Theoretical optimization of operating parameters in non-ideal displacement chromatography

Abstract A mathematical model was developed for the simulation of non-ideal displacement chromatography. The model incorporates finite mass transport to the solid adsorbent by using a linear driving force approximation with a coupled external film and internal pore mass transfer coefficient. Equilibrium adsorption at the fluid—solid interface is described using competitive langmuirian adsorption isotherms. A finite difference numerical technique was employed to approximate the system of coupled, non-linear partial differential equations. The model was used to simulate the effluent concentration profiles under various displacement chromatographic conditions. The effects of axial dispersion and finite mass transport were examined by varying the Peclet and Stanton numbers, respectively. Slow mass transfer rates were shown to have a dispersive effect on the shock waves generated in displacement chromatography, resulting in greater zone overlap. Constant pattern formation was observed under non-ideal conditions. The throughput obtained in displacement chromatography was examined as a function of feed load, flow velocity, and displacer concentration. For non-ideal systems, the throughput was shown to exhibit a maximum at unique values of these operating parameters. The effects of particle diameter and solute diffusivity on the throughput were also examined. Model predictions indicate that the use of large particles could be detrimental to the performance of displacement systems when high velocities are employed. For macromolecular separations by displacement chromatography, small particles are required regardless of the linear velocity. The model presented here is a useful tool for the optimization and scale-up of displacement chromatographic processes.