Some hydrocarbon recovery processes are characterized by the existence of sharp saturation and/or concentration fronts. Examples of such processes are VAPEX, in situ combustion, or water flooding of heavy oil reservoirs in presence of viscous fingering. In order to simulate correctly what happens around the fronts, small grid sizes need to be used. If however the whole reservoir is gridded very finely, computational time becomes prohibitive. In order to circumvent this problem, dynamic gridding, also callled, automatic mesh refinement may be used. During the computation, the computational grid is adapted to the dynamics of the flow. This requires the use of an estimator in order to decide where to refine or to coarsen the grid. In this work we studied dynamic gridding for a water flooding problem. We implemented this problem using the mixed hybrid finite element method in 2-D on a triangular grid. The resulting code was validated by comparison to a commercial reservoir simulator. From literature, we adapted an a posteriori estimator that had been derived for incompressible flow, and we used this to refine our grid on each time step. We show that the grid refinement criterion captures relatively well the sharp saturation front. Heterogeneities are also well captured. The code is able to reproduce some tendencies of viscous fingering, although more time is required to avoid definitely the numerical disperion and dynamic gridding influence. This work is a preamble for a second work considering simulation of the VAPEX process using dynamic gridding. For this we decided to switch to the finite volume method, for which a second code was developed which is shortly mentionned in the perspectives. We think that dynamic gridding may be a solution that will allow the simulation of processes such as VAPEX and in situ combustion at reservoir scale, using effective grid refinement in the region of the front.