International audienceOil extraction represents an important investment and the control of a rational exploitation of a field means mastering various scientific techniques including the understanding of the dynamics of fluids in place. This paper presents a theoretical investigation of the dynamic behavior of an oil reservoir during its exploitation. More exactly, the mining process consists in introducing a miscible gas into the oil phase of the field by means of four injection wells which are placed on four corners of the reservoir while the production well is situated in the middle of this one. So, a mathematical model of multiphase multi-component flows in porous media was presented and the cell-centered finite volume method was used as discretization scheme of the considered model equations. For the simulation on Matlab, the case of the oilfield of Tsimiroro Madagascar was studied. It ensues from the analysis of the contour representation of respective saturations of oil, gas and water phases that the conservation law of pore volume is well respected. Besides, the more one moves away from the injection wells towards the production well; the lower is the pressure value. However, an increase of this model variable value was noticed during production period. Furthermore, a significant accumulated flow of oil was observed at the level of the production well, whereas the aqueous and gaseous phases are there present in weak accumulated flow. The considered model so allows the prediction of the dynamic behavior of the studied reservoir and highlights the achievement of the exploitation process aim