650
Ind. Eng. Chem. Res. 1988,27, 650-657
the first part of this work. However, both distillation columns operate at low temperatures; therefore, the boiler energy can be supplied either by waste heat or simply by solar energy. A low boiling solvent, with properties for the ethanol extraction substantially superior to dichloromethane, has not been studied until now. However it may be possible to find a solvent with properties more favorable than dichloromethane. These properties should be those which reduce the energy of streams 5 and 9. (1) A greater distribution coefficient for ethanol is needed to increase the concentration of ethanol in stream 2 and thus to reduce the amounts of solvent to be evaporated. (2) A greater separation factor is needed to reduce the concentration of water in stream 2 and thus reduce the reflux ratio in column Q and the flow rate of stream 5. (3) The minimum-boiling heterogeneous azeotrope formed with water-ethanol-solvent should have a vaporphase composition in equilibrium with a greater water/ solvent ratio. In this way, the reflux ratio in column Q and the flow rate of stream 5 would decrease. (4) In the entire region of compositions, the relative volatilities of solvent to ethanol should be much greater than 1. Relative volatilities close to 1 should be avoided. In this way, the reflux ratio in column R and the flow rate of stream 9 would decrease. (5) The latent heat of the solvent should be less to reduce the energetic requirements of the process which needs to evaporate streams 5 and 9.
(6) If the boiling point of the solvent were lower (even slightly lower than the room temperature), extraction column P would need to be operated at pressures slightly above atmospheric. The cost of the energetic requirements of columns Q and R would however be very economical. Registry No. HOCH2CH3,64-17-5; CH2C12,75-09-2; HzO, 7732-18-5.
Literature Cited Abrams, D. S.; Prausnitz, J. M. AZChE J. 1975, 21, 116. Alekaandrova, M. V.; Boldina, L. A,; Komarova, V. F.; Kistereva, N. V.; Fedorova, T. S. Sb. Nauch. Tr. Vladimir. Politekh. Znst. 1971, 12, 140.
Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Chemistry Data Series Vol. 1, Parts 1 and 2; DECHEMA: Frankfurt, 1977. Hunter, T. J.; Nash, A. W. J. SOC.Chem. Znd. 1932, 51, 2851'. Munson, C. L.; King, C. J. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 109. Prausnitz, J.; Anderson, T.; Grens, E.; Eckert, C.; Hsieh, R.; O'Connell, J. Computer Calculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice Hall: Englewood Cliffs, NJ, 1980. Ruiz, F.; Gomis, V.; Botella, R. F. Znd. Eng. Chem. Res. 1987,26(4), 696. Stabnikov, V. N.; Matyushev, B. Z.; Protsyuk, T. B.; Yushchenko, N. M. Pishch. Prom. 1972, 15, 49. Torres-Marchal, C. Chem. Eng. 1981, 19, 134. Zacchi, G.; Aly, G.; Wennersten, R. ISEC'83, Denver, CO, 1983.
Received for review June 16, 1987 Revised manuscript received November 17, 1987 Accepted December 2, 1987
Continuous, Regenerative, Two-Dimensional Extraction. 1. Experimentation and Computer Simulation Shankar Nataraj,?William L. Wehrum, and Phillip C. Wankat* School of Chemical Engineering, Chemical and Metallurgical Engineering Building, Purdue University, West Lafayette, Indiana 18105
Experimental and computer simulation results for extraction using several variations of regenerated, two-dimensional cascades are presented. Shifts in temperature were used to regenerate the solvent for the systems diethylamine, toluene, water and citric acid, 50/50toluene-triisoctylamine, water. The modest separations achieved were in qualitative agreement with theory. Much larger separation is predicted when the equilibrium shift is larger. The basic features of continuous, regenerative, two-dimensional extraction can be demonstrated with the simplest such cascade, depicted in Figure 1. The chemical system involved is that where a single solute, say, A, is distributing between two solvents species: the solvent, S, and the diluent, D. The thermodynamic equilibrium relationship in the two-phase system, in its simplst form, is characterized by the complete immiscibility of S and D, and a linear partition coefficient, K , defined as the ratio of the concentration of A in D to that in S. To regenerate the solvent, the equilibrium distribution of A between D and S must be sensitive to some parameter such as temperature, pH, or the concentration of another ionic species. Without loss of generality, this parameter is referred to as temperature. Let the partition ratio be Kh at the hot temperature Th and K , at the cold temperature T, and assume, for specificity, that Kh >> K,. 'Current address: Air Products and Chemicals, Allentown, PA 18105. 0888-5885/88/2627-0650$01.50/0
The cascade in Figure 1 is a pair of equilibrium stages (e.g., mixer-settlers). One of these stages is held at temperature Th,the other at T,. The solvent, S, flows between the two stages with a flow rate S and is recycled. The diluent stream, containing both D and solute A dissolved in it at a concentration yo, is fed to both stages at flow rates D and nD as shown. The diluent streams exiting the two stages constitute the products of the process. The concentrations indicated for the diluent product streams in m and K , Figure 1 are for the extreme case where Kh 0. Even though these concentrations can be calculated from material balances and equilibrium relationships, physical reasoning is invoked here. In the cold stage, K , 0, and the diluent yields all of its solute to solvent S, which stores it. The diluent exits solute-free. The solute-laden solvent circulates to the hotter stage, where Kh a,and S gives up all of ita solute to D. Thus, the diluent exits this stage with its concentration increased n-fold. The temperature, in effect, acts as the signal which tells the solvent where to take up or yield the solute.
-
-
-
-
0 1988 American
Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 651 Inflow ( m l / m i n J .
1 ‘ ) c
Outflou (ml/inin).
nD.0
Figure 1. Simple two-dimemionel,regenerative,extraction cascade. In each doublet, the first symbol indicates flow rate and the second indicates solute concentration.
Concentration [ m S i
43
1.3
43
43
56
41
21
29
Figure 3. Configuration and theoretical predictions for 2 X 4 cascade with diluent recycle with system A. Run 3. Conditions are listed in Table 11.
FEED D
D
I
I
S
S
I
38
57
33
.\
I
21
Figure 2. Confiiation for 4 X 4 once-throughcascade with system A. Run 1. See Table I1 and Figure 7.
The apparatus described in the preceding paragraph is the simplest regenerative, two-dimensional cascade. Nevertheless, it illustrates most of the properties of such cascades. The process is a continuous steady-state process in which solvent S is regenerated entirely within the cascade. This regeneration is achieved by a parameter (temperature) switch between the two values T h and T,.This was possible because the system equilibrium was very sensitive to temperature. The concentration of one of the product streams is more than the feed concentration, and the other product is a “purified” diluent stream. The separation effect illustrated for this ideal extrema1 system, persists for more realistic systems. The separation can be amplified by the addition of more stages, as shown in Figure 2. The parameter switches are realized by keeping different groups of stages at T h or T,.In Figure 2 stages at the same temperature cluster into one or more “parametric bands” which can be vertical or inclined. The cascade of Figure 2 is not the most general. The parametric bands may be curved and nonparallel and need not start at the first row. The cascade need not be rectangular,and the solvent and diluent rates can vary among the different rows and columns. The chemical system need not be ideal-the multicomponent equilibria can be nonlinear and interactive, with partial miscibility of solvent and diluent. Some of the diluent streams can be recycled
D
Figure 4. The 2 X 3 countercurrent cascade without diluent reflux with system B. Run 8. Conditions are listed in Table 11.
as shown in Figure 3. Other diluent recycle methods are discussed later. We will show later that proper operation of diluent recycle can increase the separation factor. Some diluent streams can also have counterflow as illustrated in Figure 4. In this paper we will present direct computer simulation of the two-dimensional, regenerated cascade, and we will compare the theoretical predictions with experimental results obtained with two extraction systems. In part 2, more detailed theoretical analyses will be developed.
Literature Survey The application of two-dimensional systems to multicomponent separation was apparently first suggested by Martin (1949), who recommended the use of a rotating annulus for continuous chromatographic separations. Since that time a variety of two-dimensional chromatographic systems have been constructed and are reviewed by Sussman and Rathore (1975),Sussman (19761, Barker (1971), Wankat (1984, 1986), and Zakaria et al. (1983). Two-dimensional staged extraction schemes based on countercurrent distribution were developed by Meltzer (1956, 1958), Meltzer et al. (1965),Wankat (1972a,b),and Hudson and Wankat (1973). All of these two-dimensional systems feed the material to be separated at a single point in the cascade and hence greatly dilute the product, besides utilizing the cascade inefficiently. Several different physical forms of two-dimensional cascades have been studied, viz., the packed rotating annulus (Martin, 1949; Nicholas and Fox, 1969; Canon et al., 1980),the stationary annulus and rotating feedfproduct headers (Andrew, 1981), the rotating plate (Sussman et al., 1972), and the
652 Ind. Eng. Chem. Res., Vol. 27, No. 4,1988
nonrotary GLC apparatus (Turina, 1962). Other two-dimensional separations are reviewed by Wankat (1984). The idea of passing a “parameter wave” through a column to obtain a separation was apparently first used by Zhukovitskii (1960). Pressure swing adsorption, parametric pumping, and cycling zone adsorption utilize the same idea (Wankat, 1986). Two-dimensionalanalogues of such cyclic processes can be constructed by mapping time onto a second spatial dimension (Wankat, 1977). This can have two beneficial effects: (1)regeneration of separating agent by a parameter wave and (2) steady-state, multicomponent separation. Gidaspow and Onischak (1973) and Bowen (1971) report on rotating annular devices to harness the idea. Regenerative, two-dimensional extraction for both single-soluteextraction and multicomponent fractionation in test tubes was studied by Wankat et al. (1976). Rod (1984) and Hughes and Parker (1986) studied single-solute extraction with two columns (loading and regeneration) with countercurrent flow of diluent in the regeneration column. Hughes and Parker (1986) did extensive calculations and economic comparisons for copper extraction with various commercial extractants regenerated with sulfuric acid. The regenerated, two-dimensional (2D) cascades were often better than using two countercurrent cascades. Thus, there should be considerable commercial interest in these cascades. In exploring the avenues of application for 2D(R) extraction, certain features should be borne in mind. First, equilibrium of the extraction system must be sensitive to some parameter. Second, the product streams will have solvent dissolved or entrained in them. If this is not acceptable, the solvent has to be removed with further processing. Third, the product streams are solute-enriched and solute-depleted or “purified” diluent streams. The solutes can be mutually fractionated, but there are no “pure” solute streams in the sense that the diluent is still present, containing the solutes. This type of separation is useful in several applications such as water purification and preconcentration of very dilute liquors like hydrometallurgical leachates. Several extraction systems have been identified which have the appropriate properties. Extraction is used for removal of various phenols from water. The distribution of these phenols is dependent on both pH and temperature (Greminger et al., 1982; King, 1983). The distribution coefficients of lactic and citric acids also are very temperature-sensitive,and citric acid is recovered commercially in a two-temperature extraction (Baniel et al., 1981; King, 1983). The distribution coefficients of many hydrometallurgical solutions are dependent upon temperature or ion concentration such as NH,CNS* (e.g., see Asselin et al. (1950) or Levashova et al. (1955)). Many other systems are temperature-sensitive and are reviewed by Nataraj (1985).
Modeling and Computer Simulations The equilibrium stage model used for computer simulations assumes perfect equilibrium stages, no phase entrainment, and complete solvent-diluent immiscibility. Further, if the different solutes are independent of each other (do not interact), then the model discussed here is applicable to both single-solute and multisolute systems. The model, as written, is applicable to cocurrent diluent flow only-extension to countercurrent flows is obvious. For every stage, ( i , j ) ,in the ith row, j t h column of the cascade, a solute material balance may be written for each solute. six,,J + DirjYi. j = six,,1-1
DL-I~ jYi-1, J + Rg,hDg,hYz,h (1)
where RB,h is the fraction of the diluent effluent of stage (g,h)recycled to stage (i,j ). The equilibrium expression is of the general form
d~(xi,j,~i,j,Ti, j ) = 0
(2)
For linear equilibrium this simplifies to (3) = K ( T l , I)’,, j Further, solvent recycle from the last (mth) column to the first column in every row implies ~ 1 , m ‘1,o (4) The diluent feeds to the first row are fully specified (DoJ,yoJ known for all j ) as are the solvent rates at every row, S,, and the stage temperature at every stage, When there is no diluent recycle, RgVh= 0, and the diluent flow in each column is constant: D , = = Do, Thus, the composition topology of the cascade can be obtained by solving the equations row by row. For each row, a Newton-Raphson method was used for nonlinear equilibria, while for linear equilibria an analytical solution is possible (Wankat et al., 1976). For cascades with diluent recycle, the recycled diluent streams can be treated as “tear” streams. After tearing, the once-through method was used to solve the cascade iteratively, using the method of direct substitution. The composition profile of the diluent from the last row is of the most interest. Several measures of separative performance may be devised (Nataraj, 1985). The one used here, the span x, is the ratio of the maximum and minimum solute concentrations in the diluent effluent. x = ( ~ ~ j ) m a x( Y/ ~ , j ) m m (5) Y1, j
Extensive computer modeling of the toluene-water-diethylamine system was done. These results are compared with the experimental results later. Diluent Recycle. Solvent recycle, as opposed to diluent recycle, is part and parcel of 2D(R) extraction cascades. However, there are at least two advantages to recycling part of the diluent as shown in Figure 3. The first advantage is the lessening of stage requirements for a given degree of separation. It can be theoretically shown that a cascade with a single row of stages and complete recycle of each diluent stream is equivalent to another cascade, with the same row of stages repeated infinitely, and operated in a once-through manner (Nataraj, 1985). The second benefit is the increased recovery enabled by the recycle of intermediate streams. A 2D(R) cascade such as in Figure 2 has a number of effluent streams, some of which are enriched or depleted products, while others may be poorly separated. Recycle of these latter streams can increase the recovery in the product streams. By way of example, a case study of simulations done with the system diethylamine-toluene-water (described later) in a 2 row by 4 column (2 X 4) cascade with diluent recycle is presented. Three modes were studied. Mode A is a once-through cascade similar to Figure 2 except with only two rows. Mode C recycles diluent streams as in Figure 3. Mode B is similar to Figure 3 except that diluent streams are recycled to the same column. Results are given in Table I. In mode A, where there is no diluent recycle, there is a solute-rich stream from column 1,a solute-poor stream from column 3, and two streams of intermediate compositions from columns 2 and 4. The latter pair, being closer to the feed composition than the former, are of lesser value, and they decrease the recoveries in the other streams. In mode B, 90% of these two streams is recycled “directly“, Le., to the same respective columns. The jump in the
Ind. Eng. Chem. Res., Vol. 27, No.
2 3 4 SPan,X 0.1086 0.0687 0.0858 1.99 0.27 0.17 0.22 0.1185 0.0710 0.0776 1.82 0.05 0.32 0.04 0.1098 0.0608 0.0808 2.3 0.05 0.27 0.04
a Cascade: 2 rows X 4 columns. Vertical temperature bands are two stages wide. Solute: diethylamine. Solvent: toluene. Diluent: water. Solute K values: cold stages, K, = 2.66; hot stages, Kh = 1.04. Solvent rates: 21.0 mL/min per row, all rows. Solute composition in input dilent streams = 0.1 M. Stage diluent rates: 43.0 mL/min per column. Recycle ratios: 0.9 used (=amount of diluent recycled/original amount). Input diluent rates: adjusted so that stage diluent rate is 43.0; i.e., Do= 4.3 for all columns acting as recycle sources and Do = 43.0 for others. Comp. = composition. Recov. = recovery.
solute recoveries in the product streams from columns 1 and 3 is substantial, but the product quality, as measured by Ymax = ~ 2 1 , ~ m = i n ~ 2 or 3 span x ( Y 2 1 / ~ 2 3 ) is poorer than A. In mode C, an alternative “staggered” recycle scheme is shown. Among all the modes, this has the maximum recovery in stream 1. Further, it also has the highest span. Similar recycle ideas have been developed by Rieke (1984) and Frey (1982-1983) for cycling zone adsorption. Countercurrent Diluent Flows. In Figure 4 the diluent streams for regeneration flow in opposite directions. Diluent recycle can also be provided as “reflux”, and the resulting arrangement (Figure 5) mimics a conventional countercurrent cascade. The hot and cold diluent streams are the two “phases”. Obviously, they cannot be contacted directly with each other. Hence, two physically distinct stages are needed to replace each conventional “equilibrium stage”, and the solvent acts as a vehicle of solute transport. This cascade is different from a conventional extraction cascade with extract/raffinate reflux in that a different separation mechanism-that arising due to the temperature dependence of solute distribution-is employed. However, this cascade enjoys all the advantages of conventional countercurrent cascades: simultaneous realization of high solute recovery and high purity of raffinate diluent. Sensible heat (not latent heat) is exchanged at the two refluxers. Rod (1984) and Hughes and Parker (1986) have discussed a similar proposition though without reflux. The present scheme can also accommodate more columns to “fractionate” different solutes using multiple temperature switches. A simple theoretical evaluation displays the potential of countercurrent diluent flow. We consider only two columns (Figure 5) and operation at total reflux (no product or feed). Thus, the diluent rate for both columns will be the same (say, D). Stages are numbered top down. Solving mass balance, eq 1, and the two (linear) equilibrium relationships, eq (31, for any row i, it is possible to write a, 1 Yih
=
+
Z Y i - l , h
where ac = S / ( K J I )and a h = S/(K,.,D). For n rows, the “tops” and “bottoms” compositions at toal reflux and constant “overflow” are thus related by
E = Yn,h/YO,h = Yn+l,c/Yl,e =
(ac
+ l)n/(ah +
1988 653
HEAT
Table I. Comparison of Intermediate Stream Recycle Modes” effluent from column mode 1 A (Fig. 2) compn.b 0.1369 rec0v.C 0.34 B compn.b 0.1292 recov? 0.59 C (Fig. 3) compnSb 0.1399 recov.c 0.64
4,
(7)
for a linear system. For example, for citric acid distributing between water and toluene/Shellsol H, Kh = 3 at 80 “C
DEPLETED PRODL‘C‘T
I‘
!Ih
\?h
COOL
Figure 5. Countercurrent 2D(R) cascade with diluent reflux.
and K , = 3/20 at 25 “C (King, 1983). For S/D = 1, E = (23/4)”, provided the linear equilibrium is valid in the range YO,), C y C Yn,h. For n = 4,a thousand-fold enrichment/purification is thus possible!
Experimental System The objectives of these experiments were to investigate the operability of continuous, 2D(R) extraction, with and without diluent recycle, with cocurrent or countercurrent diluent flow, and to compare the experimental and theoretical results. A 4 X 4 rectangular array of mixer-settlers was fabricated. An individual mixer (Figure 6) is a 2-in. X 2-in. glass cylinder with flanged, ground ends. Four of these are stacked vertically in a column, with intervening polythene separator shelves and gaskets. The 1-in. propellers of each of the mixers are all mounted on a common drive shaft. Lip seals at each shelf materially and thermally insulate an individual mixer from ita neighbors. The temperature of a mixer is controlled by passing either hot or cold water through copper coils. Four columns are stirred by a common motor at 1100 rpm. The settlers are vertical glass cylinders (6 in. long X 50 or 75 mm) and are connected to the mixers through coalescing tubes packed with stainless steel and nylon mesh. Peristaltic pumps pump the diluent feed from storage vats to the top row of the stages. The diluent effluents from the last row flow through needle valves to the sample bottles, where they are collected and averaged for subsequent analysis. Average sample sizes ranged from 1/2 to 1h. Peristaltic pumps also circulate the solvents from their reservoirs through their respective rows in the cascade and back to the reservoirs. As the reservoirs are sealed, solvent inventory in a row loop is maintained constant. However, the solvent buildup in an individual stage in the loop is controlled by “trimming valves” placed at the solvent exit lines. In order for the position of the solvent-diluent interface in a settler to remain constant, the solvent out-
654
Ind. Eng. Chem. Res., Vol. 27, No. 4,1988
Table 11. Experimental Conditions and & E U h chem. run syst. row col. Th, "C 1 (Figure 2) A 4 4 35 2 B 2 3 55 l/row vert."band 3 (Figure 3) A 2 4 35 2/row
T,,OC 13 22 2/row vert.n band 10 2/row
product concn, mN feed, mN theory expt flow rates 37.6 see Figure 7 see Figure 7 D,= 43, S, = 21 45.0 ~ 2 . 1= 24, y z , ~ = 33 D,= 20, S, = 12.6 no D recycle y2,3 = 84, x = 3.5 37.9
y2,1=
56
Y2,2 = Y2,3=
42
A
2
4
5 (Figure 8)
A
2
4
B
6
A
7
2
1
3
4
35 2/row vert. band 35 2/row vert. band 55 l/row
10 2/row vert. band 10 2/row vert. band 22 2/row
vert. band
vert. band T3 = 34 T4 = 37
T1=8 Tz = 12
D,given in Figure 3 = 22.4
r = 0.9
y2,3
37.9
21 = 29 x = 2.67 see Figure 8
37.9
see Figure 8
see Figure 8
Y2,4
4 (Figures 3 and 8)
s, = 24
y2,J = 54.4
x = 2.43 see Figure 8
approx. same as Figure 3 r = 0.9 S, = 24, D,= 43
no D recycle 44.0
= 38, ~ = 7o
~ 2 , 1
Y2.3
= 37 S, = 12.6, Dz = D3
2 , 2
x = 1.89 y1,1 = 3.45 y1,z = 2.80
y1,1 = 2.47 y1,z = 2.32 y1,3 = 1.07
= 1.10 = 1.00 y1,c = 1.00 (normalized) (normalized,
y,13 y,14
B
8 (Figure 4)
2
3
22
55
20.6
D 1= 30.6 (includes recycle from stage (2,3))
s = 24
D1 = 42, D, = 44 D3= 40, D4 = 45 r =
m
(total recycle)
Si = 12.6, Dj = 20.6 no diluent recycle
43.9
Vert. = vertical.
k
LE
solvent, 50/50 v/v toluene + triisooctylamine, and the diluent, water. Details for system A studies are given by Nataraj (1985). System B was studied because similiar solvent systems are used for the commercial extraction of citric acid (King, 1983). In the temperature and solute-concentration ranges reported, the solvent and diluent are practically immiscible. However, diluent streams were presaturated to prevent removal of solvent from the cascade. The solute equilibrium was measured experimentally. The results are summarized by the following equations. System A was from 13 to 33 " C and 0 to 0.1 M,
System B was from 0 to 0.2 M, x = 0.0048- 3.175~+ 1760y2 x =
E
F
Figure 6. Schematic of a single mixer. Legend: P, mixer body; A, polythene stage-separator sheets; L, gaskets; B, shaft seals; M, shaft; D, propellor; C, heating/cooling coils; G , threaded rods; E, F, and J, fluid inlets/outlets; V, baffles; T, thermocouple; M and N, neighboring mixers.
flows and inflows to the settler should match. Thus, the trimming valves, needle valves, and sealed solvent reservoirs are the means for hydrodynamic control of the entire cascade. This is critical to proper cascade operation. When diluent recycle was used, extra peristaltic pumps were employed for that purpose. Two chemical systems were employed. System A consisted of the solute, diethylamine, distributing between the solvent, toluene, and the diluent, water. System B consisted of the solute, citric acid, distributing between a
(22 "C)
(9a)
-0.00004 + 1.51~+ 61.38~~ (55 "C) (9b)
Diethylamine was analyzed by titration with HCl and methyl red indicator. Citric acid was titrated with NaOH using phenolphthalein as indicator.
Experimental Results The apparatus is a set of 16 independent equilibrium stages. They may be interconnected to form any cascade, cocurrent or countercurrent, rectangular or nonrectangular, with 16 or fewer stages. All runs are summarized in Table 11. The 4 X 4 Cascade. Once-Through Diluent Flow. System A. Run 1. All 16 available stages were hooked up as the 4 X 4 cascade shown in Figure 2. The temperature bands have a slope of 2 and a width of 2 stages. The second and fourth stages of the last row yield the enriched and depleted diluent "product" effluents (concentrations y42and y44),while the others are "waste" streams. The actual flow rates and temperatures measured differed somewhat from the values of Figure 2 and among the runs themselves due to experimental limitations. The actual values were used for the theoretical prediction of the
Ind. Eng. Chem. Res., Vol. 27, No. 4, 1988 655 2.5 1
2.3 2.1
-
I 6
J
1
8
Time. hrs
Figure 7. Comparison of theory and experiments for two runs (run 1)for cascade shown in Figure 2. Conditions are listed in Table 11. Run la, top; run lb, bottom.
separation. The results from two of the runs are plotted in Figure 7. The runs were run on different days and are intended to be replicates. The temporal evolution of the composition profiles from the two product stages is plotted and compared with the theoretical (steady-state) predictions. There is evidently an oscillation in the composition profile for reasons to be discussed later. From the scatter, the 95% confidence limits can be calculated-these confidence boxes are indicated for each run separately. The boxes include only those points representing the "steady state" after the initial start-up phase. Although the 95% confidence limits overlap, a two-sided t-test showed that only the ya data points are not significantly different at a 5% level of significance. The y42 and x values were significantly different a t the 5% level of significance (Nataraj, 1985). The difficulty in repeating these experiments is probably due to the oscillations observed. The 2 X 3 Cascade. Once-Through Diluent Flow. System B. Run 2. The higher inherent separation factors for system B allowed a smaller cascade to be employed. A 2 X 3 cascade with two cold stages and one hot stage in each row was used. Results and conditions are listed in Table 11. The cold stream products showed some oscillation which is not illustrated in Table 11. A reasonable separation, xer = 3.54, is achieved with this modest cascade with mod)est temperature differences. The 2 X 4 Cascade. Diluent Recycle. System A. Runs 3 and 4. The 2 X 4 cascade with recycle using system A was illustrated in Figure 3. Vertical temperature bands were used. The effluent from the first column (y21, theory 56 mN) is the enriched product, while that from 21 mN) is the depleted product. the third (y23,theory The other two effluents have concentrations close to the feed, and hence 90% of these effluents are recycled. The input rate to the cascade is adjusted to give the same total diluent flow rate (43 mL/min) inside the cascade for each column. The results from two replicate runs (3 and 4) are listed in Table 11, and the results for run 4 are given in Figure
-
-
2
fi
4
8
10
Time, hrs
Figure 8. Comparison between theory and experiment for 2 x 4 cascade for system A. Data with diluent recycle are from run 4. Data without diluent recycle are from run 5. Conditions are listed in Table 11.
8. Runs 3 and 4 demonstrate the reproducibility of the experiment. The bottom portion of Figure 8 shows the evolution of the two product composition profiles. The dashed lines are the computed steady-state values. The outlet concentrations and x values are not significantly different at the 95% confidence level (Nataraj, 1985). These runs were more reproducible than run 1because the smaller cascade showed less oscillation and the diluent recycle appeared to reduce oscillation. In Figure 8, there is a break in the profile at about 7 h, corresponding to a discontinuation of diluent recycle. The experiments after this point constituted run 5, which is also listed in Table 11. The degradation in performance is obvious. The 2 X 3 Cascade. Diluent Recycle. System B. Run 6. The scheme and results are summarized in Table 11. The effluent from hot stage (2,3) is recycled partly to with a recycle ratio of r = 0.485. Note that cold stage (l,l), the diluent feed rates are the same to each colum and are not adjusted to give the same flow rate within all columns. A comparison of runs 2 and 6 is of interest since it shows a reduction of separation with this form of diluent recycle. This is different than runs 4 and 5 where diluent recycle increased separation. The 1 X 4 Cascade with Total Recycle. System A. Run 7. The cascade was run with a single row of four stages. The diluent effluent from each stage was fully recycled back to the same stage. One of the objectives was to examine this theoretically interesting, asymptotic operation experimentally. The run conditions and results are summarized in Table 11. The cascade was run for about 4 h. The run was then halted, and the diluent from each stage was quickly withdrawn for analysis. The values measured at each stage, normalized with respect to the concentration in the last stage, y1,4, are indicated. Also indicated are the theoretically obtained values, which, of course, are deterministic only up to an arbitrary constant. The 2 X 3 Countercurrent Cascade. Once-Through
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Diluent Flow. System B. Run 8. The final configuration examined was the counterflow cascade shown in Figure 4. There were two cold columns and one warm column. The warm diluent flowed counter to the two cold diluents. No diluent recycle or reflux was used. The conditions and results are given in Table 11. Comparison with run 2 shows that for this particular case cocurrent flow gave more separation. Since the results are not optimized, this result should not be generalized. Discussion Crucial to the operation of a continuous, two-dimensional cascade is the flow hydrodynamics and settler interface stability. The exact start-up sequence, the flowcontrol devices, and the operating policy are detailed by Nataraj (1985). The cascade should be operated so that an interface is constantly observable in each settler. When this is not possible, then the cascade should be operated with a little diluent entrainment in solvent (NOT solvent entrainment in diluent!) from some of the stages. Thus, in these stages, the solvent phase will disappear from the settlers. In the context of the sealed solvent reservoir system employed, the solvent inventory of any row loop remains constant even with diluent entrainment in solvent. There is now a net cross-flow of diluent in the direction of solvent flow. ’ Such cross-flow generally degrades the performance of the cascade. A hypothetical 10% diluent entrainment from each stage of a 4 X 4 cascade decreases the theoretical separation factor from 2.68 to 2.28 for system A. The operating policy without entrainment was successful for the cascades with diluent recycle and was illustrated in Figure 8. For the 4 x 4 once-through cascade for system A, it was necessary to resort to the operating policy with entrainment. Attempts to operate without entrainment resulted in the oscillations shown in Figure 7. The differences between theory and experiment shown in Table I1 and Figures 7 and 8 are probably due to fluctuations in the experiments and the ideal assumptions made in the theory. The experiments continually showed oscillations (e.g., see Figure 7 ) which are not included in the theory. Any residual disparity may be reasonably explained by uncertainty in the measured flow rates and temperatures which were input to the model and inadequacy of representation of the equilibria. For system A, the mass-transfer (Hausen) efficiencies of the mixers were measured to be better than 99% at conditions similar to the actual runs. It is conceivable that this was not true for system B. The apparatus was originally designed for system A, and the system B solvent is considerably more viscous, Also, the higher inherent separation factor of system B places an increased masstransfer responsibility on the mixer. System B with diluent recycle (run 6) showed less separation than expected, probably because of reduced residence times necessitated by the increase in the internal diluent rate in the first column. Commercial application of regenerated, two-dimensional cascades can only be done with chemical systems showing a relatively large shift in equilibrium when a thermodynamic parameter is changed. Since temperature shifts are used commercially for citric acid extraction (Baniel et al., 1981; King, 1983)) this is an obvious candidate. A twodimensional device with more stages such as a modified column is probably required. A second possibility is the extraction of copper using sulfuric acid (a pH shift) for regeneration. This system was studied by Hughes and Parker (1986) in a system similiar to Figure 4. They found
that the regenerated, two-dimensional cascade was economically favored in some cases. Other systems where pH shifts cause large changes in equilibrium such as the extraction of weak acids and weak bases are possible candidates for regenerated, two-dimensional cascades.
ConclusiondSummary The basic philosophy of continuous, two-dimensional, regenerative separations was introduced in the context of extraction. Possible avenues of its applications were delineated. Several different modes of continuous cascade operation were discussed. Partial recycle of the cocurrent diluent streams can enhance recovery and separation. Countercurrent flow of the diluent streams with or without reflux is suitable for very high recoveries of the solutes and very high purities of the diluent effluent. The operability and performance of such cascades were investigated experimentally with an array using a maximum of 16 mixer-settlers, and the results were compared to an ideal equilibrium stage model. Operation was done either with negligible entrainment or with small but significant diluent entrainment in the solvent. The former mode yielded the best performance (agreement of experiments with predictions), while the latter caused some degradation of performance. All cascades were shown to be operable, at least with diluent entrainment. Smaller cascades and cascades with diluent recycle were easier to operate. Acknowledgment This research was partially supported by NSF Grant CPE-8006903.
Nomenclature A , B = solute species D = diluent species D = diluent flow rate per column Do = feed diluent flow rate E = enrichment, eq 7 K = distribution coefficient, diluent over solvent M = molar concentration m = number of columns in cascade mM, mN = millimolar or millinormal concentration N = normal concentration n = any integer; number of rows in cascade R = recycled diluent flow rate r = recycle ratio = recycle rate/total rate S = solvent species S = solvent flow rate per row T = temperature, or generic parameter n = concentration of solute in solvent y = concentration of solute in diluent yo = diluent feed concentration Greek Symbols = S / K D , eq 6 x = span or separation factor, eq 5 (Y
Subscripts i, g = denote the ith or gth cascade row j , h = denote the jth or hth cascade column c, m, h = cold, medium, or hot temperature levels A, B = denote property pertaining to solute A or B 1 , 2 , 3 , 4= first subscript denotes row number, second denotes
column number
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Nataraj, S. Ph.D. Thesis, Purdue University, West Lafayette, IN, 1985. Nicholas, R. A.; Fox, J. B. J. Chromatogr. 1969,43,61. Rieke, R. D. Sep. Sci. Technol. 1984,19,261. Rod, V. Chem. Eng. J. 1984,29,77. Sussman, M. V. Chem. Technol. 1976,6,260. Sussman, M. V.; Rathore, R. N. S. Chromatographia 1975,8, 55. Sussman, M. V.; Astill, K. N.; Rombach, R.; Cerullo, A.; Chen, S. S. Ind. Eng. Chem. Fundam. 1972,Il,181. Turina, S.; Marjanovic-Krajovan, S.; Kostomaj, T. 2.Anal. Chem. 1962,189,100. Wankat, P. C. Separ. Sci. 1972a, 7, 233. Wankat, P. C. Separ. Sci. 1972b,7, 345. Wankat, P. C. AIChE J. 1977,23,859. Wankat, P. C. Sep. Sci. Technol. 1984,29,801. Wankat, P. C. Large Scale Adsorption and Chromatography; CRC: Boca Raton, FL, 1986. Wankat, P. C.; Middleton, A. R.; Hudson, B. L. Ind. Eng. Chem. Fundam. 1976,15,309. Zakaria, M.; Gonnord, M. F.; Guiochon, G. J. Chromatogr. 1983,271, 127. Zhukovitskii, A. A. In Gas Chromatography;Scott, R. P. W., Ed.; Butterworths: London, 1960; pp 293-300.
Baniel, A. M.; Blumberg, R.; Hajdu, K. U.S.Patent 4 275 234, June 23, 1981. Barker, P. E. In Preparative Gae Chromatography; Zlatkis, A., Pretorius, V., Eds.; Wiley-Interscience: New York, 1971; Chapter 10. Bowen, H. H. “Sorption Processes”. In Chemical Engineering; Coulson, J. M., Richardson, J. F., Eds.; Pergamon: Oxford, 1971; VOl. 3, pp 475-574. Canon, R. M.; Begovich, J. M.; Sisson, W. G. Sep. Sci. Technol. 1980, 15, 655. Frey, D. D. Sep. Sci. Technol. 1982-1983,17(13-14), 1485. Gidaspow, D.; Onischak, M. Can. J. Chem. Eng. 1973,51, 337. Greminger, D. C.; Burns, G. P.; Lynn, S.; Hanson, D. N.; King, C. J. Ind. Eng. Chem. Process Des. Dev. 1982,21,51. Hudson, B.; Wankat, P. C. Sep. Sci. 1973,8,599. Hughes, M. A.; Parker, N. In Chemical Separations; King, C. J., Navratil, J. D., Eds.; Litarvan Literature: Denver, 1986; Vol. I, pp 261-275. King, C. J. “Separation Processes Based upon Reversible Chemical Complexation”. Proc. Sym. Sep. Tech. National Taiwan Institute of Technology: Taipei, May 16-18, 1983; pp 139-143, 156. Levashova, L. B.; Darienko, E. P.; Degtyarev, V. F. J. Gen. Chem. USSR (Engl. Transl.) 1955,25,1025. Martin, A. J. P. Discuss. Faraday SOC.1949,7, 332. Meltzer, H. L. Fed. Proc. 1956,15,128. Meltzer, H.L. J. Biol. Chem. 1958,233,1327. Meltzer, H. L.; Buchler, J.; Frank, Z. Anal. Chem. 1965,37, 721.
Received for review June 19, 1987 Accepted December 2, 1987
GENERAL RESEARCH A Group Contribution Equation of State Based on the Simplified Perturbed Hard Chain Theory Gus K. Georgeton and Amyn S. Teja* School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
A group contribution equation of state based on the simplified perturbed hard chain theory is proposed in this work. T h e resulting GSPHCT equation of state can successfully predict binary and multicomponent phase equilibria, using group interaction parameters obtained from a limited amount of mixture information. T h e method appears to incorporate the advantages of both the simplified perturbed hard chain theory and of the group contribution concept and can easily be extended to other equations of state.
A knowledge of phase equilibria over wide ranges of pressure and temperature is required in the design of separation processes. It is often necessary to predict such information using limited experimental data-and sometimes using no experimental data at all. In practice, this is often achieved via equation of state methods or via group contribution methods. Group contribution methods such as ASOG (Derr and Deal, 1969) or UNIFAC (Fredenslund et al., 1975) are particularly attractive when experimental data are lacking. However, these methods are limited to the prediction of low-pressure phase equilibria over narrow ranges of temperature (typically 273-423 K). In contrast, equation of state methods are, in principle, applicable over wide ranges of pressure and temperature. However, these methods require data for the pure components and for the mixture. The application of the group contribution concept to equations of state has the potential to overcome the limitations of both types of methods and is therefore 0888-5885/88/2627-0657$01.50/0
receiving increasing attention in the literature. A group contribution equation of state based on the simplified perturbed hard chain theory is proposed in this work. The perturbed hard chain theory (PHCT) was proposed by Prausnitz and co-workers (Beret and Prausnitz, 1975a,b; Donohue and Prausnitz, 1978) for the calculation of the fluid-phase properties of a wide variety of substances ranging in complexity from methane to polyethylene. Their equation of state, however, is complex because they used an expression for the attractive term based on the molecular dynamic studies of Alder et al. (1972). More recently, Kim et al. (1986) developed the simplified perturbed hard chain theory (SPHCT) by replacing the attractive term in the PHCT by a term obtained from a lattice model of Lee et al. (1985). The resulting equation of state is simple to use and is valid at all densities for molecules as diverse as methane and polyethylene. Moreover, the extension of the SPHCT to 0 1988 American Chemical Society
