PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA MECÂNICA CENTRO TECNOLÓGICO PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO UNIVERSIDADE FEDERAL DO ESPÍRITO SANTO RENAN FÁVARO CALIMAN AN EXPERIMENTAL ANALYSIS OF ORIFICE PLATE WET GAS METER BY THIRD PRESSURE TAPPING FOR LIQUID LOADING ESTIMATION VITÓRIA, ES 2022 PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA MECÂNICA CENTRO TECNOLÓGICO PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO UNIVERSIDADE FEDERAL DO ESPÍRITO SANTO RENAN FÁVARO CALIMAN AN EXPERIMENTAL ANALYSIS OF ORIFICE PLATE WET GAS METER BY THIRD PRESSURE TAPPING FOR LIQUID LOADING ESTIMATION A dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Mechanical Engineering. Advisor: Prof. Rogério Ramos VITÓRIA, ES 2022 iii ACKNOWLEDGEMENTS The search for knowledge is a continuous endless ladder and the master’s is an advanced steppingstone that not only brings a better understanding on the concentration area, but a new comprehension of the world and all these were not possible alone. First, I would like to thank God for guiding me though this step. I would like to acknowledge my mother Margarida, my guardian angel, my father Valdecir and my brother Marlon for all the support and love that you have given. You are always there for me. I would like to thank my supervisor Professor Rogério Ramos for his valuable advice, guidance and opportunities given throughout these years and the trust deposited to develop such research. You provided me with the tools that I needed to choose the right direction and successfully complete my dissertation. I would also like to thank my friends Tiago Guerzet for the huge support from the company in experiments to stimulating discussions in two-phase flow topic, to Ligia Gaigher for valuable tips, to Felipe Paiva for the LabView huge support and finally, but not least to Ullices for the instrumentation expertise. In addition, my acknowledgement to Petrobras and ANP for financing the NEMOG facilities and the project that originated this work. iv ABSTRACT Wet gas flows are very common in many industrial processes, manly in oil industries. On those, flow measurement is based in differential pressure devices at least on 40% of the cases, being the orifice plate the most used one, reaching US$ 21 billion in natural gas measurement at UK industry. However, in case of two-phase flow applications, the liquid loading causes a positive bias on the pressure differential readings, due to phases interactions called over-reading and resulting in an erroneous gas flow rate prediction up to 50%. Through decades apart, many authors proposed correlations to estimate and correct this overestimation for different differential pressure devices, such as orifice plates, venturi tubes and inverted cones, but all needed some liquid content information, which real time estimation is a engineering challenge. To overcome this barrier, industry has been developing an all in on two- phase wet gas flow meters (WGFMs), with liquid loading estimation and over-reading (OR) correction on the same meter. In 2012, ISO TR 11583 (2012) released a methodology to wet gas measurement based on orifice plates or Venturi, using the pressure loss ratio (PLR) technique to liquid content relationship limited by 6D 3rd pressure tap, high pressure levels and low gas wetness. Aiming to investigate this methodology, this work relied on a gas-liquid flow circuit, located at the Research Group for Studies on Oil&Gas Flow and Measurement (NEMOG, in Portuguese), located at Federal University of Espírito Santo, Vitória, Brazil, to promote an air-water flow at 1, 3 and 5 barg pressure line (density ratio (DR) equal to 0.0025, 0.0048 and 0.0071), 360 kg/h air mass flow rate (Gas Froude number (FRg) equal to 0.74, 0.90 and 1.29) and Lockhart-Martinelli parameter (XLM) equal to 0.15 ,0.22 and 0.30 levels. With this data, the most relevant orifice plate OR correlations were tested, considering ISO TR 11583 (2012) proposal and new data fitted equations are proposed for 6D, 20D and 144D third tap distances, resulting in 10%, 10% and 15% accuracy respectively. Finally, a new methodology is proposed by combining ISO TR 11583 (2012) and Petalas and Aziz (1998) two-phase pressure drop model, with a 10% accuracy for 20D tap, but poor results for 144D due to model limitations. Keywords: Wet gas, orifice plate, over-reading, pressure loss ratio, Lockhart- Martinelli. v LIST OF FIGURES Figure 1 - Geometrical analysis of a stratified flow (Source: author) ......................... 25 Figure 2 - Geometrical analysis of a annular flow (Source: author) ........................... 28 Figure 3 - Flow approximated pressure pattern though orifice plate (Source:adapted from READER-HARRIS, FORSYTH, and BOUSSOUARA (2021)) .......................... 32 Figure 4 - Orifice plate sketch (Source: Author) ........................................................ 32 Figure 5 - Two-phase flow subsets (Source: ISO TR 12748 (2015)) ......................... 35 Figure 6 - Horizontal two-phase wet gas flow regimes (Source: adapted from ISO TR 12748 (2015)) ............................................................................................................ 36 Figure 7 - Impact of Lockhart-Martinelli definitions on over-reading estimation for a 368 kg/h air mass flow rate and 7 bara line pressure (Source: Author) ............................ 40 Figure 8 - Simplification of an orifice plate DP meter in a single-phase gas flow (Source: author) ....................................................................................................................... 43 Figure 9 - Simplification of an orifice plate DP meter in a two-phase wet gas flow (Source: author) ........................................................................................................ 44 Figure 10 - Water holdup in 4” pipe with a 0.65-beta orifice plate in stratified (left) and annular (right) flows. (Source: adapted from Steven et al. (2011)) ............................ 45 Figure 11 - Configuration of the third tapping propose by De Leeuw (Source: adapted from ISO TR 12748 (2015)) ....................................................................................... 52 Figure 12 - Illustration of pressure profile showing the Pt , PPPL and Pr for an orifice plate meter and a generic third pressure tap (Source: author) .................................. 52 Figure 13 - Venturi's PLR to XLM relation at 45 bar. (Source: De Leeuw (1997)) ....... 53 Figure 14 -The NEMOG's multiphase flow loop sketch (Source: Author) .................. 56 Figure 15 - Storage tanks flowchart (Source: author) ................................................ 57 Figure 16 - Separator vessel flowchart (Source: author) ........................................... 58 Figure 17 - Separator vessel photography (Source: author) ..................................... 58 vi Figure 18 - Compressed air supplier schematic flowchart (Source: author) .............. 60 Figure 19 - Single-phase measurement split-range configuration sketch for water and air (Source: author) ................................................................................................... 61 Figure 20 - Single-phase measurement split-range configuration photography (Source: author) ....................................................................................................................... 61 Figure 21 - High and low waterflow rate Coriolis meters in split-range arrangement photography (Source: author).................................................................................... 62 Figure 22 - The high and low mass flow rate orifice plate meters photography (Source: author) ....................................................................................................................... 63 Figure 23 - Original mixing arrangement (Source: author) ........................................ 64 Figure 24 – Final Experimental mixing arrangement (Source: author) ...................... 65 Figure 25 - Actual test loop section configuration (dimensions in millimeter) (Source: author) ....................................................................................................................... 65 Figure 26 - Test loop section photography (Source: author) ..................................... 66 Figure 27 - Fitting details of loop section, in perspective (Source: author) ................ 67 Figure 28 - Wet gas measurement pressure taps by ISO TR 12748 (2015) (Source: author) ....................................................................................................................... 67 Figure 29 - National Instruments LabVIEW multiphase flow loop supervisory system main page (Source: author) ....................................................................................... 70 Figure 30 - National Instruments LabVIEW wet gas flow parameters supervisory page (Source: author) ........................................................................................................ 71 Figure 31 - False prediction flow, PDT-3, PDT-4 and PDT-5 histograms illustration (Source: author) ........................................................................................................ 75 Figure 32 - First dry air mass flow rate measurement comparison between reference single-phase meter and test section meter (Source: author) ..................................... 78 Figure 33 - Single-Phase Meter and the Test Section Meter shift mapping with uncertainty bands (Source: author) ........................................................................... 79 Figure 34 - PLR dry test configuration (Source: author) ............................................ 81 vii Figure 35 - ISO 5167-2 (2003)’s PLR dry and the new data fit for a 0.68 orifice plate. .................................................................................................................................. 82 Figure 36 - ISO 5167-2 (2003)’s PLR dry and the new data fit for a 0.50 orifice plate. .................................................................................................................................. 82 Figure 37 - Different configurations for the third downstream pressure tap: (a) 6D, (b) 20D and (c) 144D (Source: author) ........................................................................... 84 Figure 38 - Raw data from a 0.50, 1 barg and 6D 3rd tap test (Source: author) ....... 87 Figure 39 - NEMOG’s experimental over-reading estimation based on the single-phase air flow measurement with and without the systematic shift correction (OR and XLM relative expanded uncertainties are 2.24% and 1.84% respectively) (Source: author) .................................................................................................................................. 88 Figure 40 - Over-reading experimental data points comparison with literature correlations using air-water flow with 0.50 and 0.68 beta and 1 barg line pressure (Source: author) ........................................................................................................ 90 Figure 41 - Over-reading experimental data points comparison with literature correlations for air-water flow with 0.50 and 0.68 beta and 3 barg line pressure (Source: author) ....................................................................................................................... 90 Figure 42 - Over-reading experimental data points comparison with literature correlations for air-water flow with 0.50 and 0.68 beta and 5 barg line pressure (Source: author) ....................................................................................................................... 91 Figure 43 - ISO TR 11583 (2012) XLM and DR limits of applicability with NEMOG’s data envelope (Source: author) ......................................................................................... 92 Figure 44 - ISO TR 11583 (2012) PLR to XLM extrapolation test with air-water flow (Source: author) ........................................................................................................ 93 Figure 45 - 6D PLR to XLM new data fit results for 0.50 and 0.68, 1, 3 and 5 barg and 0.15 to 0.31 Lockhart-Martinelli (Source: author) ...................................................... 95 Figure 46 - 20D PLR to XLM new data fit results for 0.50 and 0.68, 1, 3 and 5 barg and 0.15 to 0.31 Lockhart-Martinelli (Source: author) ............................................... 97 Figure 47 - 144D PLR to XLM new data fit results for 0.50 and 0.68, 1, 3 and 5 barg and 0.15 to 0.31 Lockhart-Martinelli (Source: author) ............................................... 98 viii Figure 48 - Exemplification of the third pressure tap correction from 20D to 6D using Petalas and Aziz (1998) two phase flow pressure drop model (Source: author) ....... 99 Figure 49 - Experimental configuration in two-phase pressure drop measurement for Petalas and Aziz’s (1998) model validation and adjustments (Source: author) ....... 100 Figure 50 - Petalas and Aziz (1998) two-phase pressure drop model experimental validation without pipe roughness adjustment (Source: author) .............................. 100 Figure 51 - Petalas and Aziz (1998) two-phase pressure drop model experimental validation with pipe roughness adjustment (Source: author) ................................... 101 Figure 52 - Comparison between uncorrected and corrected Lockhart-Martinelli estimation using adjusted PPL by Petalas and Aziz (1998) model in ISO TR 11583 (2012) (Source: author) ........................................................................................... 102 ix LIST OF TABLES Table 1 - Results for different definitions of Lockhart-Martinelli parameter ................ 40 Table 2 - Separator vessel technical information ....................................................... 59 Table 3 - Water pumping specifications and capabilities ........................................... 59 Table 4 - Compressed air supplier specifications and capabilities ............................ 60 Table 5 - The high and low water flow rate Coriolis meters technical information ..... 62 Table 6 - The high and low flow rate orifice plate meters technical information ........ 63 Table 7 - Wet gas measurement pressure transmitters specification ........................ 68 Table 8 - Lockhart-Martinelli and GVF ranges for NEMOG’s actual configuration..... 69 Table 9 - Normal distribution level of confidence and coverage factors (Source: JCGM (2008) ) ...................................................................................................................... 74 Table 10 - The single-phase and test section meters parameters in accordance to ISO 5167-2 (2003) ............................................................................................................ 77 Table 11 - Water mass flow rate measurement comparison between Coriolis meter and test section meter (Source: author) ........................................................................... 78 Table 12 - Single-Phase Meter and the Test Section Meter shift mapping ................ 80 Table 13 - Multiple linear regression coefficients ANOVA for the PLRdry,fit data fit .... 83 Table 14 - Wet gas flow test matrix ........................................................................... 85 Table 15 - PLRwet sensitivity in XLM estimation by ISO TR 11583 (2012) correlation . 94 Table 16 - Multiple linear regression coefficients ANOVA for 6D PLR to XLM new data fit ............................................................................................................................... 95 Table 17 - Multiple linear regression coefficients ANOVA for 20D PLR to XLM new data fit ............................................................................................................................... 96 Table 18 - Multiple linear regression coefficients ANOVA for 144D PLR to XLM new data fit ............................................................................................................................... 97 x Table 19 - ISO TR 11583 (2012) results using the adjusted Petalas and Aziz (1998) model to correct the 3rd pressure tap from 20D to 6D ............................................. 103 Table 20 - ISO TR 11583 (2012) results using the adjusted Petalas and Aziz (1998) model to correct the 3rd pressure tap from 144D to 6D ........................................... 104 xi LIST OF SYMBOLS ABBREVIATIONS ANOVA - Analysis of variance Adj MS - Adjusted mean squares Adj SS - Adjusted sums of squares CapEx - Capital expenditure DP - Differential Pressure DR - Density ratio DoF - Degree of freedom, representing the amount of data points F-value - Function value GVF - Gas volume fraction ISO - International Organization for Standardization IC - Inverted Cone LHC - Light hydrocarbon NEMOG - Núcleo de Estudos em Escoamentos de Óleo e Gás (Portuguese) N/A - Non applicable OpEx - Operational expenditure PLR - Pressure loss ratio P-value - Probability value UK - United Kingdom xii WLR - Water to liquid ratio WGFM - Wet gas flow meter LATIN SYMBOLS 𝐴 Pipe cross section area [𝑚2] 𝑎, 𝑏 𝑎𝑛𝑑 𝑐 V-cone Over-reading parameter proposed by Steven [−] 𝐶𝑑 Discharge coefficient in single-phase flow [−] 𝐶 The over-reading parameter [−] 𝑑 Orifice internal diameter [𝑚] 𝐷 Pipe internal diameter [𝑚] 𝑑𝑃 𝑑𝐿⁄ Pressure gradient [𝑃𝑎 𝑚⁄ ] 𝐸 Volume fraction [−] 𝑒 Pipe absolute internal roughness [𝑚] 𝐹𝑟 Densiometric Froude number [−] 𝑓 Friction factor [−] 𝜕𝐺 𝜕𝑦𝑖 Ith variable sensitivity coefficient at G function 𝑔 Gravity acceleration [𝑚/𝑠2] ℎ Liquid height in stratified flow [𝑚] 𝑗 Superficial velocity [𝑚/𝑠] 𝑘 Gas isentropic exponent 𝐾 Coverage factor 𝐿 Pipe length [𝑚] 𝑙 Distances from pressure tapping to downstream orifice plate face [𝑚] 𝑙′ Distances from pressure tapping to upstream plate face [𝑚] xiii �̇� Mass flow rate [𝑘𝑔/ℎ] 𝑛 Chisholm exponent [−] 𝑁 Number of experimental data points [−] 𝑂𝑅 Over-reading factor [−] 𝑂𝑅% Percentual Over-reading factor [%] 𝑃 Absolute line pressure [𝑏𝑎𝑟] 𝑄 Volumetric flow rate [𝑚3/ℎ] 𝑅 The gas constant [ 𝐽/𝑘𝑔. 𝐾 ] 𝑅𝑒 Reynolds number [−] 𝑠 Standard deviation of the measurement 𝑈𝑃 Upstream tap term of Reader-Harris/Gallagher equation [−] 𝑢𝐴 Type A standard uncertainty 𝑢𝐵 Type B standard uncertainty 𝑢 Standard uncertainty 𝑈 Expanded uncertainty 𝑉 Flow mean velocity [𝑚/𝑠] 𝑋 The original Lockhart and Martinelli (1949) parameter [−] 𝑥 Quality [−] 𝑋𝐿𝑀 Lockhart-Martinelli parameter [−] GREEK SYMBOLS 𝛽 Orifice to pipe diameter ratio [−] Δ𝑃 Differential pressure [𝑃𝑎] 𝜀 Expansibility coefficient [−] 𝜇 Viscosity [𝑃𝑎. 𝑠] xiv 𝜌 Density [𝑘𝑔/𝑚3] 𝜙 Traditional to expansion Over-reading ratio [−] 𝜃 Pipe inclination [ 𝑑𝑒𝑔𝑟𝑒𝑒] 𝜎 Superficial tension. [𝑁/𝑚] 𝜏 Shear stress [𝑃𝑎] 𝜏𝑖 Interfacial shear stress [𝑃𝑎] 𝜈𝑖 Degree of freedom of the measurement SUBSCRIPT 𝐶 Combined uncertainty 𝑐 Core property 𝑐𝑜𝑚𝑝 Compounded uncertainty 𝐶ℎ Chisholm equation 𝐷 Pipe internal diameter reference 𝑑𝑟𝑦 Dry gas flow, i.e. single phase gas flow 𝐷𝐿 De Leeuw equation for venturi meter 𝑓 Film property 𝑓𝑝 False prediction 𝑓𝑖𝑡 Data fitted property 𝑔 Gas property ℎ𝑙 Head loss reference 𝐼 Interfacial property 𝐼𝐶 Inverted cone meter 𝑖 Ith variable 𝑙 Liquid property xv 𝐿𝐻𝐶 Light hydrocarbon 𝑚 Meter reference 𝑚𝑖𝑥 Mixture property 𝑃𝑃𝐿 Permanent pressure loss 𝑟 Recovered 𝑠𝑙 Based on liquid superficial velocity 𝑆𝑡 Steven et al equation for inverted cone 𝑠𝑡𝑟𝑎𝑡 Stratified flow regime 𝑇𝑃 Two-phase 𝑡 Traditional 𝑉𝑒𝑛𝑡𝑢𝑟𝑖 Venturi meter 𝑊 Water 𝑤𝑔 Wall/gas interface 𝑤𝑙 Wall/liquid interface 𝑤𝑒𝑡 Wet gas flow, i.e. two phase gas/liquid flow 1 Upstream side reference 2 Downstream side reference xvi CONTENTS ACKNOWLEDGEMENTS .......................................................................................... III ABSTRACT ............................................................................................................... IV LIST OF FIGURES ..................................................................................................... V LIST OF TABLES ..................................................................................................... IX LIST OF SYMBOLS .................................................................................................. XI 1 INTRODUCTION ................................................................................................... 18 1.1 MOTIVATION ................................................................................................. 19 1.2 OBJECTIVES ................................................................................................. 20 1.3 DISSERTATION OUTLINE ............................................................................. 21 2 THEORICAL BACKGROUND .............................................................................. 23 2.1 TWO PHASE PRESSURE DROP MODELS .................................................. 23 2.2 SINGLE PHASE FLOW MEASUREMENT THROUGH DIFFERENTIAL PRESSURE DEVICES .............................................................................................. 31 2.3 WET GAS FLOW MEASUREMENT BY MEANS OF DIFFERENTIAL PRESSURE DEVICES .............................................................................................. 34 3 EXPERIMENTAL APPARATUS ........................................................................... 56 3.1 SECTION I: FLUID STORAGE ....................................................................... 56 3.2 SECTION II: FLUID PUMPING AND SEPARATION ...................................... 57 3.3 SECTION III: SINGLE-PHASE FLOW MEASUREMENT ............................... 60 3.4 SECTION IV: FLUIDS MIXING ....................................................................... 64 2.3.1 What is wet gas flow? .................................................................................. 34 2.3.2 Flow regimes in wet gas flows .................................................................... 36 2.3.3 Wet gas parameters ...................................................................................... 37 2.3.4 The over-reading effect ................................................................................ 43 2.3.5 History of Over-reading correction ............................................................. 45 2.3.6 PLR to XLM relationship ................................................................................ 51 3.2.1 Three-phase separator vessel ..................................................................... 57 3.2.2 Water circulation pumping .......................................................................... 59 3.2.3 Compressed air supplier .............................................................................. 59 xvii 3.5 SECTION V: TEST LOOP .............................................................................. 65 4 EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSIONS ................... 69 4.1 NEMOG’S WET GAS FLOW TEST ENVELOPE ............................................ 69 4.2 DATA ACQUISITION AND TREATMENT METODOLOGY ............................ 70 4.3 DRY AIR FLOW MEASUREMENT COMISSIONING ..................................... 75 4.4 EVALUATION OF THE ISO 5167-2 (2003) PRESSURE LOSS RATIO FOR DRY FLOW AND A NEW DATA FIT PROPOSAL ..................................................... 80 4.5 WET GAS FLOW TESTS ............................................................................... 83 5 CONCLUSION .................................................................................................... 105 5.1 FINAL REMARKS ......................................................................................... 105 5.2 CORRELATIONS SUMMARY ...................................................................... 107 5.3 PROPOSAL FOR FUTURE WORK .............................................................. 108 REFERENCES ........................................................................................................ 110 APPENDIX A .......................................................................................................... 114 APPENDIX B .......................................................................................................... 120 APPENDIX C .......................................................................................................... 125 3.5.1 Orifice plate wet gas measurement test section ........................................ 66 4.2.1 Post processing ............................................................................................ 71 4.2.2 Uncertainty evaluation ................................................................................. 72 4.5.1 Analysis of the main orifice plate over-reading correction correlations available in literature. .............................................................................................. 88 4.5.2 ISO TR 11583 (2012) PLR to 𝑿𝑳𝑴 correlation performance in air-water flow and new data fits correlations considering two extra 3rd tap configurations 92 4.5.3 Lockhart-Martinelli estimation using ISO TR 11583 (2012) equation with 3rd tap correction to 6D position using Petalas and Aziz (1998) two phase flow pressure drop model ............................................................................................... 98 18 1 INTRODUCTION Measuring is a human need since the dawn of civilizations, arising in favor to make the production management, commercial trades, group work and other tasks as easy and manageable as possible. This thought is summarized in a Willian Thomson’s, Lord Kelvin, famous quote that says “If you cannot measure it, you cannot improve it” In flow science it is not different. The need for flow measurement arose from piped water supplies management in Rome, mentioning the registers of Julius Frontinus (30 - 103 a.C), a roman engineer, evidencing the beginning of flow measurement knowledge (DELMÉE, 2003). From the Julius Frontinus studies until today’s technology frontier, the knowledge in flow measurement science has undergone great evolutions, mainly after the industrial revolution, by the mid-18th century, with the steam powered machine development, where the complex water-steam flow needed to be controlled. Even nowadays this kind of flow are present in many industrial processes, such as power production plants, food processing and mainly in oil and gas industries and still a big challenge for engineers and researchers to be understood, modeled, and predicted. A particular case of two-phase flows, like the mid-18th water-steam, are the gas-liquid flows. Present mainly in natural gas production, the so-called wet gas flow, consists of a gas as a continuous phase and a liquid as a dispersed phase combined in the same stream, a common matter that engineering must deal with. This kind of combination occurs especially in oil wells operating on the latter stage of production lives, a stage where the water content of the multiphase flow, increases and the rising of heavier hydrocarbon components condensation, due to the pressure drop in production lines (STEVEN, 2002). Additionally, depending on its efficiency, separators vessels leave amounts of liquid on the gas outlet. Therefore, to measure the flow rates, expensive two-phase meters are required on those situations. Measurement of gas flowrate is essential to industry, making possible an appropriated reservoir and well management, production optimization and allocation, flow assurance, property transfer, and legislation matters. However, in most of the gas 19 production fields, the use of complex multiphase wet gas flow meters (WGFM) is economically unviable due to its high Capital Expenditure (CapEx), as well as high Operational Expenditure (OpEx), e.g the gas measurement requirement in flairs due to legal matters. Given this scenario, the response of differential pressure (DP) meters to wet gas flows becomes an important research topic, mainly because in most of the production’s sights in Brazil, single-phase DP meters, such as orifice plates, are already installed to measure dry gas flows. Furthermore, DP meters demand a low installation and operation costs, are based on simple principles, reliable, have repeatable response, many years of operation history and have consensual operation practices consolidated in standards for single phase measurement. Even though the performance of DP meters in single-phase flows measurement is well known and consolidated in the literature, in case of two-phase applications, the liquid loading causes a positive bias on the pressure differential readings, due to phases interactions called over-reading and resulting in an erroneous gas flow rate prediction up to 50%. Aiming to correct this shift, since 1949, with Lockhart and Martinelli (1949) pioneer empirical work for predicting the pressure drop in a two-phase flow, authors are researching and developing empirical correlations based on experimental data, archiving great progress in recent years, with relatively good wet gas correction performance with a ± 2% uncertainty level on over-reading correction (STEVEN, SHUGART and KUTTY, 2018). However, those correlations need a liquid loading input to estimate the over-reading level, but this information is not available in a precise manner, remaining to use outdated information from test separators, adding huge uncertainty on the flow measurement, which turns into a supposition of the actual mass flow rate. From that need, in the last years authors have been investigating the pressure loss ratio to Lockhart-Martinelli relationship, first observed by De Leeuw (1997) and concretized for venturi and orifice plates in ISO TR 11583 (2012), to develop an all in on wet gas meter with both low CapEx and OpEx. 1.1 MOTIVATION Flow measurement in industrial facilities is based in DP devices at least on 40% of the cases, being the orifice plate the most used. To illustrate the economic impact of those 20 devices on flow measurement, the measurement of natural gas in 2006, on the UK gas industry, was estimated in £16 billion (US$ 21 billion) (READER-HARRIS, FORSYTH, and BOUSSOUARA, 2021). Furthermore, natural gas flows are often wet gas flows, as exposed on introduction. Consequently, a huge amount of money may be overpaid due to over-reading effect in property transfer, royalties, taxes and other related costs. Although the research and development on over-reading estimation has made great strides, usually over-reading correlations techniques requires a liquid flow rate estimation or some liquid content parameter to predict the bias. However, that information is not available instantly, forcing the meter operators to suppose the liquid content based on old and unprecise data, inducing an extra uncertainty on the gas flow rate prediction process. To overcome this barrier, industry has been developing an all in on two-phase wet gas flow meters (WGFMs), with liquid loading estimation and over-reading correction on the same meter. Such category of flow meter is very expensive, compared to classical ones, since it requires a set of new technologies associated. So, in 2012, ISO TR 11583 (2012) released a methodology to wet gas measurement based on orifice plates or Venturi, using the pressure loss ratio (PLR) to liquid content relationship based on a 6D 3rd pressure tap. But according to Steven, Shugart and Kutty (2018) there are some limitations with this methodology, due to very limited data used in development. Furthermore, this 6D 3rd pressure tap fixed location increases the CapEx barrier to new implementations. In 2018 Steven, Shugart and Kutty (2018) proposed a new equation set to estimate the liquid content by means of PLR for orifice meters, claiming an uncertainty less than ± 2% uncertainty for a water to liquid ratio (WLR) = 1 and for all data set tested, a global ± 4% uncertainty at a 95% confidence level, but those equations were kept confidential due to proprietary reasons. 1.2 OBJECTIVES The general objective of this study is to evaluate the PLR to liquid content relationship on different 3rd tap configurations and test the ISO TR 11583 (2012) performance, in an air-water flow by orifice plates at the NEMOG’s new gas-liquid flow loop and 21 propose new correlations and alternatives for the liquid content estimation by means of PLR. To achieve the main goal, the following specific objectives are defined: • Commissioning of single phase air flow in the multiphase circuit, evaluating the reference dry air mass flow rate uncertainty and the test meter response to dry air flow (page 75). • Evaluate the ISO 5167-2 (2003) PLRdry correlation proposing a new data fit (page 80). • Evaluate the main available orifice plate over-reading correlations performance in NEMOG’s installation (page 88). • Evaluate the ISO TR 11583 (2012) PLR to Lockhart-Martinelli (XLM) correlation performance (page 92). • Propose three new data fits of PLR vs. XLM using the traditional 6D 3rd tap and two different configuration downstream 3rd tap (page 92). • Validate the Petalas and Aziz (1998) two phase flow pressure drop model in air-water flow and evaluate the response of PLR vs. XLM and Petalas and Aziz (1998) model together (page 98). 1.3 DISSERTATION OUTLINE Chapter 1 - Introduction: this chapter provides a brief introduction to multiphase flow and delineates the motivation and research background also the objectives of this dissertation. Chapter 2 - Theorical background: this chapter presents the main literature interpretation about two phase flow pressure drop and flow measurement for single and two phase flows, important to understand the dissertation development. Moreover, the main limitations related to correlation proposals are exposed. 22 Chapter 3 - Experimental apparatus: this chapter exposes the Research Group for Studies on Oil&Gas Flow and Measurement (NEMOG in Portuguese) multiphase flow circuit, where all tests presented in this work were performed. Chapter 4 - Experimental procedures, results and discussions: this chapter consolidates the experimental procedure result and discussion for each specific objective. Chapter 5 - Conclusion: this chapter summarizes the principal conclusions of the dissertation, including the new correlations summary with the appropriate range of use. In addition, it is given a series of recommendations for future research. Appendix A: this appendix brings the calibration certificate for both Coriolis meters used to measure water mass flow rates. Appendix B: this appendix brings the calibration certificate for the pressure transmitters used to measure the manometric pressure and differential pressures. Appendix C: this appendix brings the calibration certificate for the temperature transmitter used to measure the flow temperature. . 23 2 THEORICAL BACKGROUND This chapter brings the theorical background necessary to understand the two phase flow issue and how to deal with this kind of stream in a flow measurement perspective using differential pressure orifice plate element. 2.1 TWO PHASE PRESSURE DROP MODELS Throughout history many researchers studied the liquid loading consequences in gas flows. Lockhart and Martinelli (1949) were one of the leading-edge in two-phase flow pressure drop research, suggesting that the dimensionless pressure drop in the gas (√ 𝛥𝑃𝑇𝑃,ℎ𝑙 𝛥𝑃𝑔,ℎ𝑙 ) or liquid (√ 𝛥𝑃𝑇𝑃,ℎ𝑙 𝛥𝑃𝑙,ℎ𝑙 ) phase was a unique function of the parameter 𝑋, but valid only for stratified flows (TAITEL; DUKLER, 1975). Taitel and Dukler (1975) studied this dependence, highlighting that in stratified flows it was valid only under the assumption that the gas to interfacial friction factors ratio was constant, i.e. 𝑓𝑔 𝑓𝐼 ≅ constant. In 1985 Mukherjee and Brill (1985) brought an historical review of flow pattern dependent pressure drop models for inclined pipes in addition to a new empirical model for bubble, slug and stratified flows in inclined pipes with filed data validation. Five years later Xiao, Shoham and Brill (1990) published a mechanistic model for gas- liquid two-phase flow in horizontal and near-horizontal pipelines, being able to predict firstly the flow pattern and in sequence estimate the pressure drop based on the flow regime properties for stratified, intermittent, annular, or dispersed bubble flow patterns. Aiming to synthetize all the two-phase flow modeling available in literature at the time Petalas and Aziz (1998) released a mechanistic model gathering the best of the modellings available, in addition with new empirical correlations for liquid/wall and liquid/gas friction factor in stratified flow and entrained liquid and interfacial friction factors for annular mist flows. 24 The Petalas and Aziz (1998) mechanistic model Although the modelling includes other flow patterns like dispersed bubble, bubble and intermittent, this text will focus on the stratified and annular mist regimes in wet gas flow. In the sequence of Petalas and Aziz (1998) model follows Xiao, Shoham and Brill (1990) publication, where firstly tests the hydrodynamic stabilities of the flow patterns based on the input data such as pipe internal diameter (𝐷), pipe straight length (𝐿), pipe absolute internal roughness (𝑒), fluid properties, line pressure (𝑃), temperature (𝑇) and gas (𝑗𝑔) and liquid (𝑗𝑙) superficial velocities, given by equations 1 and 2. 𝑗𝑔 = �̇�𝑔 𝜌𝑔𝐴 (1) 𝑗𝑙 = �̇�𝑙 𝜌𝑙𝐴 (2) In stratified flows liquid height (ℎ) (Figure 1) plays an important unknown role to verify the stability, , obtained as a solution of both gas and liquid momentum balance shown in equations 3 and 4. These can then be combined eliminating the pressure gradient ( 𝑑𝑃 𝑑𝐿 ). −𝐸𝑙𝐴 ( 𝑑𝑃 𝑑𝐿 ) − 𝜏𝑤𝑙𝑆𝑙 + 𝜏𝐼𝑆𝐼 − 𝜌𝑙𝐸𝑙𝐴𝑔𝑠𝑖𝑛(𝜃) = 0 (3) −𝐸𝑔𝐴( 𝑑𝑃 𝑑𝐿 ) − 𝜏𝑤𝑔𝑆𝑔 + 𝜏𝐼𝑆𝐼 − 𝜌𝑔𝐸𝑔𝐴𝑔𝑠𝑖𝑛(𝜃) = 0 (4) Where 𝐸𝑙 and 𝐸𝑔 are the liquid and gas volume fraction calculated by equations 5 and 6 and 𝑆𝑙, 𝑆𝐼 and 𝑆𝑔 are the liquid, interfacial and gas perimeters respectively, obtained geometrically in Figure 1. 25 𝐸𝑙 = 1 − 𝐸𝑔 (5) 𝐸𝑔 = 𝐷2(𝛼 − 𝑠𝑒𝑛𝛼) 𝐴 (6) Figure 1 - Geometrical analysis of a stratified flow (Source: author) The shear stresses (𝜏𝑤𝑙 , 𝜏𝑤𝑔 and 𝜏𝐼) are given by equations 7 to 9 , where 𝑉𝑙 = 𝑗𝑙/𝐸𝑙, 𝑉𝑔 = 𝑗𝑔/𝐸𝑔 and 𝑉𝐼 = 𝑉𝑔 − 𝑉𝑙 are the phases mean velocities (XIAO; SHOHAM; BRILL, 1990). 𝜏𝑤𝑙 = 𝑓𝑙𝜌𝑙𝑉𝑙 2 2 (7) 𝜏𝑤𝑔 = 𝑓𝑔𝜌𝑔𝑉𝑔 2 2 (8) 𝜏𝐼 = 𝑓𝐼𝜌𝑔𝑉𝐼|𝑉𝐼| 2 (9) 26 For the wall/liquid friction factor (𝑓𝑙) Petalas and Aziz (1998) state that a single-phase approach is not adequate, and instead, they proposed an empirical correlation based on equation 10 , where now the 𝑓𝑠𝑙 is calculated by traditional means using the liquid superficial velocity (𝑗𝑙) and pipe diameter (𝐷) on Reynolds number (equation 11). Additionally, the friction factor at wall/gas interface (𝑓𝑔) is calculated by traditional single-phase means, like Colebrook-White equation, differing only on the Reynolds number definition presented in equation 12, where 𝐷𝑔 is the hydraulic diameter for the gas phase. Finally, for the interfacial region, the liquid acts like a wall for the gas phase, therefore the shear stress (𝜏𝑖) is based on gas properties by an empirical interfacial friction factor (𝑓𝐼), given by equation 13 , where 𝐹𝑟𝑙 = 𝑉𝑙 √𝑔ℎ is the liquid Froude number. 𝑓𝑙 = 0.452 × 𝑓𝑠𝑙 0.731 (10) 𝑅𝑒𝑙 = 𝐷𝜌𝑙𝑗𝑙 𝜇𝑙 (11) 𝑅𝑒𝑔 = 𝐷𝑔𝜌𝑔𝑉𝑔 𝜇𝑔 (12) 𝑓𝐼 = ( 0.004 + 0.5 × 10−6𝑅𝑒𝑙)𝐹𝑟𝑙 1.335 [ 𝜌𝑙𝐷𝑔 𝜌𝑔𝑉𝑔2 ] (13) After determining the liquid height (ℎ), the stability of stratified flow can be verified using a Taitel and Dukler (1976) approach, based on Kelvin-Helmoholtz wave stability theory, where the wave length is verified to be smaller enough to not bridge the pipe. This is done using a limiting gas velocity, based on equation 14, and limiting liquid velocity exposed in equation 15, as proposed by Barnea (1987). 27 𝑉𝑔 < (1 − ℎ 𝐷 ) √ (𝜌𝑙 − 𝜌𝑔)𝐸𝑔𝐴 cos(𝜃) 𝜌𝑔√1 − ( 2ℎ 𝐷 − 1) 2 (14) 𝑉𝑙 < √ 𝑔𝐷 (1 − ℎ 𝐷) cos(𝜃) 𝑓𝑙 (15) Once both 14 and 15 criteria are satisfied then the stratified pattern is considered stable and the pressure gradient can be obtained from either equation 3 or 4. If not, the annular mist flow stability is tested. In annular mist flow pattern, the methodology is based on Taitel and Dukler (1976) and Oliemans, Pots and Trompé (1986) and it is similar to stratified flow test and it. The main assumption is that the film thickness is uniform and the gas core have liquid droplets entrained, but with no slip. The momentum balance equations for liquid film and gas core are given by equations 16 and 17. −𝐴𝑓 ( 𝑑𝑃 𝑑𝐿 ) − 𝜏𝑤𝑙𝑆𝑓 + 𝜏𝐼𝑆𝐼 − 𝜌𝑙𝐴𝑓𝑔 𝑠𝑖𝑛(𝜃) = 0 (16) −𝐴𝑐 ( 𝑑𝑃 𝑑𝐿 ) − 𝜏𝐼𝑆𝐼 − 𝜌𝑐𝐴𝑐𝑔 𝑠𝑖𝑛(𝜃) = 0 (17) Where 𝐴𝑓 and 𝐴𝑐 are the film and core cross section areas and 𝑆𝑓 and 𝑆𝐼 are the film, and interfacial perimeters respectively, obtained geometrically in Figure 2 28 Figure 2 - Geometrical analysis of a annular flow (Source: author) All geometric parameters can be expressed in terms of dimensionless film thickness 𝛿𝑓 = 𝛿𝑓/𝐷 and the liquid fraction entrained on the gas core (𝐹𝐸), as given by the empirical equation 18 (PETALAS; AZIZ, 1998). 𝐹𝐸 = 0.735 × [ 𝜇𝑙 2𝑗𝑙 2𝜌𝑔 𝜎𝑙 2𝜌𝑙 ] 0.074 ( 𝑗𝑔 𝑗𝑙 ) 0.2 1 + 0.735 × [ 𝜇𝑙 2𝑗𝑙 2𝜌𝑔 𝜎𝑙 2𝜌𝑙 ] 0.074 ( 𝑗𝑔 𝑗𝑙 ) 0.2 (18) Where, σl is the liquid superficial tension. The wall/liquid (𝜏𝑤𝑙) and interfacial (𝜏𝐼) shear stresses are given by equations 19 and 20 respectively, where 𝑉𝑓 and 𝑉𝑐 represents the film and core mean velocities, as shown in equations 21 and 22 respectively, 𝑉𝐼 = 𝑉𝑐 − 𝑉𝑓 is the interfacial velocity and 𝜌𝑐 is the weighted density for the core calculated as equation 23 (XIAO; SHOHAM; BRILL, 1990). 𝜏𝑤𝑙 = 𝑓𝑓𝜌𝑙𝑉𝑓 2 2 (19) 29 𝜏𝐼 = 𝑓𝐼𝜌𝑐𝑉𝐼|𝑉𝐼| 2 (20) 𝑉𝑓 = 𝑗𝑙(1 − 𝐹𝐸) 4𝛿𝑓(1 − 𝛿𝑓) (21) 𝑉𝑐 = 𝑗𝑔 + 𝑗𝑙𝐹𝐸 (1 − 2𝛿𝑓) 2 (22) 𝜌𝑐 = 𝐸𝑐𝜌𝑙 + (1 − 𝐸𝑐)𝜌𝑔 (23) Where, 𝐸𝑐 is the liquid hold up entrained on core, given by equation 24 (XIAO; SHOHAM; BRILL, 1990). 𝐸𝑐 = 𝑗𝑙𝐹𝐸 𝑗𝑔 + 𝑗𝑙𝐹𝐸 (24) For the liquid film friction factor (𝑓𝑓) Petalas and Aziz (1998) state that a single-phase approach is possible using the film Reynold number (𝑅𝑒𝑓) equation 25 , where 𝐷𝑓 is the hydraulic diameter for the liquid film. 𝑅𝑒𝑓 = 𝐷𝑓𝜌𝑙𝑉𝑓 𝜇𝑙 (25) For the interfacial friction factor (𝑓𝐼) Petalas and Aziz (1998) bring an empirical correlation exposed in equation 26 , where 𝐷𝑐 is the core internal diameter and 𝑓𝑐 is obtained by traditional means. 30 𝑓𝐼 𝑓𝑐 = 0.24 × [ 𝜎𝑙 𝜌𝑐𝑉𝑐2𝐷𝑐 ] 0.085 𝑅𝑒𝑓 0.305 (26) After determining the liquid film thickness iteratively, two stabilities criteria are tested. The first one is based on Barnea (1987) for upward flows, in which a negative film velocity profile results in instable annular flow, consequently the regime changes to intermittent flow. This transition is based in a minimal interfacial shear stress where the velocity profile changes it direction, calculated with equations 27 and 28 (PETALAS; AZIZ, 1998). 2𝑓𝑓𝜌𝑙 𝜌𝑙 − 𝜌𝑐 𝑗𝑙 2(1 − 𝐹𝐸)2 𝑔𝐷 sin(𝜃) = 𝐸𝑓 3 (1 − 3 2 𝐸𝑓) 1 − 3 2𝐸𝑓 (27) 𝐸𝑓 = 𝐴𝑓 𝐴 = 4𝛿𝑓(1 − 𝛿𝑓) (28) Solving those equations will result in a minimum film thickness (𝛿𝑓,𝑚𝑖𝑛) correspondent to a minimum interfacial shear stress. If 𝛿𝑓 > 𝛿𝑓,𝑚𝑖𝑛 the regime becomes instable. The second criterion assumes that once a limiting liquid volume fraction exceeds the value proposed by equations 29 and 30, the liquid film is unstable, causing blockages of gas core. 𝐸𝑙 = 1 − (1 − 2 𝛿�̃� 2 ) ( 𝑗𝑔 𝑗𝑔 + 𝑗𝑙𝐹𝐸 ) ; (29) 𝐸𝑙 > 0.24 (30) Once both criteria are satisfied, then the annular pattern is considered stable, and the pressure gradient can be obtained from either equation 16 and 17. 31 According to Petalas and Aziz (1998), this mechanistic model predicted the pressure drop in 59% of the -30° to +30° inclination range data within an 15% accuracy. 2.2 SINGLE PHASE FLOW MEASUREMENT THROUGH DIFFERENTIAL PRESSURE DEVICES The flow measurement by means of differential pressure devices, for single phase flows, is well known and consolidated in literature, being one of the most simple, reliable and low-cost methods used nowadays. The ISO 5167 (2003) focus on general principles and requirements to develop a low uncertainty DP meter, without requiring external calibration, by five different types of primary devices such as orifice plates, nozzles, Venturi nozzles, Venturi tubes and inverted cones. The foundation behind those devices is based on Bernoulli’s principle (equation 31), where a fluid kinetic energy increasing induces a potential energy decrease, i.e. fluid acceleration causes static pressure drop resulting in differential pressure (Δ𝑃) from upstream to downstream sides of the device, as shown in Figure 3. The acceleration is a result of an area reduction, caused by the primary device inserted on the flow, and requires the continuity equation, considering the following hypothesis: steady state and one dimension flow, incompressible fluid, as equation 32. Therefore, the flow velocity (𝑉) on the primary device can be correlated with the differential pressure (FOX, MCDONALD and MITCHELL, 2020). 𝑃 𝜌 + 𝑉2 2 + 𝑔𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (31) 𝜌𝑉𝐴 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (32) Reader-harris, Forsyth, and Boussouara (2021) inform that at least 40% of the DP based flow meters are based on orifice plates, which are ruled by ISO 5167-2 (2003). In a simple way, an orifice plate is a device with simple machining process, inserted in 32 a pipe flange, to create a flow restriction due to area reduction, as presented in Figure 4. Figure 3 - Flow approximated pressure pattern though orifice plate (Source:adapted from READER-HARRIS, FORSYTH, and BOUSSOUARA (2021)) Figure 4 - Orifice plate sketch (Source: Author) 33 Based on that, ISO 5167-2(2003) brings the mass flow rate �̇� equation for orifice plates related to the Δ𝑃 (equation 33), where 𝐶𝑑 is the discharge coefficient (equation 34), 𝛽 = 𝑑/𝐷 is the orifice to pipe diameter ratio, 𝜀 is the expansibility factor (equation 37), 𝑑 is the orifice diameter and 𝜌1 is the fluid density calculated with upstream static pressure. �̇� = 𝐶𝑑 √1 − 𝛽4 𝜀 𝜋 4 𝑑2√2𝛥𝑃𝜌1 (33) 𝐶𝑑 = 0.5961 + 0.0261𝛽2 − 0.216𝛽8 ← 𝐶∞ 𝑡𝑒𝑟𝑚 (34) +0.000521 ( 106𝛽 𝑅𝑒𝐷 ) 0.7 + (0.0188 + 0.0063𝑈𝑃)𝛽3.5 ( 106 𝑅𝑒𝐷 ) 0.3 ← 𝑆𝑙𝑜𝑝𝑒 𝑡𝑒𝑟𝑚 +(0.043 + 0.08𝑒−10𝐿1 − 0.123𝑒−7𝐿1)(1 − 0.11𝑈𝑃) ( 𝛽4 1 − 𝛽4 ) ← 𝑈𝑝𝑠𝑡𝑟𝑒𝑎𝑚 𝑡𝑎𝑝𝑝𝑖𝑛𝑔 𝑡𝑒𝑟𝑚 − 0.031(𝑀2 ′ − 0,8𝑀2 ′1.1)𝛽1.3 ← 𝐷𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑡𝑎𝑝𝑝𝑖𝑛𝑔 𝑡𝑒𝑟𝑚 +0.0011(0.75 − 𝛽) (2.8 − 𝐷 25.4 ) ← 𝐹𝑜𝑟 𝐷 < 71.12 𝑚𝑚 Where, 𝑈𝑃 = ( 19000𝛽 𝑅𝑒𝐷 ) 0.8 (35) 𝑀2 ′ = 2𝐿2 ′ 1 − 𝛽 (36) 𝜀 = 1 − (0.351 + 0.256𝛽4 + 0.93𝛽8) [ 1 − (1 − Δ𝑃 𝑃1 ) 1 𝑘 ] (37) 34 The 𝑅𝑒𝐷 term represents Reynolds dimensionless group, calculated with respect to pipe diameter 𝐷, 𝐿1 = 𝑙1/𝐷, 𝐿2 ′ = 𝑙2 ′ /𝐷, 𝑙1 and 𝑙2 ′ are the upstream and downstream tapping distances respectively measured using the respective plate face as reference. In equation 37, 𝑃1 represents the upstream absolute pressure and 𝑘 the gas isentropic exponent. For liquid flows, the compressibility is negligible the term 𝜀 is equal to the unity. Although this ISO standard is very useful in a vast range of applications, there are some limitations on its use. Those are: • The flow must be subsonic through measuring section and not pulsating. • The fluid must be single-phase. • The pipe dimeter must be within 50 mm to 1000 mm. • The flow Reynold number must be above 5000. Recently, aiming to show the 𝐶𝑑 equation reliability, Reader-Harris, Forsyth, and Boussouara (2021) publish a meticulous analysis of 𝐶𝑑 Reader-Harris/Gallagher equation uncertainty considering all the sources, finding similar results of the ISO 5167-2 original publication. The maximum discharge coefficient uncertainty found, following all the standard requirements, was 0.606% for a 0.67𝛽 orifice plate, ratifying that the correlation is very precise. 2.3 WET GAS FLOW MEASUREMENT BY MEANS OF DIFFERENTIAL PRESSURE DEVICES 2.3.1 What is wet gas flow? Wet gas flow can be classified as a subcategory of two-phase flow, as illustrated on Figure 5 scheme, where a two-phase mixture of a gas and a liquid, flows simultaneously in a pipe. The liquid parcel could be composed by a single substance or be a liquid mixture of two or more components, e.g. water and condensate hydrocarbon (ISO TR 12748, 2015). 35 Figure 5 - Two-phase flow subsets (Source: ISO TR 12748 (2015)) To establish a quantitative classification, there are two main definitions of “wet gas” based in parameters that represents the amount of liquid on the mixture. ISO TR 11583 (2012) brings the gas volume fraction (GVF) parameter (equation 38) where 𝑄𝑔 and 𝑄𝑙 are the gas and the liquid volumetric flow rates, respectively, defining wet gas flow as a two-phase mixture with a minimal GVF of 95%. The other parameter largely referenced to delimit the wet gas flow is the Lockhart- Martinelli parameter (𝑋𝐿𝑀) (equation 39), where 𝑚𝑙̇ and �̇�𝑔 are the liquid and gas mass flow rates and, 𝜌𝑙 and 𝜌𝑔 are the liquid and gas densities respectively. Steven, Shugart and Kutty (2018) state that a wet gas flow is any combination of gas and liquid with 𝑋𝐿𝑀 less or equal to 0.3, i.e., 𝑋𝐿𝑀 ≤ 0.3. Moreover, according to ISO TR 12748 (2015) this boundary value is intended to approximately separate the intermittent to non- intermittent flow regime. However, this limits for wet gas are not consensual in some regulatory texts, like API (2004) and Corneliussen et al. (2005). 𝐺𝑉𝐹 = 𝑄𝑔 𝑄𝑙 + 𝑄𝑔 (38) 36 𝑋𝐿𝑀 = 𝑚𝑙̇ 𝑚𝑔̇ √ 𝜌𝑔 𝜌𝑙 (39) Even though there are no universal definition of wet gas flow, some industries operators believes that such precise discretion is unnecessary as the meter requires the relative amount of liquid to gas flow rate, no matter how small of large is that ratio. What really matters is the capability of the meter to correct the effect caused by this liquid loading and provide an accurate gas flow rate measurement. 2.3.2 Flow regimes in wet gas flows Common single-phase characteristics such as boundary layers, turbulence, velocity profile, are not valid for two-phase flows. A proper manner to describe such flows is based on flow pattern, a physical description of the way the liquid and gas phase are interacting, whose accurate characterization depends on several parameters (CORNELIUSSEN et al., 2005). In addition, ISO TR 12748 (2015) dissert that pipe geometry, fluids properties, line pressure and temperature and phase flow rates all together in a complex phenomenon dictates the flow pattern. For example, in horizontal two-phase wet gas flows, due to inertial forces, the gas velocity is greater than liquid velocity, thus there is a relative velocity between them, called slip velocity. Moreover, the most common flow patterns are: stratified, slug and annular mist flow demonstrated in Figure 6. Figure 6 - Horizontal two-phase wet gas flow regimes (Source: adapted from ISO TR 12748 (2015)) 37 The stratified flow regime occurs mainly if the gravitational force is dominant on the liquid phase. This condition develops when the gas is flowing at low velocity, i.e low gas dynamic pressure and the line pressure is low. The result is a separated flow where the liquid moves on the downside of the pipe and the gas on the upside. The interface could be smooth or wavy depending on the velocity differences. Slug flow appears when waves in a stratified flow hit the top wall of the tube, intermittently filling the cross section with liquid. This is a unstable flow, undesirable for wet gas metering proposes. Finally annular mist flows arise at high GVF and high gas dynamic pressure, i.e high gas velocity and/or density. This pattern is characterized by an asymmetrical ring of liquid and a gas with liquid droplets core. At extreme gas dynamic pressure, the liquid is fully entrained on the gas, dispersed in little droplets, permitting a pseudo-single- phase approach on the modeling (ISO TR 12748, 2015). All these phenomena play a huge influence on the wet gas flow measurement process, so is important to stablish the flow regime because it will dictate the wet gas meter performance. 2.3.3 Wet gas parameters As GVF and 𝑋𝐿𝑀 mentioned above, many parameters are important for a wet gas flow comprehension, so this section will define the most important parameters to a better understanding of this class of flow. 2.3.3.1 The Lockhart-Martinelli parameter (𝑋𝐿𝑀) One of the most used parameters regarding wet gas flows is the Lockhart-Martinelli parameter used to characterize the flow humidity, which was named in honor of R. W. Lockhart and R. C. Martinelli. But during the history some misunderstandings involving this parameter emerged and were published though some works. This section discusses how the misleading interpretation led to the today called Lockhart-Martinelli parameter. Hall, Griffin and Steven (2007) detail the history of Lockhart-Martinelli parameter, starting with the first definition proposed. They state that Lockhart and Martinelli (1949), 38 studying the pressure losses in two phase flow, suggested a parameter denoted as 𝑋 based on generalized Blasius friction factor equation, as defined in equation 40, where Δ𝑃𝑙,ℎ𝑙 and Δ𝑃𝑔,ℎ𝑙 are the head losses of the liquid and gas phases respectively, if flowing alone on the same pipe. This definition was stated for low single phase Reynolds number, unit length, straight smooth pipe. It is clear that the first definition of Lockhart- Martinelli parameter were a pressure loss predictor instead of a liquid loading parameter. Furthermore, for Reynolds number above 2000, Lockhart and Martinelli (1949) proposed equation 41, where 𝜇𝑙 and 𝜇𝑔 are the liquid and gas viscosity respectively. 𝑋 = √ Δ𝑃𝑙,ℎ𝑙 Δ𝑃𝑔,ℎ𝑙 (40) 𝑋 = √ Δ𝑃𝑙,ℎ𝑙 Δ𝑃𝑔,ℎ𝑙 = √( 𝑚𝑙̇ 𝑚𝑔̇ ) 1.8 ( 𝜌𝑔 𝜌𝑙 ) ( 𝜇𝑙 𝜇𝑔 ) 0.2 (41) In sequence Murdock (1962) discussing the behavior of orifice plates in two-phase flows, proposed a parameter expressed by equation 42, where 𝐶𝑑𝑙 and 𝐶𝑑𝑔 represents the liquid and gas single phase discharge coefficient respectively and the subscript 𝑚 means that the pressure drop is induced by the orifice meter. This equation was unintentionally denoted by the same 𝑋 parameter and it led to confusions with Lockhart-Martinelli parameter in some derivative works, even though Murdock have never called it in this fashion. 𝑋𝑀𝑢𝑟𝑑𝑜𝑐𝑘 = √ Δ𝑃𝑙,𝑚 Δ𝑃𝑔,𝑚 = ( 𝐶𝑑𝑔 𝐶𝑑𝑙 ) 𝜀 𝑚𝑙̇ 𝑚𝑔̇ √ 𝜌𝑔 𝜌𝑙 (42) Lately Chisholm (1977) derived a new parameter as the square root of the ratio of the gas and liquid phase flows inertia, as shown in equation 43, and titled erroneously by him “… the Lockhart-Martinelli correlating group” (sic) although it has a completely 39 different equation. Despite this confusion, this new parameter has no geometrical dependence like the original Lockhart-Martinelli parameter and the Murdock parameter, being a useful non-dimensional tool to compare the liquid loading on different flows. 𝑋𝐶ℎ𝑖𝑠ℎ𝑜𝑙𝑚 = 𝑚𝑙̇ 𝑚𝑔̇ √ 𝜌𝑔 𝜌𝑙 (43) An important discussion brought by Hall, Griffin and Steven (2007) about equation 43, was related to the similarly derivation between Murdock’s one (equation 42) and the latter, with a difference related to the discharge coefficients. In that, Chisholm (1977) assumed a 𝐶𝑑𝑙 ≈ 𝐶𝑑𝑔𝜀, which has validity in some circumstances, but not all. With all that in mind, the use of these different definitions leads to different values of percentual over-reading (𝑂𝑅%), resulting in significant differences on the gas flow correction and in the prediction processes. To illustrate these shifts, let’s consider an air-water flow with a 368 kg/h air flow rate and varying only the water mass flow rate. The water mass flow rate increase results in a liquid load increase, in other words the Lockhart-Martinelli parameter increases. Considering the Chisholm (1977) equation 43 as base value for the Lockhart-Martinelli parameter, the use of different definitions as Lockhart and Martinelli (1949) - Low Re (equation 40), Lockhart and Martinelli (1949) - High Re (equation 41) and Murdock (1962) (equation 42) results in 31 to 58% of relative shift on the over-reading estimation comparing the extremes values, as shown in Figure 7 and in Table 1. This result concretizes the importance of an adequate choice of the procedure to estimate the gas wetness parameter. Thirty years after Chisholm’s publication, Hall, Griffin and Steven (2007) deducted the Lockhart-Martinelli parameter based on the square root of the gas (𝐹𝑟𝑔) to liquid (𝐹𝑟𝑙) densiometric Froude number ratio, as shown in equation 44, been one of the milestones towards the consecration of 𝑋𝐿𝑀 equation. 40 Figure 7 - Impact of Lockhart-Martinelli definitions on over-reading estimation for a 368 kg/h air mass flow rate and 7 bara line pressure (Source: Author) Table 1 - Results for different definitions of Lockhart-Martinelli parameter 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 40 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 41 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 42 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 43 OR% Highest Shift1 ṁl (kg/h) Value OR% Value OR% Value OR% Value OR% 200 0.050 7.0% 0.077 10.9% 0.048 6.8% 0.049 6.9% 58% 598 0.149 20% 0.207 28% 0.145 20% 0.147 20% 38% 798 0.199 27% 0.268 36% 0.194 26% 0.196 27% 34% 1197 0.298 40% 0.386 50% 0.291 39% 0.294 39% 29% 1 − Calculated with equation 43 OR% value as reference 𝐹𝑟𝑙 𝐹𝑟𝑔 = 𝑚𝑙̇ 𝐴√𝑔𝐷 √ 1 𝜌𝑙(𝜌𝑙 − 𝜌𝑔) �̇�𝑔 𝐴√𝑔𝐷 √ 1 𝜌𝑔(𝜌𝑙 − 𝜌𝑔) = 𝑚𝑙̇ 𝑚𝑔̇ √ 𝜌𝑔 𝜌𝑙 = 𝑋𝐿𝑀 (44) 41 Another important milestone was published by Steven (2008), where in an inspired text of dimensionless analysis of a horizonal Venturi meter operating in two-phase flow, found the equation 44 parameter as one of dimensionless group generated by Bunckinghan-Pi Theorem. This constatation cement the parameter importance for two- phase flows, so said that, in this dissertation the parameter 𝑋𝐿𝑀 (equation 43 or 44) will be called Lockhart-Martinelli parameter. Finally, to facilitate the interpretation of the 𝑋𝐿𝑀 parameter is important to establish the conversion from/to other alternative wet gas parameters like 𝐺𝑉𝐹 and quality 𝑥 = �̇�𝑔 (�̇�𝑔+ �̇�𝑙) , shown by equation 45. 𝐺𝑉𝐹 = 1 1 + 𝑋𝐿𝑀√ 𝜌𝑔 𝜌𝑙 = 1 1 + ( 1 − 𝑥 𝑥 ) 𝜌𝑔 𝜌𝑙 (45) 2.3.3.2 Density ratio (𝐷𝑅) The density ratio, expressed by equation 46 , is an important dimensionless parameter to carry the influence of line pressure on the over-reading estimation. Assuming a perfect gas model, represented by equation 47, it is possible to demonstrate that 𝐷𝑅 is a direct function of the absolute pipe internal pressure, for other parameters held constant, as liquids density, due to its negligible change for a wide range of absolute pressure. 𝐷𝑅 = 𝜌𝑔 𝜌𝑙 (46) 𝜌𝑔 = 𝑃 𝑅𝑔𝑇 (47) 2.3.3.3 Gas densiometric Froude number (𝐹𝑟𝑔) The gas densiometric Froude number, as equation 48, is a dimensionless parameter of the gas flow rate, representing the ratio of inertial to gravity forces, important to 42 evaluate the flow pattern in two-phase flows as exposed by De Leeuw (1997), where 𝐴 is the pipe cross section area, 𝑔 the gravity acceleration and 𝐷 the pipe internal diameter. 𝐹𝑟𝑔 = √ 𝑆𝑢𝑝𝑒𝑟𝑓𝑖𝑐𝑖𝑎𝑙 𝐺𝑎𝑠 𝐼𝑛𝑒𝑟𝑡𝑖𝑎 𝐿𝑖𝑞𝑢𝑖𝑑 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 𝐹𝑜𝑟𝑐𝑒 = �̇�𝑔 𝐴√𝑔𝐷 √ 1 𝜌𝑔(𝜌𝑙 − 𝜌𝑔) (48) 2.3.3.4 Water to liquid ratio (WLR) Until now, every definition was based only in one liquid specie and one gas specie, however there are situations where the liquid content is a mix of two or more liquids, like water and light hydrocarbon (LHC). So, on these situations the liquid density is a mixture density. Considering that, the liquid compounds behave as a homogeneous mixture, Steven, Shugart and Kutty (2018) say that the liquid mix density (𝜌𝑙,𝑚𝑖𝑥) is defined by equation 49, where 𝑊𝐿𝑅 is the water to liquid ratio, defined in equation 50 (�̇�𝐿𝐻𝐶 and �̇�𝑊 are the light hydrocarbon and water mass flow rates), 𝜌𝐿𝐻𝐶 and 𝜌𝑊 are the light hydrocarbon and water density, respectively. 𝜌𝑙,𝑚𝑖𝑥 = 𝜌𝑊 × 𝜌𝐿𝐻𝐶 𝜌𝐿𝐻𝐶 ×𝑊𝐿𝑅 + 𝜌𝑊 × (1 −𝑊𝐿𝑅) (49) 𝑊𝐿𝑅 = �̇�𝑊 �̇�𝑊 + �̇�𝐿𝐻𝐶 (50) 2.3.3.5 The over-reading parameter (𝑂𝑅) The most important parameter in wet gas flow measurement by DP meters is the over- reading (𝑂𝑅), representing the positive bias caused by the presence of liquid mixed in the gas flow. It is defined as the false prediction of total gas mass flow rate (�̇�𝑓𝑝) to real dry gas mass flow rate (�̇�𝑔) ratio, as equation 51 . An approximated practical way 43 to calculate the 𝑂𝑅 is given by the square root of the two-phase differential pressure (𝛥𝑃𝑇𝑃,𝑚) to gas differential pressure (𝛥𝑃𝑔,𝑚) ratio, as in many flow conditions the simplification 𝜀𝐶𝑑 ≈ 𝜀𝑇𝑃𝐶𝑑,𝑇𝑃 can be applied on the mass flow rates equations ratio equation 51. Often in literature the 𝑂𝑅 is described as a percentage, as equation 52. 𝑂𝑅 = �̇�𝑓𝑝 �̇�𝑔 ≅ √ 𝛥𝑃𝑇𝑃,𝑚 𝛥𝑃𝑔,𝑚 (51) 𝑂𝑅% = ( 𝑂𝑅 − 1) × 100% (52) 2.3.4 The over-reading effect In single-phase gas applications, a DP meter primary device causes a certain differential pressure 𝛥𝑃𝑔,𝑚 as illustrated in Figure 8. The presence of considerable liquid loading in a gas stream causes a positive bias called over-reading (𝑂𝑅), i.e the 𝛥𝑃𝑇𝑃,𝑚 in a wet gas flow is higher than the dry gas 𝛥𝑃𝑔,𝑚. as presented in Figure 9. Figure 8 - Simplification of an orifice plate DP meter in a single-phase gas flow (Source: author) 44 Figure 9 - Simplification of an orifice plate DP meter in a two-phase wet gas flow (Source: author) This phenomenon is a consequence of four main flow dynamic changes from a dry gas flow to a wet gas flow: • Phase interfacial interaction: in a single-phase flow only the fluid interacts with the pipe wall. On the other hand, when a second phase is present on the flow, a interfacial region appears, which in liquid and the gas different velocities develops a shear stress that consumes flow energy (WALLIS, 1969). • Liquid acceleration: In the acceleration process on the meter restriction, more kinetic energy is dispended on liquid acceleration than on gas phase. This is a consequence of a higher density in liquids than in gases, resulting in more energy dissipation. • Area reduction: Looking at Figure 8 and Figure 9, it is clear that the orifice area from a gas phase perspective, is reduced by the presence of a liquid phase. In such manner from equation 32 the gas velocity will be higher than if it were flowing alone, i.e more energy consumption. • Flow geometry change: in orifice-plate-based meters the plate acts like a barrier for the liquid movement, accumulating on the upstream side, causing a significant change on the flow geometry, resulting in flow dynamic changes. This phenomenon is demonstrated on Figure 10, taken in a view port of a 20-minute steady flow. 45 Adding these four main effects, the presence of liquid leads to higher pressure drop in the meter’s primary device, such as the orifice plate, than in single phase gas flow, resulting in a false prediction of total gas mass flow rate (�̇�𝑓𝑝). However, is important to call attention to low wetness (typically 𝑋𝐿𝑀 < 0.02 (ISO TR 12748, 2015)) phenomenon denominated under-reading, as described by Ting (1993), diverging from the expected behavior of wet gas flows. In that work, it was postulated that the pipe wetted internal surface decrease the wall friction, reducing the pressure drop. Figure 10 - Water holdup in 4” pipe with a 0.65-beta orifice plate in stratified (left) and annular (right) flows. (Source: adapted from Steven et al. (2011)) 2.3.5 History of Over-reading correction The first important contribution on the wet gas flow measurement field was driven by Murdock (1962), the Associated Technical Director for Applied Physics at the Naval Boiler and Turbine Laboratory, Philadelphia. Murdock published an extensive wet gas meter correlation for orifice plates based on experimental data of air-water, steam- water, natural gas-water, and natural gas-distillate flows. The correlation proposed exhibits linear behavior of liquid loading, as shown in equation 53 with a reported uncertainty of ±1.5%. Murdock recognized the significance of the term √ Δ𝑃𝑙,𝑚 Δ𝑃𝑔,𝑚 to describe the relative amount of liquid in gas flow, which lately was called Lockhart- Martinelli parameter, by other authors. 46 √ 𝛥𝑃𝑇𝑃,𝑚 𝛥𝑃𝑔,𝑚 = 1.26√ Δ𝑃𝑙,𝑚 Δ𝑃𝑔,𝑚 + 1 (53) The huge relevance on Murdock’s work is based in the publication of 90 experimental data points with a 2.5 to 4 inches pipe diameter range, a 0.26 to 0.5 orifice plate beta range and a liquid loading range, expressed in terms of 𝑋𝐿𝑀, from 0.041 to 0.25. Despite the significance of his work in wet gas knowledge, Steven et al. (2011) states that Murdock assumed a separated flow, although some of data set had other flow patterns based on the flow rates. Additionally, he did not take to account important parameters for a two-phase flow, like line pressure and slip ratio, resulting in a limited over-reading correlation, depending only on gas wetness. Chisholm (1977) continuing the 1974’s two-phase flow investigation and, motivated by the limitations of Murdock’s work, studied the pressure line influence and the slip ratio on the orifice plate over-reading in wet gas flows. According to Collins and Clark (2013), Chisholm was a National Engineering Laboratory (NEL) member, where he developed his experiments using water-vapor combinations with 10, 30, 50 and 70 bar of pressure in 21, 32 and 44mm pipe diameter. His paper introduced a new liquid loading parameter for orifice plates, called by him as Lockhart-Martinelli parameter, as defined in equation 43. Such definition was applied to develop a new over-reading correction correlation, represented by equations 54 and 55 , where the pressure influence on the over-reading was implicit on the gas to liquid density ratio (𝐷𝑅), characterized by the 𝐶𝐶ℎ term. He claimed a ±2% uncertainty performance comparing to experimental data. 𝑂𝑅𝐶ℎ𝑖𝑠ℎ𝑜𝑙𝑚 = √1 + 𝐶𝑐ℎ𝑋𝐿𝑀 + 𝑋𝐿𝑀 2 (54) 𝐶𝐶ℎ = ( 𝜌𝑔 𝜌𝑙 ) 1 4 + ( 𝜌𝑙 𝜌𝑔 ) 1 4 = (𝐷𝑅) 1 4 + ( 1 𝐷𝑅 ) 1 4 (55) 47 Steven et al. (2011) states that Chisholm’s considerations to develop the correlation were an incompressible and stratified flow, with a constant phase velocity ratio (or slip ratio) and a dependence on the gas to liquid density ratio (𝐷𝑅). These assumptions limited the correlation for a low densitometric Froude number, where the flow pattern is predominantly stratified i.e., limited in a low gas flow rate. Chisholm related the over reading as being dependent on the split ratio rather than the flow pattern. After Chisholm’s publication, a small amount of research was done on the wet gas metering by differential pressure meters field. However, with the rising interest on natural gas flows by the industry, De Leeuw (1997), a Shell Inter-national Exploration and Production employee, released research on wet gas metering with a 4”, 0.4 beta ratio Venturi, showing that the flow pattern governed the Venturi’s over-reading in addition with Lockhart-Martinelli parameter and 𝐷𝑅 relation. According to De Leeuw, the flow pattern was a gas densiometric Froude number function and hence the over- reading, with a directly proportional relation, i.e. as gas densiometric Froude number rises the over-reading rises, if all other parameters are kept unchanged. Another constatation was that Venturi’s over-reading is higher than orifice meter over-reading, demanding so, higher correction factor. A new data set was acquired from the SINTEF Multiphase Flow laboratory to a 4” diameter, 0.4 beta ratio Venturi in a Nitrogen- Diesel oil flow, covering a 15 to 90 bar pressure range, gas velocities up to 17 m/s, 1.5 ≤ 𝐹𝑟𝑔≤ 4.8 and 0 ≤ 𝑋𝐿𝑀≤0.3. With these combinations the minimal gas density tested was 17 kg/m³, becoming a limitation of the algorithm. The Venturi meter correlation proposed is shown as equation set 56 to 58 with a stated uncertainty of ±2%. 𝑂𝑅𝐷𝐿,𝑣𝑒𝑛𝑡𝑢𝑟𝑖 = √1 + 𝐶𝐷𝐿𝑋𝐿𝑀 + 𝑋𝐿𝑀 2 (56) 𝐶𝐷𝐿 = (𝐷𝑅) 𝑛 + ( 1 𝐷𝑅 ) 𝑛 (57) { 𝑛 = 0.41 𝑓𝑜𝑟 𝐹𝑟𝑔 ≤ 1.5 𝑛 = 0.606[1 − exp(−0.746𝐹𝑟𝑔)] 𝑓𝑜𝑟 𝐹𝑟𝑔 > 1.5 (58) 48 Following up the development of differential pressure technology, Stewart et al. (2002), members of NEL 1999-2002 Flow Programme, investigated the inverted cone (IC) meters performance on wet gas flows. Two IC meters, with 0.55 and 0.75 beta ratio, were used to collect new experimental data in three pressure levels 15, 30 and 60 bar, at a range of Nitrogen and Kerozene flowrates, resulting in a 0.4 to 4.0 gas densiometric Froude number range. The results indicated a strong over-reading dependence on Lockhart-Martinelli parameter, a pressure and a gas densiometric Froude number effect similar to that occurred in Venturi meters. To develop a new correlation applied to IC meters, the authors firstly tested the available data with existing Venturi correction correlations, noting that Venturi meters over-reading were higher than in IC, hence the gas flow rate error was over corrected. Based on this results, new correlations were proposed, one for each beta ratio. In 2005, Steven, Kegel and Britton (2005) unified all the IC data available at that time and slight improved the Stewart et al. (2002) correlation as shown in equations 59 to 61 resulting in a gas flow rate prediction to ±2% uncertainty. 𝑂𝑅𝑆𝑡,𝐼𝐶 = 1 + 𝑎𝑋𝐿𝑀 + 𝑏𝐹𝑟𝑔 1 + 𝑎𝑋𝐿𝑀 + 𝑏𝐹𝑟𝑔 (59) { 𝑎 = 2.431 𝑏 = −0.151 𝑐 = 1 𝑓𝑜𝑟 𝐷𝑅 < 0.027 (60) { 𝑎 = −0.0013 + ( 0.3997 √𝐷𝑅 ) 𝑏 = 0.0420 − ( 0.0317 √𝐷𝑅 ) 𝑐 = −0.7157 + ( 0.2819 √𝐷𝑅 ) 𝑓𝑜𝑟 𝐷𝑅 ≥ 0.027 (61) Steven, Ting and Stobie (2007), motivated by earlier observations about beta ratio to over-reading inverse relationship on Venturi’s, studied this behavior in orifice plates. Conclusions showed that in orifice plates this effect is far less sensitive than in Venturi, 49 smaller enough to be negligible. On the other hand, Chisholm did not report similar beta effect on his publication and De Leeuw said it is irrelevant in Venturis. Steven (2006) proceeded a theoretical derivation of Chisholm’s model for a homogeneous flow developing a correction correlation, which equations set is similar to Chisholm’s publication, but changing only the exponent from ¼ to ½. Such homogeneous model works for different types of differential pressure meters, being dependent only on Lockhart-Martinelli parameter and on gas to liquid density ratio (𝐷𝑅), regarding the fact that the flow needs to have a negligible slip. Reader-Harris, Nel and Graham (2009) continuing the de Leeuw’s studies, proposed a new correction correlation for Venturis, taking in account the Froude and beta effect. They collected new wet gas data from National Engineering Laboratory 4” loop using Nitrogen-Exxsol 80, Argon-Exxsol 80 and Nitrogen-water as two-phase fluid with 0,4 to 0.75 beta range, 15 to 60 pressure range and 0 ≤ 𝑋𝐿𝑀≤0.3. The resulting correlation is similar to De Leeuw’s correlation, substituting only the 𝑛 exponent to equation 62, where 𝛽 is the diameter ratio (beta ratio) and 𝐻 is a function of the surface tension i.e., a fluid function being 1 for hydrocarbon fluids, 1.35 for ambient temperature water and 0.79 for hot water (in a wet-steam flow). 𝑛 = max [0.583 − 0.18 × 𝛽2 − 0.578 × exp (−0.8 𝐹𝑟𝑔 𝐻 ) ; 0.392 − 0.18 × 𝛽2] (62) Another important observation made by Reader-Harris and Graham, is the fact that the discharge coefficient for wet gas flows is different from dry gas flows. The wetness results in a 𝐶𝑑 decrease. So, they proposed an appropriated empirical way to estimate the 𝐶𝑑 for wet gas flows, given by equations 63 and 64. 𝐶𝑑𝑇𝑃 = [1 − 0.0463 × exp(−0.05𝐹𝑟𝑔,𝑡ℎ)] (63) 𝐹𝑟𝑔,𝑡ℎ = 𝐹𝑟𝑔 𝛽2.5 (64) 50 Within the data set range, Reader-Harris and Graham stated a ±3% uncertainty for 𝑋𝐿𝑀 ≤ 0.15 and ±2.5% uncertainty for 0.15<𝑋𝐿𝑀≤ 0.3. Back to orifice meters studies, Steven and Hall (2009) evaluating natural gas flows with liquid loading noticed that orifice plates had the same 𝐹𝑟𝑔 and 𝐷𝑅 effect observed in Venturis i.e., an 𝐹𝑟𝑔 increase resulted in a 𝑂𝑅 increase and a 𝐷𝑅 increase resulted in a OR decrease. To improve the data set range, new experiments were done in CEESI and NEL laboratories with natural gas and nitrogen as gas phases and Stoddard solvent, Exxsol 80 and Decane as liquid phases. The geometry and properties ranges were 2” to 4” pipe diameter, 6.7 to 79 bar pressure, 0.25 to 0.73 𝛽, 1.5 to 4.8 𝐹𝑟𝑔 and 0 ≤ 𝑋𝐿𝑀≤0.55. This new data set together with the former data set available resulted in the following correlation, similar to Chisholm’s changing the 𝑛 exponent to equation 65 . Steven and Hall state a ±2% uncertainty at a 95% confidence level. { 𝑛 = 0.214 𝑓𝑜𝑟 𝐹𝑟𝑔 ≤ 1.5 𝑛 = [( 1 √2 ) − ( 0.3 √𝐹𝑟𝑔 )] 2 𝑓𝑜𝑟 𝐹𝑟𝑔 > 1.5 (65) Testing this correlation with a 0 to 100% WLR data, which was not used to develop the correlation, Steven and Hall (2009) found a slight shift on the correction up to -3%, a over-correction result. Steven et al. (2011) with more two-compound liquid loading (water + hydrocarbon) data observed that the water content on liquid mixture reduced the 𝑂𝑅, in an almost linear manner. It was a result of transition gas densiometric Froude number increase from stratified to annular mist flow pattern. As the WLR increases i.e., the water content on the liquid loading increases, the mixture surface tension increases, tending the flow pattern to separated flow. After this finding Steven et al. (2011) included the 𝑊𝐿𝑅 effect in the previously orifice plate correlation changing only de Chisholm exponent as shown in equations 66 and 67 , where 𝐹𝑟𝑔,𝑠𝑡𝑟𝑎𝑡 is the transitional gas densiometric Froude number between stratified to annular mist flow. 51 { 𝑛 = [( 1 √2 ) − ( 0.4 − 0.1 × exp (−𝑊𝐿𝑅) √𝐹𝑟𝑔,𝑠𝑡𝑟𝑎𝑡 )] 2 𝑓𝑜𝑟 𝐹𝑟𝑔 ≤ 𝐹𝑟𝑔,𝑠𝑡𝑟𝑎𝑡 𝑛 = [( 1 √2 ) − ( 0.4 − 0.1 × exp (−𝑊𝐿𝑅) √𝐹𝑟𝑔 )] 2 𝑓𝑜𝑟 𝐹𝑟𝑔 > 𝐹𝑟𝑔,𝑠𝑡𝑟𝑎𝑡 (66) 𝐹𝑟𝑔,𝑠𝑡𝑟𝑎𝑡 = 1.5 + (0.2 ×𝑊𝐿𝑅) (67) As reported by Steven et al. (2011) this algorithm corrected the data within a ±2% uncertainty at a 95% confidence level. Is important to highlight thar all these empirical correlations are based on data fitting, therefore being in some level dependent on the data set installations, where extrapolations tend to increase uncertainty. 2.3.6 PLR to XLM relationship As seen on the previous section, usually the over-reading correction correlations demand a liquid flow rate or a liquid content parameter previous knowledge, to predict the over-reading. Nonetheless this information is not available since the traditional meters were developed to measure single-phase flows. Consequently, this liquid loading info needs to be gathered from an external source like test separator, historical data, trace dilution methods or equation of state predictions, which bring high uncertainty to the measurement process, resulting in an inaccurate gas flow rate prediction (STEVEN, 2007). Aiming to mitigate this limitation De Leeuw (1997) published an important 𝑃𝐿𝑅 to 𝑋𝐿𝑀 relation. The pressure loss ratio (𝑃𝐿𝑅) is defined as the ratio between the permanent pressure loss (𝛥𝑃𝑃𝑃𝐿), measured by an extra third pressure tapping, operating in conjunction with the traditional pressure differential (𝛥𝑃𝑡), as exemplified in Figure 11 (Venturi tube application) and Figure 12 (Orifice plate application). According to De Leeuw, the 𝑃𝐿𝑅 in Venturi tube is affected by the liquid presence, increasing with it. Consequently, this relation could potentially be used to predict the liquid loading without external methods, i.e. being directly related to 𝑋𝐿𝑀 as exposed in Figure 13. However, the sensitivity of 𝑃𝐿𝑅 with the amount of liquid is variable, being wetness and 52 pressure dependent, decreasing with these parameters increasing. For Venturi tube, De Leeuw states that the use would be suitable for Lockhart-Martinelli values below 0.15 (XLM<0.15, i.e. a GVF of 98.97% at 3 barg). Despite these significant observations, no acceptable correlation formula was proposed in that work. Figure 11 - Configuration of the third tapping propose by De Leeuw (Source: adapted from ISO TR 12748 (2015)) Figure 12 - Illustration of pressure profile showing the Pt , PPPL and Pr for an orifice plate meter and a generic third pressure tap (Source: author) 53 Figure 13 - Venturi's PLR to XLM relation at 45 bar. (Source: De Leeuw (1997)) From 2001 to 2005, many reported attempts to use this method, applied to the inverted cone, have had poor results and additional methods using a second DP meter in series with inverted cone, in the expansion region tested exhaustively, had no farther results. However, in 2005 Steven, Kegel and Britton (2005) released an IC wet gas meter using the third tap to create a V-cone expansion meter correlations, which combined with the traditional V-cone correlations (equations 59 to 61) resulted in a Lockhart-Martinelli estimation based on the ratio between the traditional meter 𝑂𝑅 and the expansion meter 𝑂𝑅, as equations 68 and 69, where the subscripts TM and EM means traditional meter and expansion meter respectively. The authors stated uncertainty of ±5% for the gas mass flow rate (STEVEN, 2007). 𝜙 = 𝑂𝑅𝑇𝑀 𝑂𝑅𝐸𝑀 = (�̇�𝑓𝑝)𝑇𝑀 (�̇�𝑓𝑝)𝐸𝑀 (68) 𝑋𝐿𝑀 = (𝜙 − 1)2 4 × exp [−2.74 − 22.3 × 𝐷𝑅 − 1.27 𝐹𝑟𝑔 ] (69) 54 Back to orifice plates, Steven et al. (2011) brought back the ISO 5167-2 (2003) 𝑃𝐿𝑅𝑑𝑟𝑦 correlation for a single-phase flow as a baseline, as shown in equation 70, explaining that the discharge coefficient and consequently the pressure loss ratio have a relatively low sensitivity to Reynolds, remaining almost invariant for a given beta. Hence it could be used to predict the Lockhart-Martinelli parameter in wet gas flows. They state that 𝑃𝐿𝑅𝑤𝑒𝑡 is sensitive to 𝑋𝐿𝑀 only in orifice plates to beta larger or equal to 0.5 (β ≥ 0.5), due to 𝑃𝐿𝑅𝑑𝑟𝑦 proximity to unit at lower betas, and an extremely 𝐷𝑅 dependence. However, ISO 5167-2 (2003) stated that the 𝑃𝐿𝑅𝑑𝑟𝑦 equation is an approximation with a 𝐷 upstream and 6𝐷 downstream taps for the pressure loss and no uncertainty is mentioned. 𝑃𝐿𝑅𝑑𝑟𝑦 = √1 − [𝛽4(1 − 𝐶𝑑2)] − 𝐶𝑑𝛽2 √1 − [𝛽4(1 − 𝐶𝑑2)] + 𝐶𝑑𝛽2 (70) In face of such finding and considering the Steven and Hall (2009) and Reader-Harris, Nel and Graham (2009) correction correlations for orifice plates and Venturis respectively, the International Organization for Standardization (ISO) released the ISO TR 11583 (2012), recommending a wet gas measurement methodology based on the traditional DP meters methodology in addition to a Lockhart-Martinelli parameter estimation by means of the difference between 𝑃𝐿𝑅𝑑𝑟𝑦 and 𝑃𝐿𝑅𝑤𝑒𝑡, showed in equations 70, 71 and 72, limited by 0.5 ≤ 𝛽 ≤ 0.68, 𝑋𝐿𝑀 < 0.45𝐷𝑅0.46 and 𝐷𝑅 ≤ 0.21𝛽 − 0.09. No limitations to the pressure tapping were recommended. 𝑌 = 𝑃𝐿𝑅𝑤𝑒𝑡 − 𝑃𝐿𝑅𝑑𝑟𝑦 (71) 𝑋𝐿𝑀 = 6.41𝑌 𝛽4.9 (𝐷𝑅)0.92 (72) Steven, Shugart and Kutty (2018) argued that the 𝑃𝐿𝑅𝑑𝑟𝑦 equation (equation 70) had some shifts from the experimental data available and the 𝑋𝐿𝑀 equation (equation 72) 55 did not behave well for 𝛽 > 0.55 and was developed only for hydrocarbon liquid loading, not for water content. Other limitations exposed was about the XLM and DR parameters, resulting in a narrow range of applicability due to the reduced database used to develop this correlation. To improve these limitations Steven, Shugart and Kutty (2018) proposed a new equation set including an improving PLRdry equation. Unfortunately, for confidentiality matters, they did not expose their algorithm, but stated less then ± 2% uncertainty for a WLR = 1 and for all data set tested, a global ± 4% uncertainty at a 95% confidence level. 56 3 EXPERIMENTAL APPARATUS The Research Group for Studies on Oil&Gas Flow and Measurement (NEMOG in Portuguese) is located at Federal University of Espírito Santo, Vitória, Brazil to realize research on flow measurement field. One of the research lines is the multiphase flow measurement and characterization, relying with a new and up to date multiphase flow loop operating with air, water and mineral oil, as shown in Figure 14, pressure class #150psi (10 barG). Figure 14 -The NEMOG's multiphase flow loop sketch (Source: Author) 3.1 SECTION I: FLUID STORAGE The fluid storage counts with three steel tanks designed to store tap water, mineral oil and emulsified fluids from the separator vessel. With an 3 m³ volumetric capacity each, the tanks operate under atmospheric pressure. Figure 15 shows a schematic view of the tanks. 57 Figure 15 - Storage tanks flowchart (Source: author) 3.2 SECTION II: FLUID PUMPING AND SEPARATION This section is divided in four subsections, the three-phase separator vessel, the oil pumping, the water pumping, and the compressed air supplier. 3.2.1 Three-phase separator vessel The three-phase separator vessel, shown in Figure 16, is responsible to pre storage the water and oil before the single-phase measurement and to separate the fluid emulsion formed after the circulation on the test loop, where a schematic flowchart of the fluids before and after separation process. Figure 17 shows a separator vessel photography, and the technical information are exposed in Table 2. 58 Figure 16 - Separator vessel flowchart (Source: author) Figure 17 - Separator vessel photography (Source: author) 59 Table 2 - Separator vessel technical information Volumetric Capacity 6,7 m³ Operational Temperature 25 °C Operational Pressure 10 barg Project Limit Temperature 50 °C Project Pressure 13 barg Hydrostatic Pressure Test 20 barg Material Steel Full load weight 9300 kg 3.2.2 Water circulation pumping The water used in the flow circuit is supplied from the separator vessel and pumped by a centrifugal water pump coupled to a Weg induction electric motor controlled by an variable-frequency driver. This configuration results in the following capabilities, with operational data, shown in Table 3. Table 3 - Water pumping specifications and capabilities Water pump KSB Meganorm 80-50-125 Electric motor WEG W22 7.5 HP Driver Schneider ATV600 Maximum Pressure¹ 3.33 barg Maximum Mass Flow Rate² 42000 kg/h 1 - With no flow rate and the separator vessel, i.e. the suction line at atmospheric pressure 2 - For the actual test loop configuration, i.e. actual installed pressure drop 3.2.3 Compressed air supplier The compressed air is supplied by an Kaeser ASD 40 volumetric screw compressor that feeds an intermediary pressure vessel and goes to an air dryer, before entering the single-phase measurement, as shown in Figure 18. Since the compressor uses a 60 fixed volume screw to compress the air, the maximum air mass flow rate becomes dependent on the local air density, i.e. on the laboratory atmospheric pressure and temperature. Table 4 brings the system configuration and capability. Figure 18 - Compressed air supplier schematic flowchart (Source: author) Table 4 - Compressed air supplier specifications and capabilities Compressor Kaeser ASD 40 Maximum Pressure 8.62 barg Maximum Mass Flow Rate @ 23 °C 387 kg/h 1 Maximum Mass Flow Rate @ 30 °C 351 kg/h 1, 2 Air Vessel 13 barg , 1m³ 1 - Based on a 5 barg test loop back pressure 2 - This mass flow rate reduction occurs due to the air specific volume increase in the suction line, resulting in a volumetric efficiency reduction 3.3 SECTION III: SINGLE-PHASE FLOW MEASUREMENT The flow rate measurement of each phase is configurated in a split-range way to amplify the circuit measurement capability, as sketched in Figure 19 and Figure 20, where high flow rates and low flow rates are separated. For the water side, two different 61 flow range Coriolis flowmeters are used with technical information exposed in Table 5 and shown in Figure 21, providing both mass and volumetric flow rates. Figure 19 - Single-phase measurement split-range configuration sketch for water and air (Source: author) Figure 20 - Single-phase measurement split-range configuration photography (Source: author) 62 Figure 21 - High and low waterflow rate Coriolis meters in split-range arrangement photography (Source: author) Table 5 - The high and low water flow rate Coriolis meters technical information High flow rate Low flow rate Manufacturer Metroval Metroval Model SMT-100 SMT-50 Identifier Code FIT-05 FIT-06 Mode Totalizing Totalizing Maximum Calibrated Flow Rate 80 m³/h 20 m³/h Minimum Calibrated Flow Rate 8 m³/h 2 m³/h¹ Calibration Certificate Appendix A Appendix A 1 - Although the calibration process was performed at this minimal value, the manufacturer informed that this flow meter could measure at least 0,65 m³/h, increasing to 0,5% the measurement uncertainty. For the air side, the mass flow rate measurement are done by two different orifice plates, configurated as exposed in Table 6 and shown in Figure 22. 63 Figure 22 - The high and low mass flow rate orifice plate meters photography (Source: author) Table 6 - The high and low flow rate orifice plate meters technical information High flow rate Low flow rate Manufacturer Ituflux Ituflux Identifier code FIT-01 FIT-02 Material AISI 316 AISI 316 Tap Flange Corner Upstream/Downstream tap distance 26/26 mm 3/3 mm Pipe diameter 50.10 mm 39.10 mm Orifice diameter 25.02 mm 14.67 mm Beta ratio 0.4994 0.3752 Upstream straight pipe length 22 D 22 D Downstream straight pipe length 8 D 8 D Maximum Project Mass Flow Rate 1180 kg/h 236 kg/h Minimum Project Mass Flow Rate 236 kg/h 59 kg/h Calibration certificate N/A¹ N/A¹ 1 - The measurement uncertainty is given by ISO 5167-2 64 3.4 SECTION IV: FLUIDS MIXING The mixing section is one of the most important parts of the multiphase flow loop due to the influence on the downstream flow pattern. Considering only water and air flow, the original mixing configuration of the installation is located after the single-phase measurement and consists of two 45° Y fits, 6” pipes converging to a single 6” pipe leading to the teste loop, as shown in Figure 19 and Figure 23. Nonetheless, preliminary tests showed that the mixing upstream of the 6” to 2” reduction was resulting in an intermittent flow pattern even in low water mass flow rate, causing high range fluctuations on the test section pressure measurements downstream, leading to an inconclusive data. Following up, a new mixing section was developed and installed downstream of the pipe reduction, illustrated in Figure 24. This configuration led to a more stable two- phase flow with flow patterns from stratified to annular mist. Figure 23 - Original mixing arrangement (Source: author) 65 Figure 24 – Final Experimental mixing arrangement (Source: author) 3.5 SECTION V: TEST LOOP The experiments are performed in test loop section. It counts on interchangeable 2” sch 40 pipe spools of different lengths from 600 mm to 3000 mm, two flexible stretches and two 600 mm borosilicate pipe spools providing a set of loop configurations and inclinations. The actual installation is composed by two branches of horizontal 2” sch 40 pipes, one inlet and one in return with 6776 mm each, connected by a section with two 90° bends as shown in Figure 25 and Figure 26. Figure 25 - Actual test loop section configuration (dimensions in millimeter) (Source: author) 66 Figure 26 - Test loop section photography (Source: author) 3.5.1 Orifice plate wet gas measurement test section This section, located in the end of inlet branch, is composed by two 600 mm spools with an additional 6D ½” BSP pressure tap, measured from the orifice plate flange (flange taps). The orifice plate is fixed in-between the spools flanges, each equipped with a 25,4 mm flange pressure tap., resulting in an installation with 93D upstream and 26D downstream straight pipe length. Additionally, two extra pressure taps are provided along the test loop to enable supplementary 3rd pressure tap configurations, one located 20D and other 144D from the orifice plate downstream face as seen in Figure 25 and Figure 27. Moreover, two borosilicate translucid pipe sections are mounted to visually inspect the flow pattern behavior. 67 Figure 27 - Fitting details of loop section, in perspective (Source: author) Figure 28 exhibits the pressure transmitters taps primary configuration and Table 7 exposes the transmitters specifications. In addition, to complete the wet gas flow meter sensors, a low perturbation temperature transmitter (appendix C) is installed 14D downstream of the orifice plate. Further tests will change the Figure 28 6D 3rd tap for the 20D and 144D configuration, with more details in section 4.5. Figure 28 - Wet gas measurement pressure taps by ISO TR 12748 (2015) (Source: author) 68 Table 7 - Wet gas measurement pressure transmitters specification Identifier TAG PIT-9 PDT-3 PDT-4 PDT-5 Manufacturer Smar Code LD301- M41I- TU11-011 LD301- D31I- TU11-011 LD301- D21I- TU11-011 LD301- D21I- TU11-011 Application Manometric Differential Differential Differential Lower Range Limit (kPa) -100 -250 -50 -50 Upper Range Limit (kPa) 2500 250 50 50 Sensor type Capacitive Diaphragm 316L Stainless Steel Lower Range Calibration (kPa) 0 0 0 0 Upper Range Calibration (kPa) 1000 68.5 49.4 24.5 Calibration certificate Appendix B 69 4 EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSIONS 4.1 NEMOG’S WET GAS FLOW TEST ENVELOPE The previous chapter exposes multiphase flow circuit equipment’s ranges and with this mapping it could stablish the actual configuration wet gas parameters limits for NEMOG’s circuit. Is important call attention to the air mass flow rate maximum values exposed in Table 4, which considers a back pressure of 5 barg at the test loop. So as the pressure at the test loop increases towards the 8.62 barg compressor maximum pressure, the maximum air mass flow rate decreases. Therefore, it is decided to limit tests campaign at 5 barg pressure, starting at 1 barg in addition with a 3 barg level. That said, along with water circulation pump (Table 3) and single-phase measurements capacities (Table 5 and Table 6), Table 8 exhibit the Lockhart-Martinelli and GVF limits, as the main wet gas parameters, considering three different pressure levels and a mean air mass flow rate of 360 kg/h. Table 8 - Lockhart-Martinelli and GVF ranges for NEMOG’s actual configuration Water mass flow rate (kg/h) 645 1 945 1286 Pressure (barg) 𝑿𝑳𝑴 𝑮𝑽𝑭 2 𝑿𝑳𝑴 𝑮𝑽𝑭 2 𝑿𝑳𝑴 𝑮𝑽𝑭 2 1 0.087 99.58% 0.128 99.38% 0.174 99.16% 3 0.123 99.16% 0.180 98.78% 0.245 98.35% 5 0.150 98.75% 0.220 98.18% 0.300 97.54% 1 - Represents the minimum measurement capability of water mass flow rate by Coriolis meter 2 - Conversion as Equation 45 Analyzing Table 8 together with the forementioned pressure limitations towards the air flow, it is possible to notice that the lower limitation for Lockhart-Martinelli parameter relies on the minimal measurable water flow rate by the Coriolis meter. Thus, to establish equal levels of gas wetness for test points, it’s decided to use three 𝑋𝐿𝑀 points at 5 barg row as base values, to cover the maximum wet gas flow range considered in literature, as mentioned in section 2.3.1. To summarize, the experimental envelope for the wet gas experiments is �̇�𝑎𝑖𝑟 = 360 kg/h mean air mass flow rate as a fixed 70 value, pressures line set at 1,3 and 5 barg and Lockhart-Martinelli ranging at 𝑋𝐿𝑀 = 0.15, 0.22 and 0.30. Another important variable to determine is the beta ratios for orifice plates to be tested. The experiments aim to be validated with the Steven et al. (2011) work, where they present a relevant relation between pressure loss ratio and Lockhart-Martinelli only for 𝛽 = 0.5 or higher. Along this, an orifice plate with 𝛽 = 0.5 and 𝛽 = 0.68 are manufactured. 4.2 DATA ACQUISITION AND TREATMENT METODOLOGY The multiphase flow loop supervisory and control system is developed in the National Instruments LabVIEW platform, where the process variables are received by a 4 - 20 mA protocol for the pressure and temperature transmitters and by Modbus for the control valves, Coriolis metes, variable-frequency driver and other secondary equipment. Those variables are converted, according to the range set on the transmitter, to the respective unit selected by the user, processed on the supervisory program to result in mass flow rates (for air flow) and then recorded in a log sheet, in an approximately 0,2 second cycle period (frequency = 5Hz). Figure 29 shows the multiphase flow loop supervisory main page where the single-phase parameters are monitored and Figure 30 the wet gas parameters page view, where the main parameters involved in a wet gas flow are monitored. Figure 29 - National Instruments LabVIEW multiphase flow loop supervisory system main page (Source: author) 71 Figure 30 - National Instruments LabVIEW wet gas flow parameters supervisory page (Source: author) An important task regarding the pressure transmitters is related to the water draining from the pressure tapping tubes before each test battery. The presence of liquid in those tubes interfere in pressure measurement procedure, resulting in invalid data. 4.2.1 Post processing The data post processing procedure is an important part of the experimental research, owing to statistically extract the significant data intervals and eliminate noises and outliers. So, in this work, after the ending of an experimental campaign, the log is saved and post processed using all primary variables, such as pressure and temperature to doble check the air mass flow rates results, as calculated by the supervisory system, for both the single-phase meter, located at the single-phase flow measurement section, and the test meter, located at the test loop section. This task is performed using a Mathworks Matlab® algorithm performing the ISO 5167-2 (2003) recommendations, in addition with the uncertainty evaluation of each property, as explained in the next subsection. Further, data is transferred for a Microsoft Excel® sheet, where the statistical analysis is developed. Due to different procedures used in each experimental step, the further individual methodology executed is explained on respective chapter. 72 4.2.2 Uncertainty evaluation The uncertainty evaluation of each experimental measured variable follows the JCGM (2008) in addition with ISO 5167-2 (2003) considerations for air mass flow rate uncertainty. JCGM (2008) exposes that an uncertainty reporting is extremely important in expe