Modeling and Simulation of Non-equilibrium Liquid Chromatographic Processes in Thermally Insulated Tubular Columns and Reachors

Abstract

Modeling and Simulation of Non-equilibrium Liquid Chromatographic Processes in Thermally Insulated Tubular Columns and ReactorsLiquid chromatography is a separation technique that provides high level of purity at reasonable production cost and is widely applied in pharmaceutical, chemical, molecular biology, food industry, forensics investigation, nucleic acids research, and many other industries. The main objective of this work is the theoretical investigation of nonlinear and non-isothermal liquid chromatographic processes in thermally insulated columns and reactors. In later case, reactions and separations are occurring simultaneously inside a single unit, providing an improved selectivity, purity, and productivity. The equations of considered models constitute systems of convection diffusion partial differential equations for mass and energy balances in the bulk phase coupled with differential equations for mass and energy balances in stationary phase. The models incorporate the mixture injection in the form of a rectangular pulse at the column inlet and two types of boundary conditions. The analytical solutions are derived for Dirichlet inlet boundary conditions by implementing the Laplace transformation, Tschirnhaus-Vieta approach, the linear decomposition technique, and an elementary solution technique of ordinary differential equations. An efficient and accurate numerical Laplace inversion technique is applied to bring back the solution in the original time domain. Furthermore, the time dependent analytical temporal moments are also derived from the Laplace domain solutions to investigate front asymmetries, band broadenings, and retention times of profiles eluting the column. In the case of nonlinear models, a total variation bounded (TVB) Runge-Kutta local-projection discontinuous Galerkin (RK-LDG) finite element method is applied. The suggested numerical scheme is explicit in nature and has a potential to capture sharp peaks and abrupt changes in the solution profiles. For each of the considered model, a number of case studies are carried out considering realistic model parameters that are frequently utilized in HPLC applications. Moreover, in all the models considered, the influence of temperature on the column efficiency and separation of mixture components is analyzed with the emphasis given on the coupling of thermal and concentration fronts. To gain confidence, the results of proposed analytical and numerical methods are authenticated against the results of a high-resolution finite-volume scheme (HR-FVS). Furthermore, important parameters are identified that influence the performances of the column and reactor. The results obtained will be beneficial for interpreting mass and energy profiles in non-equilibrium and non-isothermal liquid chromatographic columns and provide deeper insight into the sensitivity of the separation process without performing costly and time-consuming laboratory experiments.