Affinity chromatography (biospecific adsorption) relies on specific interactions of biological molecules such as enzymes, antigens, antibodies, and proteins. The process consists of three steps: adsorption, washing, and elution. A mathematical model including convection, diffusion, and reversible reaction is formulated to analyse the breakthrough behaviour of the solute. A moving finite element orthogonal collocation method is applied with respect to the space variables of the governing partial differential equations of the model to evaluate the breakthrough of the solute. Danckwerts' boundary conditions are considered for the column. The validity of the numerical scheme is checked by comparison with an analytical solution for a simplified model. The results obtained from model simulation show that the breakthrough time of the solute is significantly influenced by the axial dispersion coefficient, solute concentration, ligand content, reaction kinetics, particle porosity, particle size, and flow rate. Solute recovery and bed utilisation efficiencies are evaluated for different values of the above parameters.