Unified Mechanistic Model for Steady-State Two-Phase Flow: Horizontal to Vertical Upward Flow
- L.E. Gomez (U. of Tulsa) | Ovadia Shoham (U. of Tulsa) | Zelimir Schmidt (U. of Tulsa) | R.N. Chokshi (Zenith ETX Co.) | Tor Northug (Statoil)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 2000
- Document Type
- Journal Paper
- 339 - 350
- 2000. Society of Petroleum Engineers
- 5.4.2 Gas Injection Methods, 4.2.2 Pipeline Transient Behavior, 1.6.9 Coring, Fishing, 4.1.2 Separation and Treating, 4.2 Pipelines, Flowlines and Risers, 4.6 Natural Gas, 5.3.2 Multiphase Flow, 1.10 Drilling Equipment, 3.1 Artificial Lift Systems, 4.1.5 Processing Equipment
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A unified steady-state two-phase flow mechanistic model for the prediction of flow pattern, liquid holdup and pressure drop is presented that is applicable to the range of inclination angles from horizontal (0°) to upward vertical flow (90°). The model is based on two-phase flow physical phenomena, incorporating recent developments in this area. It consists of a unified flow pattern prediction model and unified individual models for stratified, slug, bubble, annular and dispersed bubble flow. The model can be applied to vertical, directional and horizontal wells, and horizontal-near horizontal pipelines. The proposed model implements new criteria for eliminating discontinuity problems, providing smooth transitions between the different flow patterns.
The new model has been initially validated against existing, various, elaborated, laboratory and field databases. Following the validation, the model is tested against a new set of field data, from the North Sea and Prudhoe Bay, Alaska, which includes 86 cases. The proposed model is also compared with six commonly used models and correlations. The model showed outstanding performance for the pressure drop prediction, with a ?1.3% average error, a 5.5% absolute average error and 6.2 standard deviation. The proposed model provides an accurate two-phase flow mechanistic model for research and design for the industry.
Early predictive means for two-phase flow were based on the empirical approach. This was due to both the complex nature of two-phase flow and the need for design methods for industry. The most commonly used correlations have been the Dukler et al.1 and Beggs and Brill2 correlations for flow in pipelines, and the Hagedorn and Brown3 and Ros4/Duns and Ros5 correlations for flow in wellbores. This approach was successful for solving two-phase flow problems for more than 40 years, with an updated performance of ±30% error. However, the empirical approach has never addressed the "why" and "how" problems for two-phase flow phenomena. Also, it is believed that no further or better accuracy can be achieved through this approach.
A new approach emerged in the early 1980's, namely, the mechanistic modeling approach. This approach attempts to shed more light on the physical phenomena. The flow mechanisms causing two-phase flow to occur are determined and modeled mathematically. A fundamental postulate in this method is the existence of various flow configurations or flow patterns, including stratified flow, slug flow, annular flow, bubble flow, churn flow and dispersed bubble flow. These flow patterns are shown schematically in Fig. 1. The first objective of this approach is, thus, to predict the existing flow pattern for a given system. Then a separate model is developed for each flow pattern to predict the corresponding hydrodynamics and heat transfer. These models are expected to be more reliable and general because they incorporate the mechanisms and the important parameters of the flow. All current research is conducted through the modeling approach. Application of models in the field is now underway, showing the potential of this method.
The mechanistic models developed over the past two decades have been formulated separately for pipelines and wellbores. Following is a brief review of the literature for these two cases.
These models are applicable for horizontal and near horizontal flow conditions, namely, ±10°. The pioneering and most durable model for flow pattern prediction in pipelines was presented by Taitel and Dukler.6 Other studies have been carried out for the prediction of specific transitions, such as the onset of slug flow,7 or different flow conditions, such as high pressure.8 Separate models have been developed for stratified flow,6,9-11 slug flow,12-14 annular flow15,16 and dispersed bubble flow (the homogeneous no-slip model17). A comprehensive mechanistic model, incorporating a flow pattern prediction model and separate models for the different flow patterns, was presented by Xiao et al.18 for pipeline design.
These models are applicable mainly for vertical flow but can be applied as an approximation for off-vertical sharply inclined flow 60° ? 90°) also. A flow pattern prediction model was proposed by Taitel et al.19 for vertical flow, which was later extended to sharply inclined flow by Barnea et al.20 Specific models for the prediction of the flow behavior have been developed for bubble flow21,22 slug flow23-25 and annular flow.26,27 Comprehensive mechanistic models for vertical flow have been presented by Ozon et al.,28 by Hasan and Kabir,21 by Ansari et al.29 and by Chokshi et al.30
Attempts have been made in recent years to develop unified models that are applicable for the range of inclination angles between horizontal (0°) and upward vertical (90°) flow. These models are practical since they incorporate the inclination angle. Thus, there is no need to apply different models for the different inclination angles encountered in horizontal, inclined and vertical pipes. A unified flow pattern prediction model was presented by Barnea 31 that is valid for the entire range of inclination angles (?90° ? 90°). Felizola and Shoham32 presented a unified slug flow model applicable to the inclination angle range from horizontal to upward vertical flow. A unified mechanistic model applicable to horizontal, upward and downward flow conditions was presented by Petalas and Aziz,33 which was tested against a large number of laboratory and field data. Recently, Gomez et al.34 presented a unified correlation for the prediction of the liquid holdup in the slug body.
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