A new mechanistic model to predict the natural separation efficiency in deviated pumped wells has been developed based upon the combined phase momentum equations and a general slip closure relationship. The model incorporates two important parameters that are both functions of flow pattern; the local void fraction in front of the pump intake ports and the drag coefficient. The void fraction is, in turn, a function of the bubble rise velocity. The model uses existing void fraction and bubble rise velocity correlations developed by Hasan and Kabir1 for both bubbly and slug flow. The transition between bubbly and slug flow is determined by using the Hasan2 and Hasan and Kabir3 criteria. The Barnea et al.4 critical angle criterion below which bubbly flow cannot exist is also used by the model. A general drag coefficient correlation for slug flow has been developed based on data gathered by Serrano5 on a water-air system for inclination angles of 30 and 60 degrees.
Comparisons between the model's predictions and the experimental data of Serrano5 show excellent agreement. Sensitivity studies developed using the model indicates that the natural separation efficiency decreases as the liquid rate, inclination angle and gas-liquid ratio increase and as the annulus area decreases. For the wellbore configuration and operating conditions under investigation, the model predicts the existence of a minimum liquid rate below which the system reaches 100 percent gas separation efficiency.