In this research article, two standard models of liquid chromatograophy, namely the dispersive equilibrium model (DEM) and the kinetic lumped model (KLM) are approximated numerically. We studied the transport of multi components in a single column of chromatography considering non linear adsorption thermodynamics. The models are analyzed for standard Bi-Langmuir and generalized Bi-Langmuir types adsorption equilibrium isotherms using Danckwert (Robin) boundary conditions. Mathematically, the model equations form a non linear system of partial differential equations accounting for the phenomena of advection and diffusion, paired with an algebraic equation or a differential equation for adsorption isotherm. An extended semi-discrete high-resolution finite volume scheme is employed to obtain the approximate solutions of the governing model equations. The method has second to third order accuracy. Several test case studies are conducted to examine the influence of various critical parameters on the process performance. The contemplated case studies incorporate the elution process of liquid chromatography with an increasing number of components. In particular, single component, two component and three component mixtures are considered for the assessment of process performance. The formulated numerical algorithm provide an efficacious mechanism for investigating the retention behavior and the influence of mass transfer kinetics on the shapes of elution profiles.