Mechanistic Model for Upward Two-Phase Flow in Annuli

Abstract

Abstract A mechanistic model is formulated to predict the mixture behavior for upward two-phase flow in concentric annulus. The model is composed of a procedure for flow pattern prediction and a set of independent mechanistic models for calculating gas fraction and pressure drop in bubble, dispersed bubble, slug and annular flow. Small-scale experimental data from the literature validate the predictions of the model. A full-scale experimental investigation is also executed to complete the evaluation. The experiments are performed in a 1278 m vertical well in the Petrobras research facility in Taquipe, Brazil, with an 88.9 mm×159. 4 mm (3.5 in. ×6.276 in.) annulus. Test matrix covered the whole range of possible combinations of liquid and gas injection rates for an underbalanced drilling operation in a similar geometry. The overall model performance is in good agreement with the experimental data. Introduction Upward two-phase flow through an annular channel is encountered in distinct applications such as heat exchangers, power plants and production of oil and gas. However, the amount of industrial use is not reflected in research efforts. In fact, literature presents a very small number of studies related to it1–6. In the past, the interest of the oil industry for this subject was restricted to some high productivity wells flowing through the casing-tubing annulus2. In addition, some studies were motivated by oil wells lifted by sucker rod pumps5. Recently, it is gaining more relevance as grows the popularity of the underbalanced drilling technology. Considering that accurate prediction of downhole pressure is a key factor for a successful UBD operation7, the knowledge of the two-phase flow through annuli becomes more relevant. Because of the complex nature of the problem, most of the calculation approaches in current practice for UBD are based on empirical methods. As a result, the possibilities of use are restricted to particular conditions without well-defined borders8. In this scenario, similarly to the trend observed in two-phase flow in pipes, the application of mechanistic models is supposed to be the natural way for improvement. The mechanistic or phenomenological approach postulates the existence of different flow configurations and formulates separated models for each one of these flow patterns to predict the main parameters as gas fraction and pressure drop. Since the basic laws of fluid mechanics are behind the development, the results can be extended to conditions different than those used for the development. Literature Review Sadatomi et al.1 performed experiments in a 15 mm×30 mm (0.59 in. ×1.18 in.) annulus and evaluated bubble rise velocities. They also utilized the Lockhart & Martinelli relationship9 for studying pressure drops. However, their investigation did not cover all flow configurations. Caetano2 developed a mechanistic model for dealing with vertical upward two-phase flow in concentric and eccentric annulus. He also performed a comprehensive experimental investigation in a 42.2 mm×72.6 mm (1.66 in. ×3 in.) annular space using air-water and air-kerosene. This was an extensive study, but work is still needed for improvements. The sub-model for annular flow regime, for instance, tended to overestimate the total pressure gradient. As an example, the model predicted the total pressure gradients 66% higher in average than the measured values for the air-kerosene mixture. Kellessidis and Dukler3 investigated the flow pattern map for upward two-phase flow. They also performed experimental tests in a 50.8 mm×76.2 mm (2 in. ×3 in.) annular channel, although the study was limited to flow pattern definition. Literature Review Sadatomi et al.1 performed experiments in a 15 mm×30 mm (0.59 in. ×1.18 in.) annulus and evaluated bubble rise velocities. They also utilized the Lockhart & Martinelli relationship9 for studying pressure drops. However, their investigation did not cover all flow configurations. Caetano2 developed a mechanistic model for dealing with vertical upward two-phase flow in concentric and eccentric annulus. He also performed a comprehensive experimental investigation in a 42.2 mm×72.6 mm (1.66 in. ×3 in.) annular space using air-water and air-kerosene. This was an extensive study, but work is still needed for improvements. The sub-model for annular flow regime, for instance, tended to overestimate the total pressure gradient. As an example, the model predicted the total pressure gradients 66% higher in average than the measured values for the air-kerosene mixture. Kellessidis and Dukler3 investigated the flow pattern map for upward two-phase flow. They also performed experimental tests in a 50.8 mm×76.2 mm (2 in. ×3 in.) annular channel, although the study was limited to flow pattern definition.