Experimental Optimizing Control of the Simulated Moving Bed

Jun 7, 2010 - Phone: +41-44-6322456. ... Simulated moving bed (SMB) chromatography has become a well-established technique in the ... For the investig...
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Ind. Eng. Chem. Res. 2010, 49, 11996–12003

Experimental Optimizing Control of the Simulated Moving Bed Separation of Tro¨ger’s Base Enantiomers Christian Langel,† Cristian Grossmann,‡ Simon Jermann,† Marco Mazzotti,*,† Manfred Morari,‡ and Massimo Morbidelli§ ETH Zurich, Institute of Process Engineering, Sonneggstrasse 3, 8092 Zurich, Switzerland, ETH Zurich, Automatic Control Laboratory, Physikstrasse 3, 8092 Zurich, Switzerland, and ETH Zurich, Institute for Chemical and Bioengineering, Wolfgang-Pauli-Str. 10, 8093 Zurich, Switzerland

Simulated moving bed (SMB) chromatography has become a well-established technique in the pharmaceutical industry and biotechnology for the separation of enantiomers. However, exploiting the full economic potential of the process is not trivial, and therefore, we developed a “cycle-to-cycle” optimizing controller to facilitate the operation of SMB units close to the economic optimum. The proposed controller only requires the information about the linear adsorption behavior and the average porosity of the columns. This paper presents the different steps required to set up our controller for a given separation problem, namely the separation of Tro¨ger’s Base enantiomers. For the investigated system, the complete adsorption isotherm is available which allows us to carry out detailed simulations and to compare them to the actual experiments. Hence, one can judge how well the simulations can predict both the dynamic and the steady state behavior of the controller at different feed concentrations. The paper demonstrates that the control concept is simple enough to be implemented quickly and reliably for a new separation campaign within three days. Furthermore, the experimental results clearly show that despite process disturbances the controller is able to fulfill the product specifications and to improve the process performance. 1. Introduction Simulated moving bed (SMB) chromatography is a continuous countercurrent multicolumn chromatographic process that is generally applied to separate a feed mixture into two product streams.1 Because of its efficient use of the solvent and of the packing material, hence of the high productivity, SMB chromatography has become a widely applied technique especially for the separation of enantiomers.2 However, even for experienced SMB practitioners robust operation of SMB units close to the economic optimum still remains a challenge, therefore, SMBs are most often operated without exploiting the full economic potential. In order to address this issue, different research groups have developed control schemes for the operation of SMB units.3-12 In general the bottleneck of these approaches is the need for accurate adsorption data of the system under consideration, i.e. the complete binary adsorption isotherm. The control concept developed at ETH Zurich is only based on the knowledge about the linear adsorption behavior, namely the Henry’s constants and the average void fraction of the columns installed in the SMB unit. In previous publications, the effectiveness of the control scheme was proven with simulations as well as with experiments for the separation of achiral and chiral compounds under linear and nonlinear operating conditions.13-17 More recently our group developed and implemented a new automated online HPLC monitoring system to overcome the problems encountered to monitor the concentration of both enantiomers in the two product streams18 when using online optical detectors, such as UV detector and * To whom correspondence should be addressed. Phone: +41-446322456. Fax: +41-44-6321141. E-mail: [email protected]. ethz.ch. † Institute of Process Engineering. ‡ Automatic Control Laboratory. § Institute for Chemical and Bioengineering.

polarimeter.17 The quality of the concentration measurements is essential since they are required as feedback information by the controller, whose performance is directly affected by these measurements. A schematic of the proposed control scheme has been shown for example in Figure 2 of a recent paper.18 The optimizing controller is based on a simplified first principle SMB model. The required model parameters, i.e. Henry’s constants and average void fraction, can easily be obtained within short time by performing standard pulse injection experiments under diluted conditions. The measured variables are the concentrations of the two enantiomers in both product streams averaged over one cycle, which are obtained from the automated online HPLC monitoring system. The measurements together with the simplified SMB model and the Kalman filter are used to estimate the current state of the SMB unit. On the basis of the state estimate, the controller is able to predict the evolution of the separation and calculates a set of input variables, i.e. the SMB internal flow rates, for the next process cycle by minimizing a cost function which is subjected to several constraints, e.g. minimal product purity requirements and process operation constraints. The operational constraints as well as the product specifications can be imposed in a straightforward manner within the control formulation due to the model-based nature of the controller. In the present setup, a constant switch time, t*, is used which is predefined and chosen based on maximum allowable pressure drop considerations. For more details about the formulation of the optimization problem and its solution, the reader is referred to a previous paper.19 This work presents the different steps required to set up our “cycle-to-cycle” controller for a given separation problem, i.e. characterizing the system, setting up the online monitoring system and developing the controller, for the case of Tro¨ger’s Base enantiomers separation. In addition, the results of detailed simulations are compared to experiments in order to understand how well the simulations can predict both the steady state and

10.1021/ie100419w  2010 American Chemical Society Published on Web 06/07/2010

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the dynamic behavior of the controller under nonlinear chromatographic conditions. Furthermore, the disturbance rejection behavior of the controller is investigated and discussed.

Table 1. Results of the Column Pulse Injections with an Ethanol Mobile Phase and CHIRALPAK AD as the Stationary Phase at 23°Ca

2. Experimental Setup 2.1. SMB Unit. The laboratory SMB unit used eight chromatographic columns (10 cm long with 1 cm internal diameter), arranged in the 2-2-2-2 configuration, and was operated in the closed loop mode in order to reduce desorbent consumption. The SMB unit was located in a temperature controlled room to ensure isothermal operating conditions at T ) 23 °C. Note that the extra-column dead volume, VDj , was accounted for in the calculation of the dimensionless flow rate ratios mj:20 Qjt* - Vε* - VDj mj ) V(1 - ε*)

(j ) 1, ..., 4)

(1)

where V, t*, Qj, and ε* are the column volume, the switch time, the flow rate in section j, and the overall bed void fraction, respectively. For all four sections of the SMB unit, VDj ) 0.133 mL.21 2.2. Online Monitoring System. This section describes the main ideas and working principle of the automated online HPLC monitoring system (referred to as AMS) that was recently developed and presented in detail elsewhere.18 The two main parts of the AMS are an HPLC unit for sample analysis (Agilent LC 1200, Santa Clara, USA) and a custom-made automated sample collecting system for the two product streams, extract and raffinate, whose detailed flowsheet has been reported elsewhere.18 The system consists of four glass tanks (E1, E2, R1, R2) to alternately collect the two product streams over one process cycle, i.e. switch time multiplied by the number of columns present in the unit. The HPLC is equipped with an analytical CHIRALPAK AD column (25 cm × 0.46 cm) which is kept in a temperature-controlled column compartment at 23 °C. The AMS collects the two product streams in separate glass tanks (e.g., E1 and R1) over one process cycle. During the next process cycle, the AMS takes samples from these tanks and injects them to the HPLC, empties and flushes these tanks, and at the same time collects the product streams in the other two glass tanks (e.g., E2 and R2). The HPLC automatically analyzes the injected samples and returns the concentrations of the two enantiomers in both product streams averaged over one cycle as feedback information to the controller. 3. Materials and Characterization 3.1. Chiral Stationary Phase and Retention Behavior. For the experiments, a racemic mixture of Tro¨ger’s Base enantiomers (provided by Bayer Technology Services GmbH, Leverkusen, Germany) was separated using CHIRALPAK AD (Chiral Technologies Europe, Illkirch, France), an amylose based chiral stationary phase (amylose tris(3,5dimethylphenylcarbamate) coated on silica) and ethanol as mobile phase. The material has a particle size of 20 µm and was slurry packed in nine standard stainless steel columns (10 cm × 1 cm) by Bayer Technology Services GmbH, Leverkusen, Germany. Before installing the columns in the SMB unit, they had been checked using the HPLC to determine the Henry’s constants as well as the average void fraction of the columns to verify their uniform properties. Moreover, these parameters are required as input information for the simplified model of the controller.

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a

column no.

HA

HB

ε*

1 2 3 4 5 6 7 8 9 average

5.19 5.32 5.25 5.43 5.53 5.41 5.37 5.21 5.33 5.34

2.00 2.08 2.04 2.14 2.15 2.10 2.07 2.02 2.07 2.07

0.75 0.75 0.76 0.75 0.76 0.75 0.75 0.76 0.75 0.75

cA ) cB ) 0.01 g/L; Vinj ) 20 µL; Q ) 1 mL/min.

To determine the overall void fraction of the columns, pulse injection experiments are carried out injecting a nonretained compound, in this case a mixture of isopropanol and ethanol in pure ethanol, and measuring its retention time t0. The overall void fraction is given by ε* )

t0Q V

(2)

where the extra-column dead volume of the HPLC was taken into account. The Henry’s constants Hi were obtained from the retention time of the two enantiomers under linear operating conditions and calculated as Hi )

(

tR,i - t0 ε* 1 - ε* t0

)

(i ) A, B)

(3)

where tR, i is the residence time of component i corrected with the dead time of the HPLC. From now on, the more and the less retained enantiomers will be referred to as component A and B, respectively. Table 1 summarizes the results; the average values were used for the controller. For the Tro¨ger’s Base enantiomers on CHIRALPAK AD, using ethanol as the mobile phase, the bi-Langmuir adsorption isotherm was determined previously:22 ni )

Hi,1ci 1+

∑K

i,1ci

Hi,2ci

+ 1+

∑K

(i ) A, B)

i,2ci

(4)

Although the nonlinear adsorption isotherm is not needed by the controller, hence it is not used for the experiments, it is necessary in order to run virtual experiments where the real plant is replaced by the detailed process model, including the complete nonlinear adsorption isotherm. However, the isotherm above was measured on different columns and on a different batch of the same stationary phase material. As a consequence, the parameters were determined again to be consistent with those in Table 1, and the new values are reported in Table 2 and differ only slightly from the values in ref 22. 3.2. Uncontrolled SMB Experiments. The purpose of the uncontrolled runs at low feed concentration is to test and verify the separation performance of the SMB unit without applying the controller and to confirm the Henry’s constants reported in Table 1. The region of complete separation according to the triangle theory and calculated using the Henry’s constants in Table 1 is shown in Figure 1a. Five experiments were carried out at a constant switch time of 180 s and at a constant feed concentration of 0.75 g/L, i.e. under linear chromatographic conditions. The operating

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Table 2. Column and System Parameters system characteristics

A

B

Hi,1 [-] Ki,1 [L/g] Hi,2 [-] Ki,2 [L/g] ks,iav [1/s]a εbDax,i/u [m]b ε* [-]

4.28 0.011 1.06 0.601 1.81

1.74 0.013 0.34 0.136 2.96 3.01 × 10-4 0.75

a Product of mass transfer coefficient and specific surface. Coefficient to determine the dispersion coefficient, where εb is the bed void fraction and u the superficial velocity.

b

Figure 2. Typical chromatogram of the two successive sample injections at a flow rate of 1.1 mL/min, recorded at a wavelength of 260 nm.

with respect to the linear region of complete separation predicted by the triangle theory. 4. Application of the Optimizing Controller to a New Separation

Figure 1. (a) Triangles of complete separation together with the position of the operating points 1-5: linear triangle (dashed line) and triangles for increasing feed concentration, i.e. 0.75, 4.0, 8.0, 10.0, and 16.0 g/L (solid lines). (b) Product purities vs m2 for runs 1-5. The dotted lines indicate the boundaries of the complete separation region in terms of m2. Table 3. Operating Conditions and Product Purities for the Uncontrolled Experimentsa run

m1

m2

m3

m4

PE

PR

1 2 3 4 5

6.10 6.10 6.30 7.10 7.60

1.55 2.15 2.75 3.35 3.95

3.50 4.10 4.70 5.30 5.90

0.50 0.50 0.50 1.00 1.45

78.9 99.2 99.7 99.8 99.8

99.5 99.6 99.3 98.9 80.2

a

In all experiments, t* ) 180 s.

conditions in terms of mj values are listed in Table 3, and the corresponding operating points are also shown in Figure 1a. As far as sections 1 and 4 are concerned, m1 and m4 were chosen to guarantee complete regeneration of the stationary and mobile phase, respectively. The purities of the extract and raffinate averaged over one cycle at steady state are reported in Table 3; they are also plotted as a function of m2 in Figure 1b. By comparing Figures 1a and b, a good agreement can be found between the experimental separation performance and the position of the operating points

4.1. Setting up the Online Monitoring System. Two main issues have to be addressed when tuning the online monitoring system for a new separation. On the one hand, at the beginning of a new cycle, the HPLC needs to be ready for the next sample injection; hence, the time required for the HPLC analysis needs to be smaller than the cycle time of the SMB process. On the other hand, the time between the injection of two successive samples must be chosen to be long enough to avoid overlapping of the peaks. This is required to ensure baseline separation of the peaks and to allow for an accurate determination of the peak areas. Figure 2 shows a typical UV signal during the analysis of two successive samples. The analytical column in the HPLC unit was tested in the same manner as the SMB columns, thus obtaining similar values for the Henry’s constants, namely HB ) 2.05 and HA ) 5.30, while the void fraction was determined to be ε* ) 0.71. In the present case, a good compromise between resolution of the peaks and retention time was found for a flow rate of 1.1 mL/min using pure ethanol as the mobile phase and a waiting time of 8.25 min between two sample injections. Note that the mobile and stationary phases for the analysis in the HPLC and for the SMB unit do not necessarily have to be same. However, when using different solvents, it should be taken into account that injecting a sample with a mobile phase composition different from the one used in the HPLC can generate additional solvent peaks that might interfere with the product peaks. 4.2. Controller. The only information about the system behavior required by the controller is the Henry constants of the two enantiomers to be separated and the average overall void fraction of the columns used in the SMB unit. On the basis of this information, the controller’s code for the new separation task is built automatically as described elsewhere.19 In order to speed up the controller’s implementation and to prove its robustness, we used the same controller’s parameters adopted for a previous separation,23 without doing any ad hoc tuning. 5. Results and Discussion 5.1. Set Point Tracking at Increasing Feed Concentrations. This part of the work has two main purposes, namely to demonstrate that the controller can be successfully applied under

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Table 4. Initial and Final Operating Points for All Controlled Experiments Together with the Values of the Productivity Achieved at the Final Operating Pointa run A

m1 [-] m2 [-] m3 [-] m4 [-] cFT [g/L] PR [g/(min L)] a

run B

run C

run D

run E

initial point

exp

simul

exp

simul

exp

simul

simul

simul

6.23 1.73 5.93 1.531

6.37 1.90 4.96 1.20

6.06 1.95 5.12 1.34

5.92 1.75 4.55 0.05

5.68 1.77 4.56 0.53

5.28 1.58 3.98 0.18

5.52 1.67 4.22 0.29

0.10

0.47

0.46

0.80

5.47 1.63 4.09 0.16 10.0 1.03

5.38 1.55 3.79 -0.12 16.0 1.50

0.75 0.10

4.0

8.0 0.85

The switch time t* ) 180 s.

nonlinear chromatographic conditions, i.e. at high feed concentrations, and to compare the controller’s behavior when applied to the real plant and to a virtual plant, i.e. where the plant is substituted by a detailed SMB process simulator. In a series of three experiments and five simulation runs increasing total feed concentrations were considered, ranging from 0.75 to 16.0 g/L. The operating parameters of the different runs are reported in Table 4 in terms of initial mj values (same in all experiments), feed concentration, final mj values, and corresponding productivity achieved. The latter is defined as PR )

(m3 - m2)cFT QFcFT ) ncolV(1 - ε*) ncolt*

(5)

where QF, cTF, V, and ncol are the feed flow rate, the total feed concentration, the column volume, and the number of columns, respectively. All experiments and simulations were carried out at a switch time of t*) 180 s. The adsorption isotherm parameters used for the detailed simulations are those reported in Table 2. For all the runs, the same minimal purity requirements were specified, namely 98.5% for both product streams. For the experiments, the unit was always started up with clean columns, i.e. the unit was carefully flushed with pure solvent before every new experiment to remove any adsorbed component from the stationary phase material, and the lab temperature was kept constant at T ) 23 °C. Figures 3-5 show the evolution of the product purities as a function of the cycle number together with the trajectory of the operating conditions in the (m2, m3) plane for the three runs A-C. In particular, parts a and b show the results obtained for the experimental runs and for the simulations, respectively. Moreover, in the (m2, m3) plane parts of the boundaries of the corresponding triangle of complete separation, calculated for the bi-Langmuir adsorption isotherm of Table 2, are drawn for the different total feed concentrations. For the sake of comparison in Figure 1a, the entire regions of complete separation for the different feed concentrations considered in this study are shown. For all three experiments and simulations, the controller fulfills the product specifications within less than 40 process cycles, as it can be seen in Figures 3-5. With reference to run A in Figure 3, it is worth noting that the raffinate purity exhibits an overshoot with respect to the specification (at about cycle 8) and an undershoot (at about cycle 27). The same qualitative behavior is also observed in the simulations of runs A, B, and C (Figures 3b-5b). This is a consequence of the interplay between the two controller’s objectives, namely fulfilling purity specification and improving productivity. The controller typically achieves the former objective first and then the latter. Overshoots and undershoots are likely to occur in this dynamic evolution, but could in principle be eliminated by

Figure 3. Purities of the product streams as a function of time measured in cycles together with the trajectory in the (m2, m3) plane and the triangle of complete separation for cFT ) 0.75 g/L: (a) experiment; (b) simulation. The filled circle and the triangle indicate the position of the initial and final operating point, respectively.

fine-tuning of the controller’s parameters. That is exactly what we did not do (as discussed in section 4.2) in order to demonstrate the controller’s robustness. The trajectories in the (m2, m3) plane reflect the dynamic behavior of the controller: comparing the trajectories of experiment and simulation at a specific feed concentration, e.g. 4.0 g/L as shown in Figure 4, reveals that the dynamic behavior of the experimental plant is well-predicted by the detailed simulation. The same is true for the results obtained at 0.75 and 8.0 g/L, as shown in Figures 3 and 5. The final operating points reached by the controller, which correspond to the point of maximal productivity that can be achieved while guaranteeing the product specifications, are plotted using a different symbol in the (m2, m3) plane of Figures 3-5, i.e. triangles, squares, and diamonds, respectively. Plotting both the final operating points and the triangles of complete separation for the different total feed concentrations together in the same Figure 6 facilitates the comparison between experiments (filled symbols) and simulations (open symbols) and allows to identify the trends

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Figure 6. Position of the final operating points in the (m2, m3) plane for runs A-E together with the triangles of complete separation calculated for a bi-Langmuir isotherm; experiments (filled symbols), simulations (open symbol).

Figure 4. Purities of the product streams as a function of time measured in cycles together with the trajectory in the (m2, m3) plane and the triangle of complete separation for cFT ) 4.0 g/L: (a) experiment; (b) simulation. The filled circle and the square indicate the position of the initial and final operating point, respectively.

Figure 5. Purities of the product streams as a function of time measured in cycles together with the trajectory in the (m2, m3) plane and the triangle of complete separation for cFT ) 8.0 g/L: (a) experiment; (b) simulation. The filled circle and the diamond indicate the position of the initial and final operating point, respectively.

observed for increasing feed concentrations. As to the position of the final operating points, one can observe the same trend for the experiments and the simulations, namely with increasing feed concentration the final operating point shifts downward to the left. This is in good agreement with the position of the vertices of the triangles of complete separation predicted by triangle theory for a bi-Langmuir adsorption isotherm. Comparing simulations and experiments, it can readily be seen that in the case of 4.0 g/L the final operating points almost lie on top of each other, whereas in the other two cases the experimental points are shifted further downward to the left. The productivity values reported in Table 4 and calculated at steady state conditions using the final values for m2 and m3 increase with increasing total feed concentration from run A to E, as expected for a bi-Langmuir type adsorption isotherm. The experiments have shown that the optimizing controller is capable of fulfilling the process and product specifications for a separation problem governed by a bi-Langmuir adsorption isotherm well into the nonlinear chromatographic regime even though it is based on the information about the linear adsorption behavior, only. Besides, we could demonstrate that the experimental and the simulated behaviors of the controller agree well in terms of both dynamic evolution and steady state operation even under nonlinear chromatographic conditions. 5.2. Disturbance Rejection. 5.2.1. Column Overpressure. In this section, we discuss an experiment where a major problem occurred to one of the SMB columns, because it is interesting to see what reaction of the controller was triggered by it. The experiment was carried out under the same conditions as reported in Table 4 for run A. After 28 cycles, the extract purity dropped significantly below the specifications, but within 10 process cycles the controller rejected the disturbance and recovered the purity specifications, as shown in Figure 8a. During the last phase of this experiment from cycle 38 on, the controller reduced the step size and began to improve the separation performance of the unit by slowly increasing m3, i.e. increasing the feed flow rate (see Figure 7). After the experiment, the whole unit was carefully checked in order to investigate the unexpected behavior of the plant. The troubleshooting revealed that in one of the columns the stationary phase had started to leak out, possibly due to a damaged outlet frit. This incident had caused blockage of the next column inlet and had led to a steadily increasing

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Figure 7. Disturbed run due to column overpressure: trajectory in the (m2, m3) plane and the triangle of complete separation for cFT ) 0.75 g/L. The filled circle and the star indicate the position of the initial and final operating point, respectively.

Figure 9. Feed pump disturbance. (a) Product purities as a function of time measured in cycles. After 75 cycles, the feed pump delivers 7.5% more flow than its set point. Total feed concentration cFT ) 8.0 g/L. (b) Feed flow rate as a function of time measured in cycles.

Figure 8. Disturbed run due to column overpressure: (a) Purities of the product streams as function of time measured in cycles where the same conditions as in run A were applied. (b) Pressure profile at one column outlet as function of time measured in cycles. For the sake of clarity, the trend of the pressure profile is indicated with a thick solid line.

pressure inside the unit, starting at about cycle 25 as shown in Figure 8b, where the pressure profile measured within the SMB unit as a function of the cycle number is also plotted. The synchronicity between pressure increase and purity drop, as well as the fact that after replacing the leaking column the purity problem never occurred again in this form, made us to reach two conclusions. First, the two events were causally correlated. Second, the controller reacted remarkably well in a critical situation and was able to recover the specified purities in a few cycles as in all the other cases

where the operator generated a disturbance on purpose (see the next section). 5.2.2. Feed Pump Malfunctioning. The second disturbance was planned, and introduced, to simulate one of the common problems SMB practitioners experience, namely the malfunctioning of a pump. In an SMB operation, it is essential that the pumps deliver precise and constant flow rates over a long period of time to ensure the correct flows in the different sections of the SMB and to keep the unit at a constant operating point. However, in practice it is often observed that the actual flow rates of the pumps drift away from the set point implemented at the beginning of the operation. This can result in a loss of product purities. For the current case study, run C was disturbed by changing, from cycle 75, the calibration factor of the feed pump. As a result and for the rest of the operation, the flow delivered by the feed pump to the SMB unit differed from the one dictated by the controller. Note that this disturbance was unknown to the controller and that the controller could only react to the feedback information that purities were drifting away from the specified values. More specifically, after cycle 75 the feed pump delivered 7.5% more flow than assigned by the controller, as shown in Figure 9b. An increase of the feed flow rate results in an increase of the flow rates in sections 3 and 4, thus implying that the operating point is shifted upward in the (m2, m3) plane toward the region of pure extract and that a loss of raffinate purity follows as it in fact appears in Figure 9a. From cycle 80 on, the raffinate purity was below the required specifications (about 92%), but within less than 10 cycles the controller recovered the purity specifications. The disturbance rejection behavior of the controller reflects nicely its two main tasks. As soon as the controller realized that

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the raffinate purity no longer met the product specifications, it reduced the flow rate in section 3 by reducing the feed flow rate, in order to recover the raffinate purity as soon as possible (see Figure 9b). Once the purities were back in spec, the controller slowly increased the feed flow rate to improve the performance of the separation in terms of feed throughput. However, one can easily see from Figure 9b that before and after the disturbance the controller did not yet attain steady state conditions but was still increasing the feed flow rate to improve the separation performance. This result clearly demonstrates that the optimizing controller is able to efficiently reject pump disturbances and to improve the process in terms of feed throughput despite the occurrence of a feed pump disturbance. 6. Conclusions In this paper, we have presented the experimental implementation of the “cycle-to-cycle” control concept for the separation of Tro¨ger’s Base enantiomers on CHIRALPAK AD using pure ethanol as the mobile phase. It was demonstrated that the developed control concept is simple enough to be implemented quickly and reliably for a given separation campaign. In order to start the first control run, 3 days of work had to be invested to set up the whole system for the given separation task. The 3 days were used for the following activities: 1.5 days were needed to perform the system characterization, i.e. determining the void fraction and the Henry’s constants for all nine chromatographic columns; 1 day to setup the monitoring system, i.e. tuning the injection procedure; and 0.5 days to set up the controller for the new separation. In addition, a set of experimental runs was carried out to demonstrate the performance of the “cycle-to-cycle” optimizing controller under nonlinear chromatographic conditions as well as to evaluate how the controller reacts to disturbances that are likely to occur during a separation campaign. The results presented in section 5.1 clearly demonstrate the most important feature of the controller, i.e. the capability to fulfill the product specifications and to improve the performance of the process with the knowledge of the linear adsorption behavior only, although the separation carried out is governed by a bi-Langmuir type adsorption behavior. This is of great importance since the costly and time-consuming task of determining the complete adsorption isotherm for a new separation problem becomes unnecessary. Furthermore, for the first time, it was shown that the detailed simulations of the controller can well-predict the dynamic and the steady state behavior of the actual plant under nonlinear adsorption conditions. The results presented in section 5.2 show further that the controller successfully rejects unknown disturbances. The behavior of the controller is only affected by the feedback information from the plant; therefore, it is able to reject disturbances independently of their nature, as it had been shown in previous publications for the separation of Guaifenesin enantiomers.18,23 In summary, we can conclude that the “cycle-to-cycle” optimizing controller and the approach presented in this work offer a fast and reliable way to set up new chiral SMB separations and to achieve optimal separation performance in a very short time. Notations ci ) concentration of species i [g/L] Dax,i ) axial dispersion coefficient of component i [cm2/s]

Hi ) Henry constants of species i [-] ks,iav ) mass transfer coefficient of component i [1/s] Ki,j ) equilibrium constant of component i with (j ) 1, 2) [L/g] mj ) flow rate ratio in section j [-] ncol ) number of columns [-] P ) purity [-] PR ) productivity [g/(min L)] Qj ) volumetric fluid flow rate in section j [mL/min] t* ) switch time [min] t0 ) retention time of nonretained species [min] tR,i ) retention time of component i [min] V ) column volume [ml] VjD ) dead volume in section j [mL] Greek Letters ε* ) overall void fraction [-] εb ) interparticle void fraction Subscripts and Superscripts A ) more retained component B ) less retained component ave ) average D ) desorbent E ) extract F ) feed i ) component index j ) section index, (j ) 1, ..., 4) R ) raffinate

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ReceiVed for reView February 25, 2010 ReVised manuscript receiVed May 4, 2010 Accepted May 19, 2010 IE100419W