The computational reconstruction of oil and gas reservoir morphology is a challenging task and must consider several natural phenomena. In this work, a sedimentation model, coupled with the Arbitrary Lagrangian Eulerian (ALE) method for tracking bottom changes, is proposed. The scheme considers an incompressible fluid flow of diluted density currents transported by the advection diffusion equation. The stabilized SUPG/PSPG/LSIC finite element formulation is used for the Navier-Stokes equations and SUPG and discontinuity capturing formulation for the sediment transport. Turbulence is treated by a Smagorinsky model. Results show that the proposed scheme is promising and can effectively represent the phenomena of interest.