Efficient Simulation of Chromatographic Processes Using the Conservation Element/Solution Element Method

Chromatographic separation processes need efficient simulation methods, especially for nonlinear adsorption isotherms such as the Langmuir isotherms which imply the formation of concentration shocks. The focus of this paper is on the space–time conservation element/solution element (CE/SE) method. This is an explicit method for the solution of systems of partial differential equations. Numerical stability of this method is guaranteed when the Courant–Friedrichs–Lewy condition is satisfied. To investigate the accuracy and efficiency of this method, it is compared with the classical cell model, which corresponds to a first-order finite volume discretization using a method of lines approach (MOL). The evaluation is done for different models, including the ideal equilibrium model and a mass transfer model for different adsorption isotherms—including linear and nonlinear Langmuir isotherms—and for different chromatographic processes from single-column operation to more sophisticated simulated moving bed (SMB) processes for the separation of binary and ternary mixtures. The results clearly show that CE/SE outperforms MOL in terms of computational times for all considered cases, ranging from 11-fold for the case with linear isotherm to 350-fold for the most complicated case with ternary center-cut eight-zone SMB with Langmuir isotherms, and it could be successfully applied for the optimization and control studies of such processes

Optimal design and operation of compact simulated moving bed processes for enantioseparations

Simulated moving bed (SMB) chromatography is attracting more and more attention since it is a powerful technique for complex separation tasks. Nowadays, more than 60% of preparative SMB units are installed in the pharmaceutical and in the food in- dustry [SDI, Preparative and Process Liquid Chromatography: The Future of Process Separations, International Strategic Directions, Los Angeles, USA, 2002. http://www. strategicdirections.com]. Chromatography is the method of choice in these ¯elds, be- cause often pharmaceuticals and ¯ne-chemicals have physico-chemical properties which di®er little from those of the by-products, and they may be thermally instable. In these cases, standard separation techniques as distillation and extraction are not applicable. The noteworthiness of preparative chromatography, particulary SMB process, as a sep- aration and puri¯cation process in the above mentioned industries has been increasing, due to its °exibility, energy e±ciency and higher product purity performance. Consequently, a new SMB paradigm is requested by the large number of potential small- scale applications of the SMB technology, which exploits the °exibility and versatility of the technology. In this new SMB paradigm, a number of possibilities for improving SMB performance through variation of parameters during a switching interval, are pushing the trend toward the use of units with smaller number of columns because less stationary phase is used and the setup is more economical. This is especially important for the phar- maceutical industry, where SMBs are seen as multipurpose units that can be applied to di®erent separations in all stages of the drug-development cycle. In order to reduce the experimental e®ort and accordingly the coast associated with the development of separation processes, simulation models are intensively used. One impor- tant aspect in this context refers to the determination of the adsorption isotherms in SMB chromatography, where separations are usually carried out under strongly nonlinear conditions in order to achieve higher productivities. The accurate determination of the competitive adsorption equilibrium of the enantiomeric species is thus of fundamental importance to allow computer-assisted optimization or process scale-up. Two major SMB operating problems are apparent at production scale: the assessment of product quality and the maintenance of long-term stable and controlled operation. Constraints regarding product purity, dictated by pharmaceutical and food regulatory organizations, have drastically increased the demand for product quality control. The strict imposed regulations are increasing the need for developing optically pure drugs.(...

Two-Dimensional General Rate Model of Liquid Chromatography Incorporating Finite Rates of Adsorption−Desorption Kinetics and Core−Shell Particles

A two-dimensional general rate model of liquid chromatography incorporating slow rates of adsorption–desorption kinetics, axial and radial dispersions, and core–shell particles is formulated. Radial concentration gradients are generated inside the column by considering different regions of injection at the inlet. Analytical solutions are obtained for a single-component linear model by simultaneously utilizing the Laplace and Hankel transformations for the considered two sets of boundary conditions. These linear solutions are useful for simulating liquid-chromatographic columns with diluted or small-volume samples and those in which radial concentration gradients are significant. To gain further insight into the process, analytical moments are also deduced from the Laplace–Hankel-domain solutions. For situations of concentrated and large-volume samples, which are not solvable analytically, formulation of nonlinear models is necessary. In this study, a semidiscrete, high-resolution, finite-volume scheme is extended to approximate the resulting nonlinear-model equations for multicomponent mixtures. The performance of the column is analyzed by implementing a specified criterion of performance. A few numerical case studies are conducted to inspect the effects of the model parameters on the elution profiles