Comparing the optimum performance of the different modes of preparative liquid chromatography
Introduction
Several recent studies have focused on the determination of the optimum experimental conditions of binary separations in preparative liquid chromatography 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. The nonlinear nature of preparative chromatography complicates the separation process so much that the derivation of general conclusions regarding these optimum conditions is a rather difficult task. Furthermore, the very choice of the objective function of preparative chromatography is not simple. In industrial applications, the production cost would be the major factor to consider. However, many components of the production cost (e.g., overhead cost) are beyond the scope of the separation process itself. Accordingly, most previous authors have elected to study the more straightforward approach of maximizing the production rate.
Separate studies have determined the optimum experimental conditions for the maximum production rate in overloaded isocratic elution using either the ideal model 1, 2or the equilibrium-dispersive model of nonlinear chromatography 3, 4. Other works have discussed the optimization of the experimental conditions in displacement chromatography for maximum production rate 3, 5, 6, 7, 8. Production rate in gradient elution chromatography was optimized using the linear solvent strength theory 9, 10. Recently, Jandera et al. studied the optimization of gradient elution chromatography when deviations from the linear solvent strength theory take place [11].
The economic consequences of the conditions under which a separation is carried out have also been discussed. Optimum experimental conditions were determined in situations in which the cost of the solvent — a major cost factor in certain applications of preparative liquid chromatography — was also taken into account 12, 13. A hybrid objective function was recently introduced in order to weigh the importance of both the production rate (which should be as high as possible) and the solvent consumption (which should be as low as possible) [13]. Because all the modes of operation considered in this study are applied as batch processes, the recovery yield during each run is lower than unity. Some optimization for maximum production rate were undertaken with constraint of a minimum yield 3, 4, 8. A more recent study introduced a very beneficial objective function, the product of the production rate and the recovery yield [14]. It was shown that, by means of that objective function, experimental conditions can be found which are such that the production rate is only slightly lower than when the production rate is the objective function while the recovery yield is significantly improved. This trade-off of a slight decrease in the production rate for a considerable yield improvement would be most economical. The optimization of gradient elution chromatography was studied with that objective function by Felinger and Guiochon [15].
The optimization of the different modes of preparative chromatography allowed the comparison of elution and displacement chromatography 3, 16, revealing the relative advantages of either mode of separation. These studies suggested that elution can offer a larger production rate than displacement chromatography but delivers less concentrated fractions, which may significantly increase the cost of downstream processing.
The practical interest of these investigations of the optimization of the experimental conditions arises from the current availability of powerful personal computers. These machines allow the convenient calculation of the optimum conditions by using accurate models of the nonlinear separation process. The a priori knowledge of the competitive isotherms for the binary mixture of interest and of the parameters of the Knox efficiency correlation allow the rapid calculation of the band profiles of both components, their integration, the determination of the positions of the cut points, the production rate, and the recovery yield. Combining the algorithms which performs these tasks with an optimization algorithm permits the determination of the experimental conditions which maximize the relevant objective function. Then, the experimental conditions obtained by computation can be fine tuned experimentally. The introduction of the modeling step just described into the optimization process highly reduces its time and cost demand [17].
In this study, we introduce a uniform handling for the calculation of the production rate and the recovery yield achieved with the different modes of chromatography. This allows a direct comparison of their performance and an illustration of their relative advantages and drawbacks. Finally, guidelines are given to chose the parameters to be optimized.
Section snippets
Theory
The band profiles were calculated by means of the equilibrium-dispersive model of chromatography [17]. In this model instantaneous equilibrium is assumed between the stationary and the mobile phase. The concentrations in these two phases at equilibrium are simply related by the isotherm equation. An apparent dispersion term accounts for the contributions of all the sources of band broadening: axial diffusion, eddy dispersion, and the finite rate of the mass transfers. A mass balance equation is
Isotherm model
We have assumed that the adsorption behavior of the two components of the sample (and that of the displacer in displacement chromatography) can be described by competitive Langmuir isotherms
The numerical coefficients were chosen so that the saturation capacity of each solute — and that of the displacer — be the same, qs=260 mg/ml.
In reversed-phase gradient elution chromatography, the linear solvent strength model connects the mobile phase composition with the retention factor
Results and discussion
As shown above, the parameters which have to be optimized in a preparative separation are the loading factor and the number of theoretical plates in all modes of chromatography, as well as the displacer concentration in displacement chromatography and the gradient steepness in gradient elution.
Conclusions
This study confirms previous results [13]that there are only two critical parameters in the optimization of a preparative separation by elution chromatography, the loading factor and the column efficiency (assuming that it is independent of the concentration). In gradient elution and displacement chromatography, there is one more parameter, the gradient steepness or the displacer concentration, respectively. This observation simplifies markedly the solution of optimization problems.
Acknowledgements
This work was supported in part by grant CHE-9701680 from the National Science Foundation, by research grants F15700 from the Hungarian National Science Foundation (OTKA), MKM 332/1996 and FKFP 0609/1997 from the Hungarian Ministry of Education, and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory. We acknowledge support of our computational effort by the University of Tennessee Computing Center.
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