Growing energy demand requires reliable, safe and long-lasting production systems, including, according to the new legislation, periodic inspections of the pipelines. Currently, design of cleaning tools meant for oil lines, is largely based on experimental information. Big service companies and research centres, built the right tools for their operations, but questions still remain regarding the behaviour of these devices under different flow conditions. In recent years, advances in CFD have allowed to analyse complex phenomena in many industrial applications, participating in technology improvement. The present work proposes a novel 2D CFD methodology to simulate the pigging processes, considering the straight movement of a Pig through a pipeline with a two-phase flow: water-air and oil-gas. The algorithm deforms the grid and re meshes specific domain sections to account for Pig translation relative to the pipe. Three Pig models (Mandrel Pigs, Foam Pigs and Spherical Pigs) were simulated in a horizontal pipe under single-phase liquid flow conditions. Subsequently Pigs were simulated under two-phase flow air-water conditions. Pressure and velocities profiles inside the pipe, and pressure distributions around the Pig were obtained. The result helps to understand the flow behaviour during the pigging processes, providing additional insight on design and operation of these devices.