Ind. Eng. Chem. Res. 1996, 35, 993-998
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Efficient Recovery of Lanthanides by Continuous Ion Exchange Charles H. Byers and David F. Williams* Chemical Technology Division, Oak Ridge National Laboratory,‡ Oak Ridge, Tennessee 37831-6224
Continuous annular sorption is a recent innovation that uses a slowly rotating annular sorbent bed to continuously separate components as a function of angular position. The current application of this technology, continuous ion exchange (CIEx), utilizes eluent in a much more efficient manner than the previous chromatographic applications. The efficient recovery of semidilute levels (10-20 mM) of lanthanide mixtures by CIEx is demonstrated experimentally, and a mathematical model of the process is used to predict equipment performance. Results from batch shake tests and fixed-bed runs support the CIEx modeling effort and are useful separative benchmarks. The implications of the results for scaleup and economic evaluation are examined. Introduction The shortcomings of fixed-bed operation for constantduty sorption have been recognized for many years, and various methods for performing continuous adsorption have been developed as alternatives to the standard semibatch operation of fixed beds. The need for multiple columns, complicated piping and operation schedules, and tankage for blending, analyzing, and equalizing batch-to-batch variations are the typical drawbacks of batch processing. Fixed beds are often grossly oversized for the separation requirement in order to provide convenient cycle times. Despite these obvious inefficiencies, fixed beds remain a mainstay of constant-duty sorption because of their perceived simplicity, reliability, and ability to resolve complex multicomponent mixtures. The various continuous countercurrent movingbed techniques (e.g., mixer-settlers and pulsed-beds) developed in the last 40 years achieved improvements in throughput, resin utilization, and ability to handle suspended solids (Streat and Naden, 1987; Streat, 1988), but this progress was gained at the expense of separative resolution. Until recently, high-purity separation of multicomponent streams on a continuous basis could be achieved only by using a network of fixed beds. The purpose of this study is to show that the recently developed continuous annular chromatograph (CAC) can be applied to the high-purity separation of multicomponent streams in a more efficient manner. The idea of using a slowly rotating annular bed, with fixed feed and eluent positions, to continuously separate components as a function of effluent angular position was first suggested by Martin (1949) and later advocated by Giddings (1962) but was not realized as a separation technique until demonstration of the CAC by Scott (1976). The CAC concept is most readily understood by imagining the periodic and stepwise rotation of a carousel of fixed beds about a fixed feedpoint, with separate collection of effluent from each carousel position, as shown in Figure 1. Eluent transports the sorption band down a particular column during the period between feed intervals, and each component emerges at a characteristic time (and therefore carousel position) according to its relative affinity for the resin. In this manner the emergence of each sorption band is correlated with a discrete, time* Author to whom correspondence should be addressed. ‡ Managed by Lockheed Martin Energy Research Corp., under Contract No. DE-AC05-96OR224464 with the U.S. Department of Energy.
0888-5885/96/2635-0993$12.00/0
Figure 1. Continuous annular sorption concept.
invariant carousel position. Use of an annular bed eliminates the discrete elements and directly maps the effluent history into angular position. After one revolution each component forms a distinct, unchanging helical sorption band on the annular surface. Rotation transforms the unsteady-state fixed-bed process, in which a sorption wave travels down the column, into a steady-state process characterized by a standing sorption wave. What one observes is that only the annular bed movessthe feed, eluent, effluent distribution, and sorption wave remain stationary. Although simple in principle, the achievement of continuous annular sorption required ingenuity in the construction of the actual apparatus (Begovich et al., 1983). One of the important innovations introduced by Scott (1976) was the use of a distributor bed of inert material above the resin bed to segregate the feed and eluent streams in order to prevent their mixing in the entrance plenum. Since 1976, the CAC has been applied to a variety of demanding separations, including fractionation of metal (Begovich and Sisson, 1983), sugar (Howard et al., 1988), protein (Bloomingburg and Carta, 1994), and amino acid (DeCarli et al., 1989) mixtures. These studies and others have established © 1996 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 35, No. 4, 1996 Table 1. Summary of Experimental Conditions resin: Dowex 50W-X12 eluent: 5 M HNO3 50 µm average wet diameter 0.53 g dry resin per mL wet resin bed bed void fraction: 0.39
experiment batch equilibrium fixed bed CIEx-1 (basic recovery exp.) CIEx-2 (multicomponent exp.)
loaded superficial bed rotation fluid feed (all in length rate velocity 0.1 M HNO3) (cm) (deg/h) (cm/min) 10 mM Nd 10 mM Nd 10 mM Ln mixture 20 mM Ln mixture, 10 mM Cu
22.3 20.3
31
3.0 2.1
10.2
103
2.1
concentration. Therefore, batch shake tests were conducted to fill this gap in the sorption data and fixedbed tests were conducted to establish a benchmark for comparison with the CIEx test results. Figure 2. Alternate modes for continuous annular sorption: CAC vs CIEx.
that almost any chromatographic separation can be run truly continuously on the CAC. Previous continuous annular sorption studies have focused on chromatographic separations where the feed is completely resolved into its constituents by the action of an excess of carrier (i.e., eluent) flow, as shown in the left half of Figure 2. Although this arrangement provides for complete resolution of multicomponent streams, resin utilization is poor and a large eluent stream is required. A more economical contacting scheme is to reverse the role of the feed and eluent: i.e., flood the column with feed and use a minimum flow of eluent to separate the sorbed components. This more efficient mode of operation, depicted in the right half of Figure 2, is the focus of this investigation, and we distinguish it from previous chromatographic applications by referring to continuous ion exchange, or CIEx. The primary focus of this study is an experimental investigation of CIEx as applied to the recovery of lanthanides from a dilute nitric acid solution. In addition to the obvious application of rare-earth recovery for the specialty materials industry, the separation of lanthanides by ion exchange was selected because of its utility in modeling a host of radiochemical clean-up separations. The lanthanides and associated rare earths comprise a considerable fraction of the fission-product activity and also serve as excellent predictors of the behavior of the tripositive actinides (Cotton and Wilkinson, 1972). The separation of rare earths by ion exchange has been studied intensively since the 1940s. Much of that work focused on fractionation of rare-earth mixtures into pure elemental fractions by careful use of complexing agents. The focus of this study is the recovery of semidilute levels of lanthanides as a group from dilute nitric acid streams, without the use of complexing agents. Here the chemical basis for separation is straightforwardsthe Ln3+ species have a relatively high ionic charge and are most strongly held by the negatively charged resin sites. However, a gap in the ion-exchange literature still exists, because most of the published studies are restricted to dilute levels of lanthanide (Strelow et al., 1965). The few investigations of more concentrated systems did establish a Langmuirian sorption pattern for the rare earths (e.g., Tompkins and Mayer, 1947), but they are not directly applicable to this study because of differences in acid type and
Experimental Section Except for a neodymium-praseodymium mixture, all chemicals were derived from reagent-grade sources of purity greater than 99%. The large stock of lanthanide nitrate (25% Pr, 75% Nd) used in the CIEx experiments came from previous development studies, and analysis has shown that it is substantially free from metallic contaminants (>99% pure). The same lot of narrowsize-fraction (50 µm wet diameter) strong-acid cationic resin (Dowex 50W-X12) was used in all of the experiments. Absorption spectrophotometry was used to measure Nd (574, 740 nm), Pr (444 nm), Cu (710 nm), and NO3- (302 nm) concentrations. The lanthanide absorption peaks are distinct and very narrow. Although the nitrate and copper peaks are broad, they do not obscure the rare-earth peaks; therefore, extensive spectral deconvolution is not necessary. Both batch and flow-cell absorption measurements were automated using a personal computer linked to a HP8452 UVvisible spectrophotometer. For both fixed-bed and CIEx column tests, elution of sorbate was achieved with the optimal nitric acid concentration of 5 M (Nelson et al., 1964) and at a superficial velocity between 2 and 3 cm/ min. The particular experimental conditions for the various tests are summarized in Table 1. Batch Equilibration Tests. Various weights of Dowex 50W-X12 resin (50 µm wet diameter) in hydrogen form were mixed with 50 mL of 10 mM Nd(NO3)3 in 0.1 M HNO3. Equilibrium was typically achieved after overnight agitation in a shaker bath at ambient conditions (∼25 °C). The distribution coefficient at the equilibrium neodymium concentration was calculated as
D ) [(c0 - c)/c](L/S)
(1)
where D ) weight-based distribution coefficient [mL/ g], c0 ) initial (feed) Nd concentration, c ) final (equilibrium) Nd concentration, and L/S ) phase ratio ) (mL of feed solution)/(g of dry resin). The corresponding dimensionless distribution coefficient is given by the product of the weight-based distribution coefficient and the measured bulk density of the resin (FB ) 0.53 g of dry resin/mL wet resin bed). Fixed-Bed Test. The fixed-bed test consisted of measurement of the solute breakthrough curve during loading of the column to saturation and measurement
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of the concentration profile in the subsequent elution step. A standard chromatography column (1.6 cm i.d.) with low-volume inlet and outlet ports (Pharmacia XK16140) and adjustable length was used. A positivedisplacement metering pump (Alltech Model 325) was used to provide an accurate and stable 3 cm/min superficial velocity in the column during both loading and elution. The throughput (in bed volumes) during loading corresponding to an effluent concentration of half the feed concentration (i.e., 50% breakthrough) was taken as the measure of the dimensionless distribution coefficient. Continuous Ion-Exchanger Tests. The elution profile (i.e., the angular distribution of lanthanide exiting the annular column) is the critical CIEx performance parameter and the primary experimental measurement. This profile is obtained using a spectrophotometric flow cell by continuously withdrawing a side stream from one of the effluent nozzles as it rotates through the high-acid elution arc. The detailed construction of the annular bed used for these experiments has been described previously (Begovich et al., 1983). Resin is confined by a 3 × 3.5 in. annulus and rotated at a slow uniform rate during a particular experiment. The effluent is collected from a set of 90 tubes that are equally distributed below the annular resin support. Steady operation of the CIEx column is maintained by the constant feed (30 mL/min) and eluent (3 mL/min) flows provided by positive displacement metering pumps (Alltech Model 325). During the first test, CIEx-1, the column did not experience breakthrough of rare earth; i.e., a small length of unloaded resin (∼2 cm) remained below the loading band at the beginning of the elution arc. Modeling To achieve the goal of predicting the steady-state performance of CIEx separations, the defining transport equations must be supported by the attendant equilibrium and kinetic models and a practical solution scheme devised. The basic transport equation is simply the continuity equation for solute (ci) and sorbed (qi) species, which accounts for the rotation of an annular bed in a fixed cylindrical coordinate system (Howard et al., 1988)
D θ ∂2 c ∂c ∂c ∂2 c 1 - ∂q +ω +v + D )ω z 2 2 2 ∂θ ∂θ ∂z r ∂θ ∂z
(
)
(2)
∂q ) k(q* - q) ∂θ
(3)
Z ) 0, Θ > 0: 0 for rare earths/Cu ∂C ) C - Pe ∂Z ratio of eluent/feed acid for H+
〈
Z ) 1, all Θ: Θ ) 0, 0 < Z < 1:
〉
(6)
∂C/∂Z ) 0
(7)
C ) 1, Q ) 1
(8)
Except for the equilibrium relationship, all the parameters implicit in eqs 4 and 5 are readily estimated. An estimate of 8.7 × 10-4 cm2/s for the dispersion coefficient is obtained from a recent CAC study (Howard et al., 1988), and the rate parameter k is estimated to be 0.008 s-1 based upon the standard approximation (Vermuelen, 1958) and a measured diffusivity of yttrium in Dowex 50-X12 resin of 3.2 × 10-9 cm2/s (Boyd and Soldano, 1953). The equilibrium relationship for rareearth sorption at varying acid concentrations was derived both from literature studies (Strelow et al., 1965; Nelson et al., 1964) and from the shake test results of this study. At trace levels of rare earth in the presence of monovalent acid the weight-based distribution coefficient is approximated by
D [mL/g] ) 223.6[Acid]-2.6
for [Acid] < 3 M (9)
D [mL/g] ) 23.07 - 3.499[Acid] - 17.95[Acid]2 + 0.049[Acid]3 for [Acid] > 3 M (10) For nontrace levels a Langmuir fit describes the rareearth sorption
with particle-phase transport given by
ω(1 - )
St ) kL/[v(1 - )] ) Stanton number, Θ ) (θ/ω)(v/L), K0 ) q0/c0 ) reference distribution coefficient, (c0, q0) ) feed condition, and Q ) q/q0 ) q/[q*{c0}]. Equation 4 is in the same form as the standard onedimensional unsteady-state sorption equation for fixed beds if one applies the transformation θ ) ωt (Wankat, 1977). This is the mathematical representation of the analogy developed in Figure 1 (i.e., the time evolution of fixed-bed operation is mapped onto the steady-state angular distribution of continuous annular sorption). Since the elution profile governs both the separative purity and the eluent consumption, it is the primary focus of our predictions. The boundary conditions for determining the elution profile from a fully loaded bed, with eluent arc starting at θ ) 0, are
Equations 2 and 3 assume constant axial and angular dispersion (Dz and Dθ), constant rotation rate ω, constant uniaxial interstitial fluid velocity v, uniform void fraction , and a controlling particle-phase mass-transfer resistance k. In addition to the kinetic parameter k, the equilibrium relationship q* ) f(c) must be supplied over the entire range of operating conditions. Previous studies (Howard et al., 1988) indicate that the angular dispersion coefficient can be neglected (or lumped into the axial coefficient) in most cases so that a further simplification results:
Q* )
{1 +acbc}q
Fb
(11)
0
where a ) D{trace}, b ) D{trace}/q∞ ) D/4.7 mequiv/g, c ) rare-earth concentration [mequiv/mL], FB ) resin bulk density ) 0.53 g/mL, and Q* ) dimensionless equilibrium sorption referenced to feed condition ) q*/ q0. The finite-difference code GEARB (Hindmarsh, 1977) was used to solve the above system of partial differential equations by the standard “method of lines” (Silebi and Schiesser, 1992).
∂C 1 ∂2C 1- ∂Q ∂C ) K0 ∂Θ Pe ∂Z2 ∂Θ ∂Z
(4)
Results
∂Q ) [St](Q* - Q) ∂Θ
(5)
In addition to supporting the modeling effort, preliminary shake tests and fixed-bed trials provide the basic information required for planning a CIEx separation. The primary information is the distribution coefficient at the feed condition, since this factor determines
[ ]
[
]
where Z ) z/L, Pe ) (vL)/Dz ) Peclet number, C ) c/c0,
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Figure 5. Effluent profile for the recovery and separation of copper and lanthanides. Figure 3. Experimental distribution coefficient measurements of neodymium on Dowex 50W-X12 resin in 0.1 M HNO3.
Figure 4. Comparison of experimental elution curves and modeling results.
the loading capacity of the bed and, in combination with the feed flow rate, fixes the rotation rate required for a loading band which spans the entire bed length. The elution profile from a fixed-bed trial provides the volume of eluent required to completely strip the column of sorbate. This quantity is compared to the loading capacity in order to proportion the CIEx feed and eluent flows. Distribution coefficients determined from shake tests and the fixed-bed trial are summarized in Figure 3. Excellent agreement is evident between the two types of experiments. It is also apparent that at 10 mM of lanthanide the sorption is nearing the plateau level, since the sorbed amount q (q ) D[Nd]) displays only a weak concentration dependence and is approaching the total resin capacity. The sorption associated with these measurements agrees with the values predicted by eq 11. The elution profile from the fixed-bed trial is an important benchmark for evaluating both CIEx performance and the modeling results. Even for a relatively concentrated (5 M) acid eluent, the effluent profile in Figure 4 exhibits “tailing” and required 10 bed volumes to fully strip the sorbed lanthanide from the fixed-bed column. The computed profile displayed in Figure 4 was derived from the finite-difference solution of eqs 4 and 5 at the conditions of the CIEx-1 trial. Except for the minor differences in flow velocity and bed length, the
conditions of the fixed-bed and CIEx trials are “equivalent” because they produce nearly identical values of the dimensionless coefficients in eqs 4 and 5. Computed results converged after a reduction in the grid spacing to 0.05 cm. The fixed-bed profile is much sharper than the CIEx profile and shows reasonably good agreement with the modeling results given all the approximations that are contained in the numerical solution. The source of the broadening apparent in the CIEx profile is considered in the next section. The second CIEx experiment, CIEx-2, demonstrates the continuous separation and recovery of copper and lanthanides from a dilute nitric acid stream. The mode of operation in this case was slightly different because the strong sorption of lanthanides displaced copper from the column, as depicted on the right side of Figure 2. Figure 5 shows a copper breakthrough curve followed by a saturation plateau and lanthanide elution profile. It is also evident that this trial should have been conducted at a slightly slower rotation rate, since it is desirable to allow the lanthanide band to break through and completely displace the copper from the column, thereby freeing the elution arc from the presence of any copper and achieving complete separation of copper from lanthanide. Discussion Although the preceding results have established the basic soundness of operation in the CIEx mode, many important issues remain to be addressed. It is useful to organize a discussion of these topics according to (a) separative performance issues, (b) applications issues, and (c) future development issues. In the following paragraphs a closer examination of the results of this study is integrated into a discussion of these three themes. Separative performance is a key issue in the evaluation of any new sorption technology. In this study we focus upon the resolution (sharpness) of the elution profile as a measure of performance, since elution or regeneration costs dominate the economics of most sorption-based separations. The evidence presented in Figure 4, which shows the fixed-bed profile to be much sharper than the CIEx profile, does not tell the whole storysit must be put in proper context. A number of factors contribute to making the fixed-bed profile appear highly resolved in comparison with the broader CIEx profile. First, because the fixed bed used has roughly
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one-tenth the cross-section of the CIEx column and has carefully fashioned low-volume inlet and outlet piping, it represents an ideal case with the minimum of external band-broadening influences. Since increased dispersion and entrance/outlet mixing effects are known to degrade the performance of fixed beds as they are scaled up to preparative or production applications, the best comparison is between beds of equal cross section. Another performance factor to consider is the effect of discrete collection of the product from the CIEx. Each of the 90 collection ports below the resin support acts as a mixing chamber that broadens the effluent profile. Simulation of the effect of discrete collection of product by convolving the fixed-bed profile about a bandwidth (in throughput) equivalent to 4° of rotation showed that roughly half of the CIEx broadening can be attributed to this factor. For larger units this is less of a problem because of the better angular resolution (∼1°) achieved by placing more collection ports in the extended circumference at the bottom of the column. The remaining band broadening in the CIEx profile arises either from mixing in the inlet plenum or from the dispersive effect of the 2 cm length of unused resin at the bottom of the column. Our experience with different loading-band lengths leads us to believe that the inlet mixing is the more significant factor. Future tests should operate to breakthrough in order to simplify the comparison between fixed-bed and CIEx performance. It is likely that a number of external mixing effects will exert the dominant influence on the difference in separative performance between fixed beds and annular columns. Previous CAC studies have not identified a basic parameter or mechanism related to transport in the resin bed that would argue for superior performance in either device; however, there are instances in which an annular bed may offer significant advantages. For cases where separative performance degrades rapidly as the fixed-bed diameter increases, the use of an annular bed is an advantage because an equivalent flow area is achieved with a smaller effective bed diameter. Taylor dispersion for the annular geometry is also reduced because the velocity profiles develop predominantly in the radial coordinate and the resulting concentration gradients are flattened by transverse diffusion across a shallow radial gap. For those few separations that are sensitive to dispersion (e.g., those involving sharp displacement fronts), this factor may be a significant benefit. One can also imagine that the undesirable mixing present in conventional beds that arises from density-driven or viscosity-driven flow instabilities can be suppressed in a narrow-gap annular bed. At the very least we expect a carefully designed CIEx column to perform as well as a fixed-bed column. Regardless of how separative performance factors align themselves, sometimes a particular contacting scheme is favored because of the nature of the sorption application. Truly continuous operation eliminates the need for multiple columns and blend tanks, provides for automated operation, and keeps material inventory to a minimum. However, continuous operation does incur some loss of flexibility, since stable operation requires a relatively constant flow rate and feed composition. What distinguishes CIEx from the other continuous contacting schemes is that CIEx retains the capability for performing high-resolution multicomponent separations. An added benefit is that the mechanical attrition of resin associated with the other continuous movingbed contactors is absent for CIEx.
Previous work with CAC units has extended the scope of operation from laboratory-scale to large preparative operations (DeCarli et al., 1989). The barriers to CIEx scaleup are practical rather than conceptual. The model developed in this paper demonstrates that prediction of CIEx performance can be accomplished within the established fixed-bed framework. CAC units as large as 2 ft in diameter that use as much as 75% of the available area as annular bed have been used successfully for chromatographic separations. It should also be possible to configure a nested annular bed in order to increase the bed cross section and yet retain a thin annular gap. In principle, there is no barrier to constructing extremely large rotating annular beds; however, in practice, at some point the mechanics of a large piece of rotating machinery becomes cumbersome. Continued development of CIEx as an important separations device will require both refinement of equipment design and additional experimentation. Probably the most important need is for an automated effluent collection system. In the ideal system product would not be collected in discrete angular ports; instead, cuts would be made at any position automatically with the aid of on-line instrumentation. Previous attempts at improving product collection disturbed the symmetry of flow profiles in the bed and caused mixing of the separated bands. The design of a more flexible automated collection system will require some ingenuity and experimentation. The main goal of this paper is to stimulate interest in continuous annular sorption as a process separation. It should be emphasized that these trials were preliminary and that much more experimental work remains to be done. For example, the effect of extended operation was not explored in this study. Laboratory restrictions limited the extent of CIEx operation to just two or three revolutions, and although a steady-state profile was always observed after one revolution, we cannot be confident of the separative performance until more extended trials are performed. The preceding discussion also raises a number of other important issues that should be pursued in future investigations. Summary The operation of a continuous annular column in the process mode (i.e., CIEx) is a natural extension of the original continuous annular chromatograph concept. This study has established CIEx as a viable option for larger-scale separations that require more efficient use of eluent. Most of the chromatographic separations proven on the CAC can be performed more efficiently by operating in the process mode. This study has also demonstrated that CIEx performance can be predicted within the same basic framework of equations that describe fixed-bed operation. More widespread use of CIEx will require both continued experimental trials to answer questions not addressed in this study and a refined equipment design that takes full advantage of the automation potential of continuous annular sorption. Acknowledgment The authors thank W. G. Sisson for his advice on setup and operation of the continuous ion exchanger. The support of the Efficient Separations and Processing Integrated Program (ESPIP) of the Department of Energy for this research is appreciated.
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Nomenclature a ) trace level distribution coefficient, mL/g b ) Langmuir parameter, mL/g [a/q∞] c ) liquid-phase solute concentration, mequiv/mL c0 ) solute concentration in the feed, mequiv/mL C ) dimensionless liquid-phase solute concentration [c/c0] D ) weight-based distribution coefficient, mL/g Dθ ) angular dispersion coefficient, cm2/s Dz ) angular dispersion coefficient, cm2/s k ) resin-phase mass-transfer coefficient, s-1 K0 ) dimensionless distribution coefficient at the feed condition [q0/c0] L ) resin bed length L/S ) phase ratio, mL of solution/g of dry resin Pe ) vL/Dz q ) solid-phase average solution concentration, mequiv/ mL q0 ) sorbed concentration in equilibrium with the feed, mequiv/mL [q*(c0)] q* ) equilibrium sorbed concentration, mequiv/mL q∞ ) maximum sorbed concentration, mequiv/mL Q ) dimensionless sorbed concentration [q*/q0] r ) radial coordinate St ) Stanton number [kL/v(1 - )] t ) time u ) superficial velocity, cm/s v ) interstitial velocity, cm/s [u/] z ) axial coordinate with origin at the bed entrance, cm Z ) dimensionless axial coordinate [z/L] Greek Symbols ) void fraction θ ) angular displacement from the beginning of elution Θ ) dimensionless throughput [(θv/ωL) for CIEx, (tv/L) for fixed bed] FB ) resin bulk density, g of dry resin/mL of wet resin bed ω ) rotation rate, deg/h
Literature Cited Begovich, J. M.; Sisson, W. G. Continuous Ion Exchange Separation of Zirconium and Hafnium by Using an Annular Chromatograph. Hydrometallurgy 1983, 10, 11. Begovich, J. M.; Byers, C. H.; Sisson W. G. A High-Capacity Pressurized Continuous Chromatograph. Sep. Sci. Technol. 1983, 18, 1167. Bloomingburg, G. F.; Carta, G. Separation of Protein Mixtures by Continuous Annular Chromatography with Step Elution. Chem. Eng. J. 1994, 55, 19B.
Boyd, G. E.; Soldano, B. A. Self-diffusion of Cations in and through Sulfonated Polystyrene Cation-exchange Polymers. J. Am. Chem. Soc. 1953, 75, 6091. Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry; Interscience: New York, 1972; p. 594. DeCarli, J. P.; Carta, G.; Byers, C. H. Advanced Techniques for Energy-Efficient Industrial -Scale Continuous Chromatography; Oak Ridge National Laboratory: Oak Ridge, TN, 1989; ORNL/ TM-11282. Giddings, J. C. Theoretical Basis for a Continuous, Large-Capacity Gas Chromatographic Apparatus. Anal. Chem. 1962, 34, 37. Hindmarsh, A. C. GEARB: Solution of Ordinary Differential Equations Having Bounded Jacobeans; Lawrence Livermore National Laboratory: 1975; UCID-30059. Howard, A. J.; Carta, G.; Byers, C. H. Separation of Sugars by Continuous Annular Chromatography. Ind. Eng. Chem. Res. 1988, 27, 1873. Martin, A. J. P. Summarizing Paper. Discuss. Faraday Soc. 1949, 7 , 332. Nelson, F.; Murase, T.; Kraus, K. A. Ion Exchange Procedures I. Cation Exchange in Concentrated HCl and HClO4 Solutions. J. Chromatogr. 1964, 13, 503. Scott, C. D.; Spence, R. D.; Sisson, W. G. Pressurized Annular Chromatograph for Continuous Separations. J. Chromatogr. 1976, 125, 381. Silebi, C. A.; Schiesser, W. E. Dynamic Modeling of Transport Process Systems; Academic: New York, 1992; p 310. Streat, M. Ion Exchange for Industry; Halsted: New York, 1988. Streat, M.; Naden, D. Ion Exchange and Sorption Processes in Hydrometallurgy; Wiley: New York, 1987. Strelow, F. W. E.; Rethemeyer, R.; Bothma, C. J. C. Ion Exchange Selectivity Scales for Cations in Nitric Acid and Sulfuric Acid with a Sulfonated Polystyrene Resin. Anal. Chem. 1965, 37, 106. Tompkins, E. R.; Mayer, S. W. Ion Exchange as a Separation Method III. Equilibrium Studies of the Reactions of Rare Earth Complexes with Synthetic Ion Exchange Resins. J. Am. Chem. Soc. 1947, 69, 2859. Vermeulen, T. Separation by Adsorption Methods. In Advances in Chemical Engineering; Drew, T. B., Hoopes, J. W., Eds.; Academic: New York, 1958; Vol. 2, p 165. Wankat, P. C. The Relationship Between One-Dimensional and Two-Dimensional Separation Processes. AIChE J. 1977, 23, 860.
Received for review May 30, 1995 Revised manuscript received February 1, 1996 Accepted February 9, 1996X IE9503205
X Abstract published in Advance ACS Abstracts, March 15, 1996.
