Experimental study of horizontal gas-liquid fluid flow through orifice plates : Estudo experimental do escoamento horizontal gás-liquido através de placas orifício

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(1)UNIVERSIDADE ESTADUAL DE CAMPINAS Faculdade de Engenharia Mecânica. LUIS FERNANDO CAMPUZANO OJEDA. Experimental study of horizontal Gas-Liquid Flow through Orifice Plates Estudo Experimental do Escoamento Bifásico Horizontal Gás-Líquido através de Placas de Orifício. CAMPINAS 2019.

(2) LUIS FERNANDO CAMPUZANO OJEDA. Experimental study of horizontal Gas-Liquid Flow through Orifice Plates Estudo Experimental do Escoamento Bifásico Horizontal Gás-Líquido através de Placas de Orifício Dissertation presented to the School of Mechanical Engineering of the University of Campinas, in partial fulfillment of the requirements for the degree of Master in Mechanical Engineering, in the area of Thermic and Fluids.. Dissertação apresentada à Faculdade de Engenharia Mecânica da Universidade Estadual de Campinas como parte dos requisitos exigidos para obtenção do título de Mestre em Engenharia Mecânica, na Área de Térmica e Fluidos.. Orientador: Prof. Dr. Marcelo Souza de Castro. ESTE TRABALHO CORRESPONDE À VERSÃO FINAL DA DISSERTAÇÃO DEFENDIDA PELO ALUNO LUIS FERNANDO CAMPUZANO OJEDA, E ORIENTADA PELO PROF. DR. MARCELO SOUZA DE CASTRO.. CAMPINAS 2019.

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(4) UNIVERSIDADE ESTADUAL DE CAMPINAS FACULDADE DE ENGENHARIA MECÂNICA DISSERTAÇÃO DE MESTRADO ACADÊMICO. Experimental study of horizontal Gas-Liquid Flow through Orifice Plates Estudo Experimental do Escoamento Bifásico Horizontal Gás-Líquido através de Placas de Orifício Author: Luis Fernando Campuzano Ojeda Orientador: Pro. Dr. Marcelo Souza de Castro A Banca Examinadora composta pelos membros abaixo aprovou esta Dissertação: Prof. Dr. Marcelo Souza de Castro FEM/UNICAMP Prof. Dr. Jorge Luis Baliño Escola Politécnia/USP Prof. Dr. Valdir Estevam FEM/UNICAMP. A Ata de Defesa com as respectivas assinaturas dos membros encontra-se no SIGA/Sistema de Fluxo de Dissertação/Tese e na Secretaria do Programa da Unidade.. Campinas, 04 de dezembro de 2019..

(5) DEDICATION. This work is dedicated to my beloved wife Laura and my son Pedro, you fill my life with happiness and love. “It is never too late to pursue your dreams.”.

(6) ACKNOWLEDGEMENTS I wish to express my deepest gratitude to all who contributed to the development of this research study. Prominent of these are my advisors, Professor Dr. Marcelo Sousa de Castro and Dr. Charlie Van Der Geest, thank you for your guidance throughout this work, for your genuine enthusiasm, dedication, and confidence in my work. Sincere thanks go to Cepetro (Center for Petroleum Studies) Researchers Dr. Jorge Luiz Biazussi, Dr. William Monte Verde and Dr. Carlos Eduardo Perles; the ALFA research group technicians Claudio Varani and Luis Gustavo Silva, you were indispensable in the assembly and performance of the experimental study. I would like to thank my teammates Matheus Pasquini, William Fonseca, Lucas Braga, and Barbara Carnaúba for the encouragement and friendship during this master. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. Also, I would like to extend my gratitude the University of Campinas (UNICAMP), the Department of Mechanical Engineering at the School of Mechanical Engineering (FEM) and PETROBRAS and ANP for the financial support. Deep thanks to my parents for your unconditional love, you have raised me to be the person I am today. You have been supporting me in every step of my life. Thank you for everything..

(7) Resumo Na indústria de petróleo, na área de produção, existem escoamentos monofásicos e multifásicos do reservatório para o separador através de linhas horizontais e verticais. Dispositivos como singularidades podem aumentar ou diminuir a energia cinética dos fluidos para controlar o escoamento, por exemplo. Essas singularidades são comumente instaladas para vários propósitos. Esta pesquisa concentra seu estudo em dois tipos dessas singularidades: que são as placas de orifício e as válvulas choke, a primeira é destinada à medição de vazão e a outra para controle de vazão ou pressão, respectivamente. Esta tese realizou um estudo experimental do escoamento monofásico (líquido) e multifásico (gás-líquido) através de três placas de orifício de cantos vivos com diâmetro de orifício diferentes, usando ar, água e óleo como fluidos de trabalho. Para experimentos monofásicos, o padrão ASME MFC 14M foi utilizado para projetar e montar o aparato experimental, especificamente a seleção de tomadas de pressão. Além disso, o padrão ASME fornece o procedimento matemático para prever ou calcular a vazão mássica em cada condição. Experimentos monofásicos foram realizados com água e óleo mineral como fluidos de trabalho. Por outro lado, para os experimentos multifásicos ar-água e ar-óleo, os modelos de placas de orifício modelo homogêneo e os modelos não homogêneos desenvolvidos por Chisholm (1967) e Zhang et al. (2005) foram utilizados para comparação. Os modelos de válvula choke avaliados nesta pesquisa foram o modelo homogêneo desenvolvido por Sachdeva et al. (1986) e o modelo não homogêneo desenvolvido por Al-Safran and Kelkar (2009). Além disso, ao longo desta pesquisa, analisa-se o comportamento da queda de pressão e compara-se o coeficiente de descarga experimental (CD) calculado para cada modelo nas diferentes placas de orifícios contra os modelos da literatura. Finalmente, esta pesquisa estudou em detalhes a influência do comportamento do CD com números de Reynolds baixos, na região de transição e altos. Com base nesses resultados e na análise desenvolvida, é possível sugerir correlações alternativas baseadas em números adimensionais como o número de Reynolds e a razão beta, a fim de prever a vazão mássica para todos os números de Reynolds para escoamentos monofásicos e multifásicos gás-líquido. Palavras-chave: Escoamentos horizontais de gás-líquido, Placas de orifícios, Válvulas choke, Singularidades, Escoamento multifásico, Modelos de choke, Coeficiente de descarga..

(8) Abstract In the petroleum industry, in the production area, there are single and multiphase flows from the reservoir to the separator through horizontal and vertical lines. Devices such as singularities may increase or decrease fluid kinetics’ energy to control the flow. These singularities are commonly installed for multiple purposes. This research focusses its study in two types of these singularities, they are the orifice plates and the choke valves, one of them is designed to flow metering, the other one is for flow control or pressure control, respectively. This thesis performed an experimental study of single-phase (liquid) and multiphase (gasliquid) fluid flow through three sharped thin orifice plates with different orifice diameter using air, water and oil as working fluids. For single-phase experiments, the ASME MFC 14M standard was performed to design and assemble the experimental setup, specifically the pressure tappings selection. Additionally, the ASME standard provides the mathematical procedure to predict or calculate the mass flow rate. Singe-phase experiments were performed with water and mineral oil as working fluids. On the other side, for multiphase air-water and air-oil fluid flow, the orifice plates models evaluated were the homogeneous model, and the non-homogeneous models developed by Chisholm (1967) and Zhang et al. (2005). The choke valve models evaluated through this research were the homogeneous model developed by Sachdeva et al. (1986) and the non-homogeneous model developed by Al-Safran and Kelkar (2009). In addition, throughout this research, it is analyzed the behavior of the pressure drop and it is compared the experimental discharge coefficient (CD) calculated for each model on the different orifice plates against the literature models as background. Finally, this research studied in detail the influence of CD behavior throughout low, transitional and high Reynolds numbers. Based on these results and the analysis developed, it is possible to suggest alternative correlations based on dimensionless numbers such as Reynolds number and beta ratio in order to predict mass flow rate for all Reynolds numbers flow regimes for single and multiphase gasliquid flows. Keywords: Horizontal Gas-Liquid Flows, Orifice Plates, Choke Valves, Singularities, Multiphase Flow, choke models, discharge coefficient..

(9) List of Figures FIGURE 1 - TYPICAL PRODUCTION CHRISTMAS TREE CONFIGURATION (API 6A). ..................................................................... 16 FIGURE 2 - ORIFICE PLATE FLOW METER (LI ET AL. 2009) ................................................................................................. 17 FIGURE 3 - FLOW AND PRESSURE BEHAVIOR OF FLOW ACROSS A RESTRICTION (AL-SAFRAN AND BRILL, 2017). ........................... 22 FIGURE 4 - GAS-LIQUID HORIZONTAL FLOW PATTERNS (SHOHAM, 2006). ........................................................................... 23 FIGURE 5 - BEGGS AND BRILL (1973) HORIZONTAL FLOW PATTERN MAP (SHOHAM, 2006). ................................................... 25 FIGURE 6 - TAITEL AND DUKLER (1976) FLOW PATTERN MAP (SHOHAM, 2006). ................................................................... 26 FIGURE 7 - TAITEL AND DUKLER (1976) FLOW PATTERN MAP FLOW CHART PRESENTED BY AL-SAFRAN AND BRILL (2017). ............. 27 FIGURE 8 - MANDHANE ET AL. (1974) HORIZONTAL GAS-LIQUID FLOW PATTERN MAP. ............................................................ 27 FIGURE 9 - PRESSURE TAPPINGS (READER-HARRIS, 2015). ................................................................................................ 29 FIGURE 10 - ORIFICE PLATE SPECS ASME MFC 14M. ..................................................................................................... 30 FIGURE 11 - ORIFICE PLATE DISCHARGE COEFFICIENT FOR LOW REYNOLDS (MILLER, 1996)..................................................... 32 FIGURE 12 - EXPERIMENTAL SETUP SKETCH. .................................................................................................................... 45 FIGURE 13 - SHARP EDGED ORIFICE PLATE. ...................................................................................................................... 47 FIGURE 14 - DETAIL OF THE VISUALIZATION BOX AND ORIFICE PLATE (RED ARROW). ................................................................. 47 FIGURE 15 – PRESSURE TAPS AT THE ORIFICE PLATE - CORNER TAPPINGS. .............................................................................. 48 FIGURE 16 - PRESSURE TAPS LOCATION [MM]. ................................................................................................................. 48 FIGURE 17 - ORIFICE PLATE BOX DRAWING. ..................................................................................................................... 49 FIGURE 18 – HIGH SPEED CAMERA INSTALLED IN FRONT OF THE EXPERIMENTAL LINE................................................................ 50 FIGURE 19 - LABVIEW BASED PROGRAM LAYOUT............................................................................................................. 51 FIGURE 20 - OIL PROPERTIES AS A FUNCTION OF TEMPERATURE: (A) DENSITY, (B) VISCOSITY. .................................................... 52 FIGURE 21 - SCHEMATIC REPRESENTATION OF DATA ACQUISITION AND PROCESSING. ............................................................... 53 FIGURE 22 - ORIFICE PLATE MODELS PROCESSING. ............................................................................................................ 53 FIGURE 23 - CHOKE VALVES MODEL PROCESSING. ............................................................................................................. 54 FIGURE 24 - OPERATIONAL LIMITS FOR TWO-PHASE AIR-WATER EXPERIMENTS. ...................................................................... 55 FIGURE 25 - PREDICTED MASS FLOW RATE VS. MEASURED FOR WATER FLOW ASME MFC 14M ............................................... 57 FIGURE 26 – PREDICTED MASS FLOW RATE VS. MEASURED ONE FOR OIL FLUID FLOW WITH CD GIVEN BY ASME MFC 14M. ........... 59 FIGURE 27 - DETAILED RESULTS FOR Β=0.34 WITH ASME STD. .......................................................................................... 59 FIGURE 28 – PREDICTED MASS FLOW RATE VS. MEASURED FOR OIL FLUID FLOW WITH CD GIVEN BY MILLER (1996)....................... 60 FIGURE 29 - EXPERIMENTAL ANALYSIS FOR DISCHARGE COEFFICIENT VS REYNOLDS NUMBER FOR Β=0.34 ORIFICE PLATE. ................ 62 FIGURE 30 - EXPERIMENTAL ANALYSIS FOR DISCHARGE COEFFICIENT VS REYNOLDS NUMBER FOR Β =0.50 ORIFICE PLATE. ............... 63 FIGURE 31 - EXPERIMENTAL ANALYSIS FOR DISCHARGE COEFFICIENT VS REYNOLDS NUMBER FOR Β =0.67 ORIFICE PLATE. ............... 63 FIGURE 32 - FLOW PATTERN MAP FOR AIR-WATER FLOW AND EXPERIMENTAL DATA................................................................. 64 FIGURE 33 - FLOW PATTERN MAP FOR AIR-OIL FLOW AND EXPERIMENTAL DATA. ..................................................................... 65 FIGURE 34 - FLOW PATTERNS FOR HORIZONTAL AIR-WATER FLOWS. ..................................................................................... 66 FIGURE 35 - HOMOGENEOUS ORIFICE PLATE MODEL CD VS. REYNOLDS OF THE MIXTURE. .......................................................... 68 FIGURE 36 - NON-HOMOGENEOUS (CHISHOLM, 1967) ORIFICE PLATE MODEL CD VS. REYNOLDS OF THE MIXTURE. ...................... 68 FIGURE 37 - NON-HOMOGENEOUS (ZHANG ET AL., 2005) ORIFICE PLATE MODEL CD VS. REYNOLDS OF THE MIXTURE. ................... 69 FIGURE 38 – PREDICTED AIR-OIL MASS FLOW RATE VS MEASURED MASS FLOW RATE (ORIFICE PLATE MODELS). ............................ 69 FIGURE 39 – PREDICTED AIR-WATER MASS FLOW RATE VS MEASURED MASS FLOW RATE (ORIFICE PLATE MODELS). ........................ 70 FIGURE 40 - BEST PERFORMANCE MODELS FOR AIR-OIL FLOW FOR ALL OBSERVED FLOW PATTERNS. ............................................ 72 FIGURE 41 - BEST PERFORMANCE MODELS FOR AIR-WATER FLOW PATTERNS. ......................................................................... 72 FIGURE 42 - HOMOGENEOUS CHOKE VALVE MODEL CD (SACHDEVA ET AL., 1986) VS. REYNOLDS NUMBER. ................................ 73 FIGURE 43 - NON-HOMOGENEOUS CHOKE VALVE MODEL CD (AL SAFRAN AND KELKAR, 2009) VS. REYNOLDS NUMBER. ................ 73 FIGURE 45 - PREDICTED AIR-WATER MASS FLOW RATE VS MEASURED MASS FLOW RATE (CHOKE VALVE MODELS). ......................... 76 FIGURE 46 – FLOW BEHAVIOR FOR AIR-OIL FLOWS AT 𝒗𝑺𝑮=0.8 M/S AND 𝒗𝑺𝑳=0.7. ............................................................ 78 FIGURE 47 – ANNULAR FLOW BEHAVIOR FOR AIR-OIL FLOWS AT 𝒗𝑺𝑮=0.2 M/S AND 𝒗𝑺𝑳=20 M/S. ......................................... 79 FIGURE 48 – FLOW BEHAVIOR FOR AIR-OIL FLOWS AT 𝒗𝑺𝑮=0.2 M/S AND 𝒗𝑺𝑳=20 .............................................................. 81 FIGURE 49 – FLOW BEHAVIOR FOR AIR-WATER FLOWS AT 𝒗𝑺𝑮=0.7 M/S AND 𝒗𝑺𝑳=0.9. ....................................................... 85 FIGURE 50 – ANNULAR FLOW BEHAVIOR FOR AIR-WATER FLOWS AT 𝒗𝑺𝑮=0.1 M/S AND 𝒗𝑺𝑳=20 M/S. .................................... 85 FIGURE 51 – FLOW BEHAVIOR FOR AIR-WATER FLOWS AT 𝒗𝑺𝑮=0.5 M/S AND 𝒗𝑺𝑳=7.5M/S .................................................. 88.

(10) List of Tables TABLE 1 - ZHANG ET AL. (2005) COEFFICIENTS FOR EACH FLOW PATTERN ............................................................................. 35 TABLE 2 - ASHFORD AND PIERCE DISCHARGE COEFFICIENT RECOMMENDATIONS .................................................................... 38 TABLE 3 - EMPIRICAL CORRELATIONS PARAMETERS ........................................................................................................... 41 TABLE 4 - MULTIPHASE FLUID FLOW CHOKE MODELS ....................................................................................................... 43 TABLE 5 - EQUIPMENT SPECIFICATIONS ........................................................................................................................... 46 TABLE 6 - COMPARATION ASME VS. EXPERIMENTAL RESULTS (WATER SINGLE-PHASE FLOW) ................................................... 58 TABLE 7 - PREDICTED VS MEASURED MASS FLOW RATE (OIL SINGLE-PHASE). ........................................................................... 61 TABLE 8 - MEAN ERROR FOR ORIFICE PLATE MODELS (ASME CD). ....................................................................................... 70 TABLE 9 - MEAN ERROR FOR ORIFICE PLATE MODELS (SUGGESTED CD). ................................................................................. 71 TABLE 10 - DISCHARGE COEFFICIENT BEHAVIOR FOR CHOKE MODELS. ................................................................................... 74 TABLE 11 - MEAN ERROR FOR CHOKE VALVE MODELS (CONSTANT CD). ................................................................................. 74 TABLE 12 - MEAN ERROR FOR CHOKE VALVE MODELS (SUGGESTED CD). ................................................................................ 75.

(11) Nomenclature 𝐴. Area, [m²]. D. Diameter, [m]. G. Gas, [-]. L. Liquid, [-]. R. in-situ gas/liquid ratio, [-]. CD. Discharge coefficient, [-]. 𝑦!. Critical Pressure boundary regime, [-]. q. Volumetric Flow Rate, [m³/h, m³/s]. 𝑚̇. Mass Flow Rate, [kg/h, kg/s]. 𝑚̇ "#. Two Phase Mass Flow Rate (Orifice Plate Model), [kg/h, kg/s]. ∆𝑃. Pressure Drop, [Pa]. 𝜆$. non-slip holdup, [-]. 𝑣%$. Liquid Superficial Velocity, [m/s]. 𝑣%&. Gas Superficial Velocity, [m/s]. 𝑁'(. Froude Number, [-]. β. Beta Ratio, [-]. 𝛾. Gas specific gravity [-]. 𝑅𝑒. Reynolds Number, [-]. 𝐾$. Correction factor, [-]. 𝑥. Quality, [-]. 𝑋. Lockhart Martinelli, [-]. 𝑆. Slip Ratio, [-]. ∝. Void Fraction, [-]. 𝑦. Pressure Ratio, [-]. 𝑘. Heat Capacity, [J/K]. 𝑛. Gas Expansion, [-]. 𝑉&. Specific Volume Gas, [m³/kg]. 𝑉$. Specific Volume Liquid, [m³/kg]. 𝛼∗. Alpha parameter, [-]. 𝑅*. Gas Oil Ratio, [-].

(12) Subscripts. L. Liquid. G. Gas. CH. Choke. 1. Upstream condition. 2. Downstream condition. TP. Two-Phase. m. Mixture. T. Total. Abbreviations API. American Petroleum Institute. NACE. National Association of Corrosion Engineers. N&S. Needle and seat. MOV. Multi Orifice Valve. MFM. Multiphase Flow Metering. MFC. Measurement of Fluid flow in Close Conduits. A. Annular flow pattern. EB. Elongated Bubbles flow pattern. S. Slug flow pattern.

(13) Contents 1.. INTRODUCTION .............................................................................................................................. 15. 1.1. OBJECTIVES .................................................................................................................................... 17. 1.2.. WORK ORGANIZATION ............................................................................................................ 18. 2.. LITERATURE REVIEW ................................................................................................................... 20. 2.1. SINGLE PHASE FLOW THROUGH RESTRICTIONS .................................................................. 20. 2.2. TWO-PHASE HORIZONTAL GAS-LIQUID FLOW ...................................................................... 22. 2.2.1. HORIZONTAL GAS-LIQUID FLOW PATTERNS ..................................................................... 22. 2.2.2. HORIZONTAL GAS-LIQUID FLOW PATTERN MAPS ........................................................... 24. 2.3. ORIFICE PLATES ............................................................................................................................ 28. 2.3.1. ORIFICE PLATES SPECIFICATIONS ....................................................................................... 28. 2.3.2. ORIFICE PLATES TWO-PHASE FLOW MODELS................................................................... 32. 2.4 2.4.1. CHOKE VALVES .............................................................................................................................. 35 CHOKE VALVE MODELS .......................................................................................................... 36. 3.. EXPERIMENTAL SETUP ................................................................................................................ 44. 3.1. SETUP ................................................................................................................................................ 44. 3.2. ORIFICE PLATES DESIGN ............................................................................................................. 46. 3.3. VISUALIZATION SYSTEM ............................................................................................................. 49. 3.4. DATA ACQUISITION ....................................................................................................................... 50. 3.5. FLUID FLOW PROPERTIES ........................................................................................................... 51. 3.6. EXPERIMENTAL PROCEDURE ..................................................................................................... 52. 3.7. EXPERIMENTAL CONDITIONS .................................................................................................... 54. 4.. RESULTS ........................................................................................................................................... 56. 4.1. SINGLE-PHASE FLOW (WATER/OIL) .......................................................................................... 56. 4.2. TWO-PHASE GAS-LIQUID FLOWS ............................................................................................... 64. 4.2.1. ORIFICE PLATE MODELS ......................................................................................................... 67. 4.2.2. CHOKE VALVE MODELS .......................................................................................................... 72. 4.3. VISUALIZATION OF GAS-LIQUID FLOW THROUGH ORIFICE PLATES............................... 77.

(14) 4.3.1. AIR-OIL EXPERIMENTS. ........................................................................................................... 77. 4.3.2. AIR-WATER EXPERIMENTS. .................................................................................................... 83. 5.. CONCLUSIONS AND RECOMMENDATIONS .............................................................................. 89. 5.1. CONCLUSIONS................................................................................................................................. 89. 5.2. RECOMMENDATIONS .................................................................................................................... 90. REFERENCES ............................................................................................................................................ 92.

(15) 15. 1. INTRODUCTION The petroleum production system can be divided into two main regions: the reservoir and the production system. The reservoir is where the hydrocarbons are trapped, and the production system is responsible for transporting those hydrocarbons from the reservoir to the production unit. The production system is composed of multiples sections and equipment, the fluids go through several inclinations, vertical in the well and horizontal in the flowline and through several restrictions, like annular and choke valves. Al-Safran and Brill (2017) mentions that it is not usual for hydrocarbons to be in a single phase in any part of the production system. The reservoir usually contains oil, water, gas and condensates. Even if the hydrocarbons were at single phase the fluids are always exposed to many different temperatures and pressures, thus multiphase flows can occur like once the pressure drops below the bubble point. For a safe and controlled oil and gas production system, it is necessary to study the multiphase flow through restrictions or singularities such as chokes valves and orifice plates. The present research described the basic characteristics of singularities such as chokes valves and orifice plates. Also emphasize the importance of classic orifice flow parameters to better model and improve the theoretical results both for orifice plate as for choke valves models. Al-Safran and Brill (2017) described very well the multiphase flow through restrictions, saying that the fluid flow behavior is characterized by converging fluid flow in a reduction of area, and due to mass conservation, the fluid velocity increases across the reduction. Also, as the fluid velocity increases, the static pressure in the reduction must decrease due to Bernoulli equation derived from principle of conservation of momentum along a streamline. One type of restriction are valves, which intentionally dissipates an amount of flow energy to control the flowrate and pressure. Indeed, based in the principle of conservation of energy, a considerable pressure drop occurs across the restriction. The chokes are valves that particularly satisfy these characteristics and they are the reason of this research, due to their importance on the petroleum industry. A choke valve (Figure 1) is a device installed in the upstream area like in production wells, gas injection or water disposal Christmas trees. In the case of production wells, they are used to cause a restriction on the fluid flow, thus control the oil and gas production rate..

(16) 16 Choke valves are very important as a flow control device. The need for reducing large pressure fluctuations presented in slug flow arises and it is controlled for well-specific flow control. Kabir and Hasan (2018) mentioned that controlling flow rates in daily field operations is the norm in most settings. Therefore, it is important to understand the flow behavior though choke valves. It allows to maintain completion integrity, minimize the risk of excessive pressure drawdown at the sandface, manage solid production to reduce the risk of erosion and corrosion in fields with high amounts of hydrogen sulfide (H2S) and carbon dioxide (CO2). Additionally, uncertainties and inaccuracies in rate metering arise when integrity of the choke diameter decrease when erosion and cavitation appear. In order to study the two-phase fluid flow behavior in chokes, as mentioned above, the internal choke configuration can be fairy complex for the purpose of modeling and visualization, because of that, in addition and based on Sachdeva et al. (1986) analysis, a choke valve can be treated as a restriction that causes a pressure drop, same as the orifice plate. This is the reason to use orifice plates on the experimental study of this research.. Figure 1 - Typical Production Christmas Tree Configuration (API 6a). Another type of restrictions is the orifice plates or pressure drop flow meters. They are largely used in downstream transportation due to their simplicity, low cost, and easy maintainability. Because there are multiphase mixtures of oil, water and gas in the production system and this equipment is used as Multiphase Flow Metering (MFM), improvement of its accuracy is the main objective. In the petroleum industry this is important because of several.

(17) 17 areas like: flow assurance well testing, reservoir management, production allocation, production monitoring, capital and operative expenses, fiscal metering and custody transfer. The dual slotted orifice plate metering system manufactured for test and study by Li et al. (2009) is shown in Figure 2.. Figure 2 - Orifice Plate Flow Meter (Li et al. 2009) One of the most important parameters to study during this research is the discharge coefficient (CD), due to the fact that it is the parameter used to determine the pressure drop and flowrate through the restriction. This coefficient varies, depending on the size of the restriction, the CD should be adjusted to the situation, so every orifice plate may have a different discharge coefficient. The described CD is a powerful tool, the irreversible losses, heat transfer and model imperfections, are accounted in the discharge coefficient. In addition, Haug (2012) stated, that the CD also depends on the shape of the opening of the restriction.. 1.1. OBJECTIVES. The main objective of this research is to understand two-phase gas-liquid flow through restrictions. To reach that goal we did an extensive experimental study of horizontal single and two-phase flow through restrictions (modeled both as orifice plate and choke valves). Throughout this study the following specific objectives were developed: •. To carry out an experimental study of horizontal single and multiphase flow through orifice plates. The performance of these experiments is described on chapter 3 Experimental Setup..

(18) •. 18 To predict the mass flow rate through orifice plates, with the assistance of ASME standard for single-phase, and homogenous/nonhomogeneous models for horizontal GL flow through choke valves and orifice plates.. •. To compare the experimental results of mass flow rate through orifice plates with the predicted theoretical and empirical models which are commonly used on the petroleum industry.. •. Finally, as the experimental studies will be developed with assistance of videos it is possible to analyze the characteristics of gas-liquid flow patterns through singularities.. 1.2.. WORK ORGANIZATION. The organization of this thesis is as follows: Chapter 1 introduces the orifices plates and choke valves, its applications in the petroleum industry and the single and multiphase flow phenomena through singularities, this chapter is also focusing in describing the main objective and the secondary objectives that were developed in order to accomplish this main goal. Chapter 2 provides the detailed literature review used in the development of the work. It describes horizontal single and two-phase gas-liquid flow through restrictions such as orifice plates and choke valves. Also, it is presented the flow patterns in gas-liquid (G-L) two-phase flows. It is presented the standards for single-phase flow, and the theoretical and empirical models for multiphase flow through chokes and orifice plates. Finally, the calculation process to predict mass flow rate is discussed on this section. Chapter 3 involves a complete description of the experimental setup, then it will be presented a resume about the fabrication of the acrylic orifice plate cage and three orifice plates (for three different beta ratios), and a description about the data acquisition system will be shown. This section summarizes the instrumentation used to measure gauge pressure, pressure drop, mass flow rate and temperature. Finally, the fluids tested will be characterized in order to get the results presented on this research. Throughout Chapter 4 it will be presented the results of the experiments done in the experimental setup described in Chapter 3. The results are divided in different sections. The first one described the results for single-phase liquid flow through the orifice plates, for this.

(19) 19 case, the experiments were performed using water and oil separately. Second section shows the results for the two-phase flow through orifice plates, using air-oil and air-water as working fluids and comparison with literature models and new correlations for discharge coefficient are proposed. The results are shown as a resume in tables and graphs. The third section presents the visualization experiments of multiphase flow through orifice plates. To conclude, Chapter 5 presents the conclusions and perspectives for future works..

(20) 20. 2. LITERATURE REVIEW Throughout this chapter, it will be presented literature about horizontal flow through restrictions such as orifice plates and choke valves. During the first section, it is introduced the concept of single-phase flow through restrictions, separating this topic in gas single-phase flow and liquid single-phase flow. The second section is about the horizontal G-L multiphase flow, which is the focus of the research, in this section it is described the typical flow patterns and flow maps presented at this condition. The third section describes the orifice plates, it is described the main uses and characteristics about this singularity, and the standards, theoretical and empirical models. A discussion on the literature about single phase and multiphase prediction of mass flow rate through orifice plates is performed. The last section presents studies on choke valves with uses, models and characteristics.. 2.1. SINGLE PHASE FLOW THROUGH RESTRICTIONS. The single-phase liquid flow across a wellhead choke is especially rare, furthermore it is rare in the upstream petroleum industry; this can be explained by the fact that the wellhead pressure is almost always lower than the bubble pressure of the live oil. At bubble point, the liquid phase is saturated with gas and consequently the second phase appears, i.e. liquid and gas. On the other hand, for orifice plates applications (downstream sector), the single-phase flow is more typical than multiphase phase flow, especially gas single-phase flow (Kabir et al., 1990). The applications and characteristics about these singularities will be presented in detail in Section 2.3. The types of flow regimes are important when studying restrictions. Two regimes governed by different mathematical models and has different flow behaviors can be observed. The first one and most studied is critical flow, also called choked flow; it occurs when the velocity of the fluids at the smallest area reaches the sonic velocity, here the flow behavior and flow rate across the singularity, will be dependent only on upstream conditions. The second one is the subcritical regime and it happens when the velocity drops below the sonic velocity, in this case flowrate depends in both upstream and downstream conditions, in other words, changes in the downstream pressure will affect upstream pressure and flowrate as well (AlSafran and Brill, 2017)..

(21) 21 The discharge coefficient (CD), presented in Section 1, accounts irreversible losses such as friction and heat transfer. Usually it is given by the manufacturer and it depends on the type of the singularity, the restriction diameter ratio and the Reynolds number calculated at the restriction. The gas single-phase flow is more common than the liquid single-phase flow. Gas singlephase occurs across wellhead chokes when dry gas dewpoint pressure is lower than the pressure at the restriction. This kind of flow can be seen in both regimes (critical / subcritical). It is common to find in flows through restrictions, that the minimum area of the jet, which is called vena contracta, is often less than the throat area of the orifice. Figure 3 shows and sketch about some situations where the vena contracta is located after the restriction. For this reason, it is necessary to introduce into the mass flow equation, a coefficient which will consider the deviations from the theoretical value and the discharge coefficient. Considering what was said, the CD can be defined as a correction term, which is introduced into theoretical calculations, as a reason of the changes produced on the flow, due to viscosity, turbulence, and geometry of the restriction. The value of this coefficient depends of variables like density, viscosity, velocity, diameter of the flow at the restriction, geometry of the inner orifice and beta ratio which is the orifice diameter divided by the pipe diameter. The discharge coefficient is a function of the parameters described above, they are grouped in such a manner that, their resultant numerical value is dimensionless like Reynolds number and beta ratio. Regarding single-phase liquid flow, the liquid flow rate calculation through restrictions, can be calculated as given by Eq. (2.1) (Al-Safran and Brill, 2017): 𝑞$ = 𝐶+ 𝐴!, 9. -.! ∆# 0". (2.1). where qL is the liquid mass flow rate, CD is the discharge coefficient, ACH is the area at the restriction, ΔP is the pressure gradient through the restriction and ρL is the liquid density..

(22) 22. Figure 3 - Flow and Pressure behavior of Flow Across a Restriction (Al-Safran and Brill, 2017).. 2.2. TWO-PHASE HORIZONTAL GAS-LIQUID FLOW. Gas-liquid flows through pipes or horizontal lines have been extensively studied, large data sets are available for use in developing predictive tools for a wide range of conditions. Several empirical correlations and mechanistic models are also available for gas-liquid flows, like those developed by Hagedorn and Brown (1965), Beggs and Brill (1973), Taitel and Dukler (1976), and Barnea (1987), which are widely used and provide accurate results.. 2.2.1 Horizontal gas-liquid flow patterns Shoham (2006) states that the multiphase flow patterns are governed by mechanical forces such as: (i) Inertia or momentum forces, (ii) gravity force, (iii) viscous force, and (iv) surface tension forces. A carefully analysis of flow internal forces is required to characterize the multiphase flow behavior and to calculate the hydrodynamic parameters (like pressure drop and mass flow rate). For horizontal flow, as shown in Figure 4, four main flow patterns are observed which can be subdivided into additional categories. At very low liquid and gas velocities, the gas and liquid phases are separated due to density differences. Both phases flow separately: gas moving.

(23) 23 at the top and the liquid phase moving at the bottom. This flow regime is called a stratified flow. At very low velocities, the interface between gas and liquid appears very smooth, and the flow regime is called a stratified smooth flow. At slightly higher gas rates, the interface appears wavy and the flow regime is called a stratified wavy flow. As the liquid velocity increases, the liquid phase starts occupying the entire cross-sectional area. Gas travels as large, elongated bubbles in the liquid phase. At low gas velocities, we have a plug flow pattern (also called an elongated bubble flow) and at high gas velocities we have the slug flow pattern. At very high liquid velocities the gas phase moves as dispersed bubbles. This flow regime is called dispersed bubble flow. On the other hand, at very high gas velocities, the gas phase becomes continuous and the liquid phase moves as discontinuous liquid droplets entrapped in the gas phase. Some liquid phase also moves as a film adhered to the pipe wall. This flow regime is called an annular flow or an annular mist flow.. Figure 4 - Gas-Liquid Horizontal Flow Patterns (Shoham, 2006)..

(24) 24. 2.2.2 Horizontal gas-liquid flow pattern maps A flow pattern map is an illustration of transition boundaries between flow patterns. It is typically shown on logarithmic scale, which includes dimensionless parameters on both axes. As mentioned above, one of the most used empirical approach for horizontal multiphase flow is Beggs and Brill (1973). This flow pattern map was developed from a horizontal test facility of 90 ft long, pipe´s material was acrylic of 1 in and 1.5 in diameter. Nevertheless, those results were highly used in the Oil and Gas, tests fluid were air and water. On this experiment flow rates (air and water) were varied so all horizontal flow patterns were observed and recorded (Al-Safran and Brill 2017). Flow patterns and flow patterns maps have been developed based on the followed parameters: (i) Flow conditions i.e. flow velocity, and water cut; (ii) Pipe characteristics like pipe diameter, roughness, angle of inclination, and (iii) fluids properties, such as surface tension, wettability, fluid density and viscosity. This means that a significant number of different flow patterns can be obtained from different fluids characteristics. Fluids properties are extremely important on two phase flow. Viscosity and fluid density have a significant effect during the study of the behavior of two-phase flow systems, since each phase tends to flow at different velocities when the density difference between the phases is significant, the same when the difference of viscosity is present. Figure 5 illustrates Beggs and Brill (1973) revised flow pattern map. The x and y axes of the map are the non-slip liquid holdup (𝜆$ ) and the mixture Froude number (𝑁'( ), respectively. Both dimensionless parameters are given by:. 𝜆$ =. 𝑣%$ (2.2) 𝑣%& + 𝑣%$. 𝑁'(. 𝑣1 = (2.3) 𝑔𝐷. where 𝑣%$ and 𝑣%& are the liquid and gas superficial velocities (flow rate divided by the total pipe area), 𝑣1 is the mixture velocity (sum of gas and liquid superficial velocities), g is the gravity and D is the pipe diameter. Flow transition boundaries can be calculated for each condition based on 𝐿2 , 𝐿- , 𝐿3 and 𝐿4 curves which are parameters in function of the non-slip holdup 𝜆$ . Beggs and Brill (1973).

(25) 25 flow pattern map allows to determine three flow patterns: (i) Segregated, grouped in smooth and wavy stratified and annular flow; (ii) Intermittent, such as plug and slug flow; (iii) Distributed, such as dispersed bubble and mist flows. There is a fourth section called (iv) Transition, this is an unspecified combination of intermittent and segregated flow.. Figure 5 - Beggs and Brill (1973) Horizontal Flow Pattern map (Shoham, 2006). Regarding Mechanistic models, Xiao et al. (1990) modified and verified previous models such as Taitel and Dukler (1976) and Taitel and Barnea (1990), using experimental and field data, resulting into a comprehensive model. Figure 6 illustrates Taitel and Dukler (1976) flow pattern map. The y-coordinate is the Froude Number and the x-coordinate is the dimensionless 5. liquid height C 6"D. The mechanistic flow pattern, due to the liquid height determination, involves five dimensionless groups called X, Y, F, T and K. Al-Safran and Brill (2017) includes an interesting flow-chart shown in Figure 7 which helps the reader to understand the flow pattern prediction methodology in Taitel and Dukler (1976) flow pattern map..

(26) 26. Figure 6 - Taitel and Dukler (1976) flow pattern map (Shoham, 2006). A flow pattern map of air-water flow based on 5935 flow pattern observations was presented by Mandhane et al. (1974). The map is presented in Figure 8. This flow map will be used to present the observed results in the experimental campaign..

(27) 27. Figure 7 - Taitel and Dukler (1976) flow pattern map flow chart presented by AlSafran and Brill (2017).. Figure 8 - Mandhane et al. (1974) horizontal gas-liquid flow pattern map..

(28) 28. 2.3. ORIFICE PLATES. Differential Pressure devices such as orifice plates are commonly used in single-phase and multiphase flow measurements. Generally, the response of such devices for multiphase flows depends on upstream flow conditions. Based on Falcone et al. (2001) the first multiphase flow metering (MFM) appeared in the petroleum industry due to a research in early 1980’s. Inside the Oil and Gas industry the orifice plates are generally recognized in the fiscal metering or custody transfer area. They provide real-time information on variations such as gas flow rates, allowing that a commercial transaction occur so it requires a high level of accuracy.. 2.3.1 Orifice plates specifications Based on orifice plate ASME MFC 14M standard there are three location for the pressure tappings recommended: (i) flange tappings, (ii) D and D/2 tappings and (iii) corner tappings. Figure 9 describes pressure tappings alternatives and Figure 15 showed the pressure tappings used on this research. Figure 10 presents the basics specifications of an orifice plate based on the ASME standard. Also, each one of them are described as follows based on ASME MFC 14M standard:.

(29) 29. Figure 9 - Pressure Tappings (Reader-Harris, 2015).. Flange tappings: For fiscal oil and gas measurement flange tappings are normally specified: they are located in the flanges 25.4 mm (1′′) upstream of the upstream face of the plate and 25.4 mm (1′′) downstream of the downstream face of the plate. It is important to emphasize that this recommendation may be unsuitable for pipes smaller than those covered by ISO 5167-2:2003 (i.e. D < 50 mm) because the downstream tapping might be in the pressurerecovery zone, which starts a little to the right of the vena contracta, see Figure 3. For D and D/2 tappings: they are located 1D upstream and D/2 downstream, both measured from the upstream face of the orifice plate: the upstream tapping is upstream of any disturbance to the pressure from the plate; the downstream tapping is near the pressure minimum for large β (aspect ratio of the orifice plate). Corner tappings: they are located in the corners between the plate and the pipe wall. They may be either single tappings or annular slots. Recovery pressure taps are located 1 diameter upstream and 6 diameters downstream the restriction..

(30) 30. Figure 10 - Orifice Plate Specs ASME MFC 14M. Regarding Figure 10, D is the pipe diameter, d is the orifice plate diameter, a is the direction of flow, c length of upstream ring, c´ length of downstream ring, f thickness of the slot, Øj is the chamber tapping diameter, a is the width of annular slot or diameter of single tapping; g and h are dimensions of the annular chamber and s is the distance from carrier ring to upstream step. 1 is the carrier ring with annular slot, 2 is the individual tappings, 3 is the pressure tappings, 4 is carrier ring and 5 is the orifice plate. It is important to mention the corner tappings requirements as per the norm ASME and Figure 10 as reference: §. Type of Fluid: The fluids may be either compressible (gas) or incompressible (liquid). The fluids shall for all practical purposes be physically and thermally homogeneous and of single phase through the primary device.. §. The density and viscosity of the fluid at the flowing conditions must be known.. §. The inside diameter of both the upstream and downstream sections of the meter tube (i.e., pipe and flanges) shall be circular and cylindrical within a tolerance of no more than 0.025 mm..

(31) §. 31 The diameter of the meter used for all calculations shall be the average of four diameter measurement made at 6 mm from the upstream face of the orifice plate location.. §. The orifice plate shall be perpendicular to the metering section within 1 deg.. §. The orifice plate shall be centered within 0.4 mm (0.015 in) of the meter section centerline.. §. The upstream face, A, of the plate (Figure 10) shall be flat. It is considered as such when the maximum gap between it and a straight edge of length, 0, laid across it anywhere is less than 0.01(D - d)/2. It is assumed that the orifice plate mounting does not distort the plate.. §. The surface roughness of the orifice plate shall be less than 0.00127 mm.. §. There shall be no drain or vent holes in the orifice plate.. §. The orifice plate thickness, E, shall be no greater than 3.2 mm.. §. The values of E measured at different points of the plate shall not differ among themselves by more than 0.0010 mm.. §. The orifice edge thickness, e, shall not exceed 0.020 mm or 0.125d, whichever is smaller.. §. All plates must be beveled on the outlet side or the downstream side of the orifice unless their thickness is equal to or less than the orifice edge thickness. If a bevel is required, the angle of bevel, F, shall be approximate 45°.. The following equation (Eq. 2.4) is provided by ASME MFC 14M and is applicable only for corner tapping designs. The discharge coefficient equation for Reynold above 1000 is based on pipe diameter D[in], beta ratio, and Reynolds number (density, velocity of fluid, pipe diameter and viscosity):. 𝐶+ = E0.5991 + E. 7.:-×7.7-:4 +. 7.7744×7.7-:4 +. + C0.3155 +. − 0.192 + C16.48 −. 7.72;:×7.7-:4. 2.2<×7.7-:4 +. +. D × (𝛽 4 + 2𝛽2< )L × M1 − 𝛽 4 + 2=> #. D × (𝛽 4 + 4𝛽2< )L × 9. ?@$. (2.4). The discharge coefficient distribution for low Reynolds were studied by Miller (1996), The CD for the orifice plates with beta ratio of 0.5 can be directly taken from the graph of Figure 11. For the orifice plate with radio 0.67 (one of the used in the experiments) an interpolation of.

(32) 32 beta ratios about 0.6 and 0.7 is required. Finally, the CD for beta orifice below 0.5 is not presented on Miller (1996) research.. Figure 11 - Orifice Plate Discharge Coefficient for Low Reynolds (Miller, 1996). Then, in order to calculate the mass flow rate through orifice plate at corner taps, it is possible to use the Eqs. (2.5) and (2.6). 6. 𝛽 = + ; 𝐴A(BC =. D6 % 4. (2.5). -. 𝑄1 1 − 𝛽4 ∆𝑃 = R T ×R T (2.6) 𝐶+ 𝐴A(BC 2𝜌 where the beta ratio 𝛽 is in function of orifice diameter (d) and pipe diameter (D), the pressure gradient ∆𝑃 is calculated in function of the mass flow rate 𝑄1 , the discharge coefficient CD, the orifice area 𝐴A(BC and the density of the fluid 𝜌.. 2.3.2 Orifice plates two-phase flow models The models that will be presented on this research are based on the investigation performed by Oliveira et al. (2009). Indeed, the following sections have a general two-phase flow mass flow rate equation. This equations involves parameters such as the discharge coefficient for two-phase flow 𝐶+,"# which will be calculated or assumed constant, it depends.

(33) 33 on each model, the orifice area of the restriction 𝐴- , the beta ratio 𝛽 and a two-phase flow correction factor 𝐾$ , each model suggests different equations to calculate the 𝐾$ factor, the mixture density 𝜌1 , and the pressure drop across the orifice plate.. 𝑚̇ "# =. 𝐶+,"# 𝐴M1 − 𝛽 4. 𝐾$ M2𝜌1 ∆𝑃"# (2.7). The gas-liquid mixture density, 𝜌1 , can be calculated by the equation for homogeneous mixture density, it is function of the quality, x, liquid and gas densities, ρl and ρg, respectively: 1 𝑥 (1 − 𝑥) 𝑚̇& = + ; 𝑥 = (2.8) 𝜌1 𝜌F 𝜌. 𝑚̇ " The homogeneous model: the principal authors who presented this model were Carey (1992) and Collier (1996). This model treats the two-phase flow as it were a single-phase flow. The authors described the model and provides an equation to calculate the two-phase correction factor 𝐾$ based on phases density and quality factor:. 𝐾$ =. 1 [. 𝜌 𝑥 \ $ − 1] + 1 𝜌.. (2.9). The non-homogeneous model: this type of models needs two additional parameters to predict the two-phase mass flow rate. The first of them is the Lockhart-Martinelli parameter and the other one is the slip factor, as this model assumes slip between phases. Chisholm (1967) established a correlation which consider the slip between phases, the assumptions made under this model are: Ø Incompressible liquid flow. Ø No friction across the restriction. Ø Constant quality both upstream and downstream the orifice plate. The slip ratio which is necessary to calculate the two-phase correction factor 𝐾$ is calculated depending on the Lockhart-Martinelli parameter X, according to:.

(34) 34 1 − 𝑥 𝜌. 𝑋=\ ] ^ (2.10) 𝑥 𝜌$. The two-phase correction factor 𝐾$ is calculated using Eq. (2.11): a 1 1 ⃓ 𝐾$ = \ ]⃓ (2.11) 1−𝑥 ⃓ ⃓ 𝜌 1 𝜌 . $ ⃓ + 𝑆9 𝜌 ⃓ ⎛𝑆 9𝜌. ⃓ $⎞ 1 ⃓ 1+⎜ + C -D ⃓ ⎟ 𝑋 𝑋 ⃓ ⃓ ⎷ ⎝ ⎠ Depending on the Lockhart Martinelli result, the slip ratio is calculated as follows: •. For X ≥1: 𝜌$ 𝑆 = ^ (2.12) 𝜌1. •. For X <1: 2. 𝜌$ 4 𝑆 = \ ] (2.13) 𝜌1 The second non-homogeneous model studied in this section was developed by Zhang et al. (2005). The model is frequently used in Venturi Flow meters correlations. The assumptions made under this model are: Ø Incompressible liquid flow. Ø No friction across the orifice plate. Ø Air-oil with quality lower than 2%. The two-phase correction factor 𝐾$ is calculated using the following equation: 1. ∝ G 𝜌$ 𝐾$ = h𝑐 C D R T + 1j 1−∝ 𝜌.. =7.:. (2.14). The Lockhart-Martinelli parameter equation for this model is defined below:.

(35) 35 𝑋 = 𝑐, C. 𝜌. , ∝ D \ ] (2.15) 1−∝ 𝜌$. Equations (2.14) and (2.15) are based on void fraction ∝ measured by means of tomography, densities of phases, and constants like c, c´ and H which depends on the flow pattern. The constants developed on Zhang´s research are resumed in Table 1. Table 1 - Zhang et al. (2005) coefficients for each Flow Pattern Flow Pattern Bubbly and Slug Wavy Annular. 2.4. c 0.50 1.30 1.20. n 0.95 1.15 0.95. m 0.02 0.08 0.05. c' 0.51 1.25 1.21. H 0.65 0.70 0.95. CHOKE VALVES. Choke valves are very important in the oil and gas production area, mainly in natural flow production wells. Sachdeva et al. (1986) said that the principal function the choke valves have, is that they are used to control and optimize production flowrate from wells to avoid water or gas coning. Also, the choke maintains stable pressure to protect surface equipment from pressure fluctuations and prevent premature erosion (high fluid velocities) or abrasion (sand production) on surface equipment or piping components. Furthermore, chokes provide the necessary back pressure to a reservoir to avoid formation damage. Figure 1 detailed the choke valve position on a typical production Christmas tree. Another characteristic about choke valves, also described by Sachdeva et al. (1986), is regarding the types of flow regimes developed across the restriction, the critical and subcritical regimes as observed in orifice plates. Additionally, to control flow rate and pressure drop at the wellhead, the choke valve plays a very important role in Flow Assurance analysis (Falcone et al., 2001). Also, there is a research carried out at La Sapienza U., Rome, and mentioned in Falcone et al. (2001) which talk about the use of wellhead choke valves to monitor and predict well performance, bringing promising results, especially when the system is integrated with MFMSs or test separators. Such a monitoring and metering approach, from downhole to stock tank, gives a real-time picture of.

(36) 36 what is happening in the reservoir and, therefore, provides the best support to reservoir simulation. Also, as choke valves are needed in the oil industry its use as a flow meter is of interest. So, the experimental data acquired in this research will be compared with choke valves models in order to verify its performance in predicting flow rate, as a beginning of study for further works.. 2.4.1 Choke valve models Gas-liquid multiphase research through choke valves began due to a necessity to study the behavior of two-phase flow between natural gas with oil. Multiphase flow through restrictions background, was pretty well detailed by Brill et al. (1991). The first research in the area of twophase flow through restrictions was published by Tangren et al. (1949). This research assumed incompressible flow, ideal gas, homogeneous mixture (no slippage), no mass transfer between phases, isothermal, adiabatic and one-dimensional laminar flow. All those experiments were conducted under critical flow through converging-diverging duct. Then Gilbert (1954) developed experiments in gas-lift wells in California (Shell Oil Company), explained flowing and the bean (orifice) performance under two-phase vertical flow. Gilbert´s experiments were under critical flow as well, because he made no attempt to study cases where upstream pressure was less than 1.7 times the downstream pressure (subcritical flow). Then, Fortunati (1972) presented a correlation that can be used to calculate critical and subcritical two-phase flow through chokes. Ashford (1975) also developed a relation for two-phase critical flow based on the work of Ros (1960). Pilehvari (1981) also studied choke flow under subcritical conditions. The previous works were based on empirical field experiments. Then few theoretical models were implanted as Ashford and Pierce (1975) who derived an equation to predict the critical pressure ratio, the model assumes that the derivative of flow rate with respect to the downstream pressure is zero at critical conditions. Sachdeva et al. (1986) extended the work of Ashford and Pierce (1975) and proposed a relationship to predict critical pressure ratio, determine the flow regime and predict the mass flow rate assuming no slippage between phases (Homogeneous model). Al-Safran and Kelkar (2009), based on Sachdeva´s data collected, determined the flow regime and predicted the mass flow rate through positive orifice chokes taking into account the slippage between phases..

(37) 37 Homogeneous models, like Ashford and Pierce (1975), were developed based on the following assumptions: •. Isentropic flow process: adiabatic because of the instantaneous nature of the process. Reversible because friction losses are negligible compare with acceleration pressure gradient.. •. The model considers the adiabatic expansion of gas flowing simultaneously with oil and water through the orifice, using a polytropic expansion relationship.. •. Incompressible liquid phase.. •. “Frozen flow” (gas quality constant).. •. No liquid flashing occurs at the choke throat.. •. Homogeneous or uniform multiphase flow, no slip between phases.. The investigation was designed specifically to: (i) compare the predicted theoretical orifice pressure drops from known oil and gas flow rates with those measured in the well; (ii) compare the predicted theoretical flow rates through the orifice from known pressure drops with those measured in the well; and (iii) use the data to evaluate a series of orifice discharge coefficients for various bean sizes. The final Ashford and Pierce (1975) equation for critical pressure ratio is given as:. . J=2 𝑅 1 C 𝑘2 D k𝑅2 l 𝑘 − 1 m n1 − 𝑦H I J K o (1 − 𝑦H )p C 𝑘 D. 0.5[1 +. JO2 (𝑅2 )𝑦H =(2/J) ]- 𝑦H I J K. = 1 (2.16). where 𝑦H is the critical pressure ratio Eq. (2.19), 𝑘 is the heat capacity ratio of the mixture, and 𝑅2 is the superficial gas/liquid ratio at choke upstream conditions, given as the ratio of upstream superficial gas and liquid velocities.. 𝑅2 =. 𝑣%.$ (2.17) 𝑣%$$.

(38) 38 Ashford and Pierce (1975) recommend the use of the orifice discharge coefficient given in Table 2. Table 2 - Ashford and Pierce Discharge Coefficient Recommendations Choke Size (in) 32/64th 24/64th 20/64th 12/64th 8/64th. CD 0.95 0.95 0.9760 1.20 1.20. The model of Sachdeva et al. (1986) considered the conservation of mass, momentum and energy equations with the following assumptions: •. One-dimensional flow.. •. Equal phases velocities at the throat.. •. Acceleration pressure gradient is predominant (frictional and gravitational forces negligible).. •. Incompressible liquid phase.. •. “Frozen Flow”.. •. No slip between phases (homogeneous flow).. Sachdeva et al. (1986) derived an expression in order to find the boundary between critical and subcritical flow. (1 − 𝑥2 )𝑉$ (1 − 𝑦) 𝑘 ⎫ + 𝑥2 𝑉&2 𝑘−1 𝑦= - (2.18) 𝑛 𝑛(1 − 𝑥2 )𝑉$ 𝑛 (1 − 𝑥2 )𝑉$ ⎬ ⎨ 𝑘 + 2\ 𝑥 𝑉 ] ⎭ ⎩𝑘 − 1 + 2 + 𝑥2 𝑉&2 &⎧. #. where 𝑦 = #% is the pressure ratio (downstream pressure divided by upstream pressure), k is $. the heat capacity, 𝑥 is the quality, VG and VL are the specific volume of gas and liquid, and 𝑛 is the polytropic gas expansion coefficient. The subscripts 1 and 2 mean upstream and downstream conditions, respectively. Based on Sachdeva’s and Perkins’ investigations (homogeneous models), one of the most used nonhomogeneous models was developed by Al-Safran and Kelkar (2009). This model.

(39) 39 considered the conservation of mass, momentum and energy equations across the restriction, and the following assumptions: •. One-dimensional flow.. •. Acceleration pressure gradient is predominant (frictional and gravitational forces negligible).. •. Incompressible liquid phase.. •. Slippage between phases at the throat (nonhomogeneous flow).. The final Al-Safran and Kelkar equations for critical pressure ratio requires iterative solution procedure:. G=2 𝑦H I G K. −. 𝑛 𝛼 ∗ (1 − 𝑦H ) + C𝑛 − 1D 2 𝑛 𝑛 C𝑛 − 1D + C2D \1 + 𝛼 ∗ 𝑦H G ]. 𝑛 =. 𝛼 ∗ =. -. = 0 (2.19). 𝑥𝑘𝐶Q. + (1 − 𝑥)𝐶$ (2.20) 𝑥𝐶Q. + (1 − 𝑥)𝐶$. 𝑆(1 − 𝑥)𝑣$ 2.738 − log (𝛾& ) ; 𝑘 = (2.21) 𝑥𝑣.F 2.328. where 𝑦H is the critical pressure ratio, 𝑛 is the polytropic gas expansion exponent, 𝑘 is the heat capacity ratio of the mixture, 𝐶Q. is liquid specific heat, 𝑥 is quality, 𝑣. is the gas specific volume, 𝑣$ is the liquid specific volume, 𝑆 is slip ratio, 𝛾& gas specific gravity. All fluid properties are estimated at upstream pressure and temperature. The slip ratio can be calculated using the equation from Schüller et al. (2003):. 𝑆 = ^1 + 𝑥 R. 𝜌$ − 1T (1 + 0.6𝑒 =7.:R ) (2.22) 𝜌.. As per Al-Safran and Brill (2017), the ultimate goal to predict the fluid flow behavior is to determinate the volumetric flow rate of the well, which depends on the flow regime at the choke throat. For two-phase flow the condition for critical/subcritical flow is more complicated..

(40) 40 Kelkar (2008) emphasized that it is important to describe the circumstances where the restrictions must be operated under each critical or subcritical flow regime, if the objective is to separate downstream fluctuations from upstream conditions, it is a good idea to operate the restriction under critical flow. In this situation the downstream fluctuations like separator conditions will not affect the wellhead pressure, it warranties a smooth production. On the other hand, if the purpose of the restriction is to simply control the production rate, or to use it as a safety device to be closed only under emergency conditions, the pressure drop across the restriction should be minimized. For example, a subsurface safety valve operating under normal condition, it needs to cause the small pressure drop as possible. This is possible when the restriction is operated under subcritical conditions. Likewise, if a choke is used to control the flow rate, or to minimize gas hydrate blockages, it is also operated under subcritical conditions. Multiphase flow rate will be resumed on empirical and theoretical approaches, the analysis for each one depends on the flow regime mentioned before. Regarding the empirical approach it is based on Beggs et al. (1980) investigation, it was developed on offshore oil and gas wells which typically are at subcritical flow regime. Beggs established the following pressure drop equation: -. ∆𝑃 =. 𝜌G$ |𝑣1 H52 } 2𝐶+ -. (2.23). where 𝜌G$ is no-slip mixture density at upstream conditions, 𝑣1 H52 is the mixture velocity at upstream conditions based on choke diameter, ∆𝑃 pressure drop across the choke and CD is calculated as 0.5, constant. It is possible to use empirical discharge coefficient such as Beggs et al. (1980) developed for commercial valves in the oil and gas industry. In order to determinate the volumetric flow rate for critical flow, a commonly used equation is generated, it is given as: 𝑝2 𝑑 S 𝑞$&' = (2.24) 𝑏𝑅* H where the mass flow rate is 𝑞$&' , the upstream pressure is 𝑝2 , the intel temperature 𝑇2 , 𝑅* is the gas/oil ratio and d is the orifice diameter or bean size; a, b, and c parameters are empirical.

(41) 41 constants related to fluid properties of the liquid phase. Those values differ depending on each investigator, they can be summarized on Table 3. Table 3 - Empirical Correlations Parameters PARAMETER. INVESTIGATOR. a. b. c. Ros (1960). 2.00. 4.25𝑥10=3 [281.8]. 0.500. Gilbert (1954). 1.89. 3.86𝑥10=3 [194.1]. 0.546. Baxendell (1958). 1.93. 3.12𝑥10=3 [178.6]. 0.546. Achong (1961). 1.88. 1.54𝑥10=3 [89.7]. 0.650. As already mentioned, empirical correlations are developed through curve fitting based on a specific range of experimental data, these correlations cannot be extended beyond the range where they are tested, this is one of the reasons about the research on models based on theoretical approach, which involves a study about conservation of mass, momentum and energy across a restriction such as a choke valve. On the following lines, it will be described the mass flow rate equation developed on homogeneous models such as Sachdeva et al. (1986) and nonhomogeneous models such as Al-Safran and Kelkar (2009). Sachdeva et al. (1986) developed a mass flow rate equation:. 𝑚̇ = 𝐶+ 𝐴!, ^2𝑃2 (𝜌1- )- h. 𝑥$ (1 − 𝑦) 𝑘𝑥& 1 𝑦 + \ − ]j (2.25) 𝜌$ 𝑘 − 1 𝜌&2 𝜌&-. As this model assumes homogenous, incompressible fluid and polytrophic gas expansion, gas density due to the restriction can be calculates as:. . 1 1 =2 = 𝑦 J (2.26) 𝜌&2 𝜌&-. where 𝜌&2 is the upstream gas density and 𝜌&- is the downstream gas density, 𝑦 is the critical/subcritical pressure ratio and k is the heat capacity. Equation (2.25) might be used to calculate the mass flow rate for both regimes critical and subcritical..

(42) 42 Al-Safran and Kelkar (2009) nonhomogeneous model proposes the following equations in order to determinate the mass flow rate which varies depending on flow regime: Mass flow rate for subcritical flow: G a ⃓ 𝑝𝑛 𝑝- G=2 ⃓ jƒ 𝐶+ 𝐴!, 𝑝2 ‚𝛼 C1 − 𝑝 D + 𝑛 − 1 h1 − 𝑝 ⃓ ⃓ 2 2 ⃓ 𝑚̇ " = ⃓ (2.27) =2 ⃓ ⃓ 𝑝 1 ⃓ 𝑥2 𝑣.2 h𝑝- G + 𝛼j E𝑥2 + 𝑆 (1 − 𝑥2 )L 2 ⎷. where slip ratio is defined as: 7.2;. 𝜌$ 𝑆 = R T 𝜌.. (2.28). Mass flow rate for critical flow:. G 𝑛 𝐶+ 𝐴!, - 𝑝2 …𝛼(1 − 𝑦H ) + 𝑛 − 1 E1 − 𝑦H G=2 L† 𝑚̇ " = „ (2.29) =2 1 𝑥2 𝑣.2 ‡𝑦H G + 𝛼ˆ E𝑥2 + 𝑆 (1 − 𝑥2 )L. The following table resumes the empirical and theoretically models developed during the last 50 years..

(43) 43 Table 4 - Multiphase Fluid Flow Choke Models Homogeneous / Characteristics of Nonhomogeneous fluid flow. Author. Type. Tangren (1949). Correlation. Gilbert (1954). Correlation. Critical. Fortunati (1972). Correlation. Critical / Subcritical. Ashford and Pierce (1975). Theoretical. Homogeneous. isentropic. Fluid regime. Phases components. Critical. Homogeneous. Isentropic. Critical / Subcritical Critical / Subcritical. Air-water & air- kerosene. Critical / Subcritical. Oil-waternatural gas. Sachdeva et al. (1986). Theoretical. Homogeneous. Incompressible fluid and polytropic gas expansion. Perkins (1993). Theoretical. Homogeneous. Isentropic. Schüller (2003). Isentropic Theoretical Nonhomogeneous expansion through the restriction. Critical / Subcritical. Gas-water-oil. A-Safran and Kelkar (2008). Theoretical Nonhomogeneous. Critical / Subcritical. Air-water mixture. Polytropic.

(44) 44. 3. EXPERIMENTAL SETUP Throughout this chapter it will be explained the entire experimental setup used to develop this study. The setup was built at the Experimental Laboratory of Petroleum (LabPetro) of the Center for Petroleum Studies (CEPETRO) at the University of Campinas (UNICAMP). It will be shown the literature used to fabricate the three orifice plates (three different beta ratios), and the data acquisition system will be showed. Also, this section summarizes the instrumentation used to measure pressure gauge, pressure drop, mass flow rate and temperature. Finally, it will be denoted the fluids tested and the experimental process done in order to get the results presented on this research. The entire experimental setup is exposed in the Figure 12, which shows the route of each phase (liquid and/or gas) before, during, and after going through the test line.. 3.1. SETUP. The experimental setup is a closed loop for the circulation of liquid (tap water or oil), and gas (compressed air) injection in the beginning of the test section and gas-liquid separation once it goes through the test section. The apparatus consists of a liquid tank, that also works as a separation tank, booster pump for the water/oil and a compressor for the gas phase. Frequency variable drivers, pipelines for liquid, gas and two-phase flows, control valves, Coriolis flow meters, differential and gauge pressure and temperature transducers in the test section and data acquisition systems are installed and used for the experiments, as represented in Figure 12. The experimental apparatus is detailed as follows: •. A liquid tank with capacity of 500 liters and 87 cm of external diameter, that also works as a separation tank. Red label represents oil and blue label represents water.. •. A booster gear pump for the water or oil (EDRAL-ED 1 ½ x 60A), which includes a WEG motor (3 Hp, 1150rpm). The pump is controlled by frequency variable drivers or velocity speed driver (VSD).. •. Pipelines for liquid, gas and two-phase flows were fabricated in acrylic with inner diameter (I.D.) of 19 mm and external diameter (E.D.) of 25.3 mm (1¨ Nominal Diameter), the horizontal test section are about of 10.33 m long.. •. The Acrylic box along with the orifice plate is located at 5.54 m from the beginning of the test section..

(45) •. 45 A control valve and a pressure transducer device were installed on the gas line before the test line, so gas mass flow rate can be adjusted in the required value. The gas mass flow rate came from an Ingersoll Rand Rotary screw air compressor (SSR -HP50-SE).. •. Coriolis flow meters were installed: Metroval RHM 12 for liquid phase and Micromotion CMF15 for gas phase.. Figure 12 - Experimental Setup Sketch. •. Three (3) pressure transmitters, one 19 mm before the orifice plate (inside the acrylic box), other one at 5.04 m from upstream orifice plate and the second one at 3.8 m after the orifice plate.. •. Two (2) differential pressure transmitters, one at the orifice plate (corner taps) and the second for measure recovery pressure (at the upstream face of orifice plate and 114 mm downstream the orifice plate) were installed in the line.. •. Two (2) temperature transducers were installed in the test section one at the beginning and other at the end of the test line,. •. The test section and data acquisition systems include LabVIEW software and National Instrument modules.. •. Calibration equipment´s were used to setup the apparatus measured devices:.

(46) 46 o Pressure drop transducers were calibrated using a portable pressure calibrator series Druck DPI 615 (GE) with an accuracy about 0.025% full scale. o Dryblock calibrator ECIL BT was used to setup the temperature sensors with a resolution about 0.1 ºC. Table 5 details the equipment absolute uncertainty and technical specification of each device. Table 5 - Equipment specifications Device Coriolis flowmeter (MFR). Coriolis flowmeter (MFR). Pressure drop transmitter:. Pressure gauge transmitter:. Pump Compressor. 3.2. Description Model: Metroval RHM 12. Flanges: DN 25 / 1”. Max working pressure: 150 bar Range: MFR: 10 – 6000 Kg/h. Model: MicroMotion CMF15 Flanges: DN 25 / 1”. Max working pressure: 150 bar Range: MFR: Kg/h. Model: Rosemount. Range: 0-2 Bar. Max working pressure: 250 bar 4-20mA Hart Modelo: Rosemount. Range: 0-2 Bar. Max Working Pressure: 150 bar 4-20mA Hart Model: EDRAL-ED1 1/2x60A. Weg motor 3kW/100L Classe IR2; 1150RPMPower: 3 Hp Model: Ingersoll-Rand Capacity: 205 PCM (348,3 m3/h) Operational Pressure: 140 PSI (9,6 bar). Qty. Uncertainty. 1. 0.5%. 1. 0.5%. 1. 0.8%. 2. ND. 1. ND. 1. ND. ORIFICE PLATES DESIGN. Figure 13 presents each sharp-edged orifice plate used in this work, they are 1.18 mm thick plate and internal diameters (Bean Size) are 6.4 mm (~1/4 in), 9.53 mm (~3/8 in), and 12.8 mm (~1/2 in), all of them chamfered 45º towards the downstream. Those orifice plates are mounted into the test line as indicated in Figure 14. Throughout the text each orifice plate will be denoted by the special designation of 64th of inch or by the beta ratio. It is highly used in the petroleum industry because sizes in chokes valves usually increases in steps of 4/64th. Then for this study 16/64th is regarding the orifice plate with beta ratio of 0.34 (bean size of 6.4 mm or ¼ in); 24/64th is the orifice plate with beta ratio of 0.5 (bean size of 9.53 mm or 3/8 in) and 32/64th is the orifice plate with beta ratio of 0.67 (bean size of 12.8 mm or ½ in)..

(47) 47. Orifice Plate ¼ in. Orifice Plate 3/8 in. Orifice Plate ½ in. Figure 13 - Sharp edged orifice plate. Based on ASME MFC-14M–2008R the pressure drop across the restriction is measured as shown in Figure 15. Three pressure taps are located at different distances: first at one diameter upstream the restriction there is a pressure transmitter, just at the orifice plate faces a differential pressure transmitter was installed (Corner Tappings) and at six diameters downstream the restriction a differential pressure transmitter (Recovery Taps) was placed.. Figure 14 - Detail of the visualization box and orifice plate (red arrow)..

(48) 48. Figure 15 – Pressure taps at the orifice plate - Corner tappings. Figure 16 shows the distance between each pressure tap, designed as per ASME recommendations, reviewed in section 2.3.1. Also Figure 17 showed the 3-D drawing used to fabricate the acrylic box for the orifice plates experiments.. Figure 16 - Pressure taps location [mm]..

(49) 49. Figure 17 - Orifice plate box drawing.. 3.3. VISUALIZATION SYSTEM. During the multiphase flow experiments, a high-speed camera was used to analyze the different flow patterns at measured liquid and gas mass flow rates and the influence of the singularity on each flow pattern (Figure 18). A carefully analysis of the flow is required to characterize the multiphase flow behavior and to calculate the hydrodynamic parameters like pressure drop and holdup. The experimental data can improve the understanding of the phenomena involved and increase the accuracy of models used to predict mass flow rate, flow patterns and other multiphase flow characteristics across singularities. In order to visualize the two-phase flow in the annular duct, we used the shooting technique with high speed cameras. The camera model was a Phantom VEO 640 which has an acquisition rate of 1400 fps at maximum resolution of 2560 x 1600 pixels, reaching 360000 fps at lower resolutions. The camera was positioned facing the apparatus attached to tripods. The lighting equipment used were three MultiLed LT from GSVITEC each has 24 high power LEDs with a total of 7700 lumens as shown in Figure 18..