The analytical method of two-term time-fractional advection–dispersion–reaction models with sorption process

If the sorption process is described by the time fractional derivative, the traditional advection–dispersion–reaction models become two-term time-fractional ones. The analytical method built by Jiang et al. is extended to time-fractional advection–dispersion–reaction models and applied to practical models of nitrate and pollutant transport. The numerical solution adopts a fully implicit finite difference scheme, and the time fractional derivative is discretized by the L1 scheme. The analytical and numerical solutions of NO 3 − , pollutant and Cd 2+ transport models demonstrate the existence of anomalous diffusion and the evolution from the anomalous diffusion over time to the normal one and the negative correlations between the fractional order and the sorption and between the fractional order and the decay rate of solute concentration. • Write the sorption process of ions and pollutant into fractional derivative. • Build two-term time-fractional models for ions and pollutant. • Apply the analytical method of multi-term time-fractional models to practical problem. • Find the transit mechanism from subdiffusion to normal diffusion.