Estimation of the penetration depth of the pollution in the river bed for evaluation of the self-purification characteristics of the rivers by developing a novel theoretical relationship

In the current study, it was tried to determine the mechanism of the tracer penetration through the depth of the river beds to investigate the self-purification nature of the rivers. For this purpose, experimental tests were carried out, and an analytical solution was developed. The electrical conductivity sensors and sodium chloride tracer (as a conservative contaminant) were operated in the operations. Also, for the derivation of the analytical equation, a conceptual model was presented based on the hybrid cells in series model. Then, by imposing the mass conservation to each cell of depth column, the governing differential equation was obtained and solved. Next, the results were evaluated by the framework of the developed equation. Moreover, the applicability of the new model was checked and confirmed by the recreation of the breakthrough curves. The time parameters of the new model were extracted. Then, their variation by the other parameters was queried. It is observed that the sum of temporal parameters (α,T_1,T_2) have a reverse relationship with the vertical dispersion coefficient. On the other hand, its value has been raised by an increment of the bed depth. Furthermore, the product of void scale and the pore velocity has been used for calculation of the vertical dispersion coefficient. Also, the magnitudes of the pore velocity and dispersivity were commuted. It is revealed that by the increase of the bed depth, the mentioned parameters were decreased.