An analysis and interpretation of the signals in gamma-absorption measurements of liquid–gas intermittent flow
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Abstract
The intermittent flow (slug and plug type) of liquid–gas mixtures in a horizontal pipeline measured by the specific radiometric apparatus is presented. The measurement system consists of two sources of Am-241 gamma radiation and two scintillation probes. An analysis of the signals measured by the radiometric equipment is performed in the domain of time and of frequency. Recognised signal parameters are directly referred to physical quantities associated with a liquid–gas flow. The employed methodology enables determination of gas-phase flow velocity and estimation of the average depth and length of bubble gas structures. In the paper, the processing and interpretation results of the selected experiment are presented to show the in-depth description of gas structures and the type of flows recognition.
Keywords
Liquid–gas flow Slug flow Plug flow Flow structures Gamma absorption Signals analysisIntroduction
Multiphase flows, including two-phase liquid–gas and liquid–solid particle flows, are very common in industrial processes, for example in the production of crude oil, which is accompanied by natural gas extraction, in the petrochemical industry in the processing of crude oil.
Two-phase liquid–gas mixtures, depending on the angle of inclination and the diameter of the pipeline, the velocity of the transport or the relationship between the content of both phases may produce various flow structures. Therefore, it is difficult to describe and to measure such a flow. This necessitates the development of measurement technology on the basis of parameters such as flow velocity or the coefficients of the contribution of the particular phases. The recognition of the type of flow (Roshani et al. 2017b; Hanus et al. 2018) and the imaging of a multiphase flow (Mosorov 2008) also becomes crucial. The information which is provided owing to experiments enables progress as far as better mathematical modelling of such flows is concerned (Jaszczur and Portela 2008; Gulhane and Mahulikar 2009).
The advanced measurement technologies of multiphase flows include tomographic methods: electrical ones (capacitance, resistance, impedance), which use the absorption of X-rays and gamma rays, nuclear magnetic resonance (NMR) and optical ones (e.g. PIV—particle image velocimetry) (Mosorov 2006a; Powell 2008; Falcone et al. 2009; Rząsa 2009; Rahim et al. 2012; Xue et al. 2012; Tamburini et al. 2013; Banasiak et al. 2014; de Oliveira et al. 2015; Kanizawa and Ribatski 2016; Ameran et al. 2017; Vlasak et al. 2017). Tomographic methods are also used to establish crucial petrophysical parameters of rocks, such as porosity and permeability (Krakowska and Puskarczyk 2015; Jarzyna et al. 2016; Kundu et al. 2017). Although the technology of tomographic measurements is a familiar phenomenon, research in the development of such methods continues because the measurement systems usually constitute complex multi-sensor systems. As far as environment protection and hydrogeology is concerned, radiotracer methods are applied (Witczak et al. 2009; García et al. 2017; Biswal et al. 2018). The development of the aforementioned measurement methods is also facilitated by the progress in the analysis of signals which uses advanced mathematical methods. The latter are widely used, for example, in geotechnics, environment protection and geophysics (Buttkus 2000; Pietsch et al. 2007; Gołębiowski et al. 2016; Kozłowska et al. 2016; Szabó and Dobróka 2017).
Considering the fact that a significant part of the liquid–gas flows is transported in pipelines whose diameter is less than 100 mm (e.g. during the extraction of oil and natural gas in oil rigs), the problem of hydrotransport frequently may be reduced from a description in three or two dimensions to a description in one dimension. Due to this, complex systems intended for tomography may be replaced with simpler and frequently less expensive systems. That is why this article presents the application of a system which consists of two probes with NaI(Tl) scintillating crystals and two sealed sources of gamma-ray Am-241. The electrical signals which are obtained at the output of the measurement systems were subject to an analysis in the domain of time and of frequency. The properties of signals which were distinguished were related by author to physical quantities in the two-phase liquid–gas flow, such as the length and the depth of gas structures.
The measurement system
The idea of using the absorption of gamma rays in the measurements of two-phase flows was discussed in a more comprehensive way in the following articles: Chaouki et al. (1997), Johansen and Jackson (2004), Heindela et al. (2008), Kumara et al. (2010), Vlasak et al. (2014), Roshani et al. (2017a). The measurement systems which were applied are used above all to establish the contribution of the particular phases and to identify a flow structure. Therefore, the gamma-ray detectors which were used were a part of spectrometric tracks (Knoll 2000).
The research station is located in the AGH University of Science and Technology in Kraków.
Using the described measurement system, a number of experiments were carried out aimed at the development of the gamma-ray absorption method to determine the transport time delay and velocity of the dispersed phase, and recognition of flow types. The results of the experiments and the research station were detailed in the following works: Zych et al. (2014, 2015, 2016, 2018), Hanus (2015), Hanus et al. (2018).
Basic characteristics of analysed flows: υ_{L}—average velocity of water, Re—Reynolds number, Fr—Froude number, α—average void fraction of gas phase, q_{G}—air expense
Run | υ_{L} (m/s) | α (–) | Re (–) | Fr^{2} (–) | q_{G} (l/min) | Type of flow |
---|---|---|---|---|---|---|
LIW0005 | 1.66 | 0.434 | 1.9 × 10^{4} | 1.01 | 18 | Slug |
LIW0003 | 2.16 | 0.312 | 2.7 × 10^{4} | 1.14 | ||
LIW0004 | 2.92 | 0.266 | 3.7 × 10^{4} | 5.89 | Plug | |
LIW0002 | 3.28 | 0.240 | 4.3 × 10^{4} | 7.43 |
Average values of the velocity of gas phase υ_{G} and the values of the measurement uncertainty u_{c} (υ_{G}) for the flow of gas in the measurements which were analysed
Run | υ_{G} (m/s) | u_{c} (υ_{G}) (m/s) |
---|---|---|
LIW0005 | 1.325 | 0.053 |
LIW0003 | 1.792 | 0.055 |
LIW0004 | 2.059 | 0.054 |
LIW0002 | 2.304 | 0.062 |
Characteristics of analysed structures of a liquid–gas flow
The present article analyses two types of intermittent flows which are produced at various velocities of water and the contribution of water and air in the mixture (Salgado et al. 2010; Zhao et al. 2013; de Oliveira et al. 2015; Kanizawa and Ribatski 2016; Roshani et al. 2017a).
The basic quantities which describe the analysed flows are presented in Table 1.
- Reynolds number for water phase:$$Re = \frac{{\upsilon_{\text{L }} \cdot D_{\text{ch}} \cdot \rho }}{\eta }$$(1)
- Characteristic dimension for liquid phase:$$D_{\text{ch}} = r\sqrt {1 {-} \alpha }$$(3)
Methodology of signal analysis
Determining the average velocity of gas phase
The determination/evaluation of the velocity of the flow of the gas phase is crucial for a further analysis and interpretation of the measurements which are presented. It is also one of the basic parameters which characterise the two-phase liquid–gas-type flow.
Table 2 presents the average velocities of the flow of gas υ_{G} along with the uncertainties of the measurement u_{c}(υ_{G}) which were calculated for the analysed measurements.
Determining the depth of gas structures
The radiometric measurement system which is presented in the “The measurement system” section may also be utilised in a classical way to determine the density of the mixture or the void fraction α for the gas phase (Arvoh et al. 2012; Zhao et al. 2013; Roshani and Nazemi 2017). This requires prior experimental calibration of the apparatus due to which one obtains a relationship which links the number of the combined calculations I of gamma quanta registered by the scintillation probe with α. A detailed description of the process of calibration and the utilisation of the relationship which was obtained is presented in the following article: Zych et al. (2016).
Based on Eq. 9, one may evaluate the average depth of the bubbles (Zych et al. 2018).
Average values of the depths of gas structures, standard deviations and uncertainties for 50 fragments of the measurements which were analysed
Run | \(\bar{g}_{\text{l}}\) (mm) | σ_{l} (mm) | \(u_{\text{c}} \left( {\bar{g}_{\text{l}} } \right)\) (mm) | \(\bar{g}_{\text{b}}\) (mm) | σ_{b} (mm) | \(u_{\text{c}} \left( {\bar{g}_{\text{b}} } \right)\) (mm) | \(\bar{g}_{\text{sb}}\) (mm) | σ_{sb} (mm) | \(u_{\text{c}} \left( {\bar{g}_{\text{sb}} } \right)\) (mm) |
---|---|---|---|---|---|---|---|---|---|
LIW0005 | 16.0 | 0.4 | 0.1 | 25.4 | 0.5 | 0.1 | 5.4 | 1.0 | 0.1 |
LIW0003 | 12.5 | 0.6 | 0.1 | 19.1 | 1.8 | 0.3 | 4.7 | 0.8 | 0.1 |
LIW0004 | 11.7 | 2.9 | 0.4 | 17.2 | 3.2 | 0.5 | 4.4 | 2.3 | 0.3 |
LIW0002 | 10.8 | 1.8 | 0.3 | 15.8 | 2.4 | 0.3 | 4.1 | 2.1 | 0.3 |
An analysis of the graphs presented in Fig. 8 and the values of standard deviation, presented in Table 3, indicate that the flows of the slug type are characterised by a lesser extent of diversity of the average depths of gas structures (Fig. 8a, b) than the flows of the plug type (Fig. 8c, b).
- (a)the ratio of average depth of the large gas structure \(\bar{g}_{\text{l}}\) to the average depth of a large bubble \(\bar{g}_{\text{b}}\), which may be represented by the following relationship:$$\xi_{\text{l}} = \frac{{\bar{g}_{\text{l}} }}{{\bar{g}_{\text{b}} }}$$(12)
- (b)the ratio of the average depth of small gas structures \(\bar{g}_{\text{sb}}\) located between large bubbles, to the average depth of large bubbles \(\bar{g}_{\text{b}}\):$$\xi_{\text{s}} = \frac{{\bar{g}_{\text{sb}} }}{{\bar{g}_{\text{b}} }}$$(13)
Average value of the depth g_{G} of the gas phase for the particular measurements which are analysed and the values ξ_{l} and ξ_{s}, calculated on the basis of the average values in along with the uncertainties of the measurement
Run | g_{G} (mm) | u_{c} (g_{G}) (mm) | ξ_{l} (–) | u_{C} (ξ_{l}) (–) | ξ_{s} (–) | u_{C} (ξ_{s}) (–) |
---|---|---|---|---|---|---|
LIW0005 | 15.8 | 0.6 | 0.63 | 0.01 | 0.25 | 0.02 |
LIW0003 | 12.3 | 0.5 | 0.65 | 0.02 | 0.29 | 0.02 |
LIW0004 | 11.1 | 0.4 | 0.68 | 0.06 | 0.30 | 0.04 |
LIW0002 | 10.4 | 0.4 | 0.68 | 0.04 | 0.31 | 0.04 |
Determining the length of the gas structure
The length of the structures in a two-phase liquid–gas flow may be described in two basic domains: time and frequency (Zych et al. 2014). Even though both types of flow, i.e. slug and plug, are similar to each other, one may also distinguish such features in the domain of time and in the domain of frequency that set them apart.
Slug flow
Values of the frequencies which dominate in a |CSDF| spectrum for the slug-type flow and the successive numbers of the harmonic r of the basic frequency f_{0}
LIW0005 | LIW0003 | ||
---|---|---|---|
f_{r} (Hz) | r (–) | f_{r} (Hz) | r (–) |
f_{0}= 0.36 | 1 | f_{0} = 0.53 | 1 |
0.73 | 2 | 1.06 | 2 |
1.09 | 3 | 1.57 | 3 |
1.47 | 4 | 2.12 | 4 |
1.83 | 5 | 2.65 | 5 |
2.20 | 6 | 3.16 | 6 |
2.57 | 7 | 3.71 | 7 |
2.91 | 8 | 4.20 | 8 |
3.27 | 9 | 4.75 | 9 |
3.65 | 10 | 5.29 | 10 |
4.01 | 11 | 5.79 | 11 |
The linking of dominant frequencies with a flow is possible only by performing a supplementary analysis of the signal in the domain of time, i.e. by establishing the duration of a large gas structure t_{l} (Fig. 7). It is also crucial to determine the duration of a large bubble t_{b}. By taking into consideration the average velocity of the movement of the gas phase, one may calculate their lengths.
Average values of the lengths of the structures \(\overline{l}_{\text{l}}\) and \(\overline{l}_{\text{b}}\)along with the standard deviations σ_{l}, σ_{b} and the uncertainties \(u_{\text{c}} \left( {\overline{l}_{\text{l}} } \right)\), \(u_{\text{c}} \left( {\overline{l}_{\text{b}} } \right)\) for flows of the slug type
Run | \(\overline{l}_{\text{l}}\) (m) | σ_{l} (m) | \(u_{\text{c}} \left( {\overline{l}_{\text{l}} } \right)\) (m) | \(\overline{l}_{\text{b}}\) (m) | σ_{b} (m) | \(u_{\text{c}} \left( {\overline{l}_{\text{b}} } \right)\) (m) |
---|---|---|---|---|---|---|
LIW0005 | 3.59 | 0.08 | 0.14 | 1.73 | 0.11 | 0.07 |
LIW0003 | 3.38 | 0.24 | 0.11 | 1.68 | 0.26 | 0.06 |
The values of the lengths of the structures obtained on the basis of an analysis of the signal in the domain of time are congruous with the supplementary photographical documentation. On this basis, one estimated the length of a large structure, which was about 3.6 m for the LIW0005 measurement, whereas the length of the bubble was about 1.8 m. For the LIW0003 measurement, the length of a large structure was about 3.4 m, and the length of a large bubble was about 1.7 m.
Values of the average durations of gas structures \(\overline{t}_{\text{l}}\), \(\overline{t}_{\text{b}}\) and the corresponding frequencies \(\overline{f}_{\text{l}}\) and \(\overline{f}_{\text{b}}\)
LIW0005 | LIW0003 | ||||||
---|---|---|---|---|---|---|---|
\(\overline{t}_{\text{l}}\) (ms) | \(\overline{f}_{\text{l}}\) (Hz) | \(\overline{t}_{\text{b}}\) (ms) | \(\overline{f}_{\text{b}}\) (Hz) | \(\overline{t}_{\text{l}}\) (ms) | \(\overline{f}_{\text{l}}\) (Hz) | \(\overline{t}_{\text{b}}\) (ms) | \(\overline{f}_{\text{b}}\) (Hz) |
2712 | 0.37 | 1305 | 0.77 | 1885 | 0.53 | 940 | 1.06 |
A physical analysis of the successive frequencies which are multiples of f_{0} is more difficult due to the fact that their footprint in the radioisotope signal is weaker. By analysing the photographical documentation and by comparing it with the signals which were analysed, one may state that it is necessary to associate even frequencies of higher orders with the movement of smaller gas structures, located in the space between large bubbles.
Eventually, it followed from the |CSDF| analysis that the average length of gas structures for the LIW0005 measurement is \(\overline{l}_{\text{l}}\) = (3.64 ± 0.15) m, whereas for the LIW0003 it is \(\overline{l}_{\text{l}}\) = (3.37 ± 0.11) m. The average length of large bubbles for the LIW0005 measurement is \(\overline{l}_{\text{b}}\) = (1.81 ± 0.07) m, and for the LIW0003 measurement, it is \(\overline{l}_{\text{b}}\) = (1.69 ± 0.05) m. By comparing these results with the values indicated in Table 6, one may observe that there is a considerable congruity of the values obtained due to an analysis of the signal in the domain of time and frequency.
Plug flow
The flow of the plug type, despite many similarities to the flow of the slug type, also manifests features which are peculiar only to itself in reference to the signal which was registered, both in the domain of time and in the domain of frequency.
The flow of this type features a basic (large) structure which consists of a large gas bubble (whose duration is t_{l}), and whose length is considerably smaller than in the case of the slug flows (images in Fig. 3c, d), as well as the area in which smaller bubbles are located. Moreover, on the basis of an analysis of the signal, one may distinguish one more greater structure—the so-called superstructure (duration t_{ss}), which consists of a few or of up to a dozen or so basic structures.
Average values of the lengths of structures \(\overline{l}_{\text{l}}\) and \(\overline{l}_{\text{b}}\) along with the standard deviations σ_{l}, σ_{b} and the uncertainties \(u_{\text{c}} \left( {\overline{l}_{\text{l}} } \right)\), \(u_{\text{c}} \left( {\overline{l}_{\text{b}} } \right)\) for the flows of the plug type
Run | \(\overline{l}_{\text{l}}\) (m) | σ_{l} (m) | \(u_{\text{c}} \left( {\overline{l}_{\text{l}} } \right)\) (m) | \(\overline{l}_{\text{b}}\) (m) | σ_{b} (m) | \(u_{\text{c}} \left( {\overline{l}_{\text{b}} } \right)\) (m) |
---|---|---|---|---|---|---|
LIW0004 | 0.398 | 0.134 | 0.021 | 0.198 | 0.063 | 0.010 |
LIW0002 | 0.406 | 0.167 | 0.026 | 0.202 | 0.067 | 0.011 |
Average lengths of the superstructures \(\overline{l}_{\text{ss}}\) with the standard deviation σ_{ss} and the uncertainty of the measurement \(u_{\text{c}} \left( {\overline{l}_{\text{ss}} } \right)\), for the measurement of the plug type
Run | \(\overline{l}_{\text{ss}}\) (m) | σ_{ss} (m) | \(u_{\text{c}} \left( {\overline{l}_{\text{ss}} } \right)\) (m) |
---|---|---|---|
LIW0004 | 3.44 | 1.75 | 0.09 |
LIW0002 | 3.34 | 1.67 | 0.09 |
Values of the dominant frequencies f_{0} and f_{u} in the |CSDF| spectrum for the flow of the plug type
Run | f_{0} (Hz) | f_{u} (Hz) |
---|---|---|
LIW0004 | 0.60 | 5.18 |
LIW0002 | 0.67 | 5.70 |
Average values of the durations of superstructures \(\overline{t}_{\text{ss}}\) and gas structures \(\overline{t}_{\text{l}}\), \(\overline{t}_{\text{b}}\) and the corresponding frequencies \(\bar{f}_{\text{ss}}\), \(\bar{f}_{\text{l}}\) and \(\bar{f}_{\text{b}}\)
LIW0004 | LIW0002 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
\(\overline{t}_{\text{ss}}\) (ms) | \(\bar{f}_{\text{ss}}\) (Hz) | \(\overline{t}_{\text{l}}\) (ms) | \(\bar{f}_{\text{l}}\) (Hz) | \(\overline{t}_{\text{b}}\) (ms) | \(\bar{f}_{\text{b}}\) (Hz) | \(\overline{t}_{\text{ss}}\) (ms) | \(\bar{f}_{\text{ss}}\) (Hz) | \(\overline{t}_{\text{l}}\) (ms) | \(\bar{f}_{\text{l}}\) (Hz) | \(\overline{t}_{\text{b}}\) (ms) | \(\bar{f}_{\text{b}}\) (Hz) |
1670 | 0.60 | 193 | 5.17 | 96 | 10.38 | 1452 | 0.69 | 176 | 5.67 | 88 | 11.38 |
On the basis of the analyses which were performed, one may claim that the length of a superstructure calculated on the basis of the formula (Eq. 28) for the measurement LIW0004 is: \(\overline{l}_{\text{ss}}\) = (3.43 ± 0.09) m, whereas for the measurement LIW0002: \(\overline{l}_{\text{ss}}\) = (3.41 ± 0.09) m. The considerations which were conducted also indicate that the frequency f_{0} is responsible for the modulations of the amplitude of the signal in the domain of time.
Conclusion
The article presents an analysis of the signals from the radiometric measurement system for the absorption of gamma rays which consists of a set of two scintillation probes and from two sealed sources of Am-241. The analyses were performed in the time and frequency domain for intermittent flows of the slug and plug types. One distinguished the parameters of signals which were associated with physical quantities of the mixture which flowed. The amplitudes of the signals were associated with the depth of gas structures, whereas the dominant frequencies were associated with the lengths of these structures. One additionally introduced non-dimensional quantities for the description of the liquid–gas flow such as the average coefficient of the duty cycle ζ_{t}, the relationship of the average depth of the large gas structure to the average depth of a large bubble ξ_{l}, and the relationship of the average depth of small gas structures located between large bubbles to the average depth of large bubbles ξ_{s}. The obtained values of these parameters are similar for the analysed measurements.
Apart from the similarities, one also established the existence of differences of parameters of signals which occur in the time and frequency domain for the types of flows which were described.
In a flow of the slug type, there occur basic structures which consist of a large bubble and of a number of smaller structures which are situated in the space between large bubbles. The values of the amplitudes of signals from probes are at a constant level, which results in a decreased standard deviation of the estimated average depths of gas in the fragments of the gas which were analysed. In a frequency spectrum |CSDF|, there occur harmonic dominants which are even and odd multiples of the frequency f_{0}. After the results of the analysis were compared, one stated that the frequency f_{0} is associated with the movement of a large gas structure. The knowledge of the average speed of the movement of gas enables the estimation of the average length of such structures. The frequency which is the double multiple of f_{0} is associated with the average length of large bubbles in a large gas structure.
However, in the flow of the plug type, one may distinguish in the duration considerably greater superstructures, apart from large gas structures, which are similar to the ones in the flow of the slug type. In a frequency spectrum |CSDF|, this manifests itself by two salient ranges: the range of the dominant frequency f_{0}, associated with the flow and the average size of superstructures, and the range of the frequency of the useful signal. The harmonic dominant for this range f_{u} is associated with the flow and the average size of large gas structures. Hence, one may draw a conclusion that the frequency f_{0} is directly associated with the modulation of the signal, i.e. periodical change of an amplitude. As a result, the standard deviation of the changes of the depths of gas structures is greater for flows of the plug type than in the case of the flows of the slug type.
On the basis of the measurements and analyses which were performed, one may develop models of signals for the liquid–gas flows in question, studied by means of the method of the absorption of gamma rays. The results which are obtained may be used in the more efficient identification of two-phase liquid–gas flows in the installations intended for hydrotransport of gas, in which there is no optical access to the mixture which flows through.
Notes
Acknowledgements
The author would like to specially thank Prof. Robert Hanus, Prof. Marek Jaszczur, Dr Paweł Jodłowski, Prof. Volodymyr Mosorov, Dr Leszek Petryka, Prof. Dariusz Świsulski for their cooperation during the measurements and support in the writing of the manuscript.
Funding
This publication was financed by the AGH University of Science and Technology, Faculty of Geology Geophysics and Environmental Protection (Grant No 11.11.140.645).
Compliance with ethical standards
Conflict of interest
The author declares that there is no conflict of interest regarding the publication of this paper.
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