Modeling of Preparative Liquid Chromatography

C H A P T E R

18 Modeling of Preparative Liquid Chromatography T. Fornstedt *, y, P. Forsse´n *, J. Samuelsson * *

Department of Engineering and Chemical Sciences, Karlstad University, Karlstad, Sweden y Analytical Chemistry, Department of Chemistry - BMC, Uppsala University, Uppsala, Sweden

O U T L I N E 18.1. Introduction

408

18.2. Column Model 18.2.1. The Equilibrium-Dispersive Model

409 409

18.3. Adsorption Model 18.3.1. Band Shape Dependence on Adsorption 18.3.2. Adsorption Isotherms 18.3.3. Determination of Adsorption Data

410 411 413 414

18.4. Process Optimization of Preparative Chromatography 18.4.1. Empirical Optimization 18.4.2. Numerical Optimization 18.4.3. Important Operational Conditions

415 415 416 418

18.5. Case Example

422

References

422

Liquid Chromatography: Fundamentals and Instrumentation http://dx.doi.org/10.1016/B978-0-12-415807-8.00018-3

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Copyright Ó 2013 Elsevier Inc. All rights reserved.

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18.1. INTRODUCTION In preparative liquid chromatography (LC), the goal is to isolate as much as possible of the desired component(s) from a complex sample mixture. Therefore, high sample concentrations are normally injected, and because of the limited surface of the stationary phase, the column often becomes overloaded. The eluted peaks often become strongly distorted and unsymmetrical. In addition, the components compete with each other for the same surface, a thermodynamic effect that ultimately results in strong band interactions and band contaminations, described by Helfferich and Klein [1] and more recently by Guiochon et al. [2]. Preparative chromatography is especially important for purification of chiral drugs. The use of chiral stationary phases (CSPs) has become the standard methodology in pharmaceutical research and early drug development to get pure enantiomers from synthesis. Chiral-analytical LC is an important technique to support the establishment of activity profiles of chiral drug candidates in modern drug discovery. Chiral-preparative LC is essential for collecting necessary gekg amounts of the optical isomers, with high chiral purity, of each early candidate drug for toxicology tests on animals, which is recommended today after the publication of FDA’s policy statement for the development of new stereo isomeric drugs [3]. In recent years, numerous chiral phases have been developed: polysaccharide and brush-type phases, including donoreacceptor (Pirkle-type) and ionexchange-based chiral stationary phases are of particular interest for preparative purposes due to their high loading capacities [4e10]. The trend today in preparative chromatography of chiral components is toward complex and continuous operation mode systems, such as steadystate recycling or simulated moving bed [2,11]. Such complex methods, and in particular simulated moving-bed processes, are even more difficult and expensive to optimize without computer simulations than the batch mode. If the competitive adsorption isotherms have been measured, optimal operating conditions can be found, for both batch and continuous modes, by the use of computer simulations and numerical optimization as opposed to conventional trial-and-error methodologies [2]. The optimization of the experimental conditions in a preparative separation must be based on a thorough understanding and modeling of the process and its economics. Therefore, the thermodynamics and kinetics of the system must be determined. In most cases of small-drug molecule separation, the adsorption and desorption steps are many and fast and the effects of kinetics and diffusion can be lumped together. When this is not the case, in a few cases for small-drug molecules, the more-advanced general-rate model provides a reliable platform to simulate elution bands, accounting for axial dispersion and external and internal mass-transfer resistances [2,12]. But, in most cases in preparative liquid chromatography of small-drug molecules and fine chemicals, it is

18.2. COLUMN MODEL

409

more or less the thermodynamics that determine the component interactions with the phase system. More specifically, it is the adsorption isotherms and especially the ones measured under competitive conditions, that provide the essential input information that must be measured in a system prior to its modeling. There are several methods for adsorption isotherm measurements. Frontal analysis (FA) is the oldest, first suggested by Tiselius and Claeson [13], then developed and applied by James and Phillips [14]. It is considered very accurate and has been used extensively in many LC characterizations [2,15]. However, FA is time consuming; plenty of pure solute is required; and it makes analyzing multicomponent mixtures difficult [16]. As a consequence, much research has recently been done to develop new methods. This has resulted in methods like the perturbationpeak (PP) method [15,17e19], elution by characteristic points [20e23], the inverse method (IM) [24e29], the batch-uptake method [30], and the nonlinear frequency-response method [31], all of which have their advantages but also drawbacks as compared to FA. The status of the theory and the main methods of implementation of preparative liquid chromatography for small drugs are reviewed in this chapter, with a special focus on the different methods for adsorption isotherm determination. The chapter also highlights the importance of some factors or conditions that many times are neglected in the numerical process optimization of a separation problem.

18.2. COLUMN MODEL In preparative (nonlinear) LC, more advanced models must be used, since the migration rate of a solute through the column is concentration dependent. The most complete and realistic model is the general-rate model, which entails a detailed treatment of external dispersion, external mass transfer, interparticle diffusion and adsorptionedesorption kinetics. Several valuable articles and reviews describe different versions of the general-rate model [2,12]. In the opposite corner, we have the ideal model, assuming that the column has infinite column efficiency [2,32]. Based on this assumption, the shapes of the preparative bands arise only from the characteristics of the adsorption isotherms. The advantage of this model is its simplicity.

18.2.1. The Equilibrium-Dispersive Model The equilibrium-dispersive (ED) model accounts for a finite extent of axial dispersion but assumes that the mass transfer across the column is infinitely fast. In modern HPLC systems, the kinetics are very fast and the phases can be assumed to be in equilibrium. The small actual amount of nonequilibrium adds some dispersion to the solute zones and can be

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lumped with other dispersive contributions into an apparent dispersion constant. The resulting simplified model, the ED model [2], is the one most often assumed in HPLC studies. In the ED model, each solute i is described by a mass balance equation: 8 vCi ðx; tÞ vq ðx; tÞ vC ðx; tÞ v2 Ci ðx; tÞ > > ; þF i þu i ¼ Da > > vt vt vx vx2 > > > < 0  x  L; t  0; i ¼ 1; .; n; (18.1) > > > > Ci ðx; 0Þ ¼ C0;i ; > > > : Ci ð0; tÞ ¼ 4i ðtÞ: In the mass balance equation, Ci(x, t) is the mobile-phase concentration of component i at a distance x from the column inlet and at a time t after sample injection; qi is the stationary-phase concentration as described by the adsorption isotherm, F is the volumetric phase ratio, u is the linear flow rate, Da is the apparent dispersion constant, and L is the column length. F can be expressed as F ¼

Vs 1  εt ¼ V0 εt

(18.2)

where Vs and V0 are the stationary and mobile phase partial volumes and εt is the total porosity of the column. The apparent dispersion constant, Da, can be calculated from Da ¼

Lu ; 2N

(18.3)

where N is the number of theoretical plates. The last two lines in Eq. (18.1) are the initial and boundary conditions. The initial condition describes the mobile phase concentration, C0,i, at all positions x prior to the injection. Normally, C0,i ¼ 0, but as we see later, this is not always so. The boundary condition is the injection profile, 4i, that is, the shape of the injected sample zone. LC separations can be simulated by numerically estimating the solution of Eq. (18.1) at the outlet Ci(L, t), that is, estimating the elution profiles. This is usually done by the Rouchon finite-difference method or by orthogonal collocation.

18.3. ADSORPTION MODEL Functions describing the relationship between the component concentrations in the mobile and stationary phases, at a specific and constant temperature (isothermal conditions), are called adsorption isotherms. Several adsorption isotherm models are available for describing single component as well as multicomponent systems at constant temperature.

18.3. ADSORPTION MODEL

411

18.3.1. Band Shape Dependence on Adsorption In analytical LC, sample concentrations are normally very low and the corresponding adsorption isotherms are practically linear in this concentration range. This means that the adsorbed concentration is proportional to the concentration in the mobile phase. All molecules then migrate through the column, adsorb and desorb, independent of the other molecules, so each solute elutes as a Gaussian peak. The retention time of each peak depends on the initial slope of the corresponding adsorption isotherms. The peak shape deviates only slightly from the Gaussian ideal, but the chromatograms may become complex due to the multitude of solutes in the sample. In preparative LC, where concentrations are generally much higher, the adsorption-isotherm curvature and saturation capacity have an enormous impact on the peak shapes. Molecules in high-concentration zones spend relatively more time in the mobile phase due to the difficulty of finding free adsorption sites. Because of this overload, the sample zone becomes asymmetrical, elongated, and strongly dependent on the shape of the adsorption isotherm. An adsorption isotherm can be classified according to the shape of the isotherm curves, see Figure 18.1. Most reported adsorption isotherms have a convex curvature, approaching a maximum adsorbed concentration, the saturation capacity. Such models are classified as type I according to the IUPAC standard, see Figure 18.1(a), left side.

FIGURE 18.1 The most typical adsorption isotherms and the corresponding shapes of the elution profiles: (a) Type I, (b) Type II, (c) Type III adsorption behavior.

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Type III adsorption isotherms are concave with an increasing slope at high concentrations, see Figure 18.1(c), left side, whereas type II isotherms are initially convex but, after an inflection point, turn concave, see Figure 18.1(b) left,side. From Figure 18.1, it is further concluded that, if a Type I adsorption isotherm describes the adsorption process best, that is, a convex upward shape, then the overloaded eluted band has a sharp front and a diffusive rear, see Figure 18.1(a), right side. The reason is that the higher eluted concentration strives for smaller retention times, because the higher the concentration, the smaller is the degree of adsorption. But, if a Type III adsorption isotherm describes the adsorption process best, that is, a concave upwards shape, then the overloaded eluted band has the opposite shape; that is, a diffusive front and a sharp rear, see Figure 18.1(c), right side. The reason is that the higher eluted concentration strives for longer retention times, because the higher the concentration, the larger is the degree of adsorption. Type II adsorption isotherms are composed of both type I and III and have vertical asymptotes that are unrealistic in LC, because this means the saturation capacity is unlimited, resulting in a most complex band shape, see Figure 18.1(b), right side. Most reported liquidesolid adsorption processes are described with Type I adsorption isotherms. In a competitive situation, the adsorption of a component between the mobile and stationary phases depends not only on the local concentration of the component itself but also on all the other components. This ultimately results in complex chromatograms. Figurer 18.2 shows the resulting preparative chromatogram after the injection of an equal mixture of two components, assuming type I adsorption behavior. The first eluted component is displaced by the second eluted one with a mixed zone in between. We can also see that the second eluted component has a hump on its rear. This situation is much more advantageous for

FIGURE 18.2 A typical binary elution profile, assuming Type I adsorption behavior.

18.3. ADSORPTION MODEL

413

fractionation of component 1 that is enriched than if injected alone; however, it is of crucial importance to understand, predict, and control the competitive forces creating this situation. By using numerical simulation, we can predict the optimal experimental conditions for collecting pure amounts of component 1 or component 2.

18.3.2. Adsorption Isotherms Adsorption isotherms describe the equilibrium distribution of solutes between the mobile and stationary phases, q(C), in a chromatography column. The nature of the interactions varies from system to system, so there are many adsorption isotherm models. Each model consists of a number of model parameters, which define the specific adsorption isotherm for the different components. If the adsorption isotherms can be measured and fitted to the appropriate model, a lot of information is obtained about system characteristics. Furthermore, it is then possible to perform computer simulations, such as by solving Eq. (18.1). The Langmuir Adsorption Isotherm To understand the fundamentals of the adsorption mechanism at overloaded preparative conditions, it can be necessary to first study the adsorption of a single component in a chromatographic system. The Langmuir adsorption isotherm is a very simple Type I model. It assumes ideal solutions, homogeneous and independent monolayer adsorption [33]:   qs;i bi Ci ai Ci P P ¼ ; i; j ¼ 1; .; n (18.4) qi C1 ; C2 ; .; Cn ¼ 1 þ j bj C j 1 þ j bj Cj In this expression, ai is the initial slope, bi is the equilibrium constant, and qs,i ¼ ai/bi is the saturation capacity of component i. It holds that ki ¼ Fai, so the retention times of the Gaussian peaks in analytical separations are given by the initial slope of the corresponding Langmuir adsorption isotherm. Figure 18.1(a) (left side) shows an example of a single-component Langmuir adsorption isotherm. Most separation problems of practical interest involve more than a single component and the Langmuir adsorption isotherm in Eq. (18.4) can be used to model the competition between the components. Here, the adsorbed concentration of any component i depends on the concentration of all components present. Because of this, all n mass-balance equations in Eq. (18.1) are coupled and cannot be treated independently. Another common adsorption isotherm model that accounts for this experimental condition is the bi-Langmuir model [34], which is an empirical extension of the Langmuir model, with two Langmuir terms

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added to each other describing two different types of adsorption sites. The bi-Langmuir model applies to heterogeneous systems containing two separate types of adsorption sites. Examples are alkyl and silanol groups in C18 reversed-phase systems [35] and chiral selective and nonselective sites in chiral stationary phases [36]. More complex models of type II and III exist, which take lateral surface interactions, multilayer adsorption, adsorption energy distribution heterogeneity, are described elsewhere [2].

18.3.3. Determination of Adsorption Data There are several methods for determining the adsorption isotherm [2,37]. The most accurate technique today is frontal analysis [2,15], whereas the most recently developed method, the inverse method, is a better choice for process chromatography because of its rapidity [27e29]. Frontal Analysis Frontal analysis is usually carried out in a series of increasing concentration pulses [2,37]. The adsorption data for a single-component case is calculated by integrating the mass balance for those pulses: q ¼ C

VR  V0 Vs

(18.5)

where C and q are the solute concentrations in the mobile and stationary phase, and VR is the frontal breakthrough volume. FA can be used for any type of adsorption isotherm, is not effected by slow or concentrationdependent kinetics, and is therefore considered to be the most-accurate method for adsorption-isotherm determination. Due to these advantages, FA is more or less known as a reference method. For multicomponent cases, an intermediate plateau must be determined, which means that a fractionation and reinjection procedure must be followed for systems with more than two compounds. Unfortunately, it has been found that, for ternary mixtures, FA works only for high-efficiency separation systems [16]; otherwise, the erosion of the intermediate plateau is too pronounced. The major disadvantage with FA is that it is tedious and consumes a large amount of solvent and pure solute. The Inverse Method With the inverse method, adsorption-isotherm parameters are determined from overloaded elution profiles (peak shapes at sample overload are treated in Section 18.3.1). The solute consumption and time requirements are modest compared to other methods. The adsorption isotherm

18.4. PROCESS OPTIMIZATION OF PREPARATIVE CHROMATOGRAPHY

415

cannot be obtained directly from this data (as opposed to FA data). Instead, the parameters are estimated by solving the inverse partialdifferential-equation problem: Elution profiles are simulated iteratively, by solving Eq. (18.1) numerically, and the parameters are tuned by numerical optimization until the simulated and experimental profiles coincide in the least square sense. The IM is not as accurate as the FA method. However, in process chromatography, we are mainly interested in the column model’s ability, in combination with the determined adsorption isotherm, to predict elution profiles that later are going to be used for process optimization. If the determined adsorption-isotherm parameters or model is physicochemically correct or not is not a major concern in process chromatography, this makes IM a perfect candidate for adsorption-isotherm estimation.

18.4. PROCESS OPTIMIZATION OF PREPARATIVE CHROMATOGRAPHY The goal of chromatographic processes optimization, in most cases, is to produce and manufacture a high-quality product as fast and cheaply as possible, and the optimization can be performed both empirically and numerically. The empirical-process optimization approach requires extensive laboratory work to find the optimal conditions, which can be time consuming.

18.4.1. Empirical Optimization In the end, what matters to preparative chromatographers is not which model applies or the values of the model parameters. The most important thing is how much sample can be separated in a single injection and how quickly a pure component can be produced. To characterize a system, one could calculate the maximal amount of substance that is possible to inject under the condition that the component bands, or profiles, are separated. This empirical quantity is called the loading capacity. Ideally, one should use saturated solutions of the components when doing these calculations. Here, often the flow rate is fixed at as high a value as allowed and only the injection volume is varied. For example, the injection volume is increased until the maximum cross-contamination of a component exceeds 1%, that is, the component bands are no longer separated. A better optimum can be reached by allowing greater cross-contamination, performing a series of experiments with different injection volumes, then plotting the measured yield and production rate. However, this requires that the

416

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individual component bands be measured or calculated from the total response. Notice that the component bands are allowed to overlap if the minimum yield constraint is set lower than 100%, that is, if the compound is readily available and cheap compared to the chromatographic process, highly overloaded overlapping bands [38,39] are preferable.

18.4.2. Numerical Optimization The numerical approach requires considerably less laboratory work and the ability to generate fast simulations and analyze the results qualitatively and quantitatively [2]. The objective function in numerical process optimization, usually the productivity PR , is a function of the experimental conditions and depends on the adsorption mechanisms of the system, such as thermodynamics, mass-transfer rate, and dispersion. To simplify the problem, it is common to keep some process optimization parameters fixed in the objective function, that is, perform a “suboptimization.” Then, it has to be decided which parameters to include in the optimization procedure and which ones should be kept fixed. Constraints are also usually present in the optimization problem, such as on the yield (Y) and purity (PU). Increasing the yield demand often lowers the productivity, and decisions about an acceptable limit must be made. The productivity (PR,i) is how much of component i is retrieved during one injection cycle per kg CSP, mCSP, and can be written as FV PR;i ¼

tstop;i R tstart;i

Ci ðtÞdt

tcycle mCSP

(18.6)

where FV is the volumetric flow rate, tcycle is the cycle time, tstop,i and tstart,i are the end and start of the fraction collection for the ith component. The yield, Yi, is defined as how much of the injected amount of component i is collected during one injection cycle. The purity, PU,i, is the amount of component i in the collected fraction as a percent of the total amount of all collected components. General Procedures Numerical optimization of batch-process chromatography can be represented by a workflow according to Figure 18.3. First, it is important to find a suitable experimental-separation system by thorough screening of the available stationary and mobile phases. Thereafter, the adsorption isotherms for the major components must be determined. The inverse method is one of the most convenient and rapid methods for determination of competitive adsorption isotherms aimed at process

18.4. PROCESS OPTIMIZATION OF PREPARATIVE CHROMATOGRAPHY

417

Experimental system Hold up volume Calibration curve (Injection profiles)

Elution profiles

Inverse method

Column model Adsorption model Simulation algorithm

Adsorption parameters

Van Deemter curve

Process optimization

Objective function Constraints Optimization algorithm

Optimal conditions

FIGURE 18.3 Flowchart describing the most important steps in numerical optimization of process chromatography.

chromatography. The heart of the method comprises defining and solving a column mass-balance model, and the procedure involves setting an adsorption-isotherm model and parameter guesses, solving the equation and seeking to maximize the overlap of the simulated profiles to a number of elution profiles for defined overloaded injections. Therefore, a set of proper elution profiles at varying loads must be provided. The inverse solver then produces a set of adsorption isotherm parameters that best describes the system. Now it is possible to use these parameters, together with measured van Deemter functions and process conditions of the large-scale separation system, to perform process optimization with a given objective function and constraints (see Figure 18.3) [2,40]. Decision variables in the objective function are typically injection volume, injection concentration, and flow rate. Constraints are typically the maximum allowed pressure and minimum purity and yield for the target component. Numerical Injection Volume Optimization The empirical injection volume optimization just described can also be done by using computer simulations, if the adsorption-isotherm parameters and the number of theoretical plates, N in Eq. (18.3) are measured for

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both components. This numerical approach requires no advanced optimization routines, for example, “gridding” can be used that is, dividing the injection volume range using a finite number of equidistant points and calculating the objective function and the constraints in each, the one with the maximum value of the objective function that also fulfills the constraints is the estimated optimal injection volume. In a pharmaceutical setting, the yield constraint is often set to 75% and the Purity constraint to 99%. Numerical Full Optimization Here, all relevant parameters are allowed to vary: injection volume, sample concentration, and flow rate. Full optimization is difficult to perform without computer simulations and requires more-advanced optimization algorithms. We often use a response-surface global-optimization algorithm for “costly” problems, such as TOMLAB [41] combined with a modified NeldereMead simplex algorithm [42] that supports inequality constraints. In the response-surface algorithm, a global optimum is sought; this is crucial, as an ordinary local optimization algorithm might get stuck in a local minimum far from the optimal solution.

18.4.3. Important Operational Conditions Several parameters are important to model correctly if a highly accurate model prediction is needed. In this section, we discuss the holdup volume, injection profiles, and the correct accounting for additives in the modeling procedure. Holdup Volume Many articles have demonstrated the need to use the correct holdup volume (porosity) in the adsorption-isotherm determination [43e46]. All these studies were performed for single-component cases. However, from a process chromatographic point of view, it is more interesting to know how such an error affects the prediction of productivity. This was recently investigated by the determination of optimum experimental conditions using erroneous adsorption isotherms combined with a wrong holdup volume and applied in the true system to evaluate the objective functions and constraints: productivity, yield, purity [47]. It was shown that, for underestimated holdup volumes, the purity requirements are fulfilled for only the second eluted component, whereas for overestimated holdup volumes, the process requirements are fulfilled for only the first eluted component. The decreased productivity is larger for overestimated holdup volumes than underestimated volumes.

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419

Injection Profiles Injection profiles are used as boundary conditions for solving the column model, and often numerical process optimization is conducted using rectangular injection profiles, see Eq. (18.1). Normally, in numerical optimization of preparative chromatography, a rectangular injection profile is assumed instead of the “true” injection profile. The reason is that it is very time consuming and tedious to determine the injection profiles for all the different operational conditions used in the numerical optimization. However, by assuming rectangular injection profiles, large errors are introduced. In Figure 18.4, an experimental injection profile is plotted together with the corresponding rectangular injection profile, the difference in shape is striking. The injection profile depends on the flow rate, injection volume, viscosity of the solvent, and the solute size [48]. The eroded injection profiles are mainly due to radial diffusion in the injection loop that transports solutes back and forth from faster-moving regions to the slower-moving regions in the in the parabolic flow. Since it is so tedious to determine all possible injection profiles in an optimization procedure, another approach is to determine, from a few measured injection profiles, a function that describes the flow-rate and injection-volume dependence of the injection. In [47,49], it was shown that the injection profile 4i(t) in Eq. (18.1) can be described as a convolution of a Gaussian peak and an exponentially decaying pulse that has an initial constant part, the length

1

Norm. resp.

0.8

0.6

0.4

0.2

0 0

0.5

1

1.5

Volume [mL]

FIGURE 18.4 An experimental injection profile (black line) of solute omeprazole injected in 600 ml into an eluent of pure methanol at flow rate 1 ml/min overlaid with the corresponding rectangular injection profile (gray line).

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18. MODELING OF PREPARATIVE LIQUID CHROMATOGRAPHY

of which is given by q. Expressed in eluted volume, V, the convolution can be written 

    A 2V0  2V þ q 2V0 þ 2V þ q p ffiffi ffi p ffiffi ffi þ erf þ erf C V ¼ 2 2s 2s   2  A 2V þ 2V0 þ q s2 s  2Vs þ 2V0 s þ sq pffiffiffi exp þ 2 þ ln erfc 2 s 2s 2ss (18.7) where A is the area of the injection profile (related to the amount injected); s, s, V0, q are parameters and erf and erfc are the error function and the complementary error function, respectively. Here, we have that V0, Vinj/s, s, and q have a linear relationship with the injection volume, Vinj, for a constant flow rate. It is also possible to include the volumetric flow rate dependency by letting these linear relationship parameters depend on the flow rate. Modeling Additives Most often, additives are used in the mobile phases of modern separation systems, this is especially the case for chiral separation systems. However, in almost all cases of numerical modeling of such preparative systems, the additives are neglected in the modeling. The reason is that the additive is invisible to the detector, especially in such ranges, so that reliable measurements of their adsorption isotherms cannot be performed. However, this problem can be bypassed by using the inverse method. One then assumes that an “invisible” additive is present and the adsorption of it can be described by an adsorption isotherm function, such as the Langmuir function. Elution profiles are then measured for different additive levels, and due to the effect on the visible eluted peaks, the adsorption isotherm parameters of the additive also can be estimated. For example, we used the inverse solver to characterize the adsorption behavior of the FMOCeallylglycine enantiomers on the quinidinecarbamate anion exchanger by estimating both the enantiomer and the additive (acetic acid) adsorption-isotherm parameters [10]. In was shown that a simulation based on adsorption-isotherm parameters estimated by the inverse method, neglecting the additive (acetic acid) in the mobile phase, fitted an experimental overloaded profile well. However, these adsorption-isotherm parameters failed to predict the experimental elution profile when using a mobile phase with a somewhat higher level of additive concentration (see Figure 3 in [10]). Then, we used the inverse solver and accounted for the additive concentration by using elution profiles from two additive levels and including the additive level in the model. With these parameters for the

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18.4. PROCESS OPTIMIZATION OF PREPARATIVE CHROMATOGRAPHY

two enantiomers, as well as for the invisible additive, it was possible to successfully predict the elution profiles for any additive levels in between. Figure 18.5 shows the experimental and predicted binary profiles for two intermediate mobile phases and two injection volumes. It remains, however, to investigate how well the concept can be used for process optimization of a real experimental system accounting for the additive. In this context, it should be mentioned that, if the additive adsorption strength is larger than any of the injected components, very strange band shapes occur. Such profiles have been described in the literature since the 1990s [2] and the phenomenon has also been verified by computer simulations. The systems used at that time were often not of practical interested but were designed to provoke the strange effects. More recently, however, we found that the effects also take place in modern systems aimed at preparative chiral separations [50], and we can use the inverse solver approach to accurately simulate and predict cases where strong additives results in strange band shapes [51,52].

12

aII

aI

10 8 6 4

C [mg/ml]

2 0 12

bI

bII

10 8 6 4 2 0

4

6

8

10

12 4 t [min.]

6

8

10

12

FIGURE 18.5 Experimental (symbols) and predicted elution profiles using the adsorption parameters in Table 3 of [10] accounting for the additive: (a) For mobile phase 2 and (b) for mobile phase 3; here, I is a 350 ml injection and II is a 500 ml injection. The solid line corresponds to the Langmuir parameters, and the dotted line corresponds to the bi-Langmuir parameters. See Section 3 and Table 1 of [10] for experimental conditions. Source: From [10]. Copyright 2008, with permission from Elsevier.

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(a)

S

C [g/L]

6

Sum S R Cut

4

2

0

R

(b) C [g/L]

4 3 2 1 0

3

4

t [min.]

5

6

FIGURE 18.6 Overlay of experimental and simulated elution profiles for the optimal conditions on 10 mm Kromasil AmyCoat 25 3 0.46 cm column: (a) S- and (b) R-omeprazole. The solid lines are experimental UV signals representing the sum of the enantiomers, symbols are analyzed fractions, and the dashed horizontal lines represent the cut points.

18.5. CASE EXAMPLE Enantiomeric separation of omeprazole has been extensively studied regarding both product analysis and preparation using several different chiral stationary phases. We recently made a full optimization of the preparative purification of R- and S-omeprazole using columns packed with amylose tris(3,5-dimethyl phenyl carbamate) on 10 mm particles. The resulting optimal chromatogram can be seen in Figure 18.6. The thick gray lines are the experimental and the thick black line is the simulated chromatogram, thin lines are simulated for R- and S-omeprazole and symbols are fractions taken during the elution. As one can see, the model predicts the process rather well with an error in the cut point of approximately 5 sec.

References [1] Helfferich F, Klein G. Multicomponent chromatography. In: Chromatographic science series, vol. 4. New York: Marcel Dekker; 1970. [2] Guiochon G, Felinger A, Shirazi DG, Katti AM. Fundamentals of preparative and nonlinear chromatography. 2nd ed. Amsterdam: Elsevier Academic Press; 2006.

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