Numerical simulation is characterized by designing a computational model of a real case. From this model it is possible to carry out experiments and simulations, with the purpose of understanding the behavior of that projected situation. In the oil industry, cementing has the function of isolating the existing zones in the well, providing adequate support for the casing and preventing fluids from migrating. Cementing is one of the most critical operations in the process of drilling and well completion oil wells, as it is directly related to the safety of the well itself. For successful cementing operations, the cement paste needs to displace the drilling fluid completely. This displacement occurs in the annular space between the well casing and the rock formation. The objective of our proposal is to understand the behavior of the fluid in this cementing process. Motivated by these industrial processes, we will conduct direct numerical simulations of the displacement process between miscible fluids in annular spaces. In these axisymmetric displacements, we propose to investigate how different physical effects affect displacement effciency, including different viscosities and densities between injected and displaced fluids, miscibility between them, injection rate and annular space opening. For this, a numerical code based on finite differences and spectral methods will be used, written in C language, which will provide data to analyze the behavior of fluids. The reading of these data and the visualization of the two-phase flow will be done in the Matlab software.