An optimized method for solution of fixed-bed adsorption model considering particle-size distribution via method of characteristics

Fixed-bed adsorption is widely used for gas separation. In published work, to consider the impact of adsorbent particle size distribution in fixed-bed adsorption, a novel model integrating population balance equation (PBE) and mass transfer equation was proposed. However, when the PBE problem is high-dimensional, tremendous computation burden is usually unavoidable using numerical method, i.e. high-resolution finite volume algorithm. In this work, we develop an optimized solution algorithm that combines the analytical method of characteristics (MOC) and discrete numerical solving to accelerate the solution of PBE. Comparative analysis of computational performance was conducted between the optimized algorithm and the high-resolution finite volume algorithm. It was demonstrated that the optimized algorithm significantly outperforms the high-resolution method in computational resource consumption while maintaining solution consistency. Moreover, numerical dispersion was reduced. These improvements enhance the joint model's prediction accuracy and speed for adsorbent adsorption behavior considering particle size distribution, enabling the model to demonstrate strong application potential in fixed-bed adsorption simulation and prediction.