High performance finite element methods for three-dimensional chromatography models

Simple one-dimensional models are prevalently employed for numerical simulation of column liquid chromatography, irrespective of the actual size of the chromatography column. However, especially in microscale columns, which are utilized increasingly, local inhomogeneities in the packing structure as well as in the flow field and the concentration profiles can significantly influence the separation process. In order to analyze these effects and to identify potential for optimization, highly resolving three-dimensional simulations are required. The thesis at hand presents a novel, complete, and efficient simulation strategy for spatially resolved chromatography models. The focus lies on a finite element solver which has been tailored to the given fluid flow and mass transfer problems in complex geometries. A space-time Galerkin/least squares finite element method is applied to obtain stable solutions to the arising non-linear and advection-dominant problems. Suitable partitioning of the finite element mesh allows to efficiently solve realistic problems on several thousand compute cores. Selected test problems are utilized to prove that the developed simulator is able to handle realistic problems arising in column liquid chromatography. However, especially for large problems the numerical approximation error can require attention due to reduced mesh resolution. The solver is successfully employed to investigate differences in the loading behavior of two mono- and polydispersely packed microscale model columns. These novel simulations show that influences of the column confinement and of particle size, which are usually neglected in common chromatography models, can play a significant role in microscale applications and should hence be accounted for.