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Article

Optimization of X-ray Tube Voltage to Improve the Precision of Two Phase Flow Meters Used in Petroleum Industry

by
Abdullah K. Alanazi
1,
Seyed Mehdi Alizadeh
2,
Karina Shamilyevna Nurgalieva
3,
John William Grimaldo Guerrero
4,*,
Hala M. Abo-Dief
1,
Ehsan Eftekhari-Zadeh
5,*,
Ehsan Nazemi
6 and
Igor M. Narozhnyy
7
1
Department of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
2
Petroleum Engineering Department, Australian College of Kuwait, West Mishref 13015, Kuwait
3
Department of Development and Operation of Oil and Gas Fields, Saint-Petersburg Mining University, 199106 Saint-Petersburg, Russia
4
Department of Energy, Universidad de la Costa, Barranquilla 080001, Colombia
5
Institute of Optics and Quantum Electronics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, 07743 Jena, Germany
6
Imec-Vision Laboratory, Department of Physics, University of Antwerp, 2610 Antwerp, Belgium
7
Department of Commercialization of Intellectual Activity Resultse Center for Technology Transfer, Mining Oil and Gas Department, RUDN University, 117198 Moscow, Russia
*
Authors to whom correspondence should be addressed.
Sustainability 2021, 13(24), 13622; https://doi.org/10.3390/su132413622
Submission received: 18 November 2021 / Revised: 2 December 2021 / Accepted: 6 December 2021 / Published: 9 December 2021
(This article belongs to the Special Issue Computational Intelligence for Sustainable Development)
Browse Figures
Versions Notes

Abstract

:
To the best knowledge of the authors, in all the former studies, a fixed value of X-ray tube voltage has been used for investigating gas–liquid two-phase flow characteristics, while the energy of emitted X-ray radiations that depends on the tube voltage can significantly affect the measurement precision of the system. The purpose of present study is to find the optimum tube voltage to increase the accuracy and efficiency of an intelligent X-ray radiation-based two-phase flow meter. The detection system consists of an industrial X-ray tube and one detector located on either side of a steel pipe. Tube voltages in the range of 125–300 kV with a step of 25 kV were investigated. For each tube voltage, different gas volume percentages (GVPs) in the range of 10–90% with a step of 5% were modeled. A feature extraction method was performed on the output signals of the detector in every case, and the obtained matrixes were applied to the designed radial basis function neural networks (RBFNNs). The desired output of the networks was GVP. The precision of the networks in every voltage and every number of neurons in the hidden layer were obtained. The results showed that 225 kV tube voltage is the optimum voltage for this purpose. The obtained mean absolute error (MAE) for this case is less than 0.05, which demonstrates the very high precision of the metering system with an optimum X-ray tube voltage.

1. Introduction

Two-phase flow is receiving increasing attention from researchers in different study fields. The GVP and flow regime are the most important parameters utilized to measure gas–liquid two-phase flow characteristics. There are a few sustainable nondestructive techniques such as electrical capacitance [1], electromagnetic [2], ultrasonic [3], and gamma [4]/X-ray [5]/neutron [6] radiation attenuation to determine the mentioned parameters in two-phase flows.
In the last few decades, numerous researchers have conducted different investigations on measuring characteristics of two-phase flows using X-ray radiation. In 1969, G.F. Hewitt and D.N. Roberts used an X-ray tube with voltage of 100 kV and conventional X-ray radiography film to investigate flow patterns in a vertical upwards flow of air–water mixtures [7]. In 1975, O. Jone and N. Zuber used a Phillips Norelco X-ray system with tube voltage of 50 kV to investigate various flow patterns of slug, bubbly, and annular in an air–water two-phase flow inside a rectangular channel [8]. In 1999, G.D. Harvel et al. developed a high-speed X-ray CT system for measuring the GVP distribution for bubbly and slug flow patterns inside a vertical pipe [9]. Their system consisted of an X-ray tube with a tube voltage of 70 kV located in front of an array of CdWO4 scintillator detectors. In 2010, F. Fischer and U. Hampel proposed a fast response system with frame rates of 1000 images per second for determining gas–water two-phase flows [10]. Their system included an X-ray tube and 240 CZT detectors positioned in a circular array. In 2018, Song and Liu established a compact X-ray system including an X-ray tube with tube voltage of 50 kV and an array of detector for determining GVF and liquid phase’s velocity in a slug and bubbly two-phase flow [11]. In 2020, M. Roshani et al. proposed an intelligent approach using an X-ray tube with a tube voltage of 150 kV and an artificial neural network (ANN) to predict GVF in stratified and annular flow regimes of a gas–liquid two-phase flow [12]. They also used the same system in another separate study in order to determine type of flow regime in a two-phase flow [13]. In recent years, a large number of studies have been also performed on X-ray imaging of two-phase flows. S.A. Mäkiharju et al. proposed a two-dimensional X-ray system with an imaging rate of 1 kHz to determine the void fraction distribution in gas–liquid two-phase flows [14]. Their results showed that the proposed system has a good precision for void fractions above 5%. A. Tekawade et al. developed an in situ 3D synchrotron X-ray visualization system to image the two-phase flow inside a diesel injection nozzle [15]. Heindel presented a review of the current status of X-ray multiphase flow visualization methods [16].
As described in the literature review, in all the previous studies, a fixed value of tube voltage was used for investigating gas–liquid two-phase flows, while energy of emitted X-ray radiations that depend on the tube voltage can affect measurement precision of the system. In other words, once energy of X-ray radiations are less than an optimum value, they cannot penetrate well through the pipe and flow, which consequently causes reduction in measurement precision of the system. On the other hand, once the energy of X-ray radiations is higher than an optimum value, the contrast between the gas and liquid phase is decreased, which again leads to the system’s measurement precision reduction. The purpose of the present study is finding an optimum tube voltage in order to increase the measurement precision and efficiency of the X-ray radiation based two-phase flow meters. Details of the proposed system and optimization procedure are described in the following sections.

2. Materials and Method

2.1. Detection System

The investigations in the present study were performed using Monte Carlo N-Particle code (MCNPX). MCNPX code can be implemented as a powerful tool for simulating and transporting various radiations such as electrons, photons, and neutrons, etc. [17]. In has been widely used for modeling various radiation-based instruments [18,19,20,21,22,23,24]. As depicted in in Figure 1, the main components of the modeled detection system are one common commercial X-ray source and one sodium iodide detector. An electron source was defined inside the vacuum chamber of tube as the electron filament. A tungsten slab with an orientation of 20° was located inside the tube and in front of the electron source. The energy of emitted electrons from the source was changed from 125 to 300 keV with a step of 25 keV to investigate the optimum tube voltage for X-ray radiation-based two-phase flow meters. The reason of choosing 125 keV for the lower energy limit is that the generated X-rays with energies lower than this limit cannot penetrate well through the steel pipe and therefore would not be useful to be investigated in this study. It must be noted that, in all the simulations, the maximum allowed number of particles (NPS) in the MCNPX code, 2.1 billion, was used for the photon source. Using the mentioned NPS, for tube voltages in the range of 125 kV or more, a statistical error of less than 1% was achieved, which means that the obtained results are trustable [17]. For tube voltage of 100 kV or less, the obtained statistical error was about 40% or more, which means that there was too much attenuation for X-ray radiations (in other words, there was not enough penetration) and consequently enough photons did not reach the detector.
Additionally, the reason for choosing 300 keV as the upper limit is that the maximum voltage of the commercial industrial X-ray tubes does not go higher than 300 kV. It is worth mentioning that the energy of emitted electrons from the filament is almost the same as the X-ray tube voltage. In fact, the emitted electrons from the filament are accelerated inside the vacuum chamber under a high electrical potential difference and then smashed into the tungsten target. Approximately one percent of the electron’s energy is radiated as X-rays and comes out from the tube’s window. The rest of energy is converted to heat through the target.
The generated X-ray radiations form a spectrum energy with a maximum value equal to the tube voltage. The energy spectra of generated X-rays in this study for tube voltages of 125, 150, 175, 200, 225, 250, 275, and 300 kV are shown in Figure 2. For the sake of a better comparison, every energy spectrum was normalized to its sum of intensity. L-shell (with energy of 8.5 keV) and K-shell (2 peaks with energies of 59.5 and 67.5 keV) X-ray characteristic peaks of tungsten are clearly seen in Figure 2 for all the tube voltages. It can be also seen that, by increasing the tube voltage, the intensity ratio of two K-shell peaks to the L-shell peak is increased.
A steel pipe with an inner diameter of 3 inches, which is a typical size in the petroleum industry, was considered in the simulations. The thickness of mentioned pipe is 0.5 cm. A liquid–gas two-phase flow with annular pattern was also modeled inside the pipe. Air and gasoil with densities of 1.25 and 826 kg/m3 were used as the gas and liquid phases, respectively. The following mathematical equation was used for modeling various gas volume percentages inside the pipe:
GVP   ( % ) = π r g 2 π r p 2 × 100 = r g 2 r p 2 × 100
where rp, rg, and GVP are inner radius of the steel pipe, radius of the gas phase in core of the pipe, and GVP is the gas volume percentage, respectively. rp is a fixed parameter in all the simulations. For every specified GVP, the gas phase’s radius was calculated using Equation (1). For each tube voltage, different GVPs in the range of 10–90% with a step of 5% were modeled (17 totally, 136 simulations).

2.2. X-ray Tube Voltage Optimization Procedure

In order to optimize the voltage of the X-ray tube, several voltages were considered and simulated using MCNP-X code. Voltages 125, 150, 175, 200, 225, 250, 275, and 300 were considered the X-ray tube voltage and, in every voltage, several simulations in different volume fractions were performed. In fact, in every voltage, the gas volume fraction varied from 10 to 90 by steps of five. These volumes were considered as the GVPs of a typical annular two-phase flow. In every case (every voltage and every GVP), the output spectrum of NaI (Tl) detector was obtained and, accordingly, all of the required data were generated. In order to achieve the efficiency of the presented system in different voltages, the radial basis function neural network (RBFNN), which uses matrix inverse, was selected. RBFNN is a useful type of ANN. RBF can be used to approximate functions [25]. Equations (2)–(4) show the algorithm of a typical RBFNN [25].
output = ∑ ( weight × input ) +   bias
y m = e ( − ∥ x − v m ∥ 2 2 σ m 2 )
z j = ∑ m = 1 M u m j y m + b j
where x is the feature vector, v is the center position, σ is the spread, z j is the output prediction from the jth node of the output layer, u m j is weights, and b j is bias. It is worth mentioning that, in the past few decades, various advanced computational approaches, e.g., finite element, numerical linear algebra, statistics, numerical analysis, tensor analysis, and artificial intelligence, have been applied in various fields of study such as chemical engineering [26,27,28,29], electrical and computer engineering [30,31,32,33,34,35,36,37], civil engineering [38,39,40], mechanical engineering [41,42,43,44,45,46,47,48,49,50,51,52,53,54,55], petroleum engineering [56,57,58,59,60,61,62,63,64,65,66,67,68,69], environmental engineering [70,71], biomedical engineering [72,73,74,75,76], mathematics [77,78,79,80,81,82,83], etc.
The output signal (detector output spectrum) in each case was divided into several features. In fact, the continuous spectrum was transformed to discrete inputs for the training of the neural network. In this regard, each 1 keV was considered as one feature so the output spectrum in tube voltage of 125 and 275 kV was converted to 125 and 275 features, respectively. These features are extracted from the output signals and applied to the RBFNN for measuring the GVP.
For instance, the output signals related to 10% GVP and 125 kV of tube voltage with the energy of 0 to 125 keV were divided into 125 equal sections, and these sections were applied to RBFNN. This feature extraction method and applying procedure for a typical sample (10% GVP and 125 kV tube voltage) is shown in Figure 3.
RBFNN with different number of neurons in the hidden layer was used to measure the GVP of the considered annular two-phase flow. This kind of network can recognize the properties of complex and nonlinear systems such as multi-phase flows. For solving this problem, MATLAB software (version 8.1.0.604, MathWorks: Natick, MA, USA) was used to train the networks. A total of 70% were used for training, and the rest of them were used for testing. In fact, 96 samples were used for training the networks. For designing the architectures, the mean squared error goal and spread of radial basis functions were considered 0 and 1, respectively. Additionally, every X-ray tube voltage was tested in every possible neuron number in the hidden layer. In the coding, the “newrb” command was used. This command adds neurons to the hidden layer of the network until it meets the specified mean squared error goal.

3. Results and Discussion

As an example, recorded X-ray energy spectra in the detector for tube voltage of 150 kV and gas volume percentages in the range of 10–90% are depicted in Figure 4. This figure indicates that almost all the X-ray radiations with energy lower than 70 keV were fully absorbed inside the pipe. This figure also shows a regular incremental manner in the intensity of X-ray spectra once the gas volume percentage is increased.
Comparison of recorded spectra in the detector once the gas volume percentage is kept fixed at a value of 80% and the tube voltage is increased from 125 to 300 kV are shown in Figure 5. As it is observed, although the intensity of X-ray spectra are increased by increasing the tube voltage, the intensity difference between two successive tube voltages is reduced.
The mean absolute error (MAE) and mean relative error percentage (MRE %) were used to compare different X-ray tube voltages efficiency and find the optimized condition. These errors are calculated as follows:
M A E = 1 N ∑ i = 1 N | X i ( R e a l ) − X i ( M e a s u r i n g ) |
M R E % = 100 × 1 N ∑ i = 1 N | X i ( R e a l ) − X i ( M e a s u r i n g ) X i ( R e a l ) |
where N is the number of data and ‘X (Real)’ and ‘X (Measuring)’ apply for simulated data and measured data, respectively. The measured data has been obtained by ray-tracing and applying it to the presented neural networks and is considered a measured output. This value should be near the desired output, which has been considered as the real output. Therefore, the low difference between these two parameters shows the precision of the presented method. The results of obtaining GVP in an annular two-phase flow for different X-ray tube voltages and different number of neurons in hidden layer of considered RBFNN were tabulated in Table 1. In this table, MAE and MRE of both train and test sets were shown. It is clear that, by increasing the number of neurons in the hidden layer in each voltage, the MAE train and MRE train will be decreased. In the cases with very low train errors and considerable test errors, the measuring system has been encountered with an overfitting problem. In fact, a structure with minimum MAE test and MRE test and also lower MAE train and MRE train is the best structure, and its voltage is the optimum point.
Two contour graphs for showing both test errors for each case are shown in Figure 6. Additionally, a 3D plot that shows the precision (=100 − MAE) of each case is illustrated in Figure 7.
As it can be found from Table 1 and Figure 6 and Figure 7, the optimum tube voltage is 225 kV. The top three cases were achieved in this voltage. The best case is 225 kV of X-ray tube voltage and 10 neurons in the hidden layer.
The obtained results for GVP measuring in optimum condition (225 kV and 10 neurons) using RBFNN, and the comparisons with the real data are shown for training and testing sets in Figure 8 and Figure 9. Comparing the real data as the target and the measured data as the output, in a regression diagram that shows the relationship between targets and outputs, obtained RMSE errors for every case, and a histogram of obtained errors that shows the distribution of errors have been demonstrated in Figure 8a, Figure 9a and Figure 8b, Figure 9b and Figure 8c, Figure 9c and Figure 8d, Figure 9d, respectively. These graphs show the very high precision of the metering system in the optimum condition.
Usage of the X-Ray tube with a switch off/on as radiation source in flow meters has many advantages. It is safer than other systems and also can save money. To the best knowledge of the authors, there is no study in order to optimize the X-ray tube voltage in flow metering for improving the precision and efficiency. As can be seen in the Results section, a tube voltage of 225 kV is the optimum voltage for the X-ray tube and, in this condition, the precision of the metering system is more than higher and lower voltages.

4. Conclusions

In this paper, the voltage of the X-ray tube was optimized in order to increase the precision and efficiency of the X-ray radiation-based flow meters. This optimization study was performed in an annular two-phase flow. All the essential data in different tube voltages was obtained using MCNP-X code. Using MATLAB 8.1.0.604 software, a feature extraction method was performed on the output signals of the detector in every case, and the obtained matrixes were applied to the designed RBFNNs. The desired output of the networks was GVP. The precision of the networks in every voltage and every number of neurons in the hidden layer were obtained. The results show that 225 kV tube voltage is the optimum voltage for this purpose. The obtained MAE error for this case is less than 0.05, which shows the very high precision of the metering system with an optimum X-ray tube voltage.

Author Contributions

Conceptualization, S.M.A. and I.M.N.; methodology, A.K.A., K.S.N.; software, A.K.A.; investigation, K.S.N.; data curation, E.N.; writing—original draft preparation, S.M.A., J.W.G.G., E.E.-Z.; writing—review and editing, H.M.A.-D.; visualization, J.W.G.G.; supervision, E.N.; funding acquisition, I.M.N., A.K.A., E.E.-Z., K.S.N., H.M.A.-D. All authors have read and agreed to the published version of the manuscript.

Funding

We acknowledge support by the German Research Foundation and the Open Access Publication Fund of the Thueringer Universitaets- und Landesbibliothek Jena Projekt-Nr. 433052568. This work was supported by the Taif University Researchers Supporting Project grant number (TURSP-2020/266), of Taif University, Taif, Saudi Arabi. This paper has been supported by the RUDN University Strategic Academic Leadership Program. The research was performed at the expense of the subsidy for the state assignment in the field of scientific activity for 2021 No FSRW-2020-0014.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Main components of the modeled detection system.
Figure 1. Main components of the modeled detection system.
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Figure 2. The energy spectra of generated X-ray radiations in this study for tube voltages of 125, 150, 175, 200, 225, 250, 275, and 300 kV.
Figure 2. The energy spectra of generated X-ray radiations in this study for tube voltages of 125, 150, 175, 200, 225, 250, 275, and 300 kV.
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Figure 3. Applying the 125 extracted features to the RBFNN.
Figure 3. Applying the 125 extracted features to the RBFNN.
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Figure 4. Recorded X-ray energy spectra in the detector for tube voltage of 150 kV and gas volume percentages in the range of 10–90%.
Figure 4. Recorded X-ray energy spectra in the detector for tube voltage of 150 kV and gas volume percentages in the range of 10–90%.
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Figure 5. Recorded spectra in the detector once the gas volume percentage is kept fixed at a value of 80%, and the tube voltage is increased from 125 to 300 kV.
Figure 5. Recorded spectra in the detector once the gas volume percentage is kept fixed at a value of 80%, and the tube voltage is increased from 125 to 300 kV.
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Figure 6. (a) ‘MAE test’ and (b) ‘MRE test’ contour graph for all of the structures.
Figure 6. (a) ‘MAE test’ and (b) ‘MRE test’ contour graph for all of the structures.
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Figure 7. Precision of metering system in every X-ray tube voltage and number of neurons in the hidden layer.
Figure 7. Precision of metering system in every X-ray tube voltage and number of neurons in the hidden layer.
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Figure 8. Regression diagram and comparison of real and measured data for train data in the optimum voltage: (a) comparison of real and measured data, (b) regression diagram, (c) obtained RMSE error, and (d) histogram of obtained error.
Figure 8. Regression diagram and comparison of real and measured data for train data in the optimum voltage: (a) comparison of real and measured data, (b) regression diagram, (c) obtained RMSE error, and (d) histogram of obtained error.
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Figure 9. Regression diagram and comparison of real and measured data for test data in the optimum voltage: (a) comparison of real and measured data, (b) regression diagram, (c) obtained RMSE error, and (d) histogram of obtained error.
Figure 9. Regression diagram and comparison of real and measured data for test data in the optimum voltage: (a) comparison of real and measured data, (b) regression diagram, (c) obtained RMSE error, and (d) histogram of obtained error.
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Table
Table 1. The achieved results of obtaining GVP in an annular two-phase flow for different X-ray tube voltages and different number of neurons in the hidden layer of RBFNN.
Table 1. The achieved results of obtaining GVP in an annular two-phase flow for different X-ray tube voltages and different number of neurons in the hidden layer of RBFNN.
Tube Voltage 1 Neuron2 Neurons3 Neurons4 Neurons5 Neurons6 Neurons7 Neurons8 Neurons9 Neurons10 Neurons
125MAE train5.1060.210.1140.1050.1020.1020.0840.040.0360.03
MRE train (%)15.5620.8150.470.4430.4240.4240.2450.1120.0980.087
MAE test3.8520.1480.0960.1320.1440.1450.1110.0880.0870.074
MRE test (%)8.0220.3980.1510.2390.2750.2790.2910.280.2720.228
150MAE train5.2230.1460.1430.0850.0680.0450.0320.0140.0070.002
MRE train (%)15.9770.6570.6240.440.3380.1420.0690.0360.0210.006
MAE test3.9580.1070.0930.1080.2030.1130.090.1180.1810.156
MRE test (%)8.2120.3410.2660.2720.4590.2530.2210.2830.4470.381
175MAE train5.3160.1630.1580.1570.0750.0690.0490.0270.020.002
MRE train (%)16.3020.7080.6510.6590.2260.2190.1760.0690.0530.005
MAE test4.0060.1130.1150.1040.0790.0880.1290.1030.2130.166
MRE test (%)8.3130.3310.3680.3430.2230.2590.350.2910.5710.44
200MAE train5.4030.1790.1070.0620.0440.0250.0170.010.010.004
MRE train (%)16.5850.7290.3860.3060.1330.070.0530.0330.0330.009
MAE test4.0750.1110.1480.160.0950.0940.1030.1020.1050.074
MRE test (%)8.4260.3420.3790.430.240.220.2370.2430.2490.174
225MAE train5.4580.1650.1560.1380.040.0410.0340.0190.0050.002
MRE train (%)16.7690.7330.6720.6390.160.1530.1180.0570.0110.006
MAE test4.1130.1210.1070.1160.0990.0780.0540.130.0530.05
MRE test (%)8.4980.3590.3050.330.2320.2040.1540.2860.1490.14
250MAE train5.520.1540.1420.0520.0530.0350.0260.0150.0060.006
MRE train (%)16.950.6840.6250.150.1520.1210.10.0480.0140.015
MAE test4.160.1150.0970.0620.0610.0720.0810.0820.0810.083
MRE test (%)8.540.3590.3350.1780.1740.1920.2190.2190.2030.206
275MAE train5.590.1630.1220.0710.0590.0350.0250.0230.0170.009
MRE train (%)17.1580.6910.4870.2480.1850.0820.0640.0590.0440.016
MAE test4.1940.140.1330.0810.0690.0750.1150.1050.0910.101
MRE test (%)8.6080.4130.3930.2110.160.1580.2870.2540.190.229
300MAE train5.6370.180.1510.1140.0940.070.0390.0210.0090.007
MRE train (%)17.3470.7550.590.5170.3130.1720.0970.0430.030.0262
MAE test4.2240.1590.150.150.080.150.0660.0760.0640.107
MRE test (%)8.660.4620.4070.420.210.3170.1390.1590.1330.224
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Alanazi, A.K.; Alizadeh, S.M.; Nurgalieva, K.S.; Grimaldo Guerrero, J.W.; Abo-Dief, H.M.; Eftekhari-Zadeh, E.; Nazemi, E.; Narozhnyy, I.M. Optimization of X-ray Tube Voltage to Improve the Precision of Two Phase Flow Meters Used in Petroleum Industry. Sustainability 2021, 13, 13622. https://doi.org/10.3390/su132413622

AMA Style

Alanazi AK, Alizadeh SM, Nurgalieva KS, Grimaldo Guerrero JW, Abo-Dief HM, Eftekhari-Zadeh E, Nazemi E, Narozhnyy IM. Optimization of X-ray Tube Voltage to Improve the Precision of Two Phase Flow Meters Used in Petroleum Industry. Sustainability. 2021; 13(24):13622. https://doi.org/10.3390/su132413622

Chicago/Turabian Style

Alanazi, Abdullah K., Seyed Mehdi Alizadeh, Karina Shamilyevna Nurgalieva, John William Grimaldo Guerrero, Hala M. Abo-Dief, Ehsan Eftekhari-Zadeh, Ehsan Nazemi, and Igor M. Narozhnyy. 2021. "Optimization of X-ray Tube Voltage to Improve the Precision of Two Phase Flow Meters Used in Petroleum Industry" Sustainability 13, no. 24: 13622. https://doi.org/10.3390/su132413622

APA Style

Alanazi, A. K., Alizadeh, S. M., Nurgalieva, K. S., Grimaldo Guerrero, J. W., Abo-Dief, H. M., Eftekhari-Zadeh, E., Nazemi, E., & Narozhnyy, I. M. (2021). Optimization of X-ray Tube Voltage to Improve the Precision of Two Phase Flow Meters Used in Petroleum Industry. Sustainability, 13(24), 13622. https://doi.org/10.3390/su132413622

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