Discontinuous Galerkin Method for Liquid Chromatography Modelling

Sammanfattning: Chromatography is a separation technique used predominantly by the medical industry in purification and extraction of components in a solution. The setup is a column filled with resin particles where a solution of two components is filtered and separated due to different rates of interaction with the resin particles. The process is often a performed at large scale with fixed manufacturing schedules and it is suggested that simulation of the process could improve efficiency of scheduling and production, thus provide more affordable medication. The purpose of this thesis is to simulate liquid chromatography with a Discontinuous Galerkin (DG) method, which is a finite element method based derivation to solve partial differential equations. This is done by applying the DG method to a Equilibrium-Dispersive Model (EDM) for Chromatography and implementing the key functions in a Python package used in the simulation. For the flux function of the DG-method, a central flux was used and for the time domain discretization a low storage Runge-Kutta method was used. The implementation was tested with square injection profiles and compared with a equilibrium disperse model, a Laplace based solver, from which L1 and L2 error norms could be computed. The results showed that the software produced very promising results for a dispesion of $D=10-3-10-4 since the concentration curve becomes very smooth and predictable. For steeper concentration curves D<10-3 the solver created oscillations around the, almost step like curve, to account for the discontinuity leading to the error norms being higher, $errL1~ 10-1 and errL2 ~10-3. The solver responds well to grid refinement for accuracy purposes until Nt>100 and had a much faster evaluation time than the EDM-solver for this type of grid, where a linear behaviour could be noted. The evaluation time was kept bellow 21s for Nt=103 points. For time step refinement with set grid of Nt=103, a quadratic dependence in evaluation time was noted, with computational time below 10s for t 10-4 but rising above 70s for t = 10-5.