Oil production from the wells results in a mixture of various phases including water, oil, gas, solids like sand and other contaminants such as nitrogen and carbon dioxide. In this way, the primary separation of the crude oil that comes from the reservoir is a very important process in the oil production. For this purpose two main equipments can be employed: gravity separators and hydrocyclones. Despite the simplicity of the mechanism of gravity separator, it is still the best solution when considering the fluctuations of the flow rate and the complexity of the multiphase flow with solid contents. Within this context, the objective of the present work is to perform a numerical analysis of the gravity separator in order to study the primary factors that affect the efficiency of the equipment and to investigate means to improve its productivity. To met the challenging task of modeling multiphase flow inside the equipments with complex geometry, a numerical approach denominated Moving Particle Semi-Implicit (MPS) method is adopted in the present work. MPS is a particle-based Lagrangian method that solves the governing equations of the continuum. It is originally developed to model incompressible free surface flows. For the modeling of the surface tension in the free surface and in the water-oil interface, a inter-particle potential force model is used. For sack of simplicity, two dimensional models of water-oil separation are considered. At first, a simple validation of the numerical approach is carried out. After that, a simplified gravity separator is modeled and the numerical simulations are carried out to investigate the influence of the geometrical configuration on the effectiveness of the separation process.