The proposed study is important in processes related to the industry, such as cementing oil wells, fuel gas injection, cleaning equipment, among others. The concepts presented in this work are of great interest because operational problems resulting from poor predictions about the flow of immiscible fluids can lead to accidents from the simplest to the most severe. An example of this is the explosion of the Deepwater Horizon platform in the Gulf of Mexico in April 2010, where in addition to the deaths of dozens of people, it caused an oil spill in the habitat of several species of animals. The objective of this work is to present a simulation model for the flow of immiscible fluids in pipes with variable inclinations and study the effect of different liquid properties and flow conditions on the efficiency of the displacement process.