Characteristics of horizontal gas-liquid two-phase ﬂow measurement in a me dium-size d pipe using gamma densitometry

Two-phase ﬂows are common occurrences in many industrial applications. The under- standing of their characteristics in industrial piping systems is vital for the eﬃcient design, optimization, and operation of industrial processes. Most of the previous experimen- tal studies involving the use of gamma densitometers for holdup measurements in air-water mixtures are limited to smaller diameter pipes (generally regarded as those with < 50 mm in nominal diameter). Further, very few literature report experimental data obtained using gamma desitometers. This paper presents an application of a gamma densit- ometer in the measurement of two-phase ﬂow characteristics in an intermediate diameter pipe (nominal diameter between 50 mm and 100 mm). Scaled air-water experiments were performed in a 17-m long, 0.0764-m internal diameter horizontal pipe. Liquid superﬁcial velocity ranged between 0.1–0.4 m/s while gas superﬁcial velocity ranged from 0.3 to 10.0 m/s. The measured parameters include liquid holdup, pressure gradient, ﬂow pattern, and slug ﬂow features. The ﬂow patterns observed were stratiﬁed, stratiﬁed-wavy, plug, slug, and annular ﬂows. Plug and slug ﬂow patterns showed good agreement with established ﬂow pattern maps. Furthermore, the slug translational velocity was observed to increase with increasing mixture velocity, as reported by previous authors, hence establishing the reliability of the instrumentation employed. The slug body length was also measured us- ing the gamma densitometer and was found to be within the range 24–36D with a mean length of 30.6D. air suction experimental test matrix used superﬁcial water velocity ranges ( V sw ) from 0.1–0.4 m/s and for each point, the superﬁcial gas velocities ( V sg ) used are between 0.3 and 10 m/s. An experimental air-water two-phase ﬂow study has been conducted using a gamma radiation technique with two densitometers that measure slug ﬂow characteristics. Liquid holdup and slug translational velocity measurements were carried out on a 0.074-m ID horizontal test facility. Flow patterns for the experiments conducted were identiﬁed using a combination of visual observation and statistical analysis of hard gamma counts of the various ﬂow conditions. The ﬂow patterns observed were stratiﬁed, stratiﬁed-wavy, plug, slug, and annular ﬂows. A comparison of observed ﬂow patterns with established ﬂow pattern maps shows a good agreement for the dominating ﬂow pattern (plug and slug ﬂow pattern). Also, measurement of slug translational velocity and slug body length were carried out. Measured slug translational velocity


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Two-phase flows are common occurrences in many industrial applications. The understanding of their characteristics in industrial piping systems is vital for the efficient design, optimization, and operation of industrial processes. Most of the previous experimental studies involving the use of gamma densitometers for holdup measurements in airwater mixtures are limited to smaller diameter pipes (generally regarded as those with < 50 mm in nominal diameter). Further, very few literature report experimental data obtained using gamma desitometers. This paper presents an application of a gamma densitometer in the measurement of two-phase flow characteristics in an intermediate diameter pipe (nominal diameter between 50 mm and 10 0 mm). Scaled air-water experiments were performed in a 17-m long, 0.0764-m internal diameter horizontal pipe. Liquid superficial velocity ranged between 0.1-0.4 m/s while gas superficial velocity ranged from 0.3 to 10.0 m/s. The measured parameters include liquid holdup, pressure gradient, flow pattern, and slug flow features. The flow patterns observed were stratified, stratified-wavy, plug, slug, and annular flows. Plug and slug flow patterns showed good agreement with established flow pattern maps. Furthermore, the slug translational velocity was observed to increase with increasing mixture velocity, as reported by previous authors, hence establishing the reliability of the instrumentation employed. The slug body length was also measured using the gamma densitometer and was found to be within the range 24-36D with a mean length of 30.6D.

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Internal diameter [

Introduction
Two-phase flow of liquid and gas is commonly encountered in the oil and gas industry. In most cases of normal production, co-flowing liquid and gas phases are present in pipe tubing and flow lines. In the oil and gas industry, for example, to enhance oil production or transportation, gas is often injected to lower the density and mitigate serious hydrodynamic issues, especially at junctions and elbows. When a multiphase flowing mixture is encountered, the flow characteristics are completely different from those in single-phase flow. This includes flow patterns that vary depending on the fluid properties, pipe geometry, and inclination. For oil production in harsh environments, little changes in flow characteristics become critical. The pipelines used have to be able to withstand various extreme conditions of pressure, temperature, and hydraulic issues, such as slugging, liquid surges, corrosion, and erosion. Flow assurance and transportation are heavily dependent on a sufficient understanding of flow mechanisms and related behaviours such that accurate predictions can be made.
In this study, we present detailed local measurements obtained for two-phase pressure gradient, liquid holdup, and slug flow features: slug frequency, slug liquid holdup, and slug translational velocity measured using gamma densitometers in a 0.0764-m internal diameter pipe. This is generally considered as a medium-sized pipe, and is larger than many other such studies in the literature [38][39][40][41] where pipes of 0.054-m internal diameter or less have been used. Furthermore, reported studies using gamma radiation techniques in pipes are relatively scarce, and available studies have made use of smaller pipes [42][43][44] . This study, therefore, presents new intermediate diameter and gamma densitometer data for the two-phase flow community for numerical model validation and facility design.

Test facility description
The experimental test facility used for this study, shown schematically in Fig. 1 , is located at the Cranfield University's Oil and Gas Engineering Centre. The test facility is built from a tough transparent acrylic plastic (Perspex) 3-inch pipe of about 17 m in length as depicted by a simplified diagram shown in Fig. 1 . It consists of a vertical and horizontal pipe section with an observation section placed 150 pipe diameters upstream of the last injection point to ensure full development of flow in the horizontal section. The vertical section has two observation points located 10 0 pipe diameters from the base in both upwards and downwards pipeline. The following constitute its subsections i.e. the test fluid/material (air, water, oil, and slurry) section at injection point, unit operations equipment section, and the instrumentation and data acquisition section.
The air supply is obtained from a compressor with a maximum supply capacity of 400 m 3 /hr and a discharge pressure of 7 bar. For safety and accuracy, air supply from the compressor is made to pass through a dryer and a filter to ensure the presence of moisture and particles are minimised. The flow rates are measured by two flow meters: 0.5-inch vortex flow A 2-inch steel pipe is used to inject air into the mainline via about 150 pipe diameters upstream from the observation sections. Water, sourced from a water tap located in the laboratory and stored in a storage tank of 2 m 3 , is pumped into the mainline with aid of a variable speed industrial version progressive cavity pump (PCP) with 01MR2515 model number manufactured by PCM pumps limited, the UK with a maximum speed capacity of 25 m 3 /hr. The flow rate of the oil at the inlet is metered by a Coriolis flowmeter (Endress + Hauser, Promass 83F80 DN80). This flow meter with a measurement accuracy of 0.1%-0.5% has three outputs: mass flow rate, density, and viscosity.

Experimental procedure
The procedure followed for the experimental tests starts with a visual inspection of the test facility to ensure that the facility and unit operation are in good working condition. The standard operating procedures for the facility are then followed. LabVIEW software was used for flow monitoring, entering set points, and data acquisition. The video recording cameras were set up with appropriate lighting and positioned at the observation section. A Sony HDR-CX 550 camera, wide-angle, full HD 1080 was used for the video acquisition with its lens zoomed in (or out) at the interval for each test run which lasts for 30 s.
The air compressor was first powered, and the valves set appropriately based on desired liquid and gas flow rates (in m 3 /s), which were later converted to superficial velocities by dividing by the pipe cross-sectional area. The water pump suction valve and power pump are usually opened half an hour before the commencement of tests to give room for adequate circulation to achieve uniform desired viscosity with adjustment of the speed control to the desired flow rate upon start-up of the test run. Video recording and LabVIEW data acquisition were triggered to start simultaneously. Upon completion of video recording and data acquisition, the facility was shut down by safely closing the data acquisition system, oil pump, and air suction valves. The experimental test matrix used for this investigation is as follows: superficial water velocity ranges ( V sw ) from 0.1-0.4 m/s and for each point, the superficial gas velocities ( V sg ) used are between 0.3 and 10 m/s.

Gamma densitometers
Two single-beam gamma densitometers manufactured by Neftemer Limited, Russia, were used for the measurement of phase fractions. The key components of each gamma densitometer are highlighted in Fig. 2 above. They comprise a single energy source emitting gamma rays at 662 keV high energy level (hard spectrum) and the soft spectrum (i.e. lower en-

Results and discussion
Many industrial processes (i.e. nuclear industry, refrigeration, chemical systems, and air conditioning) involve the interaction of two or more phases. The interaction of these phases results in complex mixtures and flow patterns thereby making its knowledge of great interest to facilitate better and more energy-efficient designs. Air-water tests were investigated in the 3-inch horizontal facility to benchmark the results against the existing standard and generally accepted flow pattern maps and to examine the facility's reliability as well as showcase the use of a dual gamma densitometer system in a medium diameter pipe system.

Flow pattern characterization
Visual inspections and video recordings were obtained for each flow condition during experiments. The following flow patterns were observed; stratified, stratified wavy, plug, and slug flow. The individual description of the flow patterns is presented below.
Stratified flow : This flow pattern, as illustrated (in Table 1 ), occurs as the dominant flow pattern at low liquid superficial velocity at V sw = 0.1 m/s irrespective of the operating superficial gas velocity. It is characterized by complete separation of the two phases such that the less dense phase (gas) occupies the top of the pipe cross-sectional area while the denser phase (liquid) occupies the bottom owing to gravity effects with an undisturbed horizontal interface. This is not surprising since, as can be seen from the pictorial representation, the liquid height is not high enough to aid the transition to another flow regime.
Stratified wavy flow : Increasing the superficial gas velocity, provided the liquid height is less than half full will result in the interface becoming disturbed with surface ripples or small amplitudes illustrated in Table 1 . The wave pattern has been reported to have little or no effect on the pressure fluctuations [45] .
Plug flow : At a much higher liquid level and lowest gas superficial velocity, this flow regime characterized by liquid plugs with no noticeable gas entrainment and separated by elongated gas bubbles whose diameters are smaller than that of the pipe diameters are observed. Here, the elongated gas bubble is such that the phase flow in strata has the bulk of the gas at the upper periphery of the pipe while the liquid film occupies the lower periphery owing to gravity effects. Its mechanism of formation is a result of gradual build-up of the liquid level to more than half of the pipe diameter.
Slug flow : With a continuous increase in the gas velocity, a point is reached when the elongated bubble becomes similar in size as the pipe diameter moving at higher momentum with a shorter liquid body compared to plug flow. Gas entrainment is a characteristic feature of the elongated liquid body in slug flow. In comparison, however, there exists no such entrainment in plug flow. Annular flow : Further increasing the gas superficial velocity, a point is reached when the liquid holdup in the pipe becomes inadequate to form a liquid body capable of bridging the top of the pipe. This brings about the leftover liquid to be swept to the top section of the pipe forming an annulus liquid around the inner periphery of the pipe; thicker at the bottom owing to gravity effects with the gas phase flowing at the core of the pipe. This flow pattern is generally termed annular flow. Table 1 gives a pictorial description of the observed flow patterns.
The flow patterns observed are compared with established flow pattern maps [ 2 , 46 ] as presented in Fig. 3 . The choice of Beggs and Brill [46] was based on the fact that the flow pattern map was constructed over a wide range of flow condition with relatively better correlations and generally accepted in the industry while Mandhane et al . [2] flow pattern map was chosen because it has wide acceptability and simplicity. The test results agreed excellently with the Beggs and Brill [46] in the intermittent flow region than the Mandhane et al .'s [2] flow pattern map with some slight differences in the separated region which can be attributed to diameter differences yet confirming previous findings [47] which showed an increase in pipe diameter moves the transition line from separated to intermittent region towards higher liquid flow rates.

Flow pattern identification using gamma densitometer signals
Flow regime identification using the acquired gamma densitometer signals was made with signals sampled at a frequency of 250 Hz. Probability mass functions (PMF) were constructed from the time series gamma signals. The PMF structure in Fig. 4 (a) shows a bi-modal distribution with two peaks. The two-peak structure is a qualitative confirmation of visually observed intermittent flow patterns (plug and slug). The peak with the highest photon count rate is indicative of a passing film region while the smaller peak with a lower count rate is indicative of a passing slug liquid body through the detector. On the other hand, the unimodal distribution as illustrated by Fig. 4 (b) is indicative of annular flow.

Liquid holdup
Liquid holdup plays a very vital role in the oil and gas industry as its accurate prediction is crucial to the effective prediction of many two-phase flow calculations and in most cases serves as the starting point for these predictive models.
where I M = average gamma count obtained from the liquid-gas mixture in the pipe, I A = average calibration gamma data obtained for empty pipe (i.e.100% Air), I L = average calibration gamma data obtained for pipe containing pure liquid and H L = Liquid holdup. The result of the liquid holdup as presented in Fig. 5 shows the time-averaged liquid holdup measurement obtained for 30 sec exhibits a general decreasing trend for liquid holdup value as the gas superficial velocity increases. An increase in the gas superficial velocity brings about more of the gas phase occupying the total cross-sectional area of the pipe analogous to the reduction of the liquid holdup in the cross-section area of the pipe. Error bars shown on the plots were obtained as a result of conducting a set of triplicate tests to ascertain repeatability and quantify the level of uncertainty. It was found that repeated tests deviated at an average of ±8% from each other and this informed the magnitude of error bars placed on the liquid holdup measurements.

Slug translational velocity
Slug translational velocity is one of the closure parameters often utilized as an input parameter for most slug flow models. Here, it was experimentally estimated by dividing the distance between the two gamma densitometers by the time lag obtained from the cross-correlation of the signal output from the gamma densitometer. Analysis of the holdup time series result obtained from two gamma densitometers located at 103D and 124D downstream of the water injection point were utilized for translational velocity data collection as depicted in Fig. 6 . For this investigation, noisy signals associated with such phenomena were minimized by using signal filters in MATLAB (i.e. the "smooth" function).
From Fig. 6 , the distance between the two gamma densitometers is given as l Gamma and the arrival times of the slug front at first and second densitometer are denoted by T 1 and T 2 respectively. However, for fast-sampled data with large signal lengths, manual peak to peak time lag identification is not practical and an algorithm was written using MATLAB's signal processing toolbox to do this. Cross-correlation is a standard method for measuring the degree of matching between two signals to determine the time difference that exists between them. This was implemented on the two-gamma densitometer signal time series as presented. The cross-correlation function for two-time series a ( t ) and b( τ − t ) is given as where τ is the temporal lag. For two discrete signals, a ( t n ) b( τ − t n ) , where n = 1, 2, 3, …, N , sampled at an equal time interval, the cross-correlation coefficient is given as a summation rather than an integral:  This can be plotted as a distribution of time intervals τ n , such that the most probable time interval is that with the distinct highest peak of the cross-correlation coefficient C ab . Thus, the slug translational velocity is calculated using this most probable time interval as follows: where l Gamma is the distance between the two gamma densitometers. Presented in Fig. 7 (a) is measured slug translational velocity plotted as a function of mixture velocity, and this indicates a linear tendency such that slug translational velocity increases as mixture velocity increases for all the flow conditions investigated. The observed trend is consistent with previous findings [48][49][50][51] .

Evaluation of slug translational velocity and models
Measured slug translational velocity in this study was compared with prediction models in the literature [52][53][54][55][56] . The performance evaluation as presented in Fig. 7 (b) and Table 2 shows that Nicklin et al. [52] and Nicholson et al . [56] give better agreement with the present data as compared to others. Models for slug translational velocity and their model parameters have been comprehensively compiled and given in the study by Baba et al . [57] . This can be attributed to the fact that they both accounted for drift velocity which has been shown [ 56 , 58 ] to exist in horizontal cases and can even exceed the vertical case value.

Slug body length
This closure parameter is another primary variable in slug flow modelling. It was estimated by multiplying the obtained translational velocity by the time lag for the flow conditions investigated. The result shows the measured slug body length is in the region of 24-36D with a mean length of 30.6D and agrees with the work of Pan [50] . He observed an approximate length of 20-40D and a mean length of 30D for air-water and 24D for 4cP oil-air experiment in a 0.075 m ID pipe as presented in Fig. 8 showing measured slug length plotted as a function of mixture velocity. Other experimental observations [ 56 , 60-62 ] for air-water in both upward vertical and horizontal flow systems suggest that the average stable liquid slug length is relatively insensitive to the gas and liquid flow rates.  However, they noted the lengths are dependent mainly on the pipe diameter. They also concluded that the mean slug lengths are in the range of 15-40D. We found our slug lengths to be lognormally distributed, agreeing with the findings of Nydal et al. [63] . The authors carried out statistical distributions of slug characteristics in the air-water two-phase flow horizontal system for which they concluded that the cumulative probability density function of measured slug length rightskewed and fits a log-normal distribution.
Gamma readings were acquired at an average measurement time of 70 seconds for each experimental run. It is estimated that the entire sources of error in slug length measurement result in a maximum of ±5% uncertainty by the gamma densitometers. These errors include systematic errors in the Sodium Iodide (NaI) scintillation radiation by the densitometer detector and errors that arise from time-varying fluctuations of the two-phase flow in the measurement cross-section. The measured slug body length was compared with available slug body length prediction models in the literature. A comprehensive summary of slug length correlations and their model parameters has been comprehensively compiled and reported by Baba et al. [64] . Those whose performances were evaluated [65][66][67][68] are as shown in Table 3 . The prediction models of Norris [65] and Brill et al . [66] are closer and performed better when compared to Gordon and Fairhurst [67] ; Scott et al . [68] and this is not surprising since Norris [65] is a modified version of Brill et al . [66] by the exclusion of the mixture velocity term which was found to be negligible. Gordon & Fairhurst [67] and Scott et al . [68] exhibited very high discrepancy which can be attributed to the fact that both correlations were regressed from very large large-diameter oil and gas transportation pipelines where there is the possibility of long terrain-induced slugs.

Conclusion
An experimental air-water two-phase flow study has been conducted using a gamma radiation technique with two densitometers that measure slug flow characteristics. Liquid holdup and slug translational velocity measurements were carried out on a 0.074-m ID horizontal test facility. Flow patterns for the experiments conducted were identified using a combination of visual observation and statistical analysis of hard gamma counts of the various flow conditions. The flow patterns observed were stratified, stratified-wavy, plug, slug, and annular flows. A comparison of observed flow patterns with established flow pattern maps shows a good agreement for the dominating flow pattern (plug and slug flow pattern). Also, measurement of slug translational velocity and slug body length were carried out. Measured slug translational velocity plotted as a function of mixture velocity shows an increase in the translational velocity with increasing mixture velocity conforming to the findings of earlier researchers using smaller diameter pipes. Also measured was the slug body length which was found to be 24-36D with a mean length of 30.6D. The obtained result agrees with various postulations in the literature. Conclusively, this study generally demonstrates the reliability of the test facility and instrumentation used.