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Summary 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. Introduction 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. Pipeline Models. 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. Wellbore Models. 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 Unified Models. 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.

The purpose of the present study is to improve the current prediction capabilities of the entrainment fraction in horizontal gas-liquid flow. Since it is recognized that waves at the gas-liquid interface are the main source of entrainment, an experimental and theoretical work has been carried out to characterize the waves at the gas-liquid interface and to develop a model for entrainment calculations based on such characteristics. The model consists of three sub-models, namely, onset of entrainment, maximum entrainment and entrainment values in between. The onset of entrainment model determines the conditions at which the gas starts shearing the wave crests through a force balance between drag and surface tension forces. The maximum entrainment model provides the maximum fraction of liquid that can be entrained at high gas velocities by integration of the turbulent velocity profile to a determined dimensionless film thickness within the buffer sub layer. The entrainment fraction in between onset and maximum boundaries is calculated from an equilibrium between atomization and deposition rates. The atomization rate is calculated by first determining the wave mass flux in the liquid film and second by calculating the fraction of a single wave that is sheared by the gas through a force balance. The deposition rate is calculated as a linear function of the droplet concentration in the gas. Closure relationships have been developed from data for wave celerity, frequency, amplitude and width which are used in the entrainment model. A review of the most used correlations for calculating the entrainment fraction is presented and their performance evaluated. The present model shows better prediction than available models when compared to the acquired experimental data and the available experimental data in the literature.

Continuous flow gas lift is one of the most common artificial lift methods widely used in the oil industry. A continuous volume of high-pressure gas is injected as deep as possible into the tubing, to gasify the oil column, and thus facilitate the production. If there is no restriction in the amount of injection gas available, sufficient gas can be injected into each oil well to reach maximum production. However, the injection gas available is generally insufficient. An inefficient gas allocation in a field with limited gas supply reduces the revenues, since excessive gas injection is expensive due to the high gas prices and compressing costs. Therefore, it is necessary to assign the injection gas into each well in optimal form to obtain the field maximum oil production rate. The gas allocation optimization can be considered as a maximization of a nonlinear function, which models the total oil production rate for a group of wells. The variables or unknowns for this function are the gas injection rates for each well, which are subject to physical restrictions. In this work a nonlinear optimization technique, based on an objective function with constraints, was implemented to find the optimal gas injection rates. A new mathematical fit to the gas-lift performance curve (GLPC) is presented and the numeric results of the optimization are given and compared with those of other methods published in the specialized literature. The GLPC can be either measured in the field, or alternatively generated by computer simulations, by mean of nodal analysis. The optimization technique proved fast convergence and broad application.

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Summary An extensive experimental program has been conducted using a 2-in. hydrocyclone. The inlet flow conditions are: total flow rates between 18 to 27 GPM, oil-cut up to 10%, median droplet size distributions from 30 to 180 µm, and inlet pressures between 60 and 90 psia. The acquired data include the flow rate, oil-cut, and droplet size distribution in the inlet and in the underflow; the reject flow rate and oil concentration in the overflow; and the separation efficiency. Additional data were taken from the literature, especially from the Colman and Thew1 study. This experimental investigation provided insight into the hydrodynamic flow behavior in the liquid/liquid hydrocyclone (LLHC), and helped develop and refine a mechanistic model for the LLHC, which is presented in Part 2 of this paper. Introduction The petroleum industry traditionally has relied on conventional gravity-based vessels that are bulky, heavy, and expensive to separate multiphase flow. The growth of the offshore oil industry, in which platform costs to accommodate these separation facilities are critical, has provided the incentive for the development of compact separation technology. Hydrocyclones have emerged as an economical and effective alternative for produced water deoiling and other applications. The hydrocyclone is simple in design with no moving parts, easy to install and operate, and is inexpensive to purchase and maintain. Hydrocyclones have been used in the past to separate solid/ liquid, gas/liquid, and liquid/liquid mixtures. For the liquid/liquid case, both dewatering and deoiling hydrocyclones have been used in the oil industry. This study focuses only on the latter case, namely using the LLHC to remove dispersed oil from a water continuous stream. Oil is produced with a significant amount of water and gas. Typically, a set of conventional gravity-based vessels are used to separate most of the multiphase mixture. The small amount of oil remaining in the water stream, after the primary separation, has to be reduced to a legally allowable minimum level for offshore disposal. LLHCs have been used successfully to achieve this environmental regulation. There is a large quantity of literature available on the LLHC, including experimental data sets, computational fluid dynamic (CFD) simulations, and modeling. However, there is still a need for more comprehensive and detailed data sets, including measurements of the inlet and underflow droplet size distributions, utilizing appropriate sampling procedures. The objective of this study is to conduct detailed experimental investigation to provide insight into the hydrodynamic flow behavior in the LLHC and to help develop and refine a mechanistic model for the LLHC (to be presented in the second part of this paper). LLHC Hydrodynamic Flow Behavior. The LLHC, shown schematically in Fig. 1, uses centrifugal force to separate the dispersed phase from the continuous fluid. The swirling motion is produced by the tangential injection of pressurized fluid into the hydrocyclone body. The flow pattern consists of a spiral within another spiral moving in the same circular direction (Seyda and Petty2). There is a forced vortex in the region close to the LLHC axis and a free-like vortex in the outer region. The outer vortex moves downward to the underflow outlet, while the inner vortex flows in a reverse direction to the overflow outlet. Moreover, there are some recirculation zones associated with the high swirl intensity at the inlet region. These zones, with a long residence time and very low axial velocity, have been found to be diminished as the flow enters the low-angle taper section (see Fig. 1). An explanation of the characteristic reverse flow in the LLHC is presented by Hargreaves.3 With high swirl intensity at the inlet region, the pressure is high near the wall region and very low toward the centerline, in the core region. As a result of the pressure gradient profile across the diameter, which decreases with downstream position, the pressure at the downstream end of the core is greater than at the upstream, causing flow reversal. As the fluid moves to the underflow outlet, the narrowing cyclone cross-sectional area increases the fluid angular velocity and the centrifugal force. It is due to this force and the difference in density between the oil and the water that the oil moves to the center, where it is caught by the reverse flow and separated, flowing into the overflow outlet. Instead, if the dispersed phase is the heavier, like solid particles, it will migrate to the wall and exit through the underflow. Thus, for these two different separation cases, two different geometries are needed (Seyda and Petty2). In the deoiling case, usually 1 to 10% of the feed flow rate goes to the overflow. Another phenomenon that may occur in a hydrocyclone is the formation of a gas core. As Thew4 explained, dissolved gas may come out of solution because of the pressure reduction in the core region, migrating fast to the LLHC axis, and eventually emerging through the overflow outlet. An experimental study on the effect of gas on the LLHC performance is found in Smyth and Thew.5 LLHC Geometry. The deoiling LLHC consists of a set of cylindrical and conical sections. The Colman and Thew6 design has four sections, as shown in Fig. 2. The inlet chamber and the reducing section are designed to achieve higher tangential acceleration of the fluid, while reducing the pressure drop and the shear stress to an acceptable level. The latter has to be minimized to avoid droplet breakup leading to reduction in separation efficiency. The tapered section is where most of the separation is achieved. The low angle of this segment keeps the swirl intensity with high residence time. An integrated part of the design is a long tailpipe cylindrical section in which the smallest droplets migrate to the reversed flow core at the axis and are being separated flowing into the overflow exit. This configuration gives a very stable smalldiameter reversed flow core, utilizing a very small overflow port.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThe Gas-Liquid Cylindrical Cyclone (GLCC) has repeatedly proven itself in laboratory and field tests, as well as in actual field applications, as a viable alternative to the conventional gravity-based gas/liquid separator.Large conventional gravity-based vessels have been relied upon since the inception of the petroleum industry to separate oilfield production of oil, water, sand, and gas. However, economic and operational pressures continue to force the petroleum industry to seek smaller, less expensive and more appropriate separation alternatives in the form of compact separators, especially for offshore and subsea applications. As compared to the vessel-type separators, a compact separator such as the GLCC is a simple, low-cost, low-weight separator that requires little maintenance and is easy to install and operate. Furthermore, the capabilities to accurately predict various performance characteristics, e.g., liquid carry-over and gas carry-under, of the GLCC have far surpassed those capabilities for conventional vessel type separators. The scope of this paper is to present the state-of-the-art of the GLCC technology for variety of applications in the oil and gas industry.At present, over 1,000 GLCCs have been installed in fields around the world. Details of typical field applications are presented and discussed in this paper. In addition, data from field type facilities, namely, Texaco's Humble flow loop and Colorado Engineering Experiment Station Inc. (CEESI) are presented. These data illustrate GLCC performance at high pressures (up to 1,000 psi) with a variety of hydrocarbon fluids. The results presented include, gas carry-under (GCU), liquid carry-over (LCO) and GLCC control data. Additional field testing of the first integrated GLCC compact separation system carried out in Daqing oil field experiment station are also presented.The technology for state-of-the-art GLCC field applications and some laboratory and field testing results presented in this study, will help petroleum engineers to better understand, design and deploy GLCC technology in their field operations.The pioneering studies on the GLCC were conducted by Chevron (Liu &Kouba, 1994 andKouba et al. , 1995) for the development of the multiphase metering loop incorporating the Net Oil Computer © , as shown schematically in Fig. 1. The GLCC technology has been rapidly developed and disseminated by industrial cooperation, namely, through the Tulsa University Separation Technology Projects (TUSTP) industry/university research consortium.

The data reveal that LLHCs can be used up to 10% oil concentrations at the inlet, maintaining high separation efficiency. However, the performance of the LLHC is best for very low oil concentrations at the inlet, below 1%. For low concentrations, no emulsification of the mixture occurs in the LLHC. However, high inlet concentrations, up to 10%, promote emulsification posing a separation problem in the overflow stream.An existing LLHC mechanistic model is modified and refined. The main modifications carried out are improved correlation for the swirl intensity that affects the axial and tangential velocity distributions, the flow reversal radius and the inlet factor.The required inputs for the model are: LLHC geometry, fluid properties, inlet droplet size distribution and operational conditions. The model is capable of predicting the LLHC hydrodynamic flow field, namely, the swirl intensity and the axial, tangential and radial velocity distributions of the continuous-phase. The separation efficiency and migration probability are determined based on droplet trajectory analysis. The flow capacity, namely, the inlet-to-underflow pressure drop, is predicted utilizing an energy balance analysis.The LLHC mechanistic model was tested against the present study data and additional data from the literature, especially from . Very good agreement is observed between the model predictions and the experimental data with respect to the swirl intensity, axial and tangential velocity distributions, migration probability and global separation efficiency. The developed LLHC model can be used for the design of field applications for the industry. v ACKNOWLEDGEMENTS