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The aim of this work was to investigate an accurate, fast, and stable numerical scheme for solving chromatographic model equations, especially, but not limited to, those in the presence of a shock front. Existing solution techniques, such as finite-difference and finite-element methods, are briefly reviewed and compared with the finite-volume method, which so far has been applied to only a limited extent to the solution of model equations in the chromatographic community. One well-established, accurate, and stable finite-volume technique includes the application of appropriate flux limiters. Investigation of the elution profiles of linear and nonlinear chromatographic conditions were carried out over a wide range of flux limiters in terms of accuracy, stability, and computational time. Based on the simulation results, the van Leer flux limiter in the realm of finite-volume methods was found to be the most suitable in terms of accuracy and computational time for solving chromatographic model equations.

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Membrane separation technology has become an important part of process flowsheet synthesis in which it can be combined with other unit operations for enhanced separation of gasses and liquids. Since process flowsheet synthesis requires computationally efficient numerical algorithms, in this work, an accurate, fast, and robust computer model for the simulation of cocurrent hollow fiber membranes is proposed. The algorithm is based on a modified shooting method with quadratic interpolation, which requires no derivative computations versus classical optimization methods. Moreover, for solving the set of differential equations, three different integration methods were employed and compared over wide range of operating conditions. Based on both speed and robustness, the best method was found to be the variable order numerical differentiation formula as it succeeded in solving the problem fast and accurately under all tested points. The maximum computational time was 3.4 s, while the maximum absolute permeate outlet pressure estimation error was 0.37%, which is remarkable. Also, the method was validated with both experimental and simulation studies in the literature. Hence the proposed algorithm is suitable for process flowsheet synthesis, process design, and optimization studies.

This work presents experimental implementation of an improved single-column chromatographic (ISCC) separation process and its optimizing controller. A mixture of guaifenesin enantiomers has been used to evaluate the performance and integrity of (i) the ISCC process and its online monitoring system in open-loop experiments and (ii) the model predictive optimizing controller for closed-loop operation. The open-loop operation has been particularly aimed at assessing the accuracy and precision of the online monitoring system. In the closed-loop operation, the performance of the developed model predictive control (MPC) scheme has been tested for set point tracking and disturbance rejection with an objective function that reflects the process economics. The online optimal operating condition was also compared to the offline optimum condition obtained using a genetic algorithm. Results confirm that the optimizing controller is adequate to operate and maintain the ISCC process at an optimal operating point while fulfilling the product requirements.