International Max Planck Research School for Analysis, Design and Optimization in Chemical and Biochemical Process Engineering Magdeburg "Efficient and accurate numerical simulations of non-isothermal nonlinear reactive chromatographic models"

In this work models capable to describe non-reactive and reactive liquid chromatography were investigated numerically and theoretically. These models have a wide range of industrial applications e.g. to produce pharmaceuticals, food ingredients, and fine chemicals. Two established models of liquid chromatography, the equilibrium dispersive model and the lumped kinetic model, were analyzed using Dirichlet and Robin boundary conditions to solve the column balances. The models consist of systems of convection-diffusion-reaction partial differential equations with dominating convective terms coupled via differential or algebraic equations. The Laplace transformation is used to solve them analytically for the special case of single component linear adsorption. Statistical moments of step responses were calculated and compared with numerical predictions generated by using the methods studied in this thesis for both sets of boundary conditions. For nonlinear adsorption isotherms, only numerical techniques provide solutions. However, the strong nonlinearities of realistic thermodynamic functions and the stiffness of reaction terms pose major difficulties for the
numerical schemes. For this reason, computational efficiency and accuracy of numerical methods are of large relevance and a focus of this work. Another goal is to analyze the influence of temperature gradients on reactive liquid chromatography, which are typically neglected in theoretical studies. By parametric calculations the influence of  temperature gradients on conversion and separation processes during reactive liquid chromatography were analyzed systematically. Additionally, the complex coupling of concentration and thermal fronts was illustrated and key parameters that  influence the reactor performance were identified. Two numerical schemes, namely the finite volume scheme of Koren and the discontinuous Galerkin finite element method, were applied to numerically approximate the models considered.
These schemes give a high order accuracy on coarse grids, resolve sharp fronts, and avoid numerical diffusion and dispersion. Several case studies to analyze non-reactive and reactive liquid chromatographic processes are carried out. The results of the suggested numerical methods were validated qualitatively and quantitatively against some finite volume schemes from the literature. The results achieved verify that the proposed methods are robust and well suited for dynamic simulations of chromatographic processes.