Study of pollution transport through the rivers using aggregated dead zone and hybrid cells in series models

This paper aims at studying the data-based mechanistic pollution transport models of the aggregated dead zone (ADZ) and hybrid cells in series (HCIS) models. For a better understanding of them, it was tried to connect their parameters to the physical parameters of the classical advection–dispersion (ADE) model. A series of experiments were conducted using the laboratory model of the gravel bed river, and the sodium chloride solution was chosen as a conservative tracer. A new analytical solution of HCIS model, including triple dispersion cells, was developed. Also, the theoretical temporal moment equations were derived and attempted to develop explicit relationships for both ADZ and HCIS parameters based on hydraulically and geometrically variables. Detailed descriptions of the Pe number and the skewness coefficients (CSK) were presented, and the theoretical limit of CSK was extracted. It was concluded that the range of (0.93–1.24) for CSK is acceptable, which confirms the finding of previous investigators. A sensitivity analysis was operated to find the importance of different variables in estimating model parameters. Finally, the theoretical breakthrough curves of ADZ and HCIS models were drawn and confirmed with experimental BTCs. Statistical goodness of fit parameters of RMSE, DC, and MAE was calculated as triple sets of (0.0158, 0.99, 21.58 ppm), (0.0188, 0.97, 27.16 ppm), and (0.105, 0.83, 78.84 ppm) for ADZ, HCIS, and ADE models, respectively, which showed the superiority of data-based models to the classical ADE model.