An Experimental and Theoretical Investigation of Upward Two-Phase Flow in Annuli
- Antonio C.V.M. Lage (Petrobras) | Rune W Time (Stavanger U. College and RF-Rogaland Research)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2002
- Document Type
- Journal Paper
- 325 - 336
- 2002. Society of Petroleum Engineers
- 4.1.5 Processing Equipment, 4.6 Natural Gas, 2.5.2 Fracturing Materials (Fluids, Proppant), 1.7.1 Underbalanced Drilling, 1.11.5 Drilling Hydraulics, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.6.9 Coring, Fishing, 4.1.2 Separation and Treating, 1.6 Drilling Operations, 5.4.2 Gas Injection Methods, 3.1.1 Beam and related pumping techniques, 1.10 Drilling Equipment, 4.3.4 Scale, 5.3.2 Multiphase Flow, 1.6.1 Drilling Operation Management, 1.7.7 Cuttings Transport
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A steady-state mechanistic model is formulated to predict the mixture behavior for upward two-phase flow in concentric annuli. It consists of a procedure for flow pattern prediction and a set of independent models for calculating gas fraction and pressure drop in bubble, dispersed bubble, slug, and annular flow. Some aspects of churn flow are also discussed.
Experiments are performed in a 1278 m vertical well and in a small-scale U-tube, which comprises a descending pipe and an ascending annulus. Small-scale data available in the literature were also collected and catalogued.
The model is validated against the database. The performance of the model is compared with the performances of other models from the literature. It shows that the proposed model is more accurate than the alternatives.
Upward two-phase flow through an annular channel is encountered in various industrial applications such as heat exchangers, power plants, and production of oil and gas. However, the intensity of engineering use does not reflect on the research efforts because literature presents a small number of related studies.1-6
In the past, the interest of the oil industry for this subject was restricted to some high productivity wells flowing through the casing-tubing annulus.2 In addition, some studies were motivated by oil wells lifted by sucker rod pumps.5 Recently, the topic is gaining more relevance as the popularity of underbalanced drilling (UBD) technology grows. Considering that accurate prediction of downhole pressure is a key factor for a successful UBD operation,7 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 specific conditions without well defined borders.8 In this scenario, similar 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 separate models for each one of these flow patterns to predict the main parameters as gas fraction, in-situ velocities, and pressure drop. Because the basic laws of fluid mechanics are behind the development, the results can be extended to conditions different from those used for the development.
Sadatomi et al.1 performed experiments in a 15×30 mm (0.59×1.18 in.) annulus and evaluated bubble rise velocities. They also utilized the Lockhart and 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 an extensive experimental investigation in a 42.2×72.6-mm (1.66×3 in.) annular space using air/water and air/ kerosene. Despite the comprehensiveness of his study, work is still needed for improvements. For instance, the submodel for annular flow presented an overall tendency for overestimating total pressure gradients - predictions 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 50.8×76.2 mm (2×3 in.) annular channel, although the study was limited to flow pattern definition.
Nakoriakov et al.4 studied upward two-phase flow in vertical narrow annulus. In other words, the research is applicable to annular spaces where the width of channel is smaller than the capillary constant defined by:
For channels with a smaller gap than the value given by Eq. 1, capillary forces define the two-phase structure. However, usual annular configurations in the oil industry are much larger than the one defined by the capillary constant. Consequently, the flow variables keep the analogy with circular pipe situations in which surface- tension effects are not too relevant.
Papadimitriou and Shoham5 presented some improvements to Caetano's mechanistic model, but they limited their investigation to bubble- and slug-flow patterns.
Hasan and Kabir6 focused on flow pattern predictions, slip velocities, and gas fraction, but they did not treat either pressure gradients or the annular flow regime.
Scope of Work.
The main target of this investigation is on the development of a steady-state mechanistic model for upward two-phase flow in vertical and concentric annuli with channel width larger than the capillary constant. The present study focuses on two-phase mixtures formed in the absence of chemical surfactants, which means that the formation of foams is out of this investigative scope. The prediction of the flow pattern constitutes the first step in the process and the calculation of the main parameters, such as pressure and gas fraction, taking into account the predicted flow configuration, represents the second and final one. Further, the model performance is evaluated against small-scale and full-scale experimental data.
The present work extends an investigation that was already reported.10 The two-phase flow tests performed in the small-scale U-tube apparatus shown in Fig. 1 enriches the experimental database and provides additional elements for improving the mechanistic model. Besides, churn flow is further discussed based on approaches recently presented in literature.11,12 The proposed mechanistic model is evaluated against full-scale data, and its performance is compared with the performance of the Beggs and Brill13 correlation.
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