In the oil industry, it is necessary to construct submerged wells to exploit the underground oil. However, when we need to abandon these oil wells, when we do not explore it further, it needs to be isolated. For this, cement paste is placed on a layer of drilling fluid. The cement is heavier than the drilling fluid and should reach its cure time without being contaminated by the drilling fluid so that the well can be isolated. Thus, it is relevant to study how these two fluids behave when subjected to direct contact in a vertical pipe, that is, to verify how fluid 2 (well blocking) behaves when it interacts with fluid 1 (drilling fluid) both fluids have non-Newtonian behavior. This work proposes a methodology to study the problem raised above, by varying the rheological parameters of the two fluids in question, and studying how the interaction of fluids happens due to the combination of these parameters. Thus, a numerical simulation of the conservation equations that govern the flow using the Fluent program is made. The results of the identification of the interaction of the fluids, based on the different rheological characteristics of the same were very. When studying the behavior of the fluids, with the application of the properties indicated above, some behaviors typical of situations that occur in oil wells were verified, for example, the higher the density of the fluid from above, the greater the contamination, which also occurs quickly.