Mathematical modelling of a hydrocyclone for the down-hole oil–water separation (DOWS)

Abstract

In this study, a mathematical model is developed to predict the efficiency of a down-hole oil–water separation hydrocyclone. In the proposed model, the separation efficiency is determined based on droplet trajectory of a single oil droplet through the continuous-phase. The droplet trajectory model is developed using a Lagrangian approach in which single droplets are traced in the continuous-phase. The droplet trajectory model uses the swirling flow of the continuous-phase to trace the oil droplets. By applying the droplet trajectory, a trial and error approach is used to determine the size of the oil droplet that reaches the reverse flow region, where they can be separated. The required input for the proposed model is hydrocyclone geometry, fluid properties, inlet droplet size distribution and operational conditions at the down hole. The model is capable of predicting the hydrocyclone hydrodynamic flow field, namely, the axial, tangential and radial velocity distributions of the continuous-phase. The model was then applied for some case studies from the field tested DOWS systems which exist in the literature. The results show that the proposed model can predict well the split ratio and separation efficiency of the hydrocyclone. Moreover, the results of the proposed model can be used as a preliminary evaluation for installing a down-hole oil–water separation hydrocyclone system in a producing well.