- Email: [email protected]
A radiation-based hydrocarbon two-phase flow meter for estimating of phase fraction independent of liquid phase density in stratified regime
Flow Measurement and Instrumentation 46 (2015) 25–32
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
A radiation-based hydrocarbon two-phase flow meter for estimating of phase fraction independent of liquid phase density in stratified regime E. Nazemi a, S.A.H. Feghhi b, G.H. Roshani a,n, S. Setayeshi c, R. Gholipour Peyvandi d a
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran Radiation Application Department, Shahid Beheshti University, G.C., Iran c Department of Energy Engineering and Physics, Amirkabir University of Technology, Iran d Nuclear Science and Technology Research Institute, Tehran, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 15 April 2015 Received in revised form 19 August 2015 Accepted 14 September 2015 Available online 16 September 2015
The fluid properties strongly affect the performance of radiation-based multiphase flow meter. By changing the fluid properties (especially density), recalibration is necessary. In this study, a method was presented to eliminate the dependency of multiphase flow meter on liquid phase density in stratified two phase horizontal flows. At the first step the position of the scattering detector was optimized in order to achieve highest sensitivity. Several experiments in optimized position were done. Counts under the full energy peak of transmission detector and total counts of scattering detector were applied to the Radial Basis Function neural network and the void fraction percentage was considered as the neural network output. Using this method, the void fraction was predicted independent of the liquid phase density change in stratified regime of gas–liquid two-phase flows with mean relative error percentage less than 1.2%. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Radial Basis Function Radiation-based MPFM Detector Void fraction Prediction
1. Introduction The radiation-based multiphase flow meter (MPFM) is relatively new technology in Oil industry. MPFMs are used to measure the phase fractions of oil, gas and water in the flow from an oil well. The conventional methods used to measure the phase fraction in the flow for each well at wide intervals that could span over several months. The radiation-based MPFMs provide such information instantly, easing monitoring problems and enabling quick access to data, which allows rapid decisions to be made on well performance. The wealth of data accumulated by radiation-based MPFM can be fed into reservoir simulation codes to enhance their accuracy and reliability [1]. In recent years, many researchers and engineers have implemented gamma ray attenuation in order to measure volume fraction and identify the flow regime in multiphase flows. Tjugum et al. used a multibeam gamma-ray densitometry to identify flow regimes in hydrocarbon multiphase oil, water and gas pipe flows [2]. They demonstrated that a fan beam geometry with one radiation source and several collimated detectors is sufficient to provide information on the liquid–gas distribution of the pipe flow. Using 241Am source with the activity of 500 mCi and 9 CdZnTe semiconductor detectors, they identified several flow n
Corresponding author. E-mail address: [email protected] (G.H. Roshani).
http://dx.doi.org/10.1016/j.flowmeasinst.2015.09.002 0955-5986/& 2015 Elsevier Ltd. All rights reserved.
regimes in gas–liquid flows in a pipe with a diameter of 2 in. Jing et al. investigated the dual modality densitometry method using artificial neural networks (ANNs) in order to determinate the gas and water volume fraction in a three-phase flow [3]. Jing and Bai, also studied the flow regime identification in two phase flow in vertical pipe using Radial Basis Function (RBF) neural networks based on dual modality densitometry [4]. In 2014, Roshani et al. used a dual energy source consists of 241Am (59.5 KeV) and 137Cs (662 KeV) with just one transmission NaI detector to predict volume fraction in oil–water–gas three-phase flows [5]. By using ANN, they predicted the volume fraction of oil, water and gas phases with Mean Absolute error (MAE%) of less than 1%. Roshani et al. also proposed a method based on dual modality densitometry using ANN to first identify the flow regime and then predict the void fraction in gas–liquid two-phase flows [6]. They used the total count in the scattering detector, the full energy peak and photon counts of Compton edge in transmission detector as the three inputs of the ANN. By applying this method, they correctly distinguished all the three regimes of stratified, homogenous and annular and estimated the void fraction of each phase in the range of 5–95% with error of less than 1.1%. Also it has been shown that artificial neural networks could be as a useful tool for predicting, classification and optimization for industrial nuclear gauges especially in cases that lots of parameters could influence the operation of the system [7–14]. Calibration of radiation-based multiphase flow meter (MPFM)
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
depends strongly on the fluid properties [15]. By changing the fluid properties such as density, recalibration is required. Performance of radiation-based MPFMs will be improved by eliminating any dependency on the fluid properties. In all previous studies, the void fraction has been measured with a constant density liquid phase and little attention has been paid to the changes of the density of the liquid phase. Since attenuation of gamma-ray depends on both amount and density of the matter, fluctuations of the density of the liquid phase can cause significant errors in determination of the void fraction. For example, fluctuations of temperature and pressure which occur typically in pipe-lines of Oil industry, could cause changes of the liquid density and consequently measuring the void faction would deal with significant errors. In this work, an approach is proposed based on dual modality densitometry using ANN to solve the problem of measuring the void fraction in stratified regime of hydrocarbon gas–liquid twophase flows in situations that the liquid phase density is changeable. At the first step, sensitivity response of the scattering detector relative to the density changes of liquid phase in different positions around the pipe, was investigated by using Monte Carlo N Particle (MCNP) code. As much as the sensitivity is more, the ANN could predict the void fraction independent of density changes of the liquid phase with less error and consequently the measuring precision of the system would be improved. After obtaining the most sensitive position relative to density changes for the detectors by simulation, an experimental setup according to the simulated geometry was designed in order to provide the experimental required data for ANN. By applying this methodology, the void fraction was predicted independent of the liquid phase density in stratified regime of gas–liquid two-phase flows with root mean square error of less than 1.4.
2. Proposed methodology
transmission detector was kept fixed in the angle of 0° and position of 1-in. NaI scattering detector was changed from 15° to 135° respect to center of the pipe with steps of 15°. The void fractions in the range of 10–70% for stratified regime of gas–liquid two-phase flows were simulated. Distance between both the detectors and pipe was chosen 5 cm. The 137Cs source was placed 10 cm far from the pipe. Also the source was collimated in order to make a narrow beam passing through the center of the pipe. Air with density of 0.001 g/cm3 was used as the gas phase in the pipe. For making a wide range of density for liquid phase in laboratory (from 0.735 g/cm3 to 0.980 g/cm3), gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 (g/cm3), respectively, have been used as the liquid phases. Same as the experiments, in simulations these liquid phases were used, too. Since the predominant interaction mechanism for high energy photons in low atomic number materials is Compton scattering and the photoelectric interaction could be negligible, therefore, the interaction probability depends just on the density of the liquid phase regardless of its composition. Also, because the effective atomic numbers of used liquids are close to each other, it could be assumed that all of the 5 liquid phases regardless of their compositions, are considered as one liquid phase with various densities. Registered counts in both transmission and scattering detectors were calculated per one source particle in the MCNP-X code using Pulse Height Tally F8. A special tally card with the Gaussian Energy Broadening (GEB) option is also included in the model in order to take into account the Gaussian energy broadening and obtain a better and more realistic simulation of the whole spectrum in detectors. The technique consists of using a “FT8 GEB” card in the input file of MCNP code and calculating the full width at half maximum (FWHM) of the full energy peak of gamma ray with different energies in the laboratory. The tallied energy is broadened by sampling from the Gaussian function shown in Eq. (1) [16]:
2.1. Monte Carlo simulation
f (E ) = As the first step in this study, a Monte Carlo simulation model is used to obtain the best positions for the detectors in dual modality densitometry configuration. The Monte Carlo model used in this work is based on the Monte Carlo N-Particle (MCNP) code, version X, which is used for neutron, photon, electron, or coupled neutron/ photon/electron transport. In this work, a dual modality densitometry setup based on the existing devices in our laboratory has been simulated. As shown in Fig. 1, the position of 1-in. NaI
⎛ ( E − E0 ) ⎞2 ⎟⎟ −⎜⎜ Ce ⎝ A ⎠
Where, E is the broadened energy, E0 is the un-broadened energy of the tally, C is the normalization constant and also A is related to the FWHM by Eq. (2):
A=
FWHM 2 ln (2)
(2)
The desired FWHM which is specified by the user-provided
T=Transmission Detector S=Scattering Detector
pipe Shield of Source
(1)
Collimator 15
T
26
30 45 135
120 105 90 75
60
s
Fig. 1. A top view of positioning of the scattering detector in different angles used in simulated geometry in order to obtain the most sensitive position relative to density changes.
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
27
140000 120000
Count
100000 80000 60000 40000 20000 0 0
200
400
600
800
Channel
40000
Count
30000
20000
10000
0 0
200
400
600
800
Channel
16000 14000
Count
12000 10000 8000 6000 4000 2000 0 0
200
400
600
800
Channel Fig. 2. Calculation of FWHM of energy peak using experimental spectrum and Gaussian fitting function for radioactive sources of: (a)
constants (a, b, and c), has a nonlinear response relative to energy according to Eq. (3):
FWHM = a + b E + cE2
(3)
241
Am (b)
137
Cs (c)
60
Co.
Where, E is the incident gamma-ray energy. The units of “a”, “b” and “c” parameters are MeV, MeV1/2, and MeV 1, respectively. To calculate “a”, “b” and “c” parameters, one 1-in. NaI detector and 3 gamma emitter radioactive sources of 241Am (energy 60 KeV), 137 Cs (energy 662 KeV) and 60Co (energies 1173 and 1333 KeV)
28
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
0.07
FWHM (MeV)
0.06 0.05 0.04 0.03 0.02 0.01 Fig. 7. Experimental setup.
0.00 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Energy (MeV) Fig. 3. Calculation of GEB card parameters using obtained FWHM for different energies and a non-linear fitting function.
to Density Changes (percent)
Sensitivity of Scattering Detector Relate
22
241 Am, 137Cs and 60Co sources are shown in Fig. 2. The obtained FWHM from experimental spectrum is in terms of number of channels. For converting it in terms of energy (MeV) we used Eq. (4):
FWHM (MeV) =
20 18 16 14 12 10 8 6 4 2 10
20
30
40
50
60
70
Void Fraction (percent)
Fig. 4. Sensitivity of the scattering detector relative to the density changes of the liquid phase from 0.735 g/cm3 to 0.980 g/cm3 versus different void fractions.
FWHM (channel) × Energy of peak (MeV) Channel‵s number of peak (channel)
After obtaining the experimental FWHM for each energy peak, as shown in Fig. 3, FWHM (MeV) curve as a function of energy (MeV) was plotted and a non-linear fitting function (Eq. (3)) was applied to calculate the values of the “a”, “b” and “c”. Parameters of “a”, “b” and “c” were calculated 0.0109, 0.0696 and 0.0226, respectively. These parameters were used with the GEB command in the input file of MCNP code in order to take account the energy resolution of the 1-in. NaI detector in the simulations. At each position of the scattering detector, sensitivity response of this detector relative to density changes of the liquid phase from the lowest density (0.735 g/cm3 ) to the highest density (0.980 g/cm3) of liquid phase for void fractions in the range of 10– 70% was calculated according Eq. (5):
⎛ Registered count for density of 0.98 (g/cm3) ⎜ ⎜ −Registered count for density of 0.735 (g/cm3) Sensitivity = ⎜ 3 ⎜ Registered count for density of 0.98 (g/cm ) ⎜ ⎝ × 100
Fig. 5. Defined parameters in stratified regime.
including four gamma energies in the range from 60 KeV to 1333 KeV, were used. At first, FWHM of each peak of energy was determined in terms of channel. The experimental spectrums for
(4)
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (5)
Sensitivity of the scattering detector relative to the density changes of the liquid phase for different void fractions was shown in Fig. 4. As it is shown in Fig. 4, by increasing alignment angle of the scattering detector, the sensitivity increases regularly in angles from 0° to 75°, but suddenly in angle 90°, the sensitivity increases largely and becomes almost as same as the sensitivity of angle 120° and again after angle 90°, the sensitivity increases regularly. As it is obvious in Fig. 4, in angle 135° the scattering detector has the most sensitivity relative to density changes of liquid phase. Thus, angle 135° was chosen as the best position for locating of the scattering detector.
Fig. 6. Cross sectional view of the made void fractions for stratified regime in the range of 10–70%.
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
29
320000
Registered Count in the Transmission Detector (#)
310000
0.735 (g/cm3) 0.795(g/cm3)
300000
0.826(g/cm3)
290000
0.852(g/cm3)
280000
0.980(g/cm3)
270000 260000 250000 240000 230000 220000 210000 200000 190000 10
20
30
40
50
60
70
Void Fraction (percent)
Registered Count in the Scattering Detector (#)
200000
3 0.735 (g/cm )
0.795(g/cm3) 0.826(g/cm3) 180000
0.852(g/cm3) 0.980(g/cm3)
160000
140000
120000
100000
10
20
30
40
50
60
70
Void fraction (percent) Fig. 8. Registered counts versus void fraction in different densities: (a) transmission detector (b) scattering detector.
2.2. Experimental Setup An experimental setup was designed based on the obtained best positions for the detectors by simulation in order to generate required data for training and testing the artificial neural network (ANN). All the experiments were carried out in static conditions. A pipe made of Pyrex-glass with radius of 4.75 cm and wall thickness of 0.25 cm was chosen as the main pipe. For modeling the stratified regime in static conditions, PVC (polyvinyl chloride) film with thicknesses of 0.40 mm was used as a separator between liquid and gas phases. Required calculation for making various void fractions from 10% to 70% in stratified regime was done according to Eq. (6) [17]:
αs = 1 −
⎛ ⎛ R − L0 ⎞⎞⎤ ⎛ R − L0 ⎞ 1 1⎡ ⎟⎟⎥ ⎟ − sin ⎜ 2arc cos ⎜ ⎢ arc cos ⎜ ⎝ R ⎠⎠⎦ ⎝ ⎠ ⎝ R 2 π⎣
(6)
Where L 0 is the level of the liquid in the pipe, R is the radius of the pipe, and αs is the void fraction in stratified regime. These parameters are shown in Fig. 5. Although the stratified regime occurs in horizontal pipes, but in this work we located the pipe vertically to change simply the samples in the pipe. Because our experiments were carried out in
static conditions, there is no difference between locating the pipe vertically or horizontally. A cross sectional view of the made void fractions for stratified regime in the laboratory was shown in Fig. 6. Gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 g/cm3,respectively, have been used as liquid phases and also air was used as the gas phase. The void fractions of 10%, 20%, 30%, 40%, 50%, 60% and 70%, were tested for each liquid phase (5 liquid phase with different densities 7 different void fraction ¼ totally 35 tests). A 137Cs source with activity of 2 mCi and a measurement time of 600 s were chosen for all the experiments. The source was collimated (a cubic collimator with 0.8 cm width, 8 cm height and 8 cm length) in order to make a narrow beam passing through the center of the pipe. One 1-in. NaI detector was located 25 cm far from the source (5 cm far from the pipe) as transmission detector. Another 1-in. NaI detector was located 5 cm far from the pipe and in angle of 135° respect to the center of the pipe as the scattering detector. The experimental setup is shown in Fig. 7. In transmission detector, counts under the full energy peak of 137 Cs were registered, while in the scattering detector total count was registered. With the described setup and measurement time of 600 s, the relative standard deviation of registered count in both
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
Experimental Data Simulated Data
1.00
80 R.D=0%
70
0.95 R.D=0.3% 0.90 R.D=0.2% 0.85
R.D=0.8% R.D=1%
0.80 R.D=2.3%
0.75 R.D=1.7% 0.70 10
20
30
40
50
60
70
Predicted Void Fraction (%)
Registered Count (Normalised to unit)
30
Void Fraction (percent)
60 50 40 30 20
R.D=0%
0
0.95
10
20
30
40
50
60
70
40 50 Void Fraction (%)
60
70
R.D=0.5%
0.90
Void Fraction (%) R.D=1%
0.85
R.D=1.6%
0.80 0.75
70 R.D=1.7%
0.70
60 R.D=2.4%
0.65 0.60
R.D=2.8% 0.55 10
20
30
40
50
60
70
Void Fraction (percent)
Fig. 9. Comparison of experimental and simulated data for liquid phase of gasoline with density of 0.735 g/cm3: (a) transmission detector (b) scattering detector.
Predicted Void Fraction (%)
Registered Count (Normalised to unit)
10 Experimental Data Simulated Data
1.00
50
40
30
20
10 10
20
30
Fig. 11. Regression diagrams of experimental and predicted results for (a) training data (b) testing data using presented RBF neural network.
Fig. 10. Radial Basis Function structure [22].
detectors is less than 0.004. Registered counts versus void fraction for both detectors was shown in Fig. 8. In the transmission detector, by increasing the void fraction for one liquid-phase with constant density, the number of counts would increase. Also in this detector, by increasing the density for a constant void fraction, the number of counts would decrease. The scattering detector demonstrates a vice versa response in comparison with the transmission detector. By increasing void fraction for one liquid-phase with constant density, the number of counts would decrease and also by increasing the density for a constant void fraction, the number of counts would increase. The simulated results for liquid phase of gasoline with density of 0.735 g/cm3 were benchmarked toward experimental data. This step was done in order to valid the simulator MCNP code. For the sake of simplicity in evaluation of the data, both simulated and experimental data were normalized to unit. As shown in Fig. 9, the
maximum relative difference between experimental and simulated data for transmission and scattering detectors, is 2.3% and 2.8%, respectively. Results show that simulated data are in good agreement with the experimental results. The most part of observed deviations could be somewhat related to making the stratified regime phantoms in the experiments. 2.3. Artificial neural network ANN is a strong tool in order to modeling, prediction, optimization and classification. Therefore it has many applications in nuclear engineering [12–15]. In this study, the void fraction percentage was predicted using Radial Basis Function (RBF) neural network. The RBF has a feed forward ANN structure which is consists of three layers: input layer, hidden layer and output layer [18,19]. This type of neural networks is one the most famous type of feed forward networks. The RBF neural network structure has been shown in Fig. 10. The first layer is made from source nodes and the second layer consists of a set basis function units that perform a nonlinear transformation from the input space to the hidden space [20,21]. The data set required for training the network was achieved,
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
Table 1 The data that were used for training the network and predicted void fraction percentages. Density (g/cm3) Counts in trans- Counts in mitted detector scattering detector
Void fraction (%)
Predicted void fraction (%)
0.735 0.795 0.852 0.98 0.795 0.826 0.852 0.735 0.795 0.826 0.98 0.735 0.826 0.852 0.735 0.795 0.852 0.98 0.795 0.826 0.852 0.735 0.795 0.826 0.98
10 10 10 10 20 20 20 30 30 30 30 40 40 40 50 50 50 50 60 60 60 70 70 70 70
9.709535 10.23984 9.934259 10.01297 19.58138 20.51575 19.82555 30.49037 30.84105 30.08618 29.88916 42.14215 40.44589 38.55896 48.33656 50.91241 47.71875 50.52808 60.01559 60.74899 61.58983 70.21274 69.92444 69.68112 69.05846
236,403 226,957 219,932 198,375 242,468 239,534 235,672 262,678 255,449 252,142 229,422 275,463 264,871 261,091 286,000 281,233 274,083 259,783 296,428 293,021 290,476 316,349 312,781 309,375 294,942
153,319 163,893 172,704 200,901 155,704 160,128 164,551 138,847 147,747 151,308 179,789 130,341 141,947 145,518 119,993 127,157 133,425 154,021 112,506 117,006 120,606 93,892 97,503 101,115 118,268
31
From Tables 1 and 2 and Fig. 11, clearly the predicted void fraction percentage by presented model is close to the experimental results. These results show the applicability of ANN as an accurate and reliable model for the prediction of void fraction percentage according to the counted gamma photons in transmission and scattering detectors. Two types of errors (mean relative error percentage (MRE%) and the root mean square error (RMSE)) were used in order to show the precision of the proposed neural network .The MRE% and the RMSE of the network are calculated by:
MRE% = 100 ×
1 N
N
∑ j=1
Xj (Exp) − Xj (Pred) Xj (Exp )
2
N
RMSE =
(7)
∑ j = 1 ( Xj (Exp) − Xj (Pred) ) N
(8)
where N is the number of data and ‘X (Exp)’ and ‘X (Pred)’ stand for experimental and predicted (ANN) values, respectively. Obtained MRE percentages for training and testing sets were 0.0795 and 1.1140, respectively. Obtained RMSE for training and testing sets were 1.2660 and 1.3589, respectively. These low errors show the accuracy and precision of the presented RBF neural network.
4. Conclusion Table 2 The data that were used for testing the network and predicted void fraction percentages. Density(g/cm3) Counts in transmitted detector
Counts in scattering detector
Void Fraction (%)
Predicted Void Fraction (%)
0.826 0.735 0.98 0.852 0.795 0.98 0.826 0.735 0.98 0.852
168,299 145,973 191,092 154,868 138,376 166,944 129,843 108,005 137,707 103,823
10 20 20 30 40 40 50 60 60 70
10.40418 22.47479 19.22676 28.14699 41.58127 39.85354 48.40015 59.33674 58.56083 69.25613
223,844 252,419 215,284 248,219 268,277 244,324 278,073 299,999 276,190 306,835
using described experiment. The number of samples for training and testing data were 25 (about 72%) and 10 (about 28%) respectively. For training the RBF model, a program was developed using MATLAB 8.1.0.604 software. The best structure of network (spread and number of neurons in hidden layer) was founded using an iterative loop in written program. In this iterative loop the spread and the number of neurons in hidden layer were changed step by step and finally, the best structure with minimum error was saved. In the best structure, the spread was 0.7 and the number of neurons in hidden layer was 10.
Attenuation of gamma-ray strongly depends on density of matter; therefore the density fluctuation of the liquid phase can cause significant errors in determination of the void fraction. In this study, a method was presented based on dual modality densitometry using RBF neural network for determining the void fraction independent of the density changes in stratified regime of two-phase flows. The presented RBF neural network has 2 inputs and 1 output. The inputs were counts of full energy peak of transmitted detector and total count of scattering detector and the output was the void fraction percentage. Trained network predicted void fraction percentage with root mean square error less than 1.4. These results show the applicability of RBF as an precise, accurate and reliable model for the prediction of void fraction according to the registered counts in two detectors independent of the liquid phase density change. The proposed methodology could be applied for measuring the volume fraction in situations where the density of liquid phase could be changed. For instance, in situations where the gas void fraction (GVF) is low and the water cut of liquid is high. In such situations, salinity changes of the water could lead to density changes of water and consequently would cause error in measuring the volume fraction. As another example, in situations where the temperature is variable and consequently the density of liquid phase would change, the proposed methodology could be as a good choice for measuring the volume fraction.
References 3. Results and discussion The relation between the experimental and predicted results using the presented RBF model for training and testing data in two regression diagrams, have been shown in Fig. 11. These diagrams show the high accuracy and precision of the presented model. The predicted void fraction percentages for training and testing samples were tabulated in Tables 1 and 2, respectively.
[1] F. Abu-Jarad, Application of radiation sources in the oil & gas industry and shortages in their services, in: Proceedings of the International Symposium on the Peaceful Applications of Nuclear Technology in the GCC Countries, Jeddah, 2008. [2] S.A. Tjugum, B.T. Hjertaker, G.A. Johansen, Multiphase flow regime identification by multibeam gamma-ray densitometry, Meas. Sci. Technol. 13 (2002) 1319–1326. [3] C.G. Jing, G.Z. Xing, B. Liu, Q.G. Bai, Determination of gas and water volume fraction in oil water gas pipe flow using neural networks based on dual
32
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
modality densitometry. in: Advances in Neural Networks, Lecture Notes in Computer Science, 3973, Springer–Verlag, New York, 2006, pp. 1248–1253. C.G. Jing, Q. Bai, Flow regime identification of gas/liquid two-phase flow in vertical pipe using RBF neural networks, in: Proceedings of the Chinese Control and Decision Conference (CCDC), 2009. G.H. Roshani, S.A.H. Feghhi, A. Mahmoudi-Aznaveh, E. Nazemi, A. AdinehVand, Precise volume fraction prediction in oil-water-gas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector, Measurement 51 (2014) 34–41. G.H. Roshani, E. Nazemi, S.A.H. Feghhi, S. Setayeshi, Flow regime identification and void fraction prediction in two-phase flows based on gamma ray attenuation, Measurement 65 (2015) 25–32. C.M. Salgado, L.E.B. Brandao, R. Schirru, C.M.N.A. Pereira, A. Xavier da Silva, R. Ramos, Prediction of volume fractions in three-phase flows using nuclear technique and artificial neural network, Appl. Radiat. Isot. 67 (2009) 1812–1818. C.M. Salgado, C.M.N.A. Pereira, R. Schirru, L.E.B. Brandao, Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks, Prog. Nucl. Energy 52 (2010) 555–562. C.M. Salgado, L.E.B. Brandao, C.M.N.A. Pereira, W.L. Salgado, Salinity independent volume fraction prediction in annular and stratified (water–gas– oil) multiphase flows using artificial neural networks, Prog. Nucl. Energy 76 (2014) 17–23. G.H. Roshani, S.A.H. Feghhi, F. Shama, A. Salehizadeh, E. Nazemi, Prediction of materials density according to number of scattered gamma photons using optimum artificial neural network, Comput. Methods Phys. (2014), Article ID 305345, 6 pp. E. Nazemi, S.A.H. Feghhi, G.H. Roshani, Void fraction prediction in two-phase flows independent of the liquid phase density changes, Radiat. Meas. 68 (2014) 49–54.
[12] T. Cong, G. Su, S. Qiu, W. Tian, Applications of ANNs in flow and heat transfer problems in nuclear engineering: A review work, Prog. Nucl. Energy 62 (2013) 54–71. [13] M. Khorsandi, S.A.H. Feghhi, A. Salehizadeh, G.H. Roshani, Developing a gamma ray fluid densitometer in petroleum products monitoring applications using Artificial Neural Network, Radiat. Meas. 59 (2013) 183–187. [14] G.H. Roshani, S.A.H. Feghhi, A. Adineh-Vand, M. Khorsandi, Application of adaptive neuro-fuzzy inference system in prediction of fluid density for a gamma ray densitometer in petroleum products monitoring, Measurement 46 (2013) 3276–3281. [15] S. Corneliussen, J.P. Couput, E. Dahl, E. Dykesteen, K.E. Frøysa, E. Malde, H. Moestue, P.O. Moksnes, L. Scheers, H. Tunheim, Handbook of Multiphase Flow Metering, Norwegian Society for Oil and Gas Measurement, Oslo, 2005. [16] D.B. Pelowitz, MCNP-X TM User’s Manual, Version 2.5.0. LA-CP-05e0369, Los Alamos National Laboratory, 2005. [17] E. Abro, G.A. Johansen, Improved void fraction determination by means of multibeam gamma-ray attenuation measurements, Flow Meas. Instrum. 10 (2) (1999) 99–108. [18] S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, USA, 1999. [19] A. Shahsavand, A. Ahmadpour, Application of optimal Rbf neural networks for optimization and characterization of porous materials, Comput. Chem. Eng. J. 29 (2005) 2134–2143. [20] B. Yu, X. He, Training radial basis function networks with differential evolution, PWASET 11 (2006) 57–160. [21] E.J. Hartman, J.D. Keeler, J.M. Kowalski, Layered neural networks with Gaussian hidden units as universal approximators, Neural Comput. (1990) 210–215. [22] M. Hayati, A. Rezaei, L. Noori, Application of radial basis function network for the modeling and simulation of turbogenerator, J. Adv. Inf. Technol. 4 (2) (2013) 76.
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
A radiation-based hydrocarbon two-phase flow meter for estimating of phase fraction independent of liquid phase density in stratified regime E. Nazemi a, S.A.H. Feghhi b, G.H. Roshani a,n, S. Setayeshi c, R. Gholipour Peyvandi d a
Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran Radiation Application Department, Shahid Beheshti University, G.C., Iran c Department of Energy Engineering and Physics, Amirkabir University of Technology, Iran d Nuclear Science and Technology Research Institute, Tehran, Iran b
art ic l e i nf o
a b s t r a c t
Article history: Received 15 April 2015 Received in revised form 19 August 2015 Accepted 14 September 2015 Available online 16 September 2015
The fluid properties strongly affect the performance of radiation-based multiphase flow meter. By changing the fluid properties (especially density), recalibration is necessary. In this study, a method was presented to eliminate the dependency of multiphase flow meter on liquid phase density in stratified two phase horizontal flows. At the first step the position of the scattering detector was optimized in order to achieve highest sensitivity. Several experiments in optimized position were done. Counts under the full energy peak of transmission detector and total counts of scattering detector were applied to the Radial Basis Function neural network and the void fraction percentage was considered as the neural network output. Using this method, the void fraction was predicted independent of the liquid phase density change in stratified regime of gas–liquid two-phase flows with mean relative error percentage less than 1.2%. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Radial Basis Function Radiation-based MPFM Detector Void fraction Prediction
1. Introduction The radiation-based multiphase flow meter (MPFM) is relatively new technology in Oil industry. MPFMs are used to measure the phase fractions of oil, gas and water in the flow from an oil well. The conventional methods used to measure the phase fraction in the flow for each well at wide intervals that could span over several months. The radiation-based MPFMs provide such information instantly, easing monitoring problems and enabling quick access to data, which allows rapid decisions to be made on well performance. The wealth of data accumulated by radiation-based MPFM can be fed into reservoir simulation codes to enhance their accuracy and reliability [1]. In recent years, many researchers and engineers have implemented gamma ray attenuation in order to measure volume fraction and identify the flow regime in multiphase flows. Tjugum et al. used a multibeam gamma-ray densitometry to identify flow regimes in hydrocarbon multiphase oil, water and gas pipe flows [2]. They demonstrated that a fan beam geometry with one radiation source and several collimated detectors is sufficient to provide information on the liquid–gas distribution of the pipe flow. Using 241Am source with the activity of 500 mCi and 9 CdZnTe semiconductor detectors, they identified several flow n
Corresponding author. E-mail address: [email protected] (G.H. Roshani).
http://dx.doi.org/10.1016/j.flowmeasinst.2015.09.002 0955-5986/& 2015 Elsevier Ltd. All rights reserved.
regimes in gas–liquid flows in a pipe with a diameter of 2 in. Jing et al. investigated the dual modality densitometry method using artificial neural networks (ANNs) in order to determinate the gas and water volume fraction in a three-phase flow [3]. Jing and Bai, also studied the flow regime identification in two phase flow in vertical pipe using Radial Basis Function (RBF) neural networks based on dual modality densitometry [4]. In 2014, Roshani et al. used a dual energy source consists of 241Am (59.5 KeV) and 137Cs (662 KeV) with just one transmission NaI detector to predict volume fraction in oil–water–gas three-phase flows [5]. By using ANN, they predicted the volume fraction of oil, water and gas phases with Mean Absolute error (MAE%) of less than 1%. Roshani et al. also proposed a method based on dual modality densitometry using ANN to first identify the flow regime and then predict the void fraction in gas–liquid two-phase flows [6]. They used the total count in the scattering detector, the full energy peak and photon counts of Compton edge in transmission detector as the three inputs of the ANN. By applying this method, they correctly distinguished all the three regimes of stratified, homogenous and annular and estimated the void fraction of each phase in the range of 5–95% with error of less than 1.1%. Also it has been shown that artificial neural networks could be as a useful tool for predicting, classification and optimization for industrial nuclear gauges especially in cases that lots of parameters could influence the operation of the system [7–14]. Calibration of radiation-based multiphase flow meter (MPFM)
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
depends strongly on the fluid properties [15]. By changing the fluid properties such as density, recalibration is required. Performance of radiation-based MPFMs will be improved by eliminating any dependency on the fluid properties. In all previous studies, the void fraction has been measured with a constant density liquid phase and little attention has been paid to the changes of the density of the liquid phase. Since attenuation of gamma-ray depends on both amount and density of the matter, fluctuations of the density of the liquid phase can cause significant errors in determination of the void fraction. For example, fluctuations of temperature and pressure which occur typically in pipe-lines of Oil industry, could cause changes of the liquid density and consequently measuring the void faction would deal with significant errors. In this work, an approach is proposed based on dual modality densitometry using ANN to solve the problem of measuring the void fraction in stratified regime of hydrocarbon gas–liquid twophase flows in situations that the liquid phase density is changeable. At the first step, sensitivity response of the scattering detector relative to the density changes of liquid phase in different positions around the pipe, was investigated by using Monte Carlo N Particle (MCNP) code. As much as the sensitivity is more, the ANN could predict the void fraction independent of density changes of the liquid phase with less error and consequently the measuring precision of the system would be improved. After obtaining the most sensitive position relative to density changes for the detectors by simulation, an experimental setup according to the simulated geometry was designed in order to provide the experimental required data for ANN. By applying this methodology, the void fraction was predicted independent of the liquid phase density in stratified regime of gas–liquid two-phase flows with root mean square error of less than 1.4.
2. Proposed methodology
transmission detector was kept fixed in the angle of 0° and position of 1-in. NaI scattering detector was changed from 15° to 135° respect to center of the pipe with steps of 15°. The void fractions in the range of 10–70% for stratified regime of gas–liquid two-phase flows were simulated. Distance between both the detectors and pipe was chosen 5 cm. The 137Cs source was placed 10 cm far from the pipe. Also the source was collimated in order to make a narrow beam passing through the center of the pipe. Air with density of 0.001 g/cm3 was used as the gas phase in the pipe. For making a wide range of density for liquid phase in laboratory (from 0.735 g/cm3 to 0.980 g/cm3), gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 (g/cm3), respectively, have been used as the liquid phases. Same as the experiments, in simulations these liquid phases were used, too. Since the predominant interaction mechanism for high energy photons in low atomic number materials is Compton scattering and the photoelectric interaction could be negligible, therefore, the interaction probability depends just on the density of the liquid phase regardless of its composition. Also, because the effective atomic numbers of used liquids are close to each other, it could be assumed that all of the 5 liquid phases regardless of their compositions, are considered as one liquid phase with various densities. Registered counts in both transmission and scattering detectors were calculated per one source particle in the MCNP-X code using Pulse Height Tally F8. A special tally card with the Gaussian Energy Broadening (GEB) option is also included in the model in order to take into account the Gaussian energy broadening and obtain a better and more realistic simulation of the whole spectrum in detectors. The technique consists of using a “FT8 GEB” card in the input file of MCNP code and calculating the full width at half maximum (FWHM) of the full energy peak of gamma ray with different energies in the laboratory. The tallied energy is broadened by sampling from the Gaussian function shown in Eq. (1) [16]:
2.1. Monte Carlo simulation
f (E ) = As the first step in this study, a Monte Carlo simulation model is used to obtain the best positions for the detectors in dual modality densitometry configuration. The Monte Carlo model used in this work is based on the Monte Carlo N-Particle (MCNP) code, version X, which is used for neutron, photon, electron, or coupled neutron/ photon/electron transport. In this work, a dual modality densitometry setup based on the existing devices in our laboratory has been simulated. As shown in Fig. 1, the position of 1-in. NaI
⎛ ( E − E0 ) ⎞2 ⎟⎟ −⎜⎜ Ce ⎝ A ⎠
Where, E is the broadened energy, E0 is the un-broadened energy of the tally, C is the normalization constant and also A is related to the FWHM by Eq. (2):
A=
FWHM 2 ln (2)
(2)
The desired FWHM which is specified by the user-provided
T=Transmission Detector S=Scattering Detector
pipe Shield of Source
(1)
Collimator 15
T
26
30 45 135
120 105 90 75
60
s
Fig. 1. A top view of positioning of the scattering detector in different angles used in simulated geometry in order to obtain the most sensitive position relative to density changes.
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
27
140000 120000
Count
100000 80000 60000 40000 20000 0 0
200
400
600
800
Channel
40000
Count
30000
20000
10000
0 0
200
400
600
800
Channel
16000 14000
Count
12000 10000 8000 6000 4000 2000 0 0
200
400
600
800
Channel Fig. 2. Calculation of FWHM of energy peak using experimental spectrum and Gaussian fitting function for radioactive sources of: (a)
constants (a, b, and c), has a nonlinear response relative to energy according to Eq. (3):
FWHM = a + b E + cE2
(3)
241
Am (b)
137
Cs (c)
60
Co.
Where, E is the incident gamma-ray energy. The units of “a”, “b” and “c” parameters are MeV, MeV1/2, and MeV 1, respectively. To calculate “a”, “b” and “c” parameters, one 1-in. NaI detector and 3 gamma emitter radioactive sources of 241Am (energy 60 KeV), 137 Cs (energy 662 KeV) and 60Co (energies 1173 and 1333 KeV)
28
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
0.07
FWHM (MeV)
0.06 0.05 0.04 0.03 0.02 0.01 Fig. 7. Experimental setup.
0.00 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Energy (MeV) Fig. 3. Calculation of GEB card parameters using obtained FWHM for different energies and a non-linear fitting function.
to Density Changes (percent)
Sensitivity of Scattering Detector Relate
22
241 Am, 137Cs and 60Co sources are shown in Fig. 2. The obtained FWHM from experimental spectrum is in terms of number of channels. For converting it in terms of energy (MeV) we used Eq. (4):
FWHM (MeV) =
20 18 16 14 12 10 8 6 4 2 10
20
30
40
50
60
70
Void Fraction (percent)
Fig. 4. Sensitivity of the scattering detector relative to the density changes of the liquid phase from 0.735 g/cm3 to 0.980 g/cm3 versus different void fractions.
FWHM (channel) × Energy of peak (MeV) Channel‵s number of peak (channel)
After obtaining the experimental FWHM for each energy peak, as shown in Fig. 3, FWHM (MeV) curve as a function of energy (MeV) was plotted and a non-linear fitting function (Eq. (3)) was applied to calculate the values of the “a”, “b” and “c”. Parameters of “a”, “b” and “c” were calculated 0.0109, 0.0696 and 0.0226, respectively. These parameters were used with the GEB command in the input file of MCNP code in order to take account the energy resolution of the 1-in. NaI detector in the simulations. At each position of the scattering detector, sensitivity response of this detector relative to density changes of the liquid phase from the lowest density (0.735 g/cm3 ) to the highest density (0.980 g/cm3) of liquid phase for void fractions in the range of 10– 70% was calculated according Eq. (5):
⎛ Registered count for density of 0.98 (g/cm3) ⎜ ⎜ −Registered count for density of 0.735 (g/cm3) Sensitivity = ⎜ 3 ⎜ Registered count for density of 0.98 (g/cm ) ⎜ ⎝ × 100
Fig. 5. Defined parameters in stratified regime.
including four gamma energies in the range from 60 KeV to 1333 KeV, were used. At first, FWHM of each peak of energy was determined in terms of channel. The experimental spectrums for
(4)
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (5)
Sensitivity of the scattering detector relative to the density changes of the liquid phase for different void fractions was shown in Fig. 4. As it is shown in Fig. 4, by increasing alignment angle of the scattering detector, the sensitivity increases regularly in angles from 0° to 75°, but suddenly in angle 90°, the sensitivity increases largely and becomes almost as same as the sensitivity of angle 120° and again after angle 90°, the sensitivity increases regularly. As it is obvious in Fig. 4, in angle 135° the scattering detector has the most sensitivity relative to density changes of liquid phase. Thus, angle 135° was chosen as the best position for locating of the scattering detector.
Fig. 6. Cross sectional view of the made void fractions for stratified regime in the range of 10–70%.
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
29
320000
Registered Count in the Transmission Detector (#)
310000
0.735 (g/cm3) 0.795(g/cm3)
300000
0.826(g/cm3)
290000
0.852(g/cm3)
280000
0.980(g/cm3)
270000 260000 250000 240000 230000 220000 210000 200000 190000 10
20
30
40
50
60
70
Void Fraction (percent)
Registered Count in the Scattering Detector (#)
200000
3 0.735 (g/cm )
0.795(g/cm3) 0.826(g/cm3) 180000
0.852(g/cm3) 0.980(g/cm3)
160000
140000
120000
100000
10
20
30
40
50
60
70
Void fraction (percent) Fig. 8. Registered counts versus void fraction in different densities: (a) transmission detector (b) scattering detector.
2.2. Experimental Setup An experimental setup was designed based on the obtained best positions for the detectors by simulation in order to generate required data for training and testing the artificial neural network (ANN). All the experiments were carried out in static conditions. A pipe made of Pyrex-glass with radius of 4.75 cm and wall thickness of 0.25 cm was chosen as the main pipe. For modeling the stratified regime in static conditions, PVC (polyvinyl chloride) film with thicknesses of 0.40 mm was used as a separator between liquid and gas phases. Required calculation for making various void fractions from 10% to 70% in stratified regime was done according to Eq. (6) [17]:
αs = 1 −
⎛ ⎛ R − L0 ⎞⎞⎤ ⎛ R − L0 ⎞ 1 1⎡ ⎟⎟⎥ ⎟ − sin ⎜ 2arc cos ⎜ ⎢ arc cos ⎜ ⎝ R ⎠⎠⎦ ⎝ ⎠ ⎝ R 2 π⎣
(6)
Where L 0 is the level of the liquid in the pipe, R is the radius of the pipe, and αs is the void fraction in stratified regime. These parameters are shown in Fig. 5. Although the stratified regime occurs in horizontal pipes, but in this work we located the pipe vertically to change simply the samples in the pipe. Because our experiments were carried out in
static conditions, there is no difference between locating the pipe vertically or horizontally. A cross sectional view of the made void fractions for stratified regime in the laboratory was shown in Fig. 6. Gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 g/cm3,respectively, have been used as liquid phases and also air was used as the gas phase. The void fractions of 10%, 20%, 30%, 40%, 50%, 60% and 70%, were tested for each liquid phase (5 liquid phase with different densities 7 different void fraction ¼ totally 35 tests). A 137Cs source with activity of 2 mCi and a measurement time of 600 s were chosen for all the experiments. The source was collimated (a cubic collimator with 0.8 cm width, 8 cm height and 8 cm length) in order to make a narrow beam passing through the center of the pipe. One 1-in. NaI detector was located 25 cm far from the source (5 cm far from the pipe) as transmission detector. Another 1-in. NaI detector was located 5 cm far from the pipe and in angle of 135° respect to the center of the pipe as the scattering detector. The experimental setup is shown in Fig. 7. In transmission detector, counts under the full energy peak of 137 Cs were registered, while in the scattering detector total count was registered. With the described setup and measurement time of 600 s, the relative standard deviation of registered count in both
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
Experimental Data Simulated Data
1.00
80 R.D=0%
70
0.95 R.D=0.3% 0.90 R.D=0.2% 0.85
R.D=0.8% R.D=1%
0.80 R.D=2.3%
0.75 R.D=1.7% 0.70 10
20
30
40
50
60
70
Predicted Void Fraction (%)
Registered Count (Normalised to unit)
30
Void Fraction (percent)
60 50 40 30 20
R.D=0%
0
0.95
10
20
30
40
50
60
70
40 50 Void Fraction (%)
60
70
R.D=0.5%
0.90
Void Fraction (%) R.D=1%
0.85
R.D=1.6%
0.80 0.75
70 R.D=1.7%
0.70
60 R.D=2.4%
0.65 0.60
R.D=2.8% 0.55 10
20
30
40
50
60
70
Void Fraction (percent)
Fig. 9. Comparison of experimental and simulated data for liquid phase of gasoline with density of 0.735 g/cm3: (a) transmission detector (b) scattering detector.
Predicted Void Fraction (%)
Registered Count (Normalised to unit)
10 Experimental Data Simulated Data
1.00
50
40
30
20
10 10
20
30
Fig. 11. Regression diagrams of experimental and predicted results for (a) training data (b) testing data using presented RBF neural network.
Fig. 10. Radial Basis Function structure [22].
detectors is less than 0.004. Registered counts versus void fraction for both detectors was shown in Fig. 8. In the transmission detector, by increasing the void fraction for one liquid-phase with constant density, the number of counts would increase. Also in this detector, by increasing the density for a constant void fraction, the number of counts would decrease. The scattering detector demonstrates a vice versa response in comparison with the transmission detector. By increasing void fraction for one liquid-phase with constant density, the number of counts would decrease and also by increasing the density for a constant void fraction, the number of counts would increase. The simulated results for liquid phase of gasoline with density of 0.735 g/cm3 were benchmarked toward experimental data. This step was done in order to valid the simulator MCNP code. For the sake of simplicity in evaluation of the data, both simulated and experimental data were normalized to unit. As shown in Fig. 9, the
maximum relative difference between experimental and simulated data for transmission and scattering detectors, is 2.3% and 2.8%, respectively. Results show that simulated data are in good agreement with the experimental results. The most part of observed deviations could be somewhat related to making the stratified regime phantoms in the experiments. 2.3. Artificial neural network ANN is a strong tool in order to modeling, prediction, optimization and classification. Therefore it has many applications in nuclear engineering [12–15]. In this study, the void fraction percentage was predicted using Radial Basis Function (RBF) neural network. The RBF has a feed forward ANN structure which is consists of three layers: input layer, hidden layer and output layer [18,19]. This type of neural networks is one the most famous type of feed forward networks. The RBF neural network structure has been shown in Fig. 10. The first layer is made from source nodes and the second layer consists of a set basis function units that perform a nonlinear transformation from the input space to the hidden space [20,21]. The data set required for training the network was achieved,
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
Table 1 The data that were used for training the network and predicted void fraction percentages. Density (g/cm3) Counts in trans- Counts in mitted detector scattering detector
Void fraction (%)
Predicted void fraction (%)
0.735 0.795 0.852 0.98 0.795 0.826 0.852 0.735 0.795 0.826 0.98 0.735 0.826 0.852 0.735 0.795 0.852 0.98 0.795 0.826 0.852 0.735 0.795 0.826 0.98
10 10 10 10 20 20 20 30 30 30 30 40 40 40 50 50 50 50 60 60 60 70 70 70 70
9.709535 10.23984 9.934259 10.01297 19.58138 20.51575 19.82555 30.49037 30.84105 30.08618 29.88916 42.14215 40.44589 38.55896 48.33656 50.91241 47.71875 50.52808 60.01559 60.74899 61.58983 70.21274 69.92444 69.68112 69.05846
236,403 226,957 219,932 198,375 242,468 239,534 235,672 262,678 255,449 252,142 229,422 275,463 264,871 261,091 286,000 281,233 274,083 259,783 296,428 293,021 290,476 316,349 312,781 309,375 294,942
153,319 163,893 172,704 200,901 155,704 160,128 164,551 138,847 147,747 151,308 179,789 130,341 141,947 145,518 119,993 127,157 133,425 154,021 112,506 117,006 120,606 93,892 97,503 101,115 118,268
31
From Tables 1 and 2 and Fig. 11, clearly the predicted void fraction percentage by presented model is close to the experimental results. These results show the applicability of ANN as an accurate and reliable model for the prediction of void fraction percentage according to the counted gamma photons in transmission and scattering detectors. Two types of errors (mean relative error percentage (MRE%) and the root mean square error (RMSE)) were used in order to show the precision of the proposed neural network .The MRE% and the RMSE of the network are calculated by:
MRE% = 100 ×
1 N
N
∑ j=1
Xj (Exp) − Xj (Pred) Xj (Exp )
2
N
RMSE =
(7)
∑ j = 1 ( Xj (Exp) − Xj (Pred) ) N
(8)
where N is the number of data and ‘X (Exp)’ and ‘X (Pred)’ stand for experimental and predicted (ANN) values, respectively. Obtained MRE percentages for training and testing sets were 0.0795 and 1.1140, respectively. Obtained RMSE for training and testing sets were 1.2660 and 1.3589, respectively. These low errors show the accuracy and precision of the presented RBF neural network.
4. Conclusion Table 2 The data that were used for testing the network and predicted void fraction percentages. Density(g/cm3) Counts in transmitted detector
Counts in scattering detector
Void Fraction (%)
Predicted Void Fraction (%)
0.826 0.735 0.98 0.852 0.795 0.98 0.826 0.735 0.98 0.852
168,299 145,973 191,092 154,868 138,376 166,944 129,843 108,005 137,707 103,823
10 20 20 30 40 40 50 60 60 70
10.40418 22.47479 19.22676 28.14699 41.58127 39.85354 48.40015 59.33674 58.56083 69.25613
223,844 252,419 215,284 248,219 268,277 244,324 278,073 299,999 276,190 306,835
using described experiment. The number of samples for training and testing data were 25 (about 72%) and 10 (about 28%) respectively. For training the RBF model, a program was developed using MATLAB 8.1.0.604 software. The best structure of network (spread and number of neurons in hidden layer) was founded using an iterative loop in written program. In this iterative loop the spread and the number of neurons in hidden layer were changed step by step and finally, the best structure with minimum error was saved. In the best structure, the spread was 0.7 and the number of neurons in hidden layer was 10.
Attenuation of gamma-ray strongly depends on density of matter; therefore the density fluctuation of the liquid phase can cause significant errors in determination of the void fraction. In this study, a method was presented based on dual modality densitometry using RBF neural network for determining the void fraction independent of the density changes in stratified regime of two-phase flows. The presented RBF neural network has 2 inputs and 1 output. The inputs were counts of full energy peak of transmitted detector and total count of scattering detector and the output was the void fraction percentage. Trained network predicted void fraction percentage with root mean square error less than 1.4. These results show the applicability of RBF as an precise, accurate and reliable model for the prediction of void fraction according to the registered counts in two detectors independent of the liquid phase density change. The proposed methodology could be applied for measuring the volume fraction in situations where the density of liquid phase could be changed. For instance, in situations where the gas void fraction (GVF) is low and the water cut of liquid is high. In such situations, salinity changes of the water could lead to density changes of water and consequently would cause error in measuring the volume fraction. As another example, in situations where the temperature is variable and consequently the density of liquid phase would change, the proposed methodology could be as a good choice for measuring the volume fraction.
References 3. Results and discussion The relation between the experimental and predicted results using the presented RBF model for training and testing data in two regression diagrams, have been shown in Fig. 11. These diagrams show the high accuracy and precision of the presented model. The predicted void fraction percentages for training and testing samples were tabulated in Tables 1 and 2, respectively.
[1] F. Abu-Jarad, Application of radiation sources in the oil & gas industry and shortages in their services, in: Proceedings of the International Symposium on the Peaceful Applications of Nuclear Technology in the GCC Countries, Jeddah, 2008. [2] S.A. Tjugum, B.T. Hjertaker, G.A. Johansen, Multiphase flow regime identification by multibeam gamma-ray densitometry, Meas. Sci. Technol. 13 (2002) 1319–1326. [3] C.G. Jing, G.Z. Xing, B. Liu, Q.G. Bai, Determination of gas and water volume fraction in oil water gas pipe flow using neural networks based on dual
32
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
E. Nazemi et al. / Flow Measurement and Instrumentation 46 (2015) 25–32
modality densitometry. in: Advances in Neural Networks, Lecture Notes in Computer Science, 3973, Springer–Verlag, New York, 2006, pp. 1248–1253. C.G. Jing, Q. Bai, Flow regime identification of gas/liquid two-phase flow in vertical pipe using RBF neural networks, in: Proceedings of the Chinese Control and Decision Conference (CCDC), 2009. G.H. Roshani, S.A.H. Feghhi, A. Mahmoudi-Aznaveh, E. Nazemi, A. AdinehVand, Precise volume fraction prediction in oil-water-gas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector, Measurement 51 (2014) 34–41. G.H. Roshani, E. Nazemi, S.A.H. Feghhi, S. Setayeshi, Flow regime identification and void fraction prediction in two-phase flows based on gamma ray attenuation, Measurement 65 (2015) 25–32. C.M. Salgado, L.E.B. Brandao, R. Schirru, C.M.N.A. Pereira, A. Xavier da Silva, R. Ramos, Prediction of volume fractions in three-phase flows using nuclear technique and artificial neural network, Appl. Radiat. Isot. 67 (2009) 1812–1818. C.M. Salgado, C.M.N.A. Pereira, R. Schirru, L.E.B. Brandao, Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks, Prog. Nucl. Energy 52 (2010) 555–562. C.M. Salgado, L.E.B. Brandao, C.M.N.A. Pereira, W.L. Salgado, Salinity independent volume fraction prediction in annular and stratified (water–gas– oil) multiphase flows using artificial neural networks, Prog. Nucl. Energy 76 (2014) 17–23. G.H. Roshani, S.A.H. Feghhi, F. Shama, A. Salehizadeh, E. Nazemi, Prediction of materials density according to number of scattered gamma photons using optimum artificial neural network, Comput. Methods Phys. (2014), Article ID 305345, 6 pp. E. Nazemi, S.A.H. Feghhi, G.H. Roshani, Void fraction prediction in two-phase flows independent of the liquid phase density changes, Radiat. Meas. 68 (2014) 49–54.
[12] T. Cong, G. Su, S. Qiu, W. Tian, Applications of ANNs in flow and heat transfer problems in nuclear engineering: A review work, Prog. Nucl. Energy 62 (2013) 54–71. [13] M. Khorsandi, S.A.H. Feghhi, A. Salehizadeh, G.H. Roshani, Developing a gamma ray fluid densitometer in petroleum products monitoring applications using Artificial Neural Network, Radiat. Meas. 59 (2013) 183–187. [14] G.H. Roshani, S.A.H. Feghhi, A. Adineh-Vand, M. Khorsandi, Application of adaptive neuro-fuzzy inference system in prediction of fluid density for a gamma ray densitometer in petroleum products monitoring, Measurement 46 (2013) 3276–3281. [15] S. Corneliussen, J.P. Couput, E. Dahl, E. Dykesteen, K.E. Frøysa, E. Malde, H. Moestue, P.O. Moksnes, L. Scheers, H. Tunheim, Handbook of Multiphase Flow Metering, Norwegian Society for Oil and Gas Measurement, Oslo, 2005. [16] D.B. Pelowitz, MCNP-X TM User’s Manual, Version 2.5.0. LA-CP-05e0369, Los Alamos National Laboratory, 2005. [17] E. Abro, G.A. Johansen, Improved void fraction determination by means of multibeam gamma-ray attenuation measurements, Flow Meas. Instrum. 10 (2) (1999) 99–108. [18] S. Haykin, Neural Networks: A Comprehensive Foundation, Prentice-Hall, USA, 1999. [19] A. Shahsavand, A. Ahmadpour, Application of optimal Rbf neural networks for optimization and characterization of porous materials, Comput. Chem. Eng. J. 29 (2005) 2134–2143. [20] B. Yu, X. He, Training radial basis function networks with differential evolution, PWASET 11 (2006) 57–160. [21] E.J. Hartman, J.D. Keeler, J.M. Kowalski, Layered neural networks with Gaussian hidden units as universal approximators, Neural Comput. (1990) 210–215. [22] M. Hayati, A. Rezaei, L. Noori, Application of radial basis function network for the modeling and simulation of turbogenerator, J. Adv. Inf. Technol. 4 (2) (2013) 76.