Chiral separation by two-column, semi-continuous, open-loop simulated moving-bed chromatography

Journal of Chromatography A, 1217 (2010) 5407–5419

Contents lists available at ScienceDirect

Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma

Chiral separation by two-column, semi-continuous, open-loop simulated moving-bed chromatography João M.M. Araújo 1 , Rui C.R. Rodrigues, Mário F.J. Eusébio, José P.B. Mota ∗ Requimte/CQFB, Departamento de Química, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

a r t i c l e

i n f o

Article history: Received 28 November 2009 Received in revised form 24 January 2010 Accepted 16 June 2010 Available online 23 June 2010 Keywords: Simulated moving bed Open-loop configuration Two-column process Chiral separation

a b s t r a c t A two-column version of a multicolumn, semi-continuous, open-loop chromatograph for chiral separation is presented and validated experimentally. The heart of the process is a flexible node design and cyclic flow-rate modulation that succeed at keeping the mass-transfer zone inside the system without resorting to any recycling technique. One advantage of this streamlined design is the simplicity of its physical realization: regardless of the number of columns, it only requires two pumps to supply feed and desorbent into the system, while the flow rates of liquid withdrawn from the system are controlled by material balance using simple two-way valves. A rigorous model-based optimization approach is employed in the optimal cycle design to generate a solution that is physically realizable in the experimental apparatus. The optimized scheme for two-column operation supplies fresh feed into the system where the composition of the circulating fluid is closest to that of the feedstock fluid, and recovers the purified products, extract and raffinate, alternately at the downstream end of the unit while desorbent is supplied into the upstream end of the system. The feasibility and effectiveness of the two-column process are verified experimentally on the separation of reboxetine racemate, a norepinephrine re-uptake inhibitor, under overloaded conditions. Our set-up employs an automated on-line enantiomeric analysis system, comprising an analytical HPLC set-up with two UV detectors to monitor the composition profile at the downstream end of one of the columns; this monitoring system does not use a polarimeter. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The production of pure enantiomers is one of the major fields of application of preparative chromatography in the pharmaceutical industry, which is subject to stringent constraints on product purity imposed by pharmaceutical and food regulatory organizations, such as the American FDA [1]. Batch chromatography is usually the preferred method when amounts from a few milligrams to about 100 g of purified substance are needed. When larger amounts are required, ranging from several hundred grams to kilograms, the simulated moving bed (SMB) is often a more efficient alternative [2]. Over the last decade, SMB chromatography has been increasingly applied to the separation of pure substances in the pharmaceutical, fine chemistry, and biotechnological industries, at all production scales [3]. The increasing use of the SMB as a multipurpose unit in the pharmaceutical industry, where SMB units can be applied to different separations at all stages of the drug-development cycle,

∗ Corresponding author. Tel.: +351 212 948 385; fax: +351 212 948 550. E-mail address: [email protected] (J.P.B. Mota). 1 Current address: ITQB-UNL, Av. da República, Estac¸ão Agronómica Nacional, 2780-157 Oeiras, Portugal. 0021-9673/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2010.06.040

has led to the development of novel operating schemes, some of which are substantially different from the classical process. Broadly speaking, the new operating schemes introduce modulations of selected control parameters into the operating cycle. Concepts such as asynchronous port switching [4–6], cyclic modulation of the feed concentration [7,8], time-variable manipulation of the flow rates [9–13], and modulation of solvent strength during process operation [14–16], have been thoroughly analyzed. The extra degrees of freedom available with the non-classical schemes improve the separation efficiency, thus allowing the units to have fewer columns. The advantages are obvious: less stationary phase is used, the setup is more economic, and the overall pressure drop can be reduced. Furthermore, switching from one mixture to another is easier and faster than with more columns. Alternative SMB schemes with less zones than the classical, fourzone SMB implementation, with one or more columns per zone, have also been studied. For example, the three-zone SMB configuration [17–19] takes the four-zone, open-loop SMB and removes zone IV. If the amount of adsorbent allocated to each zone is properly optimized by means of asynchronous port switching, then a threezone, asynchronous SMB can perform better than a standard (i.e., synchronous) four-zone SMB [20–22]. The advantages and drawbacks of the three-zone SMB have been discussed by Chin and Wang [23].

5408

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

Nomenclature c DL k K L nQ N Pe q Q t

v x

solute concentration (g/L) axial dispersion coefficient (cm2 /min) LDF coefficient (s−1 ) Henry constant column length (cm) number of intervals for piecewise-constant modulation number of columns Péclet number adsorbed concentration (g/L) flow rate (mL/min) time (min) linear velocity (cm/min) dimensionless axial position, z/L

Greek letters ˛ selectivity, K2 /K1 ˛ separation factor, (1 + ˇK2 )/(1 + ˇK1 ) ˇ phase ratio, (1 − )/ total porosity   switching interval (min)  dimensionless time, t/ Subscripts and superscripts E eluent F feed i solute index I–IV zone index in inlet effluent j column index out outlet effluent R raffinate X extract 1 (R, R)-reboxetine 2 (S, S)-reboxetine

A two-zone SMB with continuous feeding and partial withdrawal was developed by Lee [24] for glucose-fructose separation; this process appears to be more suitable for enriching products than for high-purity separations [23]. Another two-zone SMB scheme uses intermittent feeding and withdrawal to achieve ternary separations [25]. More recently, Wankat et al. [26,27] developed two-zone SMBs for binary separation, which incorporate a storage tank to temporarily hold desorbent for later use. The results show that good separation can be achieved with their two-zone SMB systems, but with more desorbent than required by a four-zone SMB. However, partial feed was shown to improve the product purities and recoveries considerably. One-column processes that reproduce the cyclic behavior of multicolumn SMB chromatography, by means of a recycle lag, have also been proposed [28–30]. We have recently developed a semi-continuous, two-column chromatograph with a flexible node design, robust pump configuration, and cyclic flow-rate modulation to exploit the benefits of both batch and simulated counter-current modes [31]. The cycle itself is optimized and adapted to the difficulty of separation and process specifications. The feasibility of the proposed two-column system was demonstrated on a linear problem with a separation factor, ˛ , of only 1.1, where ˛ represents the ratio of factors by which the solute velocities are reduced with respect to the fluid

Fig. 1. Flow diagram for the different types of port configuration: (a) complete direction of flow to the next column; (b) downstream frozen bed; (c) upstream frozen bed; (d) flow addition to circulating stream; (e) partial withdrawal; (f) complete withdrawal and flow injection at the same node, and (g) partial withdrawal and flow addition at the same node. Configurations (e) and (g) are not considered in the present work, as they imply partial withdrawal of the exit stream from a column.

velocity: ˛ =

1 + ˇK2 , 1 + ˇK1

(1)

Here, ˇ = (1 − )/ is the phase ratio,  is the bed porosity, and Ki is the Henry constant for component i. We favor the use of ˛ over the standard definition of selectivity, ˛ = K2 /K1 , because the latter does not properly represent the difficulty of separation for small Ki . The separation is somewhat arbitrarily classified as hard for ˛ ≈ 1.1, moderate for ˛ ≈ 1.5 and easy for ˛ > 4 [32]. Fig. 1 shows the different port configurations that can be achieved with our original node design; they are the building blocks for establishing the cyclic operating schemes reported in [31]. Streams can be partially, or totally, added or removed, or flown to the next column; an inlet port and an outlet port can be simultaneously open at the same node, and the flow through a column can be temporarily frozen. In the present study we are particularly interested in streamlined versions of our original design. A first step towards this goal is to suppress partial withdrawal, i.e., to discard port configurations e and g from the design. It is worth noting that partial withdrawal is a direct consequence of the analogy between the steady state of the true moving bed (TMB) process and the cyclic steady state of the analogous SMB. However, when very few columns are considered, as is the case here, the analogy between TMB and SMB is only weak, to say the least.2 For example, batch chromatography and steady-state recycling [33–35] do not employ partial withdrawal; instead, product or waste fractions are always obtained by completely withdrawing the outlet stream of a column over a certain period of the cycle. Another, less obvious, consequence of discarding port configurations e and g is that internal recycling can only be carried out by circulating the fluid without supplying any external fluid into the beds or withdrawing any fluid from the system. Interestingly, this recirculation step is similar to the step implemented in the improved SMB (I-SMB) process [36], where the inlet and outlet ports are closed and the internal flow through the four sections is set to move the concentration profiles along the columns and adjust their relative position with respect to the outlet ports.

2 This, however, may not be as clear-cut as it seems because of a few counterexamples; e.g., single-column processes can match exactly the cyclic behavior of multicolumn SMB chromatography, by means of a recycle lag [29].

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

Fig. 2. Chemical structure of reboxetine enantiomers.

Yet another consequence of discarding port configurations e and g is that at any time the number of active inlets must be equal or greater than the number of active outlets. For example, one can feed and elute the system at the same time, at different locations, while collecting product from another column. However, it is not possible to feed the system while collecting both extract and raffinate at the same time. A typical example where all inlets and outlets are active is that of eluting a given column and collecting extract from its outlet while feeding the other column and collecting raffinate from its outlet. One advantage of this streamlined design is the simplicity of its physical realization: regardless of the number of columns, it requires as many pumps as the number of input streams and one internal circulating pump to implement the recirculation step. The flow rates of fluid withdrawn from the system are controlled by material balance using valves. For example, each distinct outlet can be controlled using one three-way valve per column: setting the valve to one position diverts the exit fluid from the column to the corresponding collecting tank; switching the valve to the other position, allows the exit fluid to circulate to the upstream column. Alternatively, four two-way valves per column can also be used. It is thus clear that the equipment employed in the apparatus is simple. The apparatus can be simplified to a greater extent if the internal recirculation step is eliminated; in this case, the internal recirculation pump is unnecessary and only two pumps are required to run the process. The resulting node design gives rise to a class of semicontinuous, open-loop, multi-column chromatographic processes, which can achieve efficient binary separation despite employing simple equipment. The purpose of the present work is to report on a two-column version of such class of processes for chiral separation. The paper is organized as follows. We start by describing the experimental apparatus where the proof of concept was realized. Our set-up employs an automated on-line enantiomeric analysis system, comprising an analytical HPLC set-up with two UV detectors sharing the same light source, to monitor the composition profile at the downstream end of one of the columns; this monitoring system does not use a polarimeter. Next, the procedure for optimal cycle design is discussed, followed by a description of the numerical approach used to solve the resulting nonlinear programming problem. Finally, the feasibility and effectiveness of the proposed two-column, open-loop chiral chromatograph are demonstrated experimentally on the separation of reboxetine racemate on an amylose-based chiral stationary phase. Reboxetine, (RS)-2-[(RS)-˛-(2-ethoxyphenoxy)benzyl]morpholine (see Fig. 2 for its chemical structure), is an antidepressant drug which belongs to the so-called norepinephrine re-uptake inhibitors (NRI drugs), because it selectively inhibits the uptake of this important neurotransmitter from the presynaptic neurones [37]. Reboxetine has been approved in over sixty countries as an antidepressant, and is marketed in Europe and Latin America under the trade names Edronax, Norebox, Prolifit, Vestra, and Integrex. Reboxetine has two asymmetrical carbons, thus it

5409

Fig. 3. Schematic of node design. Note that an on/off valve is placed between the outlet and inlet lines; this valve is normally open and is only closed when the effluent from the upstream column is totally withdrawn as product or the fluid in the column needs to be temporarily frozen. Notation is as follows: E, eluent inlet; F, feed inlet; X, extract outlet; R, raffinate outlet; Q, internal flow rate.

can exist as two enantiomeric pairs; however, due to the stereoselectivity of the synthesis (as declared by the manufacturer) only the (R, R)-, (S, S)-pair (Fig. 2) is present as a racemic mixture in the active principle and commercial formulations [38]. Recent pharmacological studies support the hypothesis that the (S, S)enantiomer is a more potent norepinephrine re-uptake inhibitor than the (R, R)- and that it is responsible for the vasomotor and cardiac side effects of reboxetine [39]. 2. Experimental set-up Fig. 3 shows a schematic of the node configuration employed in our prototype apparatus. As stated above, the flow rate of liquid that is withdrawn at each node is controlled by material balance. The experimental implementation of the schematic in Fig. 3 depends essentially on the versatility of the valves—the portion of the equipment that controls the port switching—to realize the port configurations (a)–(d) and (f) depicted in Fig. 1. We use a distributed valve design based on two-way valves, since they allow independent port switching and are quite versatile. Two-way valves allow the flow either to go through or not to go through. Each valve is attached to the transfer line between columns by a tee. A two-way valve is placed immediately downstream of the two outlet ports of each column, but preceding the two inlet ports, to control the flow rate of liquid from the column that is circulated to the other column (cf. Fig. 3). This valve is normally open and is only closed when the effluent from the upstream column is totally withdrawn as product or the fluid in the column needs to be temporarily frozen. Overall, our set-up employs 10 twoway valves to control the port switching. The two-way valves are model SFVO from Valco International (Schenkon, Switzerland) with pneumatic actuation. Each valve is automated by means of a single computer-controlled three-way solenoid: application of 50 psi opens the valve; venting the air allows the spring to return the valve to the closed position. Two HPLC pumps, model K-501 from Knauer (Berlin, Germany) with 10 mL heads, and controlled via RS232 communication protocol, are employed to supply feed and desorbent to the system. The experimental set-up is fully automated and driven by an inhouse developed automation system [40] using LabView software (National Instruments). A schematic diagram of the apparatus is shown in Fig. 4. It is current practice to install a fraction collector on the recycle line of the SMB loop to allow an internal sample to be periodically collected and analyzed by off-line HPLC. This way, the internal composition, at either the inlet of the downstream column or outlet of the upstream column (depending on the exact placement of the collector), can be measured. As the composition profile circulates around the ring of columns, the periodic sampling of the internal composition at that fixed position allows the measurement of the internal composition profile in the system. This profile is of major importance to optimize the SMB process [41].

5410

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

At fixed time intervals the six-port valve is switched to the ‘load position’ to divert the effluent exiting the column into the injection loop for collecting an internal sample. The total enantiomeric concentration in the sample is determined by averaging the measured upstream UV signal over the duration of the loop filling. Mobile phase, previously in the loop, is pushed to the downstream column while the loop is being filled. Thus, the recirculation flow rate in the two-column apparatus is not interrupted. Furthermore, by working with a sufficiently small injection loop, the sample volume drawn from the system will have an insignificant impact on the composition profile circulating around the two-column unit and, therefore, will not perturb its operation. When the injection loop is filled, the valve is switched back to its original position (‘inject position’), and the normal recirculation flow is resumed. When the six-port valve is periodically switched back to ‘inject position,’ the injection loop is placed within the flow path of mobile phase that is being pumped into the analytical column. The sample in the injection loop is thus pushed onto the analytical column for analysis and the injection loop is washed with mobile phase. The second UV detector is placed at the outlet of the analytical column for automated analysis of the chromatograms and their conversion into concentrations. The procedure is described in more detail elsewhere [48]. 3. Procedure for optimal cycle design Fig. 4. Schematic diagram of semi-continuous, two-column, open-loop chromatograph for chiral separation.

Alternatively, the enantiomeric composition can be monitored with two on-line optical detectors in series [42,43]: an UV detector to measure the absorbance of light and a polarimeter to measure the rotation of polarized light. This is a straightforward solution for chiral analysis. However, the polarimeter—an instrument which, by the way, the authors do not currently have—is an expensive analyzer. Furthermore, it has been shown that the high sensitivity of the accuracy of the polarimeter detector to experimental factors, such as impurities in the system, or pressure fluctuation in the measuring cell, has a direct impact on the accuracy and robustness of the measurements [44–47]. In the present work we employ an automated on-line enantiomeric monitoring system, comprising an analytical HPLC set-up with two UV detectors, which does not require the use of a polarimeter. The analytical HPLC column is packed with the same (or similar) stationary phase as that used in the two-column chromatograph, though this is not mandatory, but with smaller particle size to achieve lower retention times for the same peak resolution. By selecting an appropriate particle size, the monitoring scheme can achieve a sampling rate faster than the overall dynamics of the two-column apparatus. The on-line monitoring system is illustrated in Fig. 5. It comprises an electrically-actuated, six-port, two-position valve from Knauer (Berlin, Germany), an analytical HPLC column, one K-501 HPLC pump with 10 mL head, and two multi-wavelength UV detectors (USB2000/ USB4000 from Ocean Optics, USA) with attenuator, sharing the same DH-2000-S-DUV light source (Micropack, Ostfildern, Germany) by means of a bifurcated optical fiber assembly. One of the UV detectors is placed in the circulation line of the two-column apparatus, at the outlet of one of the columns, for measuring the total enantiomeric concentration at that fixed point of the unit. The UV detector is followed by the six-port valve, which is also positioned on the circulation line immediately downstream of the UV. Most of the time, the effluent from the column flows through the UV measuring cell and through the six-port valve, following the red flow path depicted in Fig. 5, and is directed to the other column.

The port configurations (a)–(d) and (f) shown in Fig. 1 are the building blocks for establishing the cyclic operating scheme of the two-column, open-loop chiral chromatograph. The periodic movement of the active inlet and outlet ports, one column ahead in the direction of the fluid flow, which occurs in a standard SMB to simulate the counter-current contact between the solid and the fluid, is also implemented in our process.3 Because the two columns are assumed to be identical, the cycle can be divided into two intervals of equal length, , where  is equivalent to the switching interval of a standard SMB. At the end of each interval, i.e. every  time units, the active inlet/ outlet ports are switched, and the columns reverse roles. As described next, the feed and eluent flow rates are modulated in time as a convenient means of solving the design problem. This has the fortunate side effect of providing an optimal cycle with better performance than one operated with constant flow rates. For convenience, the -periodic modulations implemented in the present work are piecewise constant. In practice, the switching interval is divided into a given number nQ of steps of equal length, and the flow rates are kept constant over each step before jumping discretely to different values over the next step. The adopted formulation does not explicitly track the port switching over the cycle; instead, the state of each two-way valve is inferred from the piecewise-constant flow-rate profiles. If in Fig. 3, for example, Ej = 0 over a given step of the switching interval, then the two-way valve that connects the eluent pump to the inlet of column j is closed, otherwise it is open. Similarly, if Qj = 0 or Xj + Rj = Qj then the two-way valve located between the inlet/ outlet ports downstream of column j is closed, otherwise it is open. This formulation is highly flexible and has the advantage of eliminating the integer nature of the design problem, since the only remaining

3 Note, however, that moving forward the input and withdrawal ports in a twocolumn SMB loop is exactly the same as moving them backwards. Thus, in such case it is equally valid to state that the co-current contact between the solid and the fluid is being simulated. This illustrates the very loose analogy between the class of processes under consideration, when realized with just two columns, and a TMB process.

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

5411

Fig. 5. Schematic diagram of on-line chiral monitoring system. The main equipment comprises an electrically-actuated, six-port, two-position valve, an analytical HPLC column, an HPLC pump, and two UV detectors sharing the same light source by means of a bifurcated optical fiber assembly. The set-up is fully automated.

degrees of freedom are the switching interval and the time-variable flow rates. A rigorous model-based optimization approach is employed to determine the optimal operating parameters. The purpose of the nonlinear programming problem (NLP) is to guarantee the fulfillment of product and process specifications, such as minimal purities and maximal operating flow rates, while optimizing process performance in terms of productivity and eluent consumption. At each step of the flow-rate modulation, the following basic restrictions must be satisfied: 0 ≤ Ej ≤ Qmax ,

Xj ≥ 0,

(2)

0 ≤ Fj ≤ Qmax ,

Rj ≥ 0,

(3)

0 ≤ (Xj + Rj ) ⊥ (Qj − Xj − Rj ) ≥ 0,

(4)

0 ≤ E1 ⊥ E2 ≥ 0,

(5)

E1 + E2 + F1 + F2 ≥ Qmin ,

(6)

where Qmax is the capacity of the installed HPLC pumps, Qmin is a positive constant whose purpose is explained below, and ⊥ is the complementarity operator enforcing at least one of the bounds to be active. The complementarity constraint 0 ≤ x ⊥ y ≥ 0 implies the following [49]: x=0

or

y = 0,

x ≥ 0, y ≥ 0.

PR ≥ PRmin ,

PX ≥ PXmin ,

(10)

RRmin ,

RXmin ,

(11)

RR ≥

(8)

(9)

RR ≥

where P and R denote product purity and recovery, respectively, the ‘min’ script stands for their minimal admissible values, and the subscripts ‘R’ and ‘X’ identify the extract and raffinate streams, respectively; these performance parameters are defined as follows:

 t+

PR =

(7)

Here the or operator is inclusive as both variables x and y may be zero. The constraints defined by Eqs. (2)–(6) guarantee that the solution is physically realizable with our experimental set-up. Eq. (4) ensures that product withdrawal can be implemented with onoff valves: either nothing is withdrawn as product from column j (Xj + Rj = 0 is active) and the flow is totally circulated to the other column, or the exit stream from column j is totally withdrawn as product (Qj − Xj − Rj = 0 is active). Note that the complementarity constraint implicitly enforces the condition Qj ≥ Xj + Rj .

This constraint is of utmost importance, as it prevents the withdrawal of product at a flow rate larger than that provided by the column—otherwise the packed bed would dry out and no longer be saturated with fluid. Eq. (5) enforces the use of a single pump for supplying desorbent to the system.4 Eq. (6) is one way to handle the condition of open-loop configuration, as it enforces at least Qmin amount of fluid to be supplied into the system at every step. Note that Eq. (6) is not, by itself, a sufficient condition for open-loop operation; however, when Eqs. (4) and (6) are applied together, the desired effect is achieved. Our experience with the type of problems under consideration here has shown that Eq. (6) offers an efficient method of defining the open-loop condition in a NLP formulation. Product purity and recovery are enforced through the following constraints:

t

 t+ t

out + c out )R dt (c1,j j 2,j

t

out R dt c1,j j

 t+ RR =

 t+

out R dt c1,j j

 t+ F

c1

t

Fj dt

,

,

RX =

PX =

 t+ t

 t+ t

t

out X dt c2,j j

out + c out )X dt (c1,j j 2,j

out X dt c2,j j

 t+ F

c2

t

.

,

(12)

(13)

Fj dt

Eqs. (12) and (13) have been written under the assumption that component 1 is the least retained species and component 2 the more retained one.

4 In principle, a similar condition should also be applied to the feed pump; it was observed, however, that the optimal solutions naturally discard feed strategies that require two pumps. Note also that in the present work only the case of one feed inlet and one desorbent inlet is discussed; however, a few configurations with one feed inlet and two distinct desorbent inlets have also been analyzed but are not reported here.

5412

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

In the present work, the objective function, fobj , is chosen to be the maximization of productivity, or feed throughput: ¯ fobj = max F,

F¯ =

1 



t+

(F1 + F2 ) dt = t

2 



t+2

Fj dt t

(j = 1, 2), (14)

where F¯ is the average feed flow rate per cycle. It is worth noting, however, that in general the optimization of a chromatographic process is a multi-objective optimization problem in which productivity is to be maximized and eluent consumption is to be minimized [31]. This issue is not tackled here. The NLP problem is formulated with a single-column analog model that reproduces the cyclic steady state (CSS) of the twocolumn unit [29,50], together with a full-discretization approach for steady period dynamics. For this purpose, a full-discretization method is applied to the single-column model in which the time coordinate is discretized over a full cycle (2 time units) and the CSS conditions are directly imposed [21,51]. The interested reader is referred to Fig. 4 of Ref. [31] for an explanatory image of the computational domain and governing equations, as well as for a schematic diagram of the single-column model. Discretization is handled via collocation, using 15 cubic Hermite elements [52] for the spatial domain and 10N = 20 Radau elements (with two interior points) for the time domain. The latter type of collocation elements is especially suitable for handling process dynamics with frequent discontinuities in time [54]. The flow rates remain constant over the Radau elements of a step, but are allowed to change discretely to different values across steps. This means that the maximum number of steps into which the switching interval can be divided for the piecewise-constant modulation of the flow rates is nQ = 10. This is perfectly adequate for every practical application, since higher resolutions have little impact on process performance; actually, the results presented here were obtained with nQ = 5. The complementarity conditions, Eqs. (4) and (5), are reformulated as NLP constraints using a relaxed formulation [53]. As proposed by Biegler et al. [20,54], the nonlinear programming problem obtained after discretization and relaxation of the complementarity conditions is formulated in AMPL [55] and solved using IPOPT 3.2.3 [56]. This solution strategy has been previously employed with success by our group on a broad class of SMB problems [21,22,57]. IPOPT implements a primal-dual interior-point method, and uses line searches based on filter methods; it directly exploits the first and second derivative (Hessians) information provided by AMPL via automatic differentiation. 4. Chromatographic column model The isothermal operation of a chromatographic column is adequately described by a dispersed plug-flow model with lineardriving-force approximation for mass transfer. These assumptions are standard practice in preparative chromatography and SMB modeling [58]. The lumped solid-diffusion version of the model can be written as ∂ci ∂q v +ˇ i = L ∂ ∂



∂qi = ki (q∗i − qi ), ∂

∂c 1 ∂2 ci − i Pe ∂x2 ∂x



(0 < x < 1),

(15)

(16)

where subscript i is the solute index;  = t/ and x = z/L, the dimensionless temporal and axial coordinates, respectively; ˇ = (1 − )/, the phase ratio; L, the column length; v, the linear velocity of fluid; Pe = vL/DL , the Péclet number; DL , the axial dispersion coefficient; q∗i (c1 , c2 ), the adsorption isotherm for solute i; and ki ,

Fig. 6. Analytical chromatogram of reboxetine racemate on Chiralpak AD (20 ␮m), 100 × 10 mm i.d.; mobile phase: hexane/ ethanol/ DEA (90:10:0.2 v/v-%) at 25 ◦ C; flow rate: 0.8 mL/min; injection: 75 ␮L @ 1.1 g/L of racemate; detector: UV @ 276 nm.

the linear-driving-force (LDF) coefficient for mass transfer. The reference time, , for rendering the time coordinate dimensionless, is chosen to be equal to the switching interval of the two-column process. Eq. (15) is subjected to the usual boundary conditions ci −

1 ∂ci = ciin Pe ∂x

∂ci =0 ∂x

for x = 0,

for x = 1,

(17) (18)

where ciin is the inlet concentration of solute i. 5. Experimental The feasibility and effectiveness of the proposed two-column chiral chromatograph were assessed experimentally on the separation of reboxetine racemate, using Chiralpak AD as stationary phase and a mixture of 90:10 hexane/ ethanol with 0.2% diethylamine (DEA) (basic modifier) as eluent. The solvent composition was not thoroughly optimized. Daicel’s Chiralpak AD (Chiral Technologies Europe, Illkirch, France), a 20-␮m silica-based packing material coated with amylose tri-(3,5-dimethylphenyl carbamate), is convenient for the separation of aromatic enantiomers. Racemic reboxetine was kindly supplied by Pfizer (Compound Control Center, Pfizer Global Research and Development). Fig. 6 shows an analytical chromatogram of the racemic mixture. According to the literature [38,59], the elution order of the two enantiomers and the assignment of their absolute configurations are as follows: the first-eluting enantiomer is identified as (R, R)-reboxetine and the second-eluting one as (S, S)-reboxetine. It is clear from the analysis of Fig. 6 that the chromatographic conditions are unfavorable for HPLC separation of the racemic mixture due to the low selectivity and poor resolution; it is thus difficult to resolve the two enantiomers with high purity and yield by HPLC for the chosen chromatographic conditions. 5.1. Materials and methods The chromatographic columns employed in the two-column system are thermojacketed Superformance 10 mm i.d. glass columns (Götec Labortechnik, Germany). The stationary phase was slurry packed into each column to a bed height of L = 10.0 cm. The solvents used, HPLC-grade n-hexane (Sigma–Aldrich, Germany),

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

5413

Table 1 Column characterization and adsorption parameters for the separation of reboxetine enantiomers on Chiralpak AD, using hexane/ ethanol/ DEA (90:10:0.2 v/v-%) as mobile phase. Scripts ‘1’ and ‘2’ denote the less-retained [(R, R)-] and more-retained [(S, S)-] enantiomers, respectively; the Henry constants were determined from diluted pulse experiments. Column length, L (cm) 10.0 Péclet number, Pe Column diameter, d (cm) 1.0 LDF coefficients, ki (s−1 ) Total porosity,  0.57 Feed (overloaded), c F (g/l) 4.93, 5.48 Henry constants, Ki Linear-Langmuir isotherm, q∗i (g/L) = (4.452 cA , 5.031 cB ) + (0.443cA , 1.273cB )/(1 + 10.79cA + 15.44cB )

539.1 8.72, 8.72 1.1

Table 2 ¯ are: Operating parameters of optimal cycle for overloaded separation of reboxetine enantiomers (cf. Table 1). The parameter values of the NLP design problem (fobj = max F) nQ = 5, Qmax = 9.5 mL/min, Qmin = 0.5 mL/min, PXmin = 98.8% and RRmin = 90.0%. Flow rates are expressed in mL/min and denoted as follows: F, feed; E, eluent; X, extract, R, raffinate; Qj , zone j of equivalent two-column SMB.  (min) Step

4.226 F

E

X

R

Q1

Q2

Q3

Q4

1 2 3 4 5

0.642 0 0 0 0

0.618 3.091 1.553 1.618 1.679

0 0 1.553 1.618 1.679

1.260 3.091 0 0 0

0.618 3.091 1.553 1.618 1.679

0.618 3.091 0 0 0

1.260 3.091 0 0 0

0 0 0 0 0

Average

0.128

1.712

0.970

0.870

1.6 a

0a

0.4 a

0a

a

Average length, Nj , of the jth zone (j = I, . . . ,IV) of an equivalent two-column SMB, expressed as fractional number of columns.

ethanol (Panreac, Spain), and DEA (Sigma–Aldrich, Germany), were mixed in the appropriate volumetric proportions after filtration. The system was operated isothermally at 25 ◦ C. The analytical HPLC column is 150 × 4.6 mm i.d., packed with Chiralpak IA [amylose tri-(3,5-dimethylphenyl carbamate) immobilized on 5 ␮m silica gel], purchased from Daicel Chemical Industries Ltd (Chiral Technologies Europe, Illkirch, France). The UV detector placed in the circulation line of the two-column set-up (labeled as ‘Total signal’ in Fig. 4) at the outlet of column 1, was calibrated at a wavelength of 276 nm; the second UV detector, placed at the outlet of the analytical HPLC column, was calibrated at a wavelength of 230 nm. The sampling frequencies of the two UV’s were both fixed at 0.25 s−1 . The total bed porosity () was determined from the retention time of 1,3,5-tri-tert-butylbenzene (TTBB) (Sigma–Aldrich, Germany); this solute is not retained by the stationary phase but can access its internal porosity. The packing reproducibility was assessed by comparing the peak shapes and retention times of the chromatograms obtained with the two preparative columns; both columns were found to be identically, and reasonably well, packed. Extra-column volumes in the experimental set-up were estimated from TTBB pulse experiments with and without the two chromatographic columns. In the working range of fluid velocity used in preparative chromatography the Van Deemter plot is well approximated by a straight line [58]. The intercept and slope for each enantiomer, expressed here in terms of the Péclet number (Pe) and linear-driving-force (LDF) coefficient for mass-transfer (ki ), were determined by fitting the experimental dependence of the plate height on flow rate for diluted pulses of racemic mixture. The estimated values of these parameters are listed in Table 1. The experimental determination of adsorption isotherms is of utmost importance for the design and operation of any cyclic adsorption process. This statement holds true for the two-column chromatographic process under consideration, since its operating conditions cannot be properly determined without knowledge of the competitive isotherms of the two enantiomers. In the present work, the competitive isotherms were estimated with good accuracy by applying a hybrid inverse method described in detail elsewhere [60]. Briefly, a prescribed adsorption isotherm model—in the present case, the linear-Langmuir model—was coupled with the chromatographic column model described earlier

and fitted to experimental band profiles from overloaded injections of the racemic mixture and breakthrough data from a single frontal experiment. The latter were included to reduce the uncertainty on the estimated saturation capacity, due to dilution of the chromatograms with respect to the injected concentrations. The numerical constants of the isotherm model were tuned so that the calculated and measured band profiles matched as much as possible. The fitted parameters of the linear-Langmuir model are listed in Table 1.

6. Results and discussion From the Henry constants given in Table 1 it is possible to determine the value of ˛ under linear separation conditions (linear isotherm): ˛ = 1.088 [cf. Eq. (1)]; this value places the separation in the classification of difficult ones, as defined in Section 1. It is thus difficult to obtain both enantiomers with high purity and yield by HPLC for the chosen chromatographic conditions. Traditional solutions to this problem consist of increasing the column length or implementing a recycling strategy (e.g., steady-state recycling [33–35]). These modifications lead to a reduction of the specific productivity. Moreover, even though steady-state recycling increases purity and yield with respect to batch chromatography, it is difficult to apply in supercritical fluid chromatography because fluid recirculation is difficult to implement under those conditions. The process disclosed in the present work provides increased purity and yield using simple equipment and without the need for a recirculation pump. The optimal cycle for the two-column chromatograph was determined by solving the NLP design problem with the chromatographic parameters listed in Table 1, subject to minimal product purity and recovery, PXmin = 98.8% and RXmin = 90.0%, respectively (in the case of reboxetine’s racemate, the more retained enantiomer is the desired product). Five sub-divisions (nQ = 5) per switching interval were allocated for the piecewise-constant modulation of the flow rates, and Qmax was fixed at 9.5 mL/min. The optimal operating parameters are listed in Table 2 and schematic diagrams of the corresponding cycle are shown in Fig. 7. Fig. 7b shows a schematic of the port configuration’s chronogram for a full cycle of the two-column, open-loop chromatograph after merging identical steps into a single, larger step. Note that the

5414

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

Fig. 7. Chronogram of port switching and location of active inlet/ outlet lines for the two-column, open-loop chromatograph’s operating cycle. (a) Schematic for the nQ = 5 steps of the first switching interval of the cycle; the steps for the second switching interval of the cycle are identical but the column positions are reversed. (b) Schematic for a full cycle (2) after merging identical steps into a single (larger) step; the equivalent lengths of a standard four-zone SMB are indicated at far right. The steps delineated by a red, dotted outline provide the best schematic of the switching interval. Symbols F, R, E, and X denote the active feed, raffinate, eluent, and extract lines, respectively.

sequence in Fig. 7b is circular: the first step follows the last one, and that last precedes the first. Given that the step length is uniform, the switching interval may start with any of the steps shown in Fig. 7b, and not just with the uppermost one, as long as the ordering of the steps is obeyed. In fact, the clearest picture of the port configuration’s chronogram for a switching interval is given by the sequence of steps delineated by a red, dotted outline in Fig. 7b, and not by the three uppermost steps. The cycle is very simple and follows two rules: (i) the positioning of the feed step within the cycle follows the “golden rule” of counter-current processes—fresh feed is supplied into the system where the composition of the circulating fluid is closest to that of the feedstock fluid; and (ii) the two purified products are recovered alternately at the downstream end of the unit while desorbent is supplied into the upstream end of the system. These two rules characterize the distinctive aspects or properties of the process that differentiate it from other two-column configurations.

Fig. 8 shows the steady periodic solution of the enantiomeric concentration profiles at the outlet of the two columns for the first switching interval of the cycle, as well as the intervals over which the extract and raffinate products are collected. The same information is conveyed in Fig. 9 under the form of exit concentration profiles for column 1 over a full cycle (i.e., during two consecutive switching intervals). The intervals during which the extract and raffinate products are collected from column 1 are indicated, as in Fig. 8; also, the total enantiomeric concentration for the outlet effluent of column 1, which is the variable monitored by the UV labeled ‘Total signal’ in Fig. 5, is shown as a solid line. It is worth noting that Figs. 8 and 9 illustrate the two equivalent ways of looking at the cyclic steady state of the two-column chromatograph: either by tracing the steady periodic dynamics of the two columns over a single switching interval (Fig. 8) or by tracing the steady periodic dynamics of one of the columns over a full cycle (Fig. 9).

Fig. 8. Steady periodic solution of the enantiomeric concentration profiles (- - -, less retained; · · · , more retained) at the outlet of the two columns, over the first switching interval of the cycle, for the optimized scheme given in Table 2. Symbols R and X indicate the raffinate and extract withdrawal intervals, respectively.

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

Fig. 9. Steady periodic solution of the enantiomeric concentration profiles (- - -, less retained; · · · , more retained; —, total) at the outlet of column 1, over a full cycle, for the optimized scheme given in Table 2. Symbols R and X indicate the raffinate and extract withdrawal intervals, respectively.

It is tempting to explore the analogy between the operating cycle of the two-column chromatograph and that of an SMB, despite the concerns expressed in Section 1 about making such type of analogy. The cycle can be broadly classified as a NI /0/NIII /0 open-loop configuration with partial feed and selective product withdrawal, where NI , . . . , NIV are the standard four zones of the SMB and NI + NIII = 2; in the present case, NI = 1.6 and NIII = 0.4. This can be inferred from the last four columns of Table 2, which report the flow rates in terms of the standard four zones of an SMB, and from Fig. 7(b), which shows the chronogram of port switching and positioning of the active inlet/outlet lines over a cycle. The terms ‘partial’ and ‘selective’ are employed here to recognize that the system is only semi-continuous: it is not fed continuously but in pulsed form, and the two product streams are delivered alternately. Suppose that all four inlet/outlet ports are open in a two-column SMB; the only feasible port configuration that can accommodate this is the 1/0/1/0. With the purpose of exploring the analogy between the two systems, we therefore set both NII and NIV to zero and ensure that NI + NIII = 2. Moreover, a column is assumed to be in zone I of a classical SMB if it is supplied with fresh eluent or if it delivers extract; likewise, a column is assumed to be in zone III of a classical SMB if it is supplied with fresh feed or if it delivers raffinate. According to these rules, during the first two steps of the cycle column 2 plays the role of zone I of a classical SMB whereas column 1 plays the role of zone III; during the last three steps of the first switching interval both columns play the role of zone I. Over the second switching interval of the cycle the column positions are reversed, as seen in Fig 7(b). The material balance between columns provides the flow rates for zone II and zone IV. Thus the average length of zone I is

5415

Fig. 10. Temporal profile of total enantiomeric concentration for the outlet effluent of column 1. ◦, profile measured by the UV labeled ‘total signal’ in Fig. 4 at each sampling interval of the automated HPLC collector; —, steady periodic solution of the process model.

Fig. 11. Temporal profiles of individual enantiomer concentration for the outlet effluent of column 1. Symbols denote experimental data and lines represent the steady periodic solution of the process model (less-retained enantiomer: , ——; more-retained enantiomer: , - - - -). R and X denote the raffinate and extract withdrawal periods, respectively.

It is worth noting that the 1.6/0/0.4/0 port configuration is specific to the particular separation under study. The values of , NI , and NIII change whenever the process specifications or the difficulty of separation are altered5 . The difficulty of separation is, in

turn, governed by the separation factor, ˛ , and, to a lesser extent, by band broadening, which depends on the values of Pe and ki . The optimal cycle given in Table 2 was reproduced experimentally in our prototype apparatus. Upon completion of 11 cycles, a cyclic steady state was reached after which three more cycles were carried out to obtain the concentration curves shown in Figs. 10 and 11. The graph in Fig. 10 compares the simulated curve of total enantiomeric concentration for the outlet effluent of column 1 with the measurements obtained over the 11th–14th cycles using the UV detector labeled ‘Total signal’ in Fig. 5. The open circles are the conversion into concentration of the average UV signal for each sample collected in the automated analysis of the composition profile. There is excellent agreement between experimental

5 Our own experience [61,62] with different separations has shown that the period during which fresh feed is supplied into the system varies with ˛ and may

occur while raffinate is being collected, or while extract is being withdrawn, or may cross the boundary between raffinate and extract collects; see also [63].

¯I = N

3 2 × (1 column) + × (2 columns) = 1.6 columns 5 5

(19)

and that of zone III is ¯ III = N

2 × (1 column) = 0.4 columns. 5

(20)

5416

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

Fig. 12. Snapshot of BioCtr’s monitoring console taken when the concentrations of both enantiomers in the exit effluent of column 1 were high.

Fig. 13. Snapshot of BioCtr’s monitoring console taken while raffinate was being collected from the downstream end of column 1.

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

5417

Fig. 14. Snapshot of BioCtr’s monitoring console taken while extract was being collected from the downstream end of column 1.

and simulation profiles; they are quantitatively and qualitatively similar. Fig. 11 compares the individual enantiomeric concentration profiles at the outlet of column 1, measured during the 11th–14th

cycles of operation, with those predicted by process simulation. The symbols are the experimental profiles determined by HPLC analysis of the collected fractions in combination with the total UV measurement. Again, it is seen that there is a good match between the

Fig. 15. HPLC analysis of the extract and raffinate fractions collected during the 11th and 14th cycles of operation. Analytical chromatograms on Chiralpak IA (5 ␮m), 150 mm×4.6 mm i.d.; mobile phase: hexane/ethanol/DEA (90/10/0.2 v/v-%) at 25 ◦ C; flow rate: 3.3 mL/min; injection 100 ␮L; detector UV @ 276 nm. Symbols are experimental UV data, whereas lines (red, (R, R)-; blue, (S, S)-; green, total-reboxetine) represent the fitted sum of two EMG functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

5418

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

discrete concentration measurements and the simulated profiles; they are quantitatively and qualitatively similar. The method implemented to calculate the enantiomeric composition employs the chromatograms from the analytical column to compute the enantiomeric purity, which is then converted into individual concentrations using the total concentration value measured independently by the UV detector installed in the twocolumn apparatus. Each pair of chromatographic peaks detected per injection were fitted to the sum of two exponentially modified Gaussian functions (one per peak), by nonlinear least-squares curve fitting, to estimate the area under each peak. The procedure is described in more detail elsewhere [48]. The productivity achieved by the optimized cycle is 13.0 g of processed racemate per liter of column per day, while keeping the extract (where the desired product is collected) purity and recovery within the desired specifications (PXmin = 98.8%, RXmin = 90.0%). The productivity is expressed in terms of process parameters as

 Productivity

g L × day



=

c F F¯ , 2Vc

(21)

where F¯ is the average feed flow rate per cycle, c F is the total feed concentration (racemic mixture) and Vc is the column volume. Figs. 12–14 show snapshots of the BioCtr’s monitoring graphical interface taken at three instants of the cycle when the composition profiles at the downstream end of column 1 were significantly different from each other. Fig. 12 depicts BioCtr’s monitoring console when the concentration of both enantiomers was high; at this point, fresh feed was being supplied into the system at the upstream end of column 2. Fig. 13 was taken while raffinate was being collected from column 1. Fig. 14, on the other hand, was taken while extract was being collected from column 1. In all three figures, the upper-left window displays the variations in the flow rates of the two HPLC pumps, which supply feed and eluent to the system. The upper-right window shows a plot of total absorbance, which is proportional to the total enantiomeric concentration, measured by the UV detector labeled ‘Total signal’ in Fig. 5 and placed at the downstream end of column 1. The lowerleft window monitors the individual chromatograms of the two enantiomers, measured by the second UV detector placed at the outlet of the analytical HPLC column (Fig. 5). The window at lower right shows the periodic variation in the state of the six-port, twoposition valve. Most of the time, the six-port valve is in ‘inject position’ (value equal to zero) to direct the exit effluent of column 1 to column 2 along the red path depicted in Fig. 5. At fixed time intervals the six-port valve is switched to ‘load position’ (value equal to one) to divert the exit effluent of column 1 into the injection loop for collecting an internal sample. In all four windows, the monitored data are plotted as time-series with a moving x-axis, whose scale can be altered by the user at any time. As a final experimental verification that the process accomplished what it was intended to do, the extract and raffinate fractions collected during the 11th and 14th cycles of operation were stored separately and post-processed by off-line HPLC to determine their purities. The enantiomeric purity of each collected fraction was determined by fitting the sum of two EMG functions to the experimental chromatograms with the same analysis tools employed by the automated on-line enantiomeric monitoring system. The chromatograms shown in Fig. 15 indicate that the experimental extract purity is within the desired specification (PXmin ≥ 98.8%). Using the experimental values of the extract and raffinate purities, PX = 0.989 and PR = 0.901, respectively, and the flow rate data listed in Table 2, it is possible to determine the extract recovery; its value, RX = 0.891, is practically within specification (RXmin ≥ 90.0%).

Fig. 16. Influence of raffinate purity, PR (%), on productivity (expressed by the aver¯ solvent consumption, E/ ¯ F, ¯ and switching interval, , for the age feed flow rate, F), separation of reboxetine enantiomers by the two-column, open-loop chromatograph; the extract purity is fixed at PX = 99%. Each trend line is scaled by the value of the corresponding performance parameter obtained for PR = 90%.

If we concluded at this point, it would be legitimate to question whether the two-column chromatograph can handle or not higher purity constraints on both products. Fig. 16 shows that it can. This figure displays the influence of the raffinate purity (PR ) on the pro¯ solvent consumption (E/ ¯ F), ¯ ductivity (which is proportional to F), and switching interval () for a fixed extract purity of PX = 0.99; the extract purities range from 0.90 to 0.99. The trend lines were scaled by the values of the corresponding performance parameters obtained for PR = 90% in order to plot the lines on a single graphic. Given that the extract recovery correlates very well with the raffinate purity, RX can replace PR on the x-axis of Fig. 16. Either way, Fig. 16 shows that the two-column, open-loop cycle depicted in Fig. 7 can resolve both enantiomers with 99% purities and similarly high recoveries. As expected, the process is forced to decrease its productivity and to augment its solvent consumption in order to meet an increasing raffinate purity (or extract recovery). If PR is increased ¯ F¯ increases by 23%. For from 0.9 to 0.99, F¯ diminishes by 20% and E/ the separation under study, the interval during which fresh feed is supplied into the system occurs always while extract is being collected. As PR is increased, the extract is collected over a larger time interval, whereas both the feed and raffinate-withdrawal steps are shortened. Consequently, NI grows smaller and NIII larger as PR is increased. This also explains why the switching interval is insensitive to changes in PR . 7. Conclusions In the present work, a two-column, semi-continuous, openloop chromatograph for enantioseparation, which is particularly effective when the resolution is limited, was presented. The experimental set-up and its operation are nearly as simple as those of batch chromatography and not more complex than those of batch chromatography with recycle. The compact two-column system relies on a flexible node design and optimized flow-rate modulation to implement a hybrid scheme between batch and simulated counter-current chromatography modes. It is worth pointing out, however, that our process can also be operated with desorbent being supplied to the system at a constant flow rate. The two-column chromatograph is a compromise between continuous multi-column processes and traditional batch chromatography,

J.M.M. Araújo et al. / J. Chromatogr. A 1217 (2010) 5407–5419

constrained by the requirement of an open-loop configuration; it combines the simplicity and flexibility of the batch process and the increased productivity of multi-column chromatography. A proof of concept and experimental validation were successfully accomplished using the separation of the enantiomers of reboxetine under overloaded conditions. When applied to this unfavorable chiral separation, the two-column chromatograph yielded good purity and recovery. In the context of chiral considerations and chiral switches, compact two-column, open-loop chromatography is an attractive method, because of its simplicity of implementation, low running costs, and easiness of scaling-up. Acknowledgements Financial support from FCT/ MCTES (Portugal), through grants SFRH/ BD/13721/2003, SFRH/ BPD/48366/2008, and PTDC/ EBBBIO/101992/2008 is gratefully acknowledged. References [1] Food and Drug Administration, Chirality 4 (1992) 338. [2] R.M. Nicoud, G. Fuchs, P. Adam, M. Bailly, E. Küsters, F.D. Antia, R. Reuille, E. Schmid, Chirality 5 (1993) 267. [3] M. Juza, M. Mazzotti, M. Morbidelli, Trends Biotech. 18 (2000) 108. [4] P. Adam, R.M. Nicoud, M. Bailly, O. Ludemann-Hombourger, US Patent 6,136,198 (2000). [5] O. Ludemann-Hombourger, R.M. Nicoud, M. Bailly, Sep. Sci. Technol. 35 (2000) 1829. [6] A. Toumi, F. Hanisch, S. Engell, Ind. Chem. Res. 41 (2002) 4328. [7] H. Schramm, M. Kaspereit, A. Kienle, A. Seidel-Morgenstern, Chem. Eng. Technol. 25 (2002) 1151. [8] H. Schramm, A. Kienle, M. Kaspereit, A. Seidel-Morgenstern, Chem. Eng. Sci. 58 (2003) 5217. [9] M.M. Kearney, K.L. Hieb, US Patent 5,102,553 (1992). [10] E. Kloppenburg, E.D. Gilles, Chem. Eng. Technol. 22 (1999) 813. [11] Z.Y. Zhang, M. Mazzotti, M. Morbidelli, J. Chromatogr. A 1006 (2003) 87. [12] Z. Zhang, M. Mazzotti, M. Morbidelli, AIChE J. 50 (2004) 3. [13] Y.F. Zang, P.C. Wankat, Ind. Eng. Chem. Res. 41 (2002) 2504. [14] T.B. Jensen, T.G.P. Reijns, H.A.H. Billiet, L.A.M. van der Wielen, J. Chromatogr. A 863 (2000) 149. [15] D. Antos, A. Seidel-Morgenstern, J. Chromatogr. A 944 (2002) 77. [16] S. Abel, M. Mazzotti, M. Morbidelli, J. Chromatogr. A 994 (2002) 23. [17] D.M. Ruthven, C.B. Ching, Chem. Eng. Sci. 44 (1989) 1011. [18] J.P. Meissner, G. Carta, Ind. Eng. Chem. Res. 41 (2002) 4722. [19] Y. Zang, P.C. Wankat, Ind. Eng. Chem. Res. 41 (2002) 5283. [20] Y. Kawajiri, L.T. Biegler, Ind. Eng. Chem. Res. 45 (2006) 8503. [21] R.C.R. Rodrigues, J.M.M. Araújo, J.P.B. Mota, J. Chromatogr. A 1162 (2007) 14. [22] J.P.B. Mota, I.A.A.C. Esteves, M.F.J. Eusébio, AIChE J. 53 (2007) 1192. [23] C.Y. Chin, N.H.L. Wang, Sep. Purif. Rev. 33 (2004) 77. [24] K. Lee, Sep. Sci. Technol. 35 (2000) 519. [25] M. Ando, M. Tanimura, M. Tamura, US PAtent 4,970,002 (1990). [26] W. Jin, P.C. Wankat, Ind. Eng. Chem. Res. 44 (2005) 1565. [27] W. Jin, P.C. Wankat, Ind. Eng. Chem. Res. 45 (2006) 2793.

[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

[41] [42] [43] [44] [45] [46] [47]

[48] [49] [50] [51] [52] [53] [54] [55]

[56] [57] [58] [59] [60] [61] [62]

[63]

5419

N. Abunasser, P.C. Wankat, Ind. Eng. Chem. Res. 43 (2004) 5291. J.P.B. Mota, J.M.M. Araújo, AIChE J. 51 (2005) 1641. J.M.M. Araújo, R.C.R. Rodrigues, J.P.B. Mota, Ads. Sci. Tech. 25 (2007) 647. R.C.R. Rodrigues, T.J.S.B. Canhoto, J.M.M. Araújo, J.P.B. Mota, J. Chromatogr. A 1180 (2008) 42. P.C. Wankat, Ind. Eng. Chem. Res. 40 (2001) 6185. C.M. Grill, J. Chromatogr. A 796 (1998) 101. C.M. Grill, L. Miller, J. Chromatogr. A 827 (1998) 359. ˜ I. Quinones, C.M. Grill, L. Miller, G. Cuiochon, J. Chromatogr. A 867 (2000) 1. M. Tanimura, M. Tamura, T. Teshima, Japanese Patent JP-B-H07-046097 (1995). P. Dostert, M.S. Benedetti, I. Poggesi, Eur. Neuropsychopharm. 7 (1997) 23. P. Melloni, A. Delia Torre, E. Lazzari, G. Mazzini, M. Meroni, Tetrahedron 41 (1985) 1393. T. Denolle, C. Pellizzoni, M.G. Jannusso, I. Poggesi, Clin. Pharmacol. Ther. 66 (1999) 282. M.F.J. Eusébio, Development of an Universal Interface for Monitoring and Control of Chemical and Biochemical Processes, Ph.D. Thesis. Universidade Nova de Lisboa, Lisboa, Portugal, 2006 (in Portuguese). O. Ludemann-Hombourger, R.M. Nicoud, M. Bailly, Sep. Sci. Technol. 35 (2000) 1829. ¨ F. Kastner, A. Mannschreck, J. Chromatogr. 351 (1986) 346. K.-H. Rimbck, G. Zenoni, M.P. Pedeferri, M. Mazzotti, M. Morbidelli, J. Chromatogr. A 888 (2000) 73. C. Roussel, N. Vanthuyne, M. Serradeil-Albalat, J.-C. Vallejos, J. Chromatogr. A 995 (2003) 79. A. Ghanem, J. Chromatogr. A 1132 (2006) 329. M. Morari, Presentation 287a at 2006 AIChE Annual Meeting, San Francisco, CA, November, 2006. M. Mazzotti, Presentation L-201 at PREP 2007—20th International Symposium on Preparative/ Process Chromatography, Baltimore MD June 3–6, 2007, pp. 12–17. J.M.M. Araújo, R.C.R. Rodrigues, M.F.J. Eusébio, J.P.B. Mota, J. Chromatogr. A 1189 (2008) 292. M.C. Ferris, J.S. Pang (Eds.), Complementarity and Variational Problems: State of the Art, SIAM Publications, Philadelphia, PA, 1997. J.M.M. Araújo, R.C.R. Rodrigues, J.P.B. Mota, Ind. Eng. Chem. Res. 45 (2006) 5314. J.M.M. Araújo, R.C.R. Rodrigues, J.P.B. Mota, J. Chromatogr. A 1132 (2006) 76. J.P.B. Mota, E. Saatdjian, D. Tondeur, A.E. Rodrigues, Comp. Chem. Eng. 21 (1997) 387. B.T. Baumrucker, J.G. Renfro, L.T. Biegler, Comput. Chem. Eng. 32 (2008) 2903. Y. Kawajiri, L.T. Biegler, AIChE J. 52 (2006) 1343. R. Fourer, D.M. Gay, B.W. Kernighan, AMP: A Modeling Language for Mathematical Programming, 2nd edition, Brooks/Cole-Thomson Learning, Pacific Grove, CA, 2003. A. Wachter, L.T. Biegler, Math. Prog. 106 (2005) 25. R.C.R. Rodrigues, J.M.M. Araújo, M.F.J. Eusébio, J.P.B. Mota, J. Chromatogr. A 1142 (2006) 69. G. Guiochon, S. Golshan-Shirazi, A. Katti, Fundamentals of Preparative and Nonlinear Chromatography, Academic Press, Boston, MA, 1994. M.A. Raggi, R. Mandrioli, C. Sabbioni, C. Parenti, G. Cannazza, S. Fanali, Electrophoresis 23 (2002) 1870. J.M.M. Araújo, R.C.R. Rodrigues, J.P.B. Mota, J. Chromatogr. A 1189 (2008) 302. R.C.R. Rodrigues, Compact SMB Chromatography for Binary Separation, PhD Thesis, Universidade Nova de Lisboa, Portugal, 2008. J.M.M. Araújo, Optimal Design and Operation of Compact Simulated MovingBed Processes for Enantioseparations, PhD Thesis, Universidade Nova de Lisboa, Portugal, 2009. E. Valéry, O. Ludemann-Hombourger, World Patent WO 2007/012750 A2.