of water, the scale of the abscissa in Figure 2a is 10 times larger than that in Figure 2b. After extraction, the concentration of acetic acid in raffinate is decreased to 0.0109 (xAR1) as shown by line cd. Its flow rate is 0.0250 mol (nAR1). The area of the shaded rectangle aceb for the decrease in concentration is related to energy utilization, and its meaning will be explained in the following section. The transfer rate δA1 of acetic acid from raffinate to extract phases is shown by the width of dotted line de. Then, line d′e′ shows that 90% of acetic acid (nAE1 ) 0.225 mol) is recovered in extract at xAE1 ) 0.043. Only the width of a line shows an available value so that the absolute value in the abscissa has no meaning. An arrow with a solid line links the concentrations of acetic acid between two phases under equilibrium (i.e., at outlet of extraction). For convenience, the arrow with a dotted line is also drawn. Its length shows a logarithm of a distribution coefficient of acetic acid (i.e., ln KxA1 ) ln xAE1 - ln xAR1). We can evaluate the value as KxA1 ) 3.98 for this extraction. Second, let us examine MUD for water as shown in Figure 2b. There are two vertical axes, of which scales are 10 times larger than that for acetic acid. The axis on the left-hand side is for the raffinate phase, whereas that on the right-hand side is for the extract phase. Then, the area in Figure 2b has the same scale as the

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area in Figure 2a. Line ab represents a concentration (xWR1,in ) 0.950) and a flow rate (nWR1,in ) 4.718) of water in the feed. Those in raffinate are changed to 0.981 (xWR1) and 2.228 mol (nWR1) as shown by line cd, meaning an increase in concentration. The dotted area for the increase in concentration is used in the discussion in the following section. Hence, about 52.8% of water in the feed is transferred to extract (nWE1 ) 2.490 mol). It is shown by line d′e′ at xWE1 ) 0.476, which is smaller than that in raffinate. The distribution coefficient of water, KxW1, is also obtained by the vertical length of the arrow with a dotted line having the same scale as the ordinate in Figure 2a. It is shown on the right edge of Figure 2b as KxW1 ) xWE1/xWR1 ) 0.486. We can draw MUD for each component in a multicomponent system. The distribution behavior of all of the components can be represented so that its comparison is also possible on MUD. When we look at parts a and b of Figure 2 simultaneously, we can graphically evaluate the selectivity of acetic acid as β ) 8.19 by adding two vertical lengths of arrows, because the following relation holds:

ln β ) ln KxA1 - ln KxW1

(1)

This is an advantage of a logarithmic scale of MUD. Third, let us examine features of cyclohexanol on MUD shown in Figure 2c. There are also two vertical axes, of which scales are adjusted to the same scale of the area in parts a or b of Figure 2. The solvent is assumed to be pure so that the supplied solvent is represented by line a′b′ at xSE1,in ) 1 with its width of 2.522 mol (nSE1,in). The display of a flow rate for a solvent is another attractiveness of MUD. Although 99.2% of cyclohexanol remains in extract as shown by line d′e′, its concentration becomes low (i.e., xSE1 ) 0.480) because of the transfer of 2.490 mol (nWE1) of water. The drop of xSE1 indicates the miscibility of water with cyclohexanol. On the other hand, 0.8% of cyclohexanol (nSR1 ) 0.019 mol) is discharged in raffinate at xSR1 ) 0.0085 as shown by line cd. Despite a quite small value of xSR1, the logarithmic scale can show it precisely. The difference between xSE1 and xSR1 is represented on the right edge of Figure 2c. Hence, we can evaluate the distribution coefficient of cyclohexanol as KxS1 ) 56.5. (b) Features of Extraction from a Thermodynamic Viewpoint. Let us consider a liquid-liquid extraction in a multistage operation at temperature T and pressure P. Solute A in the mixture of A and diluent W is extracted by solvent S. We assume that δji mol of component j is transferred from raffinate to extract phases at stage i. Entropy change ∆Si and enthalpy change ∆Hi of the extraction at stage i are obtained as follows:10

∑j njRi,outsjjRi,out + ∑j njEi,outsjjEi,out) (∑njRi,in sjjRi,in - ∑njEi,insjjEi,in) j j

∆Si ) (

)

∑j

[

( )] ( )∑

δji ∆S°ji - R ln

ajEi,out

ajRi,out

∑j njRi,inR ln a

-

ajRi,out

jRi,out

-

njEi,inR ln

j

( ) ajEi,out

ajEi,out

(2)

and

∑j njRi,outhh jRi,out + ∑j njEi,outhh jEi,out) (∑njRi,inh h jRi,in - ∑njEi,inh h jEi,in) j j

∆Hi ) (

)

∑j δji∆H°ji

(3)

In deriving eqs 2 and 3, we have assumed that partial h j of molar entropy sjj and partial molar enthalpy h component j are obtained as

sjj ) s°j - R ln(aj)

(4)

h h j ) h°j

(5)

and

where s°j and h°j are the entropy and enthalpy, respectively, of 1 mol of pure component j at T and standard pressure P0. Moreover, we have also assumed the following relations: ∆S°ji ) s°jEi - s°jRi and ∆H°ji ) h°jEi - h°jRi. Exergy change ∆i of the extraction at stage i is defined by

∆i ) ∆Hi - T0∆Si

(6)

where T0 is an environmental temperature. By introducing eqs 2 and 3 into eq 6, we have exergy loss for the extraction as follows:

EXLi ) -{∆i + (-∆Hi)[1 - T0/T]} )-

( ) ( )∑

∑j njRi,inRT0 ln

∑j

njEi,inRT0 ln

ajRi,out

-

ajRi,in

ajEi,out ajEi,in

+

δjiRT0 ln

j

( ) Kji

Kji′

(7)

In eq 7, we have introduced the equilibrium constant Kji and the ratio of activities Kji′ of component j at an outlet of stage i

Kji )

ajEi,eq ajRi,eq

and

Kji′ )

ajEi,out ajRi,out

(8)

The first term of the right-hand side of eq 7 is the summation of exergy loss caused by the decrease in activity of component j in the raffinate phase, whereas the second term is that of exergy loss in the extract phase. These exergy losses of mixing13 are generated by the addition of a solvent for carrying out an extraction. The third term of the right-hand side of eq 7 is exergy loss, which is generated by the deviation of activity from an equilibrium value at an outlet of the stage. Hence, this term becomes zero when the extraction reaches equilibrium. Because exergy loss indicates inefficiency, large exergy loss suggests a potential to be improved. Therefore, the simultaneous examination of exergy loss as well as the distribution behavior is inevitable for examining characteristic features of extraction. When we have the activity of each component, we can show exergy loss based on eq 7. In this paper, however,

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Figure 3. MUD for countercurrent six-stage extraction using cyclohexanol (system I).

we use the mole fraction instead of the activity and evaluate temporary exergy loss by the change in the mole fraction under equilibrium conditions as follows:

EXLi ) -

∑j njRi,inRT0 ln(xjRi,out/xjRi,in) ∑j njEi,inRT0 ln(xjEi,out/xjEi,in)

(9)

We notice that the relation of eq 9 is represented by a rectangular area on MUD. Hence, exergy loss for the decrease in concentration of acetic acid in the raffinate phase is estimated by the area of the shaded rectangle aceb in Figure 2a as 0.95 kJ (EXLA). On the other hand, the concentration of water in raffinate is increased after the extraction, as shown in Figure 2b. For this case, the sign of the first term of the right-hand side of eq 9 becomes negative, giving rise to exergy gain which is calculated by

EXGW ) nWR1,inRT0 ln(xWR1/xWR1,in) ) 0.38 kJ (10) The area of the shallow dotted rectangle cabe shows this EXGW. For cyclohexanol, the drop of xSE1 (0.480) causes a large exergy loss of 4.58 kJ (EXLS), as shown by the shaded area a′c′e′b′ in Figure 2c. The total exergy loss generated in system I is obtained by

EXLtotal ) (EXLA - EXGW + EXLS) ) 5.15 kJ (11) The large EXLtotal implies an insufficiency in the singlestage extraction of system I. When we look at MUDs in Figure 2, we may find that a large EXLS deteriorates the efficiency. MUD helps such intuitive recognition. The simultaneous representation of both distribution and exergy features is a typical attractiveness of MUD. (c) Advantage of Multistage Extraction. MUD in Figure 2 suggests two schemes for reducing EXLS (i.e., reduction of nSEi,in and reduction of -ln(xSEi,out/xSEi,in)). A multistage operation is a major option for carrying out the former scheme. Let us consider a countercurrent six-stage extraction using cyclohexanol. The extraction feed is supplied to stage 1, whereas the solvent is fed to stage 6. The extract and raffinate streams flow in opposite directions from each other. Figure 3 shows MUD of this extraction. The scales of abscissa and ordinate in the three diagrams are specified one by one. On the other hand, the scale of the area

is common. At stage 1, only 0.01 mol (δA1) of acetic acid is transferred from the feed to the extract, yielding xAR1 ) 0.0477 in the raffinate phase as shown by line cd in Figure 3a. Because the concentration of acetic acid in the extract, xAE1, is determined by the product of xAR1 and KxA1 at stage 1, a high concentration of xAR1 contributes to a high concentration of xAE1. Despite the small distribution coefficient at stage 1, KxA1 ) 2.386, we have xAE1 ) 0.114, which is higher than xAE1 (0.0432) in the single-stage operation because of high xAR1. Hence, we can find the reason that the countercurrent multistage operation can push up xAE1. Tracing changes in a concentration and a flow rate is helpful to understand the mechanism. The transfer rates δAi at the following stages are δA2 ) 0.046, δA3 ) 0.048, δA4 ) 0.047, δA5 ) 0.039, and δA6 ) 0.035, giving rise to xAR6 ) 0.0069 of acetic acid in the raffinate. These values of δAi are much smaller than 0.225 (δA1) in the single-stage extraction. Then, the requirement of cyclohexanol is also reduced to nSE6,in ) 0.585 mol, as shown by line a′b′ in Figure 3c. This advantage is induced by the multistage scheme. Concentrations of cyclohexanol in the extract phase are getting lower from stage 6 to stage 1. Especially at stage 6, the largest fall is observed, as shown by line c′d′ in Figure 3c. When cyclohexanol mixes with the extraction feed at stage 1, 0.066 mol (-δS1) of cyclohexanol is transferred from the extract phase to the raffinate phase, as shown by dotted line e′f′ in Figure 3c. On the contrary, a fraction of it returns to the extract phase at the following stages 2-6. Finally, 0.028 mol (nSR6) of cyclohexanol is discharged in the raffinate at xSR6 ) 0.00803. This means that 95.2% of cyclohexanol (nSE1 ) 0.557 mol) remains in the extract. The flow pattern makes a closed loop in the countercurrent multistage scheme. As for water, a fraction of water is transferred from the raffinate phase to the extract phase at each stage, as shown in Figure 3b. The concentration of water at stage 1 in the raffinate phase is decreased to xWR1 ) 0.939 (line cd) from xWR1,in ) 0.950 (line ab) in the feed. However, the concentrations of water at the following stages are gradually increased until xWR6 ) 0.985, which is shown by line fg at stage 6. Because we expand or reduce the scales of ordinate as well as abscissa for unifying the scale of area on MUD, features of changes in concentration within a narrow range (e.g., for water) are also clearly drawn. On the other hand, the flow rate in the raffinate phase at stage

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6 is 3.501 mol (nWR6), and that in the extract phase is 0.534 mol (nWE6) at 0.460 (xWE6). Namely, the mixing of this large quantity of water gives rise to a low concentration of cyclohexanol, xSE6 (line c′d′), in the extract phase at stage 6. The concentration of water in the extract phase goes on increasing from 0.460 to 0.602 (xWE1). Then, the flow rate of water in the extract becomes 1.217 mol (nWE1). Here, we introduce the overall distribution coefficient Kxj,ov and the overall selectivity βov as follows:

Kxj,ov ) xjE1/xjR6

(12)

βov ) KxA,ov/KxW,ov

(13)

The values of KxA,ov for acetic acid and KxW,ov for water are graphically obtained as 16.55 and 0.61, respectively, yielding high selectivity βov ) 27.1, which is about 3.3 times as large as β in a single-stage extraction. According to MUDs in Figures 2 and 3, we can find that the high selectivity is accomplished mostly by the enlargement of KxA,ov on the basis of large xAE1 and small xAR6. This is also a preferable feature developed by the multistage operation. However, KxS,ov (35.4) is smaller than KxS1 (56.5) in a single-stage extraction. Let us examine the advantages of the multistage extraction from an exergy viewpoint. Exergy loss for the change in concentration of acetic acid in the raffinate phase is calculated by

EXLAR )

Figure 4. Relationship between EXLtotal and βov in countercurrent multistage operations.

∑i [-nARi,inRT0 ln(xARi,out/xARi,in)] ) 0.583 kJ (14)

which is represented by summation of the area of the shaded rectangles in Figure 3a. On the other hand, an exergy gain of 0.256 kJ (EXGAE) is generated by the progress of separation in the extract phase. The summation of area of the dotted rectangles in Figure 3a shows this. Hence, the net exergy loss for acetic acid is obtained as

EXLA,net ) EXLAR - EXGAE ) 0.327 kJ

(15)

which is smaller than that in a single-stage extraction. For water, exergy loss is generated in the raffinate phase at stage 1, whereas at the following stages, exergy gain is produced. On the other hand, at each stage in the extract phase, exergy gain is generated. The net exergy gain for water is EXGW,net ) 0.901 kJ, which is represented by the summation of the dotted area in Figure 3b. For solvent, exergy loss is generated in each phase, giving rise to EXLS,net ) 1.918 kJ, which is represented by the summation of the shaded area in Figure 3c. This means that small nSE6,in in the multistage scheme reduces 58% of EXLS in a single-stage extraction. Total exergy loss in a countercurrent sixstage extraction is also decreased to 1.34 kJ (EXLtotal). The method presented in this paper offers a visualization tool for displaying both features about concentration and exergy correctly. The common scale of area on MUD is available to point out the portions to be improved on the basis of exergy loss. In Figure 3, we may find that the largest exergy loss is observed for a solvent, and especially at stage 6 in the extract phase, about half of EXLS,net is generated. This is caused by the large drop of xSE6. Hence, we notice the importance

Figure 5. Contribution of small EXLtotal to the reduction of the requirement of a solvent: (1) single-stage, (3) countercurrent threestage, and (6) countercurrent six-stage operations.

of trial to raise xSE6 or selection of another solvent for further improving EXLS,net. Let us examine the relationship between EXLtotal and βov in a countercurrent multistage extraction. The effect of three solvents (i.e., cyclohexanol, nitromethane, and R-furan aldehyde) is represented in Figure 4. The stage numbers 1, 3, and 6 in the abscissa correspond to singlestage, countercurrent three-stage, and countercurrent six-stage operations, respectively. The solid and dashdotted curves show EXLtotal and βov, respectively. The value of EXLtotal for each system is decreased as the total number of multistage operation is increased. On the contrary, the values of βov are getting larger with the number. Although the absolute value of βov itself depends on the solvent species, the reduction of EXLtotal relates to the high selectivity in a specified system. Because EXLtotal is mainly caused by mixing, the flow rate of the supplied solvent may affect its value. Figure 5 shows a relationship between EXLtotal and the flow rate in single-stage, countercurrent three-stage, and countercurrent six-stage operations. In the region of EXLtotal in this study, the supplied rate of the solvent is almost proportional to EXLtotal. Therefore, a trial to reduce EXLtotal may lead to the reduction of the quantity of the employed solvent and elevation of the selectivity. The clarification of the location of large exergy loss gives us a hint for modifying the extraction system. 3. Effect of Solvent Species Drawn on MUD Extraction behavior is strongly affected by the solvent species. Let us discuss the differences of the behavior

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Figure 6. Effect of nitromethane on the extraction behavior in a countercurrent six-stage operation (system III).

on MUD. Figure 6 shows MUD of the countercurrent six-stage extraction for system III using nitromethane. A typical feature of system III is that a large quantity of the solvent, nSE6,in ) 4.227 mol, is required. This value is more than 7 times as large as that of cyclohexanol. However, a high xSE1 (0.831) is obtained as shown by line f ′g′ in Figure 6c. This is caused by the poor miscibility of water with nitromethane. Namely, about 97.6% of the supplied nitromethane (nSE1 ) 4.127 mol) remains in the extract, and only 0.762 mol (nWE1) of water is discharged from stage 1 at xWE1 ) 0.124, which is much lower than xWE1 in Figure 3b, as shown by line a′b′ in Figure 6b. On the other hand, in a raffinate phase, because 0.261 mol (nSR1) of nitromethane is moved into the raffinate phase at stage 1, the concentration of water xWR1 is decreased to 0.907, as shown by line cd in Figure 6b from 0.950 in the feed. Concentrations of water in the raffinate phase are conversely increased at the following stages until 0.959 (xWR6) at stage 6. Low xWE1 and high xWR6 give small KxW,ov (0.129), which is evaluated by the long arrow at the right edge of Figure 6b. The concentration of acetic acid in the extract is 0.0453 (xAE1), as shown by line a′b′ in Figure 6a. The reason for this low value is based on the small distribution coefficient, KxA1 ) 1.099, at stage 1. The decrease in xAR1 (0.0413) shown by line cd also affects a low xAE1. The distribution of acetic acid, however, proceeds by the multistage operation, yielding KxA,ov ) 7.87. Hence, 61.01 of βov is realized. When we compare Figure 6 with Figure 3, we may find that the change of the solvent species has a substantial effect on the behavior of water as well as that of acetic acid and that a small KxW,ov in system III makes a significant contribution to a large βov. This is a remarkable feature of system III. It is important to trace not only a target solute but also every component in the process. The precise description of changes in concentrations and flow rates on MUD is helpful to understand the effect of the specific solvent on the extraction process.

As for exergy features, we have EXLA,net ) 0.241 kJ, EXGW,net ) 0.753 kJ, and EXLS,net ) 2.177 kJ. Although a large quantity of solvent is supplied, EXLS,net is not enlarged so much because of the small values for the terms, -ln(xSEi,out/xSEi,in). Then, the total exergy loss in system III is EXLtotal ) 1.67 kJ. As shown in Figures 4 and 5, EXLtotal, βov, and the quantity of the supplied solvent of system III in single-stage extraction are 5.87 kJ, 14.63, and 21.30 mol, respectively. The reduction of EXLtotal by applying a multistage operation to system III has a good effect on the increase in βov and the decrease in the supplied solvent. Figure 7 shows the effect of R-furan aldehyde (system II) on the countercurrent six-stage extraction. For a comparison of the effect of the solvent species, first, we evaluate the concentration of acetic acid in the extract as xAE1 ) 0.0962, which is based on xAR1 (0.0454) and KxA1 (2.12) at stage 1 as shown in Figure 7a. Then, the value of KxA,ov becomes 14.71, which is inferior to that in system I. Second, from Figure 7b, we notice that KxW,ov in system II is 0.501, which is preferred to that in system I but is not better than that in system III, giving rise to βov ) 29.33. This value is a little higher than βov in system I but much lower than that in system III. Third, we may find that the supplied rate of R-furan aldehyde is 1.041 mol (nSE6,in), which is about 1.8 times as large as nSE6,in in system I, but about 94% of it (nSE1 ) 0.975 mol) is recovered in the extract, as shown in Figure 7c. When we compare Figures 3, 6, and 7 simultaneously, we recognize the importance of poor miscibility of a diluent with a solvent for realizing high selectivity. The reason for this is that the small value of KxW,ov largely depends on the interaction between the diluent and the solvent, whereas the value of KxA,ov can become larger by employing a multistage scheme. According to examination, we perceive that the feature of R-furan aldehyde is similar to that of cyclohexanol rather than to nitromethane. For the exergy features, the net exergy loss and gain for acetic acid and water are EXLA,net ) 0.285 kJ and EXGW,net ) 1.202 kJ,

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Figure 7. Effect of R-furan aldehyde on the extraction behavior in a countercurrent six-stage operation (system II).

respectively. Although, as shown by line f ′g′ in Figure 7c, xSE1 (0.414) in system II is higher than xSE1 (0.284) in system I, a large exergy loss for the solvent (EXLS,net ) 2.678 kJ) is generated, giving rise to EXLtotal ) 1.76 kJ, which is the largest one in the three systems. The large EXLtotal does not indicate the suitableness of R-furan aldehyde for this extraction system from a viewpoint of thermodynamics.

T0 ) environmental temperature (K) x ) mole fraction of substance

4. Conclusions

Subscripts

(1) A new graphical method using MUD is applied to an extraction of acetic acid from its aqueous solution by three solvents (i.e., cyclohexanol, nitromethane, and R-furan aldehyde). The scales of ordinate and abscissa are properly chosen for unifying a scale of area on MUD for every component. (2) There are two main advantages of the present method: (i) changes in concentration in wide or narrow range are followed precisely and (ii) a portion with a large exergy loss is detected visually. (3) The use of cyclohexanol in a countercurrent multistage scheme leads to a high concentration of acetic acid in the extract and a small EXLtotal, which relates to a low supply rate of cyclohexanol. (4) A large exergy loss for a solvent indicates the importance of selection of the solvent species. (5) The detailed description of changes in concentration of water depicts the significance of immiscibility with a solvent for raising the selectivity. (6) Drawing MUD for solute, diluent, and solvent is necessary to evaluate the effect of the specific solvent on extraction characteristics.

A ) acetic acid E ) extract phase eq ) equilibrium i ) ith stage in ) inlet of a process j ) component j out ) outlet of a process ov ) overall R ) raffinate phase S ) solvent x ) mole fraction W ) water

Nomenclature a ) activity EXL ) exergy loss (kJ) EXG ) exergy gain (kJ) K ) equilibrium constant for Kj or distribution coefficient for Kxj n ) quantity of substance (mol) R ) gas constant (kJ mol-1 K-1)

Greek Letters β ) selectivity ∆H ) enthalpy change of substance (kJ) ∆S ) entropy change of substance (kJ K-1) ∆ ) exergy change of substance (kJ) δ ) extent of transfer (mol s-1)

Literature Cited (1) Kotas, T. J. The Exergy Method of Thermal Plant Analysis; Butterworth: London, U.K., 1985. (2) Ishida, M.; Nakagawa, N. Exergy Analysis of Pervaporation System and Its Combination with a Distillation Column Based on an Energy-Utilization Diagram. J. Membr. Sci. 1985, 24, 271. (3) Jin, H.; Ishida, M.; Kobayashi, M.; Nunokawa, M. Exergy Evaluation of Two Current Advanced Power Plants: Supercritical Steam Turbine and Combined Cycle. Trans. ASME: J. Energy Resour. Technol. 1998, 250. (4) King, C. J. Acetic Acid Extraction. In Solvent Extraction Handbook; Lo, T. C., Bard, M. H. I., Hanson, C., Eds.; WileyInterscience: New York, 1983. (5) Poole, L. J.; King, C. J. Regeneration of Carboxylic AcidAmine Extracts by Back-Extraction with an Aqueous Solution of a Volatile Amine. Ind. Eng. Chem. Res. 1991, 30, 923. (6) Harrowfield, J. M.; Mocerino, M.; Peachey, B. J.; Skelton, B. W.; White, A. H. Rare-Earth-Metal Solvent Extraction with Calixarene Phosphate. J. Chem. Soc., Dalton Trans. 1996, 1687.

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Received for review May 31, 2001 Revised manuscript received October 17, 2001 Accepted October 23, 2001 IE010484N