Analysis of longitudinal dispersion equations in streams and rivers

Contaminants and effluents, after they are discharged into a river, are subjected to transport and mixing processes, such as advection, molecular and turbulent diffusion and dispersion. Their effect could be accounted for the three-dimensional advection-diffusion equation, which forms the basis for the analysis of mixing problems in rivers. Once the cross-section mixing is complete, the process of longitudinal dispersion is the most important mechanism, erasing all longitudinal concentration gradients. The present paper proposes a comparison among nine literature predictive equations for the longitudinal dispersion coefficient using a set of 150 field data collected in 61 rivers through-out the world. The comparison was performed using well-known statistical parameters, such as discrepancy ratio, accuracy and standard deviation and comparing DL measured data with DL predicted values. Most of the considered equations had an accuracy in the range from 40% to 53%. However, further analysis led to prefer as more accurate Kashefipour-Falconer and Deng et al. equations to the remaining formulas. Finally, Kashefipour-Falconer equation was modified to point out a direct relationship between longitudinal dispersion coefficient DL and the discharge for unit width q.