SPE 164443

From Empirical to Micro-scale Modeling of Multiphase Flow; Bridging the Gap of R&D Abdullah Al Qahtani, Abdullah Al Sultan and Luai Hadhrami, King Fahd University, Research Institute

Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Middle East Oil and Gas Show and Conference held in Manama, Bahrain, 10–13 March 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract In the petroleum industry, multiphase flows are complex phenomena and can be found in a variety of situations. The three more common working fluids (oil, natural gas and water) can have four different two-phase flow permutations of the three types of fluids. Multiphase flow modeling/metering is a key factor for optimal flow design and realizing optimal recovery of hydrocarbons. Over the last few decades, scientists developed the math of pressure and flow rate relationship in multiphase flow. A number of empirical correlations and mechanistic models have been developed for predicting pressure drop and other fluid flow characteristics during multiphase flow in wellbores and flow lines. Similarly, the emerging sensing and measurement tools were adapted for application of multiphase flow in oil and gas fields. With all calculation being computer-assisted and after many years of development and experimental research, the computer based numerical analysis methods have been evolved to solve the large number of equations and correlation coefficients. With the vast application of high performance computing, computational time is not an issue anymore but accuracy. The challenges associated with multiphase flow modeling/metering include accuracy, size, application, and cost. The need for efficient and cost effective modeling/measurement systems in oil and gas fields have kept and will continue the need for active participation of R&D and better integration with sensing systems. This paper reviews the state of art of modeling of multiphase flow and the major headways that led the way for subsequent research in this regard, and potential ways to promote accuracy and reduce cost. These are potential research projects being evaluated / proposed in the research institute in King Fahd University of Petroleum & Minerals in collaboration with international service providers and national field operators. Introduction Multiphase flow refers to a mixture of different phases or components flowing at the same time and can be found in a variety of situations. Multi-phase flow is very common in industrial processes and its applications were already in use for ages. Multiphase flow is not unique to the petroleum industry, and is in many other industries. What makes multiphase flow unique in the petroleum industry are the complexity of fluids encountered, the larger diameters and longer lengths of the pipes, and often the hostile environments.

Multiphase flow can occur throughout the entire production system involved in flowing fluids from oil and gas reservoirs to processing facilities at the surface. The production system includes the well completion, and surface facilities including pipelines that carry produced fluids to other processing facilities. Multi-phase flow phenomena can be found in a wide range of length scales of interest and instead, multiphase flow structures are classified in terms of flow regimes, which are functions of varied parameters such as transients, geometry/terrain and hydrodynamics.

The multiphase flow encountered in producing oil and gas can be any combination of a saturations phase, a hydrocarbon liquid phase, and a water phase. The three more common working fluids (oil, natural gas and water) can have four different

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multi-phase flow permutations: gas–liquid, liquid–liquid, solid–liquid and solid–gas flows. The significantly different densities and viscosities of these fluids make multiphase flow much more complicated than the single-phase flow. The distribution of phases in space and time differs for each flow regime. The different types of flow regime can be grouped into dispersed flow (bubble flow and mist flow), separated flow (stratified and annular flow) and intermittent flow (churn and slug flow). The whole science of multiphase flow modeling is now based on these types of flow regime. Since these flow regimes are dynamic in nature and not under the control of an engineer or an operator, it is challenging to fully understand multiphase flow modeling and characteristics.

The petroleum industry constantly faces challenging flow-assurance problems as it pursues assets in more difficult producing environments. This guarantees the interest for multiphase flow modeling in future. Unlike single-phase flows, multiphase flows are complex phenomena and cannot be predicted or modeled easily. Predicting multiphase-flow behavior in an oil and gas production system is further complicated by complex heat transfer that occurs as fluids flow through the piping system and the mass transfer that takes place among hydrocarbon fluids as pressure and temperature change. These phenomena are governed by conservation of mass, momentum, and energy, coupled with fundamental thermodynamics and heat transfer Multi-phase Flow Modeling Flow simulation and modeling has been a key tool for providing an understanding of how and how much fluid flows through a flow conduit. This was prompted by the need for production design and processing systems in oil and gas fields. Understanding fluid flow inside hydraulic structures is a critical factor in the design of production systems and facilities. Flow modeling is a tool that can be used in the design process to simulate various design alternatives, identify flow problems, develop solutions and evaluate operating strategies. Being able to better simulate flow systems will enable having energy-efficient to debottleneck any design constraints and alleviate potential operational upsets. The major headways in fluid flow modeling was hinged and gone side by side with the evolution of flow measurement or metering. Initially, flow metering was used to develop and validate semi analytical or empirical models used to describe pressure traverse in wells and flow lines. Nowadays, flow modeling is becoming an assimilated portion of metering and flow measurement. Modeling is used to calculate some parameters, such as fluid properties and pressure traverse calculations, and to cross correlate results. Recently, the industry realized its importance in the use of virtual metering, to utilize readily available data to estimate flow, and infer some flow conditions in wells and flow networks. The development of multi-phase flow large-scale analysis in the petroleum industry has been divided into three partially overlapping periods; the empirical period, the awakening years and the modeling periods which together encompass the second half of the past century. During the empirical period, all efforts were focused on correlating data from laboratory and field facilities in an attempt to encompass the widest range of operational conditions possible. The earliest attempt to empirically predict multi-phase flow pressure drops for horizontal pipes is the well-known work of Lockhart and Martinelli. Followed by number of new correlations, they claimed to be progressively more applicable for a wider range of operational conditions. It was used as a classic against which subsequent correlations were compared for improvident. Along with a number of modifications applied to it, Beggs and Brill’s correlation became one of the most extensively used correlations. In general, the reliance on the empirical approach was always limited by the uncertainty of their application to systems operating under different conditions than those from which the correlations were originally proposed. Nonetheless, calculating and designing flow lines in multi-phase production facilities on the basis of empirical correlations were the norm until well into the 1980s. Past attempts in the modeling approach used different conservation equations for predicting flow pattern and pressure gradient using empirical correlations. Industry realized that empirical correlations all suffer from significant errors in some ranges of input variables and cannot be improved because of their simplistic nature. Later, the mechanistic models develoed to be more accurate, more sophisticated, and are more physically based (mechanistic or phenomenological) approaches into multi-phase flow calculations. i.e. models trying to capture specific features of individual flow patterns in which simplified conservation equations are invoked while the main focus is the prediction of pressure drop and hold-up. The main goal remains an attempt to reduce the impact of empirical correlations on multi-phase predictions. The advent of the personal computer during the 1980s dramatically enhanced the capabilities of handling progressively more complex design situations, which is why this period has been called ‘the awakening years’. Much of the petroleum research on multi-phase flow during these years and the subsequent modeling period was enriched by the progress already made by other industries.

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The modeling period began in the 1980's, when the petroleum industry faced challenges that required a much better understanding of multiphase-flow technology. Early research of multiphase flow led the way towards more involved flow modeling and analysis. These seed efforts are the genesis of the well-known fast transient multi-phase-flow codes introduce a fully phenomenological description of how transitions occur among the different flow patterns. This work led the way for subsequent research in the area, and most of their transition criteria are still in use in more recent multi-phase flow models. Simulations tools used in the past for design and operation of pipelines and pipeline networks were of steady-state type. Such tools cannot capture the dynamic behavior of the systems, and can lead to false confidence and conclusions, if used uncritically. Application of dynamic simulation tools become vital for better understanding of pipelines and networks as fields mature, and as we production of existing fields increases. Successful operation of production systems also requires the ability to predict flow behavior when flow rates change in pipes. This occurs frequently when adding production from new wells and fields into a pipeline, or reducing production because of flow-assurance problems, maintenance issues, or other factors. Transient flow becomes dominant in such pipelines and pipeline networks, with the inevitable consequence this has on well backpressures and operation of receiving facilities (slug catchers, compression, piping, pumping, etc.). Simulating these time-dependent behaviors requires a sophisticated commercial multiphase-flow simulator like OLGA that is based on conservation equations that retain time-dependent terms. OLGA also involves flow-pattern predictions and requires closure relationships similar to steady-state flow. One of the major simulation advances that were developed to have more insight into the physical flow behavior and provide quantitative and qualitative understanding of fluid flow is the computational fluid dynamics, CFD. The most fundamental consideration in CFD is how one treats a continuous fluid in a discretized fashion on a computer. One method is to discretize the spatial domain into small cells to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion (Euler equations for in viscid, and Navier-Stokes equations for viscid flow). CFD method usually aims at solving the Navier-Stokes equations on a computational mesh grid adapted to the geometry of the system in study with different methods such as finite differences, finite elements, finite volumes and spectral methods. The complexity of the non-linear Navier-Stokes equations (Partial Differential Equations) impact the method used and on the quality of the results. Traditionally, computational fluid dynamics (CFD) is applied to model the flow in the control device and flow control valves in wells. An alternative to the CFD to avoid using a mesh-based method is to use Lattice Boltzmann Methods, which simulate an equivalent mesoscopic system on a Cartesian grid, instead of solving the macroscopic system (or the real microscopic physics). Moreover, the LBM require less computational efforts in terms of number of equations to solve and spending less coding time with results as accurate as those provided by classic CFD. Furthermore, the LBM can use any programming language and simple coding to simulate the case. Lattice Boltzmann methods are based on kinetic theory and thus no Navier-Stokes equations are solved. Instead, the method considers a typical volume element of fluid to be composed of a collection of ‘particles’ that are represented by a particle velocity distribution function for each fluid component at each grid point. In this approach, the rules governing the motion and collisions of these ‘particles’ are designed in such a way that the time-average motion of the particles is consistent with the Navier-Stokes equation. In these implementations the physical rules are implemented straight forward and have the advantage of relatively easy computations and simple implementation in complex geometries since there is no specific mesh. This last feature permitted to users of LBM to solve successfully complicated fluid flow applications with interfacial dynamics and singular boundaries. Some other small-scale modeling approaches use the Lagrangian frame of reference for fluid motion. In Lagrangian methods, the numerical grid follows the fluid and deforms with it. In this approach, the motion of the fluid interface needs to be modeled in simulate dispersed flows: the Eulerian-Eulerian or the Eulerian- Lagrangian approach. In the Eulerian-Eulerian approach, separated equations are solved for the dispersed and the continuous phase. Large-scale Interest Perhaps one of the most fundamental and rigorous approaches to the study of large-scale multi-phase flow currently in use in the petroleum industry is the mechanistic model. In the multi-fluid model, separate conservation equations (mass, momentum and energy) are written for each of the multiphases for a total of six equations. These equations are coupled with terms describing the interaction between phases. In this multi-phase flow method of analysis, as well as in all the others, empiricism cannot be completely avoided, since additional closure relationships are needed. Small-scale Interest and Computational Physics The study of small-scale multi-phase flow has proved to be extremely difficult for researchers due to the elusive nature of the phenomena comes into the picture during attempts to model the variety of constitutive relationships that show up in conservation equations. A great deal of progress has been made on the development of useful small-scale experimental studies, but numerical experiments or models still remain the most effective way of studying such detailed flow behavior. The challenge of

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modeling small-scale multi-phase flow resides in the finite nature of the computer power typically available to the modeler and the difficulty of tracking separated phases (and interfaces between them) with sharply different properties. In multi-phase flow modeling within small-scale interest, the Navier-Stokes equations, with the appropriate boundary conditions – are solved through a suitable numerical method, e.g. finite volumes, finite differences, finite elements or spectral methods. The main problem arises when considering that some boundary conditions are time-dependent, since they are located at phase boundaries, which are free to move, deform, break up or coalesce. Modeling business needs Production systems today are not only more complicated, but often involve comingling of dissimilar fluids from several wells, zones, and fields. The higher pressures and lower temperatures encountered can result in serious flow-assurance issues such as pipe erosion and corrosion, and total or partial plugging of piping systems from paraffin deposition on pipe walls and the formation of hydrate plugs. Many solutions were invented to mitigate operational problem related to multiphase flow. The effectiveness of such solutions often depends on the flow pattern in the pipe. Knowing the flow characteristics in production system, the right solution is proposed. This includes empirical correlations for predicting flow patterns, liquid holdup, and pressure drop. During the last century petroleum industries propelled intense research activity on the area. Their efforts have been aimed at the demystification of the mechanisms taking place during this complex flow situation. Since multi-phase flow phenomena can be found in a wide range of length scales of interest. Therefore, the most suitable approach to study multi-phase flows will largely depend on the length scale of interest. Typically, in the petroleum industry, attention was given to large-scale phenomena in multi-phase flows, as no detailed flow behavior is needed for routine design and operation. In pipeline, the interest is only in the pressure drop and liquid hold-up. As flow measurement technology evolves, with increasingly mounting business needs in oil fields for precise and more measurements frequency, more needs arise to have better modeling schemes and coverage for systems in play and applications. More modeling schemes are developed to describe new systems in place. This trend is gathering more momentum as the philosophy of intelligent fields mounts and as more measurement and flow analysis are needed to have more efficient and lower cost operations. This need entails having inline systems, which requires integration in terms of system design or modeling scheme, compact, this requires relatively smaller scale modeling, and larger number of units which require having a cost effective systems to be installed in more points or on individual wells. Integration with downhole conditions is becoming more important to cover operation with special application like pumping, separation and back injection of separated water. An accurate measurement the flow rates of multiphase fluids is a very challenging process and of great importance in the petroleum industry. It is difficult to measure the flow rate due to the inherent complex nature of the multiphase mixture. The multiphase flow metering system consists of a combination of devices for phase fraction measurement and phase velocity measurement which is being used to measure the flow rates of multiphase fluids. The flow measurement does not solely rely on physical measurement but also make use of modeling and interpretation of flow characteristics. The Venturi meter is frequently used for the velocity measurement of the mixture. Over the last decade, the measurement of multiphase flows has been the center of attention in the industry. Hence, multiphase meters provide other real-time information such as water content. Such information allows rapid operator intervention and optimization of production. Modeling of multiphase flow though ESP has not been fully covered in oil industry literature. Additionally, ESP design software is short of properly model and design ESP’s with multiphase flow. Given the fact that ESPs’ curves are based on water tests, the behavior of an ESP handling two-phase flow is a subject of concern, especially in oil wells, where significant amounts of free gas may be produced with oil. For this, some advanced flow simulations utilize an equivalent pump curves to simulate ESP in oil wells. This, however, is in short of simulating the effect of gas volume fraction in the ESP and its impact of degradation of head produced by the ESP. Hence, flow simulation may over predict ESP/well performances. Another area in ESP modeling may consider the transient flow during intermittent flow and shut-ins of ESP-lifted wells. Research gap of multiphase flow modeling Modern multi-phase flow analysis models the flow of oil and gas through pipelines by invoking the basic principles of continuum mechanics and thermodynamics. In previous decades, the challenge of modeling multi-phase flows by invoking such fundamental laws had been circumvented by reliance on empirical and semi-empirical correlations in the oil industry. Nowadays, the petroleum industry might be ready to explore new research avenues in multi-phase flow analysis, with the incorporation of the increasingly sophisticated modeling tools that have become available in the last few years.

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The most suitable approach to study multi-phase flows will largely depend on the length scale of interest. Typically, in the petroleum industry, attention is given to large-scale phenomena in multiphase flows, as no detailed flow behavior is needed for routine design and operation. In pipeline, only in the pressure drop and liquid hold-up are important to know. Other than the effect of the local flow pattern variables, detailed flow phenomena are not important. However, small-scale studies of multi-phase flows are very important because large-scale phenomena are controlled by small-scale physics. That is, the transition from one flow pattern to another is driven by local small-scale phenomena. One of the most important problems to be addressed by the researchers is the development of an improved understanding of transitions from one flow regime to another. This can be achieved only through small-scale studies of multi-phase flows. In addition, for the improved understanding of the operation of process equipment such as separators in the petroleum industry, it is necessary to understand the small-scale phenomena associated with large-scale phenomena to mimic reality in the field. With the evolving tools and sensing technologies, and corresponding business needs in industry research needs evolve and list of priority for research, driven by needs, is to be developed to bridge the gap of research and provide better research deliverables. This master plan covers three and interrelated focus areas, namely; flow characterization, sensing/measurement, and computation. In each area, research will have a bundle of research topics to address and develop new techniques utilizing emerging tools. In the area of flow characterization, where industry have used more defined flow patterns , like flow through venture, choke, or any throttling system where flow undergo a physically defined flow regimes, a new systems and setup are to be explored and augmented to the other proposed focus areas. In the area of sensing/measurement, the crossover from different scientific disciplines to adapt technologies for the petroleum industry, has been of a great addition to enhance the frequency and accuracy of data acquisition. Not forgetting also new sensing techniques that emerge from other disciplines. In the area of computation, the adaptation of numeral computation techniques was used primarily for multiphase flow and production optimization calculations but was not used as such in the field of flow modeling and metering. Artificial intelligence is an area that is not fully exploited in the multiphase flow modeling. The overlaps of the three areas also create a big area of research and potential technology development. The overlap between the flow characterization and sensing could include flow modeling of online metering, production optimization, and flow assurance, while the overlap between flow characterization and computation could include micro-scale modeling, LBM or Lagrangian methods using application of mathematical principles of classical fluid mechanics to describe some fluid flow. The overlap between Computation and sensing could include new techniques of improving fluid properties characterization and modeling and hence improve virtual metering. In addition, ways to reduce inherent errors of the classical PVT empirical correlation is area that warrants a big attention. An augmentation of effect or implicit calculation could reduce errors of using such correlations. Moreover, the thermal effect on multiphase flow could be included in the research. Overlap of the three areas could include an advance ways of modeling multiphase flow. This could include pattern recognition that could revolutionize the virtual modeling and metering. Another major area of research is to develop techniques that could augment the micro-scale modeling into the large-scale model, i.e. small flow conduit like a control valve which requires more insight calculations and production network. This could drive to developing sort of proxy models to have more efficient way of computation. Transient flow simulation is area that will always draw attention due to its severity and unforgettable impact on production systems. Consideration of downhole flow conditions and augmentation with surface flow has been a challenge due to the computational time required and research will always worthwhile in this area. Conclusions and Recommendations The petroleum industry is full of challenges for multiphase flow modeling and hence metering that warrant a lot of research. The motivations are not only to improve modeling but also to have more efficient modeling schemes from the computational aspects and accurate enough to serve production optimization and allocation purposes. The evolving sensing technologies and adaptation to the petroleum industry put pressure on researcher to develop matched modeling schemes and techniques. The micro-scale modeling needs is mounting as wells and fields are equipped more sophisticated equipment, both surface and subsurface, to serve new production philosophy like digital oil fields. It is widely expected that the demystification of micro-scale intricacies of multi-phase flow phenomena can greatly help large-scale modeling in the foreseeable future. The simultaneous implementation of large-scale and small-scale simulation represents a powerful combination that can significantly improve our understanding of multi-phase flow phenomena and may play an important role in significantly improving the nature and reliability of the semi-empirical relationships needed by large-scale simulation models. The industry is in quest for integrated modeling approach to maximize accuracy and reduce equipment and operating cost. It is recommended to use the mechanistic approach for complex flow when the combined estimation of velocity and holdup is required. It is important to consider more complex models, which are applicable for all range of flow rates in the field, and in which wellbore inclination and the flow regime dependency can be easily accounted for by incorporating rigorous transition

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mechanisms. It is recommended to incorporate the flow regime in estimation procedure or to obtain flow regime information using other methods as it is expected to have a slug flow dominating in oil/gas wells. Moreover, in reality, the wellbore profile is usually more complex than the idealized systems considered in studies. Multiple flow obstructions and rapid changes of the wellbore geometry affect greatly the dynamic inflow response and should be accounted for. This is especially true with pumping wells connected to large flow networks. It also recommended employing ensemble Kalman filter for more complex and dynamic models in the field using data assimilation concepts. In addition, the use of soft-sensing in downhole and surface may be still an area of further investigation and improvement for better utilization of readily available real-time data. Finally, the experimental setups of flow loops could be dramatically improved by the evolution of computation and visualization to have inline validation systems. References

1. Beggs, H. D. and Brill, J. P.: .A Study of Two-Phase Flow in Inclined Pipes, J. Pet. Tech. (May 1973) 607-617. 2. Hagedorn, A. R. and Brown, K. E.: .Experimental Study of Pressure Gradients Occurring during Continuous Two-Phase Flow in

Small Diameter Vertical Conduits, J. Pet. Tech. (Apr. 1965) 475-484. 3. Orkiszewski, J.: .Predicting Two-Phase Pressure Drops in Vertical Pipe, J. Pet. Tech. (Jun. 1967) 829-838. 4. Rastoin S., Schmidt Z., and Doty D.R. A review of multiphase flow through chokes. Journal of energy resources technology,

119:10, 1997. 5. Sarica C. and Shoham O. A simplified transient model for pipeline-riser systems. Chemical Engineering Science, 46(9):2167–

2179, 1991. 6. Taitel Y., Vierkand S., Shoham O., and Brill J.P. Severe slugging in a riser system: experiments and modeling. International

journal of multiphase flow, 16(1):57–58, 1990. 7. Alvarez C. J. et al. SPE 56463. ”Wet Crude Transport through a Complex Hilly Terrain Pipeline Network”, the SPE Annual

Technical Conference in Houston, 3-6 October, 1999. 8. Zarei, R. and Alvarez, C.J. SPE 91043. “Transport of Ethane-Rich Gases Using an Extensive Gas Pipeline System”. The Annual

SPE Technical Conference and Exhibition, Houston TX, 26-29 September 2004. 9. Xu, Z., G., and Shea, R. “Important Tips for Setting Up Simulation Models for Multiphase Flow in Pipelines”, the BHR Group

2001 Multiphase Technology Conference, 2001. 10. Bendiksen, K.H., Malnes, D., Moe, R, and Nuland, S. “The Dynamic Two-Fluid Model OLGA: Theory and Application”,

SPEPE, May 1991, pp. 171-180. 11. Espedal, M., Langsholt, M., Fuchs, P. H. “Holdup Discontinuities in Stratified Two-Phase Flow”, International Conference on

Multiphase Flow ’98”, Lyon, France, June 8 – 12, 1998. 12. Williams, J.: “Status of Multiphase Flow Measurement Research,” paper SPE 28515 presented at the 1994 SPE Annual Technical

Conference and Exhibition, New Orleans, 25–28 September. 13. Hatton, G.J.: “Multiphase Flow Meters and Application Trends,” paper OTC 8547 presented at the 1997 Offshore Technology

Conference held in Houston, 5–8 May. 14. Alimonti, C. and Bilardo, U.: “Measurement of Three-Phase Flow Rates Using Neural Network Approach,” presented at the 2001

International Conference on Multiphase Flow, New Orleans, 27 May–1 June. 15. Hall, A.R.W., Whitaker, T.S., and Millington, B.C.: “Multiphase Flow Metering: Current Status and Future Developments,”

paper OTC 8553 presented at the 1997 Offshore Technology Conference, Houston, 5–8 May. 16. Piantanida, M. et al.: “Multiphase Metering: Experimental Results From the Analysis of Acoustic Noise Through a Choke,”

paper SPE 50681 presented at the 1998 SPE European Petroleum Conference, The Hague, 20–22 October. 17. Aspelund, A., Midttveit, O., and Richards, A.: “Challenges in Downhole Multiphase Measurements,” paper SPE 35559 presented

at the 1996 European Production Operations Conference and Exhibition, Stavanger, 16–17 April. 18. G. P. Lucas and N. D. Jin, “A new Kinematics Wave Model for Interpreting Cross Correlation Velocity Measurements in

Vertically Upward, Bubbly Oil-In-Water Flows,” Measurement Science and Technology, Vol. 12, No. 9, 2001, pp. 1538-1545. 19. L. A. Xu, “The State-Of-Art and Developing Trend of Correlated Flow Measuring Techniques,” Process Automation

Instrumentation, Vol. 9, No. 3, 1988, pp. 1-4. 20. X. B. Liu, “Downhole Measurement of Oil/Water Two-Phase Flows,” Ph.D. Thesis, Harbin Institute of Technology, Harbin,

1996. 21. Elperin T, Fominykh A, Klochko M. 2002, “Performance of a Venturi meter in gas–liquid flow in the presence of dissolved

gases”, Flow Measurement and Instrumentation, vol. 13 pp. 13-16. 22. Emilio E.P, Clovis R.M. 2002, “The Effect of the Slip Velocity on the Differential Pressure in Multiphase Venturi Flow Meters”,

ASME International Conference. 23. Rosa E.S., Morales R.E.M., 2004, “Experimental and Numerical Development of a Two-Phase Venturi Flow Meter”, Journals of

Fluid Engineering, vol. 126 pp.457-467. 24. Zhiyao H, Dailiang X, Hongjian Z, Haiqing L., 2005, “Gas–oil two-phase flow measurement using an electrical capacitance

tomography system and a Venturi meter”, Flow Measurement and Instrumentation, vol. 16 pp.177-182. 25. A. J. Chorin, Numerical Solution of Navier-Stokes Equations, J. Comput. Math., vol. 22, p. 745, 1968. 26. S. V. Pantankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980. 14. D. B. Kothe and R. C. Mjolsness,

IPPLE: A New Model for Incompressible Flows with Free Surfaces, AIAA J., vol. 30, pp. 2694–2700, 1992. 27. M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, J.

Comput. Phys., vol. 20, pp. 1165–1191, 1994.

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28. L.-S. Luo, The lattice-gas and lattice Boltzmann methods: Past, Present, and Future, Proceedings of the International Conference on Applied Computational Fluid Dynamics, Beijing, China, pp. 52-83, 2000.

29. Abdullah M. Al-Qahtani, and Mikal Espedal, “Birding the gap in Electric Submersible Pump Flow modeling and Design” internal report. June 2004.

30. Abdullah M Al Qahtani. “Flow Simulation in Inflow Control Valves Using Lattice Boltzmann Modeling “SPE SA 0532presented at the 2010 SPE/DGS Annual Technical Symposium and Exhibition held in Al-Khobar, Saudi Arabia, 04–07 April 2010.

31. Mikal Espedal, Abdullah M. Al-Qahtani, and Carlos J. Alvarez. “Multiphase flow in pipeline networks – Future challenges in Saudi Aramco” SPE SA 0532 presented at the 2005 SPE Technical Symposium of Saudi Aramco held in Dhahran, Saudi Arabia, 14-16 May 2005.