Dimensionless analytical model for non-ideal breakthrough in fixed beds: Application to trivalent amphoteric oxide sorbent materials

Novel analytical solutions were developed to simulate breakthrough curves from flow-through columns with trivalent amphoteric oxide sorbent material. When the rate of sorption is slow compared to the rate of advection, sorption is limited by the rate of mass transfer of pollutants from the liquid to the solid phase. The two coupled differential equations for liquid and solid phase concentrations were solved analytically and valuable, simple analytical solutions emerged with two dimensionless parameters: 1) γ, the sorptive potential of the material, and 2) Da, the Dämkohler number, representing the ratio of mass transfer rate to the advection rate through the material. The solutions can guide the design of sorption systems to achieve a target removal percent or determine the number of pore volumes that can be treated before the material must be disposed or regenerated. The equations were tested using experimental data from four columns operated with phosphate sorption media at varying hydraulic loading rates to evaluate the analytical approach's scalability. The analytical solution captured the breakthrough curves using a least square fit. A noted advantage of the analytical solutions is the ease of application to rapidly screen sorptive materials and to select suitable hydraulic and pollutant loading rates.