Abstract:
Theoretical Analysis of Dynamic Behaviors in Liquid Chromatography
The chromatographic techniques are used on laboratory and industrial scales for the sepa-
ration of substances that under the traditional processes, such as distillation or extraction,
are neither technically nor economically feasible. It is an important separation technique in
the petrochemical industry and becomes more and more exploited in fine chemical, phar-
maceutical and biotechnical industries. For instance, this attractive technology is used to
separate chiral molecules, enzymes, sugar and to purify proteins or to produce insulin.
This thesis project is concerned with the analytical and numerical solutions of three stan-
dard liquid chromatographic models namely, the equilibrium dispersive model (EDM), the
lumped kinetic model (LKM) and the general rate model (GRM). Each model consid-
ers different levels of complexities to describe the process. These models are systems of
convection-diffusion partial differential equations with dominating convective terms and
coupled through differential or algebraic equations.
The Laplace transformation is applied to derive the analytical solutions of the EDM and
LKM considering the special case of single-component linear adsorption isotherm, contin-
uous or finite width pulse injections, two different sets of boundary conditions and fully
porous particles. For further analysis of the solute transport behavior, the analytical tem-
poral moments are derived from the Laplace-transformed solutions and are compared with
the numerical solutions of a semi-discrete high resolution finite volume scheme (HR-FVS).
For nonlinear adsorption isotherms, numerical techniques are the only tools to provide solu-
tions. However, the strong nonlinearities of realistic thermodynamic functions pose major
difficulties for the numerical schemes. For that reason, computational efficiency and accu-
racy of the numerical methods are highly important. The suggested HR-FVS is extended
to approximate these nonlinear model equations. The numerical results of the suggested
HR-FVS are compared with some other finite volume schemes available in the literature.
Different case studies are considered covering a wide range of mass transfer kinetics. The
results obtained verified the correctness of analytical results and accuracy of the suggested
HR-FVS.
An interesting aspect of this thesis project is the application of GRM to fixed-bed chro-
matographic columns packed with core-shell or fully porous particles. Due to their proven
performance and improved availability, core-shell particles are increasingly applied for chro-
matographic separations. Such particles are useful for highly efficient and fast separation
of complex samples with a reasonably low back pressure. Cored beads provide advantages
over fully porous beads, such as reduced diffusional mass transfer resistances in particle
macropores and separation times. The concept has improved column efficiency by shorten-
ing the diffusion path that molecules have to travel and thus, has improved the diffusional
mass transfer kinetics in particle macropores. Once again, both single-component linear
and multi-component nonlinear GRM models are considered. The above mentioned ana-
lytical and numerical solution techniques are applied to solve the model equations. The
potential of the solutions is demonstrated by considering different case studies that quan-
tify the effects of the relative core size, axial dispersion, film mass transfer resistance and
intraparticle diffusion resistance in the porous layer on the elution curves.