Studies have shown that humankind will experience a water shortage in the coming decades. It is therefore paramount to develop new techniques and models with a view to minimizing the impact of pollution. It is important to predict the environmental impact of new emissions in rivers, especially during periods of drought. Computational fluid dynamics (CFD) has proved to be an invaluable tool to develop models able to analyze in detail particle dispersion in rivers. However, since these models generate grids with thousands (even millions) of points to evaluate velocities and concentrations, they still require powerful machines. In this context, this work contributes by presenting a new three-dimensional model based on CFD techniques specifically developed to be fast, providing a significant improvement in performance. It is able to generate predictions in a couple of hours for a one-thousand-meter long section of river using Pentium IV computers. Commercial CFD packages would require weeks to solve the same problem. Another innovation inb this work is that a half channel with a constant elliptical cross section represents the river, so the Navier Stokes equations were derived for the elliptical system. Experimental data were obtained from REPLAN (PETROBRAS refining unit) on the Atibaia River in São Paulo, Brazil. The results show good agreement with experimental data.