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Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow
Progress in Nuclear Energy xxx (2017) 1e9
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Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow G.H. Roshani a, E. Nazemi b, *, M.M. Roshani b a b
Electrical Engineering Department, Kermanshah University of Technology, Kermanshah, Iran Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 March 2016 Received in revised form 29 December 2016 Accepted 14 February 2017 Available online xxx
Changes of fluid properties, especially density, strongly affect the performance of radiation-based multiphase flow meter and could cause error in volume fraction measuring. One solution in such situations is continuous recalibration of the system, which is a difficult and long time task. In this study, a new methodology is presented for identifying flow regime and estimating the void fraction in gas-liquid flows independent of liquid phase density changes. The approach is based on gamma-ray attenuation and scattering combined with artificial neural networks (ANNs). The detection system uses a fan beam geometry, comprised of one 137Cs source and three NaI(Tl) detectors. Two of these three detectors were implemented to measure transmitted photons and the third one was used to measure scattered photons. Also, four ANNs were used in this study, the first one for identifying the flow regime independent of liquid phase density changes and the other three ANNs for predicting void fraction independent of liquid phase density changes. Using this methodology, three flow regimes of annular, stratified and bubbly were correctly distinguished in liquid phase density changes range of 0.735e0.980 g/cm3 and void fraction was predicted with a mean relative error (MRE) of less than 4.3%. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Gamma-ray Flowmeter Void fraction Flow regime Neural network Independent density
1. Introduction The accurate flow metering of oil well products is of great importance to the oil industry. The high cost of sub-sea production has led to the use of multiphase pipelines to transfer mixture of oil and gas. This provides a requirement for multiphase metering in which the flow rates of oil and gas can be determined with sufficient accuracy for reservoir management, for monitoring the withdrawal of fluids from a reservoir, and for custody transfer purposes. Ideally the measurements should be carried out nonintrusively. To this end, nuclear techniques, notably neutron interrogation and activation and also gamma densitometry have an important part to play (Bishop and James, 1992). Using gamma attenuation techniques are also more conventional in comparison with neutron scattering and attenuation techniques. Difficulty in obtaining a sufficiently strong neutron source to provide an adequate counting statistics for transient measurements, is one of the limitations of using neutron techniques. In recent years, some studies have been done on measuring the
* Corresponding author. E-mail address: [email protected] (E. Nazemi).
volume fraction and determining the flow regime in multiphase flows by means of gamma-ray attenuation techniques. El Abd showed that usage of Compton-Compton scattering is more precise than transmission and traditional Compton scattering for determining the void fraction in stratified regime of two phase flows (El Abd, 2014). 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 (Roshani et al., 2015). They used the total count in the scattering detector, the full energy peak and photon counts of Compton edge in transmission detector which were obtained by simulations, 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 5e95% with error of less than 1.1%. Faghihi et al. modeled three basis two-phase flow regimes including homogenous, stratified and annular in a vertical pipe by using polyethylene phantoms (Faghihi et al., 2015). For all three modeled flow regimes all transmitted and scattered gamma rays in all directions were measured by setting a gamma ray source and detector around the pipe. Finally, they presented innovative correlations to predict the void fraction in two-phase flow in a vertical pipe. Also it has been shown
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Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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that artificial neural networks could be used for predicting, classification and optimization for radiation-based multiphase flow meters and generally industrial nuclear gauges specially in cases that lots of parameters could influence the operation of the system (Salgado et al., 2009, 2010, 2014; Jing et al., 2006; Roshani et al., 2014a,b, 2016a,b, 2017a,b; Cong et al., 2013; Jing and Bai, 2009; Nazemi et al., 2016a; Yadollahi et al., 2016a,b; Eftekharizadeh et al., 2016; Zahakifar et al., 2017). Calibration of radiation-based multi-phase flow meters (MPFMs), depends strongly on the fluid properties (Corneliussen et al., 2005). By changing the fluid properties such as density, recalibration is required. Performance of MPFMs would be improved by eliminating any dependency on the fluid properties. In Fig. 1. Defined parameters in stratified regime.
Fig. 2. Schematic cross sectional view of different void fractions in the range of 10%e70% in stratified regime.
Fig. 3. Schematic cross sectional view of different void fractions in the range of 10%e70% in annular regime.
Fig. 4. Schematic cross sectional view of different void fractions in the range of 10%e70% in bubbly regime.
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Fig. 5. (a) Experimental setup. (b) Schematic view of experimental setup.
Fig. 6. Architecture of the proposed MLP model in order to identify flow regime independent of liquid phase density changes.
all previous studies, the flow regime identification and void fraction measurement have been done by considering this point that, the density of the liquid phase was constant and little attention has been paid to the changes of the density of the liquid phase. Fluctuations of the density due to temperature and pressure changes in pipelines, can cause significant errors in identification of flow regime and also determination of the volume fraction in radiationbased multiphase flow meters.
In our previous studies, we presented a method based on dual modality densitometry using ANN to measure only the void fraction independent of the liquid phase changes in annular and stratified regime of gas-liquid two phase flows (Nazemi et al., 2014, 2015). We also proposed a multi-beam gamma ray attenuation technique method for measuring void fraction independent of flow regime (Nazemi et al., 2016b). In this study, we developed previous methods in order to identify the flow regime in addition to
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Table 1 Specification of proposed classifying ANN model. Neural network
MLP
Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron
3 3 1 260 tansig
Table 2 Specification of 3 proposed ANN models for predicting void fraction independent of liquid phase density changes. Type of Regime
Neural network
MLP
Annular
Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron
3 5 1 125 tansig 3 3 1 245 tansig 3 3 1 250 tansig
Stratified
measuring void fraction independent of the liquid phase changes. Proposed methodology is based on combination of multi-beam gamma ray attenuation and dual modality densitometry techniques using artificial neural network. One 137Cs source, three NaI detectors and four ANNs were implemented in this work in order to identify the flow regime and determine the phase fraction in gasliquid two phase flows independent of the liquid phase changes. 2. Experimental setup An experimental setup was designed in static conditions in order to generate required data for ANN in order to identify the flow regime and predict the void fraction independent of liquid phase density changes. Three flow regimes of annular, stratified and bubbly with void fractions of 10, 20, 30, 40, 50, 60 and 70 percent and liquid phase density in the range of 0.735e0.988 g/cm3 were modeled in the experiments (3 different flow regime 7 different
Bubbly
void fraction 5 different liquid phase density ¼ totally 105 tests). PVC (Polyvinyl Chloride) films with thickness of 0.40 mm were used inside the main pipe made of Pyrex-glass, for modeling different flow regimes and void fraction in static conditions. For stratified regime, various void fractions would be calculated by using equation (1) (Abro et al., 1999):
Fig. 7. The general pattern of the 4 separated networks for identifying the flow regime and predicting void fraction independent of liquid phase density.
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
Table 3 The data that were used for training the networks and predicted gas percentage. Type of regime
First Transmission detector Second transmission detector Scattering detector count count count
Liquid density
Gas percentage
Predicted gas percentage independent of liquid density
Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly
275,221 295,940 327,242 339,852 353,852 267,004 287,643 307,657 349,239 361,763 264,058 305,750 320,471 333,565 361,472 260,597 281,835 319,316 331,619 345,580 245,672 268,112 308,167 322,936 354,861 270,616 283,031 296,939 323,031 336,906 260,894 276,457 288,247 316,708 331,565 345,688 273,515 286,106 299,725 330,072 344,135 253,147 282,732 296,606 312,116 342,716 233,389 267,774 297,145 314,627 281,825 295,825 310,825 339,825 357,825 255,026 287,382 301,302 336,599 353,358 283,418 296,732 315,001 244,613 261,166 280,363 293,748 330,618 348,995 239,283 255,792 277,119 315,886 339,489 294,568
0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.98 0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.98 0.98
10 20 40 50 60 10 20 30 60 70 10 30 40 50 70 10 20 40 50 60 10 20 40 50 70 10 20 30 50 60 10 20 30 50 60 70 20 30 40 60 70 10 30 40 50 70 10 30 50 60 20 30 40 60 70 10 30 40 60 70 30 40 50 10 20 30 40 60 70 20 30 40 60 70 50
10.1 21.7 43.3 52.7 61.7 10.4 18.6 30.8 60.88 69.8 10.0 28.7 40.5 48.3 69.8 9.5 17.8 41.9 48.8 57.1 11.1 20.7 40.4 47.0 69.8 9.70 22.3 30.1 55.0 58.2 12.7 22.0 33.2 54.9 62.0 69.5 19.0 33.5 40.4 60.2 68.9 7.3 28.6 34.6 49.8 69.1 10.0 29.8 40.7 56.9 20.0 35.4 44.2 65.1 71.4 18.1 30.9 43.5 59.7 71.1 32.3 39.9 52.1 17.9 16.1 33.7 38.4 60.0 69.4 15.4 22.9 29.3 54.0 61.9 48.4
223,058 224,817 227,591 238,072 255,810 220,448 221,140 222,097 254,707 277,011 216,781 219,952 221,194 232,328 275,061 215,518 216,059 218,471 228,549 247,774 202,311 203,105 205,402 219,738 270,563 242,125 244,157 248,788 271,618 285,425 234,369 236,110 243,236 265,834 279,506 294,699 233,381 240,525 252,047 278,203 293,634 229,173 237,970 249,357 261,022 291,974 214,217 223,453 251,456 266,302 258,129 266,129 278,129 296,129 304,129 243,560 260,435 271,633 293,991 303,571 257,368 267,836 280,636 237,464 248,012 254,568 265,498 290,239 301,108 233,205 243,364 253,521 281,940 295,403 265,450
450,762 420,010 355,583 321,767 285,589 472,135 437,915 405,458 295,528 255,403 482,383 407,799 376,893 338,346 259,357 490,700 454,281 382,627 346,269 305,890 540,377 498,574 415,447 375,986 280,143 483,585 455,613 428,493 356,969 321,832 501,815 473,706 444,357 371,630 332,495 289,516 482,980 450,156 416,246 337,242 293,563 524,536 459,968 426,050 385,699 296,925 584,754 503,814 420,064 372,472 453,178 417,128 373,569 302,474 263,931 503,912 438,349 395,354 313,863 272,430 447,931 409,534 361,256 524,687 491,423 456,608 418,004 325,125 282,105 541,547 500,852 462,413 356,009 307,721 413,187
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Table 4 The data that were used for testing the network and predicted gas percentage. Type of regime
First Transmission detector Second Transmission detector Scattering detector count count count
Liquid density
Gas percentage
Predicted gas percentage independent of liquid density
Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly
312,832 364,852 322,829 335,781 284,983 347,409 303,234 358,132 288,287 337,796 310,267 349,999 301,924 257,071 314,652 269,753 326,785 251,902 281,272 333,899 270,673 318,151 250,521 265,472 220,218 334,199 350,924 266,330 323,825 310,915
0.735 0.735 0.795 0.795 0.826 0.826 0.852 0.852 0.98 0.98 0.735 0.735 0.795 0.826 0.826 0.852 0.852 0.98 0.98 0.98 0.795 0.795 0.826 0.826 0.98 0.826 0.826 0.735 0.735 0.852
30 70 40 50 20 60 30 70 30 60 40 70 40 10 50 20 60 20 40 70 20 50 10 20 10 60 70 10 50 50
29.3 69.3 43.9 50.7 16.5 59.9 30.1 67.5 30.4 55.7 40.0 70.5 42.3 11.6 51.3 16.3 62.3 20.3 29.4 62.4 16.5 50.3 15.1 15.0 10.8 61.7 70.2 14.9 51.3 50.0
225,970 278,066 223,629 235,546 218,683 253,094 217,222 272,727 204,020 242,746 258,563 297,490 253,693 231,871 263,703 230,364 275,242 218,318 238,187 285,606 253,391 283,591 240,941 250,807 223,251 291,705 302,218 251,703 288,129 278,928
R L0 1 R L0 sin 2arccos as ¼ 1 arccos 2 p R R 1
386,371 246,178 372,664 332,985 442,563 300,107 417,691 263,441 457,172 328,950 395,694 279,390 410,700 510,641 378,632 494,185 343,185 544,917 462,117 322,386 473,290 352,830 516,200 484,271 587,294 318,933 277,543 481,955 337,914 368,178
(1)
where, L0 is the level of the liquid in the pipe, R is the radius of the pipe and as is the void fraction in stratified regime. These parameters are shown in Fig. 1. Schematic cross sectional view of void fractions in the range of 10%e70% for stratified regime, is shown Fig. 2. Also for annular regime, different void fractions could be calculated from equation (2) (Abro et al., 1999):
aa ¼
pr2 r2 ¼ pR2 R2
(2)
Where R is the radius of the pipe, r is radius of the gas phase which is located in the center of the pipe, and aa is the void fraction in annular regime. Since the radius of the pipe (R) is constant, different void fractions could be calculated just by changing the radius of the gas phase (r). The void fractions in the range of 10%e 70% in annular regime, are shown schematically in Fig. 3 from a top side view. In the case of bubbly regime, an arrangement with 80 hollow cubic plastic straws distributed over the whole pipe cross section was used. We considered these hollow straws as gas phase, because they were filled with air. When we fill one of these straws with liquid, we consider this straw as liquid phase. By dividing the cross section area of straws filled with air by the cross section area of straws filled with liquid and air (total of 80 straws), the void fraction is calculated. Since in real situations there are many small gas bubbles over the cross section of pipe, distribution of them is almost uniform, but in our study we could not make area of straws as small as the gas bubbles in real situation. Therefore, in order to keep uniformity of distribution of gas phase respect to attenuation
of gamma rays, for each of the two straws covered by the measurement volume between the 1st detector and source, a corresponding number of straws (6) over the total pipe cross section, was treated the same way. A schematic cross sectional view of the various void fractions in the range of 10e70 percent is shown in Fig. 4. In the case of boundary between straws (thickness of plastic straws), it should be said that they are very thin and could be negligible in comparison with cross section area of straws. In general it should be noted that, although this model is a little different from real bubble regime which takes place in dynamic two-phase flows, but it is good for primary studies in the laboratory, because making bubble regime in static experimental condition is almost impossible and it could be made in dynamic condition. For liquid phase, 5 liquids of gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 g/cm3 have been used instead of one liquid with different densities, respectively. The predominant mechanism of interaction for high energy photons is Compton scattering and the photoelectric interaction can be negligible. Therefore, the probability of interaction depends just on the density of the liquid phase regardless of its composition. Because the effective atomic numbers of used liquids are close to each other, it can be assumed that all of them are one liquid phase with different densities. The air was also used as the gas phase. A137Cs source with activity of 74 MBq and a measurement time of 600 s were chosen for all the experiments. Since in this work three parameters (void fraction, flow regime and liquid phase density) were variable, at least three features or data about the flow were required in order to identify the flow regime and predict the void fraction independent of liquid phase changes. For this purpose, 3 detectors (2 transmission detectors and one scattering detector) and a fan beam source were implemented. A collimator with the
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Fig. 8. Comparison of experimental and predicted gas percentage for e Annular regime (a) training data (b) testing data e Stratified regime (c) training data (d) testing data and e Bubbly regime (e) training data (f) testing data.
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Table 5 Obtained errors for training and testing results of the proposed ANN models. Type of regime
Error
Train
Test
Annular Annular Stratified Stratified Bubbly Bubbly
MRE% RMSE MRE% RMSE MRE% RMSE
0.3227 2.4313 0.7797 3.8852 0.4026 2.9241
4.2128 4.1330 3.9599 6.4020 0.5275 5.7692
open of 36 was used in order to make a broad beam. Two NaI detectors with dimensions of 25.4 mm diameter and 25.4 mm thickness, were located 25 cm far from the source as transmission detectors. The 1st detector was placed in direction of 0 and 2nd one was placed in direction of 13 respect to the source. In both transmission detectors, which were connected to two MultiChannel Analyzers (MCA), only the transmitted photons (photo peaks) were registered (those within an energy interval of 650e670 keV). Another 25.4 25.4 mm NaI detector, was used as the scattering detector. In the 3rd detector which was located in the angle of 90 and was connected to a counter, total count was registered. The experimental setup is shown in Fig. 5. 3. Methods application and results
the following. Usually the precision of the ANNs are indicated using regression diagram. The more precise the network is, the closer the data to the x ¼ y line. Fig. 4 shows the comparison between the experimental and predicted results using the proposed ANN models for training and testing data using regression diagrams. The comparison between experimental and predicted (ANN) results for training and testing data are tabled in Table 3 and Table 4, respectively. From Table 3, Table 4 and Fig. 8, it is clear that the predicted gas percentage independent of the liquid phase density by ANN models is close to the experimental results. These results show the applicability of ANN as an accurate and reliable model for predicting of the gas percentage according to the registered counts in first transmission detector, second transmission detector, and scattered detector. Table 5 shows the obtained errors for the proposed predicting ANN models, where the mean relative error percentage (MRE %) and the root mean square error (RMSE) of the networks are calculated by:
N 1 X Xj ðExpÞ Xj ðPredÞ MRE% ¼ 100 N j¼1 Xj ðExpÞ 2P RMSE ¼ 4
N j¼1 Xj ðRealÞ
Xj ðPredÞ
N
2 30:5 5
(3)
(4)
3.1. Regime identification The proposed Multi-layer perceptron (MLP) model which was used for identifying the flow regime independent of liquid phase density, has been shown in Fig. 6, where the inputs are registered counts in first transmission detector, second transmission detector, and scattered detector and the output is the type of flow regime. The annular, stratified and bubbly regimes were considered as 1, 2 and 3 respectively. It means that for example if the regime is bubbly the network output will be number 3. By using the experimental set up, the data set required for training the network was achieved. The training of presented MLP network was done by Levenberg-Marquardt (LM) algorithm. In this method, first derivative and second derivative (hessian) are used for network weight correction (Hagan and Menhaj, 1994). The number of samples for training and testing data are 75 (about 70%) and 30 (about 30%), respectively. In this study, different ANN structures were tested and optimized for obtaining the best ANN configuration. Many different structures with one, two and three hidden layers with different number of neurons in each layer were tested. MATLAB 8.1.0.604 software was used for training the ANN model. Table 1 shows the specification of the proposed ANN model used in order to determine the flow regime independent of liquid phase density changes. Using this trained network, the type of regime was recognized with 100% accuracy. 3.2. Percentages prediction After identification of flow regime, 3 separate ANNs were implemented to predict the void fraction for each flow regime. The inputs of these 3 ANNs are same as the mentioned ANN for regime identification and the output is void fraction percentage. The procedure of flow regime identification and void fraction measurement independent of liquid phase density changes, is shown in Fig. 7. The specifications of the proposed ANN models used in order to predict the gas percentage independent of the liquid phase density, were tabled in Table 2. The precision of these prediction networks will be discussed in
Where N is the number of data and ‘X (Exp)’ and ‘X (Pred)’ stand for experimental and predicted (ANN) values, respectively. 4. Conclusions In this work, based on our previous studies, we combined multibeam gamma ray attenuation and dual modality densitometry techniques in order to identify the flow regime in addition to measuring void fraction independent of the liquid phase changes. A fan beam geometry, comprised of one 137Cs source and three 1 inch NaI(Tl) detectors were used in the detection system. Two of these three detectors were implemented to measure transmitted photons and the third one was used to measure scattered photons. Also, four ANNs were used in this study, the first one for identifying the flow regime independent of liquid phase density changes and the other three ANNs for predicting void fraction independent of liquid phase density changes. Using this methodology, three flow regimes of annular, stratified and bubbly were correctly distinguished in liquid phase density changes range of 0.735e0.980 g/cm3 and void fraction was predicted with a mean relative error (MRE) of less than 4.3%. The proposed methodology could be applied for identifying flow regime and measuring the void fraction in situations where the density of liquid phase of gas-liquid two phase flows could be changed. For instance, 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 Abro, E., Khoryakov, V.A., Johansen, G.A., 1999. Determination of void fraction and flow regime using a neural network trained on simulated data based on gamma-ray densitometry. Meas. Sci. Technol. 10, 619e630. http://dx.doi.org/ 10.1088/0957-0233/10/7/308. Bishop, C.M., James, G.D., 1992. Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nucl. Instrum. Methods 327, 580e593. http://dx.doi.org/10.1016/0168-9002(93)90728-Z. Cong, T., Su, G., Qiu, S., Tian, W., 2013. Applications of ANNs in flow and heat transfer problems in nuclear engineering: a review work. Prog. Nucl. Energy 62, 54e71.
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Roshani, G.H., Feghhi, S.A.H., Mahmoudi-Aznaveh, A., Nazemi, E., Adineh-Vand, A., 2014b. Precise volume fraction prediction in oilewateregas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector. Measurement 51, 34e41. http://dx.doi.org/10.1016/ j.measurement.2014.01.030. Roshani, G.H., Nazemi, E., Feghhi, S.A.H., Setayeshi, S., 2015. Flow regime identification and void fraction prediction in two-phase flows based on gamma ray attenuation. Measurement 62, 25e32. http://dx.doi.org/10.1016/ j.measurement.2014.11.006. Roshani, G.H., Nazemi, E., Feghhi, S.A.H., 2016a. Investigation of using 60Co source and one detector for determining the flow regime and void fraction in gasliquid two-phase flows. Flow Meas. Instrum. 50, 73e79. http://dx.doi.org/ 10.1016/j.flowmeasinst.2016.06.013. Roshani, G.H., Nazemi, E., Roshani, M.M., 2017a. Intelligent recognition of gas-oilwater three-phase flow regime and determination of volume fraction using radial basis function. Flow Meas. Instrum. 54, 39e45. http://dx.doi.org/10.1016/ j.flowmeasinst.2016.10.001. Roshani, G.H., Nazemi, E., Roshani, M.M., 2016b. Flow regime independent volume fraction estimation in three-phase flows using dual-energy broad beam technique and artificial neural network. Neural Comput. Appl. http://dx.doi.org/ 10.1007/s00521-016-2784-8. Roshani, G.H., Nazemi, E., Roshani, M.M., 2017b. Usage of two transmitted detectors with optimized orientation in order to three phase flow metering. Measurement 100, 122e130. http://dx.doi.org/10.1016/j.measurement.2016.12.055. Salgado, C.M., Brandao, L.E.B., Schirru, R., Pereira, C.M.N.A., Xavier da Silva, A., Ramos, R., 2009. Prediction of volume fractions in three-phase flows using nuclear technique and artificial neural network. Appl. Radiat. Isot. 67, 1812e1818. http://dx.doi.org/10.1016/j.apradiso.2009.02.093. Salgado, C.M., Pereira, C.M.N.A., Schirru, R., Brandao, L.E.B., 2010. Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks. Prog. Nucl. Energy 52, 555e562. http://dx.doi.org/10.1016/j.pnucene.2010.02.001. Salgado, C.M., Brandao, L.E.B., Pereira, C.M.N.A., Salgado, W.L., 2014. Salinity independent volume fraction prediction in annular and stratified (water-gas-oil) multiphase flows using artificial neural networks. Prog. Nucl. Energy 76, 17e23. http://dx.doi.org/10.1016/j.pnucene.2014.05.004. Yadollahi, A., Nazemi, E., Zolfaghari, A., Ajorloo, A.M., 2016a. Application of artificial neural network for predicting the optimal mixture of radiation shielding concrete. Prog. Nucl. Energy 89, 69e77. http://dx.doi.org/10.1016/ j.pnucene.2016.02.010. Yadollahi, A., Nazemi, E., Zolfaghari, A., Ajorloo, A.M., 2016b. Optimization of thermal neutron shield concrete mixture using artificial neural network. Nucl. Eng. Des. 305, 146e155. http://dx.doi.org/10.1016/j.nucengdes.2016.05.012. Zahakifar, F., Keshtkar, A.R., Nazemi, E., Zaheri, A., 2017. Optimization of operational conditions in continuous electrodeionization method for maximizing Strontium and Cesium removal from aqueous solutions using artificial neural network. Radiochim. Acta. http://dx.doi.org/10.1515/ract-2016-2709.
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Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow G.H. Roshani a, E. Nazemi b, *, M.M. Roshani b a b
Electrical Engineering Department, Kermanshah University of Technology, Kermanshah, Iran Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 March 2016 Received in revised form 29 December 2016 Accepted 14 February 2017 Available online xxx
Changes of fluid properties, especially density, strongly affect the performance of radiation-based multiphase flow meter and could cause error in volume fraction measuring. One solution in such situations is continuous recalibration of the system, which is a difficult and long time task. In this study, a new methodology is presented for identifying flow regime and estimating the void fraction in gas-liquid flows independent of liquid phase density changes. The approach is based on gamma-ray attenuation and scattering combined with artificial neural networks (ANNs). The detection system uses a fan beam geometry, comprised of one 137Cs source and three NaI(Tl) detectors. Two of these three detectors were implemented to measure transmitted photons and the third one was used to measure scattered photons. Also, four ANNs were used in this study, the first one for identifying the flow regime independent of liquid phase density changes and the other three ANNs for predicting void fraction independent of liquid phase density changes. Using this methodology, three flow regimes of annular, stratified and bubbly were correctly distinguished in liquid phase density changes range of 0.735e0.980 g/cm3 and void fraction was predicted with a mean relative error (MRE) of less than 4.3%. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Gamma-ray Flowmeter Void fraction Flow regime Neural network Independent density
1. Introduction The accurate flow metering of oil well products is of great importance to the oil industry. The high cost of sub-sea production has led to the use of multiphase pipelines to transfer mixture of oil and gas. This provides a requirement for multiphase metering in which the flow rates of oil and gas can be determined with sufficient accuracy for reservoir management, for monitoring the withdrawal of fluids from a reservoir, and for custody transfer purposes. Ideally the measurements should be carried out nonintrusively. To this end, nuclear techniques, notably neutron interrogation and activation and also gamma densitometry have an important part to play (Bishop and James, 1992). Using gamma attenuation techniques are also more conventional in comparison with neutron scattering and attenuation techniques. Difficulty in obtaining a sufficiently strong neutron source to provide an adequate counting statistics for transient measurements, is one of the limitations of using neutron techniques. In recent years, some studies have been done on measuring the
* Corresponding author. E-mail address: [email protected] (E. Nazemi).
volume fraction and determining the flow regime in multiphase flows by means of gamma-ray attenuation techniques. El Abd showed that usage of Compton-Compton scattering is more precise than transmission and traditional Compton scattering for determining the void fraction in stratified regime of two phase flows (El Abd, 2014). 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 (Roshani et al., 2015). They used the total count in the scattering detector, the full energy peak and photon counts of Compton edge in transmission detector which were obtained by simulations, 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 5e95% with error of less than 1.1%. Faghihi et al. modeled three basis two-phase flow regimes including homogenous, stratified and annular in a vertical pipe by using polyethylene phantoms (Faghihi et al., 2015). For all three modeled flow regimes all transmitted and scattered gamma rays in all directions were measured by setting a gamma ray source and detector around the pipe. Finally, they presented innovative correlations to predict the void fraction in two-phase flow in a vertical pipe. Also it has been shown
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that artificial neural networks could be used for predicting, classification and optimization for radiation-based multiphase flow meters and generally industrial nuclear gauges specially in cases that lots of parameters could influence the operation of the system (Salgado et al., 2009, 2010, 2014; Jing et al., 2006; Roshani et al., 2014a,b, 2016a,b, 2017a,b; Cong et al., 2013; Jing and Bai, 2009; Nazemi et al., 2016a; Yadollahi et al., 2016a,b; Eftekharizadeh et al., 2016; Zahakifar et al., 2017). Calibration of radiation-based multi-phase flow meters (MPFMs), depends strongly on the fluid properties (Corneliussen et al., 2005). By changing the fluid properties such as density, recalibration is required. Performance of MPFMs would be improved by eliminating any dependency on the fluid properties. In Fig. 1. Defined parameters in stratified regime.
Fig. 2. Schematic cross sectional view of different void fractions in the range of 10%e70% in stratified regime.
Fig. 3. Schematic cross sectional view of different void fractions in the range of 10%e70% in annular regime.
Fig. 4. Schematic cross sectional view of different void fractions in the range of 10%e70% in bubbly regime.
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Fig. 5. (a) Experimental setup. (b) Schematic view of experimental setup.
Fig. 6. Architecture of the proposed MLP model in order to identify flow regime independent of liquid phase density changes.
all previous studies, the flow regime identification and void fraction measurement have been done by considering this point that, the density of the liquid phase was constant and little attention has been paid to the changes of the density of the liquid phase. Fluctuations of the density due to temperature and pressure changes in pipelines, can cause significant errors in identification of flow regime and also determination of the volume fraction in radiationbased multiphase flow meters.
In our previous studies, we presented a method based on dual modality densitometry using ANN to measure only the void fraction independent of the liquid phase changes in annular and stratified regime of gas-liquid two phase flows (Nazemi et al., 2014, 2015). We also proposed a multi-beam gamma ray attenuation technique method for measuring void fraction independent of flow regime (Nazemi et al., 2016b). In this study, we developed previous methods in order to identify the flow regime in addition to
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Table 1 Specification of proposed classifying ANN model. Neural network
MLP
Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron
3 3 1 260 tansig
Table 2 Specification of 3 proposed ANN models for predicting void fraction independent of liquid phase density changes. Type of Regime
Neural network
MLP
Annular
Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron Number of neurons in the input layer Number of neurons in the first hidden layer Number of neurons in the output layer Number of epochs Activation function of each neuron
3 5 1 125 tansig 3 3 1 245 tansig 3 3 1 250 tansig
Stratified
measuring void fraction independent of the liquid phase changes. Proposed methodology is based on combination of multi-beam gamma ray attenuation and dual modality densitometry techniques using artificial neural network. One 137Cs source, three NaI detectors and four ANNs were implemented in this work in order to identify the flow regime and determine the phase fraction in gasliquid two phase flows independent of the liquid phase changes. 2. Experimental setup An experimental setup was designed in static conditions in order to generate required data for ANN in order to identify the flow regime and predict the void fraction independent of liquid phase density changes. Three flow regimes of annular, stratified and bubbly with void fractions of 10, 20, 30, 40, 50, 60 and 70 percent and liquid phase density in the range of 0.735e0.988 g/cm3 were modeled in the experiments (3 different flow regime 7 different
Bubbly
void fraction 5 different liquid phase density ¼ totally 105 tests). PVC (Polyvinyl Chloride) films with thickness of 0.40 mm were used inside the main pipe made of Pyrex-glass, for modeling different flow regimes and void fraction in static conditions. For stratified regime, various void fractions would be calculated by using equation (1) (Abro et al., 1999):
Fig. 7. The general pattern of the 4 separated networks for identifying the flow regime and predicting void fraction independent of liquid phase density.
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
Table 3 The data that were used for training the networks and predicted gas percentage. Type of regime
First Transmission detector Second transmission detector Scattering detector count count count
Liquid density
Gas percentage
Predicted gas percentage independent of liquid density
Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly
275,221 295,940 327,242 339,852 353,852 267,004 287,643 307,657 349,239 361,763 264,058 305,750 320,471 333,565 361,472 260,597 281,835 319,316 331,619 345,580 245,672 268,112 308,167 322,936 354,861 270,616 283,031 296,939 323,031 336,906 260,894 276,457 288,247 316,708 331,565 345,688 273,515 286,106 299,725 330,072 344,135 253,147 282,732 296,606 312,116 342,716 233,389 267,774 297,145 314,627 281,825 295,825 310,825 339,825 357,825 255,026 287,382 301,302 336,599 353,358 283,418 296,732 315,001 244,613 261,166 280,363 293,748 330,618 348,995 239,283 255,792 277,119 315,886 339,489 294,568
0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.98 0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.735 0.735 0.735 0.735 0.735 0.795 0.795 0.795 0.795 0.795 0.826 0.826 0.826 0.852 0.852 0.852 0.852 0.852 0.852 0.98 0.98 0.98 0.98 0.98 0.98
10 20 40 50 60 10 20 30 60 70 10 30 40 50 70 10 20 40 50 60 10 20 40 50 70 10 20 30 50 60 10 20 30 50 60 70 20 30 40 60 70 10 30 40 50 70 10 30 50 60 20 30 40 60 70 10 30 40 60 70 30 40 50 10 20 30 40 60 70 20 30 40 60 70 50
10.1 21.7 43.3 52.7 61.7 10.4 18.6 30.8 60.88 69.8 10.0 28.7 40.5 48.3 69.8 9.5 17.8 41.9 48.8 57.1 11.1 20.7 40.4 47.0 69.8 9.70 22.3 30.1 55.0 58.2 12.7 22.0 33.2 54.9 62.0 69.5 19.0 33.5 40.4 60.2 68.9 7.3 28.6 34.6 49.8 69.1 10.0 29.8 40.7 56.9 20.0 35.4 44.2 65.1 71.4 18.1 30.9 43.5 59.7 71.1 32.3 39.9 52.1 17.9 16.1 33.7 38.4 60.0 69.4 15.4 22.9 29.3 54.0 61.9 48.4
223,058 224,817 227,591 238,072 255,810 220,448 221,140 222,097 254,707 277,011 216,781 219,952 221,194 232,328 275,061 215,518 216,059 218,471 228,549 247,774 202,311 203,105 205,402 219,738 270,563 242,125 244,157 248,788 271,618 285,425 234,369 236,110 243,236 265,834 279,506 294,699 233,381 240,525 252,047 278,203 293,634 229,173 237,970 249,357 261,022 291,974 214,217 223,453 251,456 266,302 258,129 266,129 278,129 296,129 304,129 243,560 260,435 271,633 293,991 303,571 257,368 267,836 280,636 237,464 248,012 254,568 265,498 290,239 301,108 233,205 243,364 253,521 281,940 295,403 265,450
450,762 420,010 355,583 321,767 285,589 472,135 437,915 405,458 295,528 255,403 482,383 407,799 376,893 338,346 259,357 490,700 454,281 382,627 346,269 305,890 540,377 498,574 415,447 375,986 280,143 483,585 455,613 428,493 356,969 321,832 501,815 473,706 444,357 371,630 332,495 289,516 482,980 450,156 416,246 337,242 293,563 524,536 459,968 426,050 385,699 296,925 584,754 503,814 420,064 372,472 453,178 417,128 373,569 302,474 263,931 503,912 438,349 395,354 313,863 272,430 447,931 409,534 361,256 524,687 491,423 456,608 418,004 325,125 282,105 541,547 500,852 462,413 356,009 307,721 413,187
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Table 4 The data that were used for testing the network and predicted gas percentage. Type of regime
First Transmission detector Second Transmission detector Scattering detector count count count
Liquid density
Gas percentage
Predicted gas percentage independent of liquid density
Annular Annular Annular Annular Annular Annular Annular Annular Annular Annular Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Stratified Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly Bubbly
312,832 364,852 322,829 335,781 284,983 347,409 303,234 358,132 288,287 337,796 310,267 349,999 301,924 257,071 314,652 269,753 326,785 251,902 281,272 333,899 270,673 318,151 250,521 265,472 220,218 334,199 350,924 266,330 323,825 310,915
0.735 0.735 0.795 0.795 0.826 0.826 0.852 0.852 0.98 0.98 0.735 0.735 0.795 0.826 0.826 0.852 0.852 0.98 0.98 0.98 0.795 0.795 0.826 0.826 0.98 0.826 0.826 0.735 0.735 0.852
30 70 40 50 20 60 30 70 30 60 40 70 40 10 50 20 60 20 40 70 20 50 10 20 10 60 70 10 50 50
29.3 69.3 43.9 50.7 16.5 59.9 30.1 67.5 30.4 55.7 40.0 70.5 42.3 11.6 51.3 16.3 62.3 20.3 29.4 62.4 16.5 50.3 15.1 15.0 10.8 61.7 70.2 14.9 51.3 50.0
225,970 278,066 223,629 235,546 218,683 253,094 217,222 272,727 204,020 242,746 258,563 297,490 253,693 231,871 263,703 230,364 275,242 218,318 238,187 285,606 253,391 283,591 240,941 250,807 223,251 291,705 302,218 251,703 288,129 278,928
R L0 1 R L0 sin 2arccos as ¼ 1 arccos 2 p R R 1
386,371 246,178 372,664 332,985 442,563 300,107 417,691 263,441 457,172 328,950 395,694 279,390 410,700 510,641 378,632 494,185 343,185 544,917 462,117 322,386 473,290 352,830 516,200 484,271 587,294 318,933 277,543 481,955 337,914 368,178
(1)
where, L0 is the level of the liquid in the pipe, R is the radius of the pipe and as is the void fraction in stratified regime. These parameters are shown in Fig. 1. Schematic cross sectional view of void fractions in the range of 10%e70% for stratified regime, is shown Fig. 2. Also for annular regime, different void fractions could be calculated from equation (2) (Abro et al., 1999):
aa ¼
pr2 r2 ¼ pR2 R2
(2)
Where R is the radius of the pipe, r is radius of the gas phase which is located in the center of the pipe, and aa is the void fraction in annular regime. Since the radius of the pipe (R) is constant, different void fractions could be calculated just by changing the radius of the gas phase (r). The void fractions in the range of 10%e 70% in annular regime, are shown schematically in Fig. 3 from a top side view. In the case of bubbly regime, an arrangement with 80 hollow cubic plastic straws distributed over the whole pipe cross section was used. We considered these hollow straws as gas phase, because they were filled with air. When we fill one of these straws with liquid, we consider this straw as liquid phase. By dividing the cross section area of straws filled with air by the cross section area of straws filled with liquid and air (total of 80 straws), the void fraction is calculated. Since in real situations there are many small gas bubbles over the cross section of pipe, distribution of them is almost uniform, but in our study we could not make area of straws as small as the gas bubbles in real situation. Therefore, in order to keep uniformity of distribution of gas phase respect to attenuation
of gamma rays, for each of the two straws covered by the measurement volume between the 1st detector and source, a corresponding number of straws (6) over the total pipe cross section, was treated the same way. A schematic cross sectional view of the various void fractions in the range of 10e70 percent is shown in Fig. 4. In the case of boundary between straws (thickness of plastic straws), it should be said that they are very thin and could be negligible in comparison with cross section area of straws. In general it should be noted that, although this model is a little different from real bubble regime which takes place in dynamic two-phase flows, but it is good for primary studies in the laboratory, because making bubble regime in static experimental condition is almost impossible and it could be made in dynamic condition. For liquid phase, 5 liquids of gasoline, kerosene, gasoil, lubricant oil, and water with the densities of 0.735, 0.795, 0.826, 0.852, and 0.980 g/cm3 have been used instead of one liquid with different densities, respectively. The predominant mechanism of interaction for high energy photons is Compton scattering and the photoelectric interaction can be negligible. Therefore, the probability of interaction depends just on the density of the liquid phase regardless of its composition. Because the effective atomic numbers of used liquids are close to each other, it can be assumed that all of them are one liquid phase with different densities. The air was also used as the gas phase. A137Cs source with activity of 74 MBq and a measurement time of 600 s were chosen for all the experiments. Since in this work three parameters (void fraction, flow regime and liquid phase density) were variable, at least three features or data about the flow were required in order to identify the flow regime and predict the void fraction independent of liquid phase changes. For this purpose, 3 detectors (2 transmission detectors and one scattering detector) and a fan beam source were implemented. A collimator with the
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
G.H. Roshani et al. / Progress in Nuclear Energy xxx (2017) 1e9
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Fig. 8. Comparison of experimental and predicted gas percentage for e Annular regime (a) training data (b) testing data e Stratified regime (c) training data (d) testing data and e Bubbly regime (e) training data (f) testing data.
Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004
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Table 5 Obtained errors for training and testing results of the proposed ANN models. Type of regime
Error
Train
Test
Annular Annular Stratified Stratified Bubbly Bubbly
MRE% RMSE MRE% RMSE MRE% RMSE
0.3227 2.4313 0.7797 3.8852 0.4026 2.9241
4.2128 4.1330 3.9599 6.4020 0.5275 5.7692
open of 36 was used in order to make a broad beam. Two NaI detectors with dimensions of 25.4 mm diameter and 25.4 mm thickness, were located 25 cm far from the source as transmission detectors. The 1st detector was placed in direction of 0 and 2nd one was placed in direction of 13 respect to the source. In both transmission detectors, which were connected to two MultiChannel Analyzers (MCA), only the transmitted photons (photo peaks) were registered (those within an energy interval of 650e670 keV). Another 25.4 25.4 mm NaI detector, was used as the scattering detector. In the 3rd detector which was located in the angle of 90 and was connected to a counter, total count was registered. The experimental setup is shown in Fig. 5. 3. Methods application and results
the following. Usually the precision of the ANNs are indicated using regression diagram. The more precise the network is, the closer the data to the x ¼ y line. Fig. 4 shows the comparison between the experimental and predicted results using the proposed ANN models for training and testing data using regression diagrams. The comparison between experimental and predicted (ANN) results for training and testing data are tabled in Table 3 and Table 4, respectively. From Table 3, Table 4 and Fig. 8, it is clear that the predicted gas percentage independent of the liquid phase density by ANN models is close to the experimental results. These results show the applicability of ANN as an accurate and reliable model for predicting of the gas percentage according to the registered counts in first transmission detector, second transmission detector, and scattered detector. Table 5 shows the obtained errors for the proposed predicting ANN models, where the mean relative error percentage (MRE %) and the root mean square error (RMSE) of the networks are calculated by:
N 1 X Xj ðExpÞ Xj ðPredÞ MRE% ¼ 100 N j¼1 Xj ðExpÞ 2P RMSE ¼ 4
N j¼1 Xj ðRealÞ
Xj ðPredÞ
N
2 30:5 5
(3)
(4)
3.1. Regime identification The proposed Multi-layer perceptron (MLP) model which was used for identifying the flow regime independent of liquid phase density, has been shown in Fig. 6, where the inputs are registered counts in first transmission detector, second transmission detector, and scattered detector and the output is the type of flow regime. The annular, stratified and bubbly regimes were considered as 1, 2 and 3 respectively. It means that for example if the regime is bubbly the network output will be number 3. By using the experimental set up, the data set required for training the network was achieved. The training of presented MLP network was done by Levenberg-Marquardt (LM) algorithm. In this method, first derivative and second derivative (hessian) are used for network weight correction (Hagan and Menhaj, 1994). The number of samples for training and testing data are 75 (about 70%) and 30 (about 30%), respectively. In this study, different ANN structures were tested and optimized for obtaining the best ANN configuration. Many different structures with one, two and three hidden layers with different number of neurons in each layer were tested. MATLAB 8.1.0.604 software was used for training the ANN model. Table 1 shows the specification of the proposed ANN model used in order to determine the flow regime independent of liquid phase density changes. Using this trained network, the type of regime was recognized with 100% accuracy. 3.2. Percentages prediction After identification of flow regime, 3 separate ANNs were implemented to predict the void fraction for each flow regime. The inputs of these 3 ANNs are same as the mentioned ANN for regime identification and the output is void fraction percentage. The procedure of flow regime identification and void fraction measurement independent of liquid phase density changes, is shown in Fig. 7. The specifications of the proposed ANN models used in order to predict the gas percentage independent of the liquid phase density, were tabled in Table 2. The precision of these prediction networks will be discussed in
Where N is the number of data and ‘X (Exp)’ and ‘X (Pred)’ stand for experimental and predicted (ANN) values, respectively. 4. Conclusions In this work, based on our previous studies, we combined multibeam gamma ray attenuation and dual modality densitometry techniques in order to identify the flow regime in addition to measuring void fraction independent of the liquid phase changes. A fan beam geometry, comprised of one 137Cs source and three 1 inch NaI(Tl) detectors were used in the detection system. Two of these three detectors were implemented to measure transmitted photons and the third one was used to measure scattered photons. Also, four ANNs were used in this study, the first one for identifying the flow regime independent of liquid phase density changes and the other three ANNs for predicting void fraction independent of liquid phase density changes. Using this methodology, three flow regimes of annular, stratified and bubbly were correctly distinguished in liquid phase density changes range of 0.735e0.980 g/cm3 and void fraction was predicted with a mean relative error (MRE) of less than 4.3%. The proposed methodology could be applied for identifying flow regime and measuring the void fraction in situations where the density of liquid phase of gas-liquid two phase flows could be changed. For instance, 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 Abro, E., Khoryakov, V.A., Johansen, G.A., 1999. Determination of void fraction and flow regime using a neural network trained on simulated data based on gamma-ray densitometry. Meas. Sci. Technol. 10, 619e630. http://dx.doi.org/ 10.1088/0957-0233/10/7/308. Bishop, C.M., James, G.D., 1992. Analysis of multiphase flows using dual-energy gamma densitometry and neural networks. Nucl. Instrum. Methods 327, 580e593. http://dx.doi.org/10.1016/0168-9002(93)90728-Z. Cong, T., Su, G., Qiu, S., Tian, W., 2013. Applications of ANNs in flow and heat transfer problems in nuclear engineering: a review work. Prog. Nucl. Energy 62, 54e71.
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Please cite this article in press as: Roshani, G.H., et al., Identification of flow regime and estimation of volume fraction independent of liquid phase density in gas-liquid two-phase flow, Progress in Nuclear Energy (2017), http://dx.doi.org/10.1016/j.pnucene.2017.02.004