This work presents an in-house two-dimensional two-phase model to describe oil spill in river sections. A two-dimensional geometry was adopted since the oil flows on the water. Due to the irregular geometry of rivers banks, the momentum and mass equations were written in curvilinear coordinates. An orthogonal grid method was especially developed to represent the river surface, since the finite volume method requires orthogonal grids. An eulerian-eulerian approach was used for the mass and momentum balances, written in curvilinear coordinates. A zero-order turbulence model was used to account for turbulence. The model can also be used to predict miscible effluent dispersion in a river section. A software has been developed from the model and results for both miscible effluent dispersion and oil spill are presented.