Introducing a Precise System for Determining Volume Percentages Independent of Scale Thickness and Type of Flow Regime

Abstract

When fluids flow into the pipes, the materials in them cause deposits to form inside the pipes over time, which is a threat to the efficiency of the equipment and their depreciation. In the present study, a method for detecting the volume percentage of two-phase flow by considering the presence of scale inside the test pipe is presented using artificial intelligence networks. The method is non-invasive and works in such a way that the detector located on one side of the pipe absorbs the photons that have passed through the other side of the pipe. These photons are emitted to the pipe by a dual source of the isotopes barium-133 and cesium-137. The Monte Carlo N Particle Code (MCNP) simulates the structure, and wavelet features are extracted from the data recorded by the detector. These features are considered Group methods of data handling (GMDH) inputs. A neural network is trained to determine the volume percentage with high accuracy independent of the thickness of the scale in the pipe. In this research, to implement a precise system for working in operating conditions, different conditions, including different flow regimes and different scale thickness values as well as different volume percentages, are simulated. The proposed system is able to determine the volume percentages with high accuracy, regardless of the type of flow regime and the amount of scale inside the pipe. The use of feature extraction techniques in the implementation of the proposed detection system not only reduces the number of detectors, reduces costs, and simplifies the system but also increases the accuracy to a good extent.

1. Introduction

Gas volume fraction (GVF) is one of the important parameters in describing biphasic flows in the oil industry because calculating the empty fraction is necessary to predict values such as heat transfer, pressure drop, and critical two-phase flow occurrence to calculate the empty fraction. Quantitative knowledge of these parameters is required in the oil industry. Various methods can be used to measure the empty fraction [1]. Although the main axis of diagnosis in this study is gamma radiation, hydrostatic, hydrometric, and ultrasonic are other useful alternative techniques for detecting the volume fraction of multiphase flow. In [2], an artificial neural network (ANN) and extraction of various features were used to increase the accuracy of two-phase flowmeters based on X-ray radiation. An X-ray tube for sending photons, a NaI detector for absorbing photons, and a Pyrex glass pipe through which the photons pass form the structure used in this paper. The Monte Carlo MCNP-X code was used to model the geometry. Feature extraction was performed in the time domain with five features and was given as input to the neural network. Multi-Layer Perceptron (MLP) was applied to approximate the function related to the output–input relationship. The procedure proposed by Basahal et al. was able to accurately obtain the flow pattern and predict the volume fraction of two-phase flow components. The root mean square error (RMSE) was less than 0.51, the mean absolute error (MAE) was less than 0.4, and the mean absolute error percentage (MAPE) was less than 1.16%. Taylan et al. [3] conducted related research and used a combination almost identical to the previous study. Their structure consists of a Pyrex glass pipe in the middle, an X-ray tube on one side, and two detectors on the other side. The difference was in the number of detectors. Flow regime and volume percentage in a three-phase flow of oil, water, and gas were calculated. As usual, the simulation procedure was performed by MCNP-X code. The signals were collected and the simulations were completed, then the Fast Fourier Transform (FFT) was used to convert to the frequency domain. The first and second dominant frequency amplitudes were used as neural network inputs. Three RBFNN networks were trained to predict the type of regime and the volume percentage of gas and water. Correct diagnosis of all flow regimes and determination of volume percentages with Mean Relative Error (MRE) less than 2.02% shows that the use of frequency features can be effective in determining these important parameters. The scale formation inside a few pipes can be seen in Figure 1. The proposed structure also includes two detectors, one that absorbs the transmitted photons and the other the scattered photons.

Roshani and his colleagues in [4] attempted to use the obtained absorption spectra to train and test the multilayer perceptron network (MLP) using an X-ray source, a detector, and other routine procedures. After training, MLP neural networks can conjecture the volume ratio of each petroleum product with an average absolute error of 2.72. Sattari et al., in two studies [5,6], examined the time characteristics to determine the volume percentages and the type of flow regimes. Research [5] extracted a large number of time-domain characteristics and identified the most effective ones in a creative way. In [6], time characteristics were considered the input of the GMDH neural network. Although the accuracy of the obtained networks was very high in these studies, not considering the scale thickness in the oil pipes was one of the weaknesses of these studies. In [7], GMDH neural networks were used to determine the volume percentages, but with the difference that the neural network inputs were features named count under Compton continuum, count under photopeak of 1.173 MeV, count under photopeak of 1.333 MeV, and the average value of the recorded spectrum. In other studies, signal frequency characteristics [8] and signal wavelet transform characteristics [9,10] were used to determine the volume percentages. The deposition of scale over time in oil pipelines is undeniable, which reduces the efficiency of oil industry systems and devices. Sedimentation of the scale inside the pipe causes non-invasive detection systems to fail to function properly. In all the mentioned studies, failure to investigate the effects of scale thickness on the detection of multiphase flow parameters can be introduced as a major shortcoming. In [11], a method of attenuation of gamma through a dual-energy source with an RBFNN neural network is proposed to determine the thickness of the scale formed in oil pipelines. Failure to extract the appropriate characteristics from the received signals and the use of raw signals as input to the neural network has not only imposed a large computational load on the system but has also prevented access to high accuracy. In research [12], although both the effects of scale thickness and frequency characteristics of signals were investigated, the lack of high accuracy in the detection system indicates the inadequacy of frequency characteristics in determining the type of flow regimes and predicting volume percentages. Inspired by previous research, this study attempted to measure the volume percentage under conditions where the scale was deposited inside the pipe. For this purpose, different conditions, including three different flow regimes in different volume percentages, as well as the number of different scales in the pipe, were simulated so that these different conditions can be considered as neural network inputs for training. Wavelet features were used to reduce computational costs and better interpret data as well as achieve high accuracy. Additionally, in this research, the number of volume percentages independent of the type of flow regime and the amount of scale inside the pipe can be identified with very high accuracy, which are the most important contributions of this research. The proposed method can be used in many fields of science, including medicine [13], chemical [14], and micro and nanofluidics [15,16], which can be the subject of future studies.

2. Simulation Setup

The modeling part of the detection system of this research was performed using version X of the Monte Carlo Particle Code (MCNPX) [17]. The mentioned diagnostic system is illustrated in Figure 2. There is a dual-source with a protective housing that directs gamma radiation to a pipe containing fluid at the top of the image. In the middle of the image is a pipe containing fluid, inside which a scale is also formed. At the bottom of the image, a detector was placed that absorbs photons passing through the pipe and collects the data. The attenuation for a narrow gamma-ray beam follows Lambert–Beer’s law according to the following equation:

$$I=I_0{e}^{-\mu \rho x}$$

(1)

where the intensity of uncollided and primary photons are shown by I and I₀, respectively. µ and $\rho$ represent the mass attenuation coefficient and density of absorber material, respectively. x is the beam path length through the absorber

The energy source of the structure is a gamma source with two isotopes, cesium-137 and barium-133, the former operating at 0.662 MeV and the latter at 0.356 MeV. Three homogeneous, annular, and stratified flow regimes with steps of 15% in a volume percentage of 10% to 85% with seven various scale thicknesses (0 cm, 0.5 cm, 1 cm, 1.5 cm, 2 cm, 2.5 cm, and 3 cm) was simulated. Inside the pipe, there was a symmetrical layer of BaSO₄ with various thicknesses. In fact, the effects of changing the velocity, temperature, and pressure of each phase showed themselves in the type of flow regime formed inside the pipe [18,19]. For example, if the velocity of the gas phase inside the pipe is too high, it will cause the liquid phase to stick to the wall of the pipe, resulting in the formation of an annular phase. If in a horizontal pipe, the pressure of both phases is low and in the same range, due to the density difference between the two materials, the liquid phase is placed at the bottom of the pipe, and the gas phase is placed on top of it. This type of flow regime is called stratified. The recorded spectra for different scale thicknesses of 1 cm and different empty space fractions are shown in Figure 3. What was achieved in this study was confirmed by several experiments that were already performed in our previous articles [20]. The obtained detector responses were compared in experimental and simulation. Since the Tally output in the MCNP code is per source particle, both were normalized to units. The value of 2.2% for the detector response was the maximum relative difference between the simulation data and the experimental data. As can be seen, a good agreement was obtained between the experimental data and the simulation results. It is worth noting that the experiments and, consequently, the simulations were performed in static conditions. The actual working conditions were dynamic, but the reference points for flowmeter training were fixed and could be considered static. In real conditions, multiphase flow meters were used to train flowmeters to determine the volume fraction and detect flow regimes. One of the cases in which rapid active gamma-ray neutron analysis was used for quantitative analysis for fast, non-intrusive, and online measurements of multiphase oil/gas/seawater flow is [21]. In the research that was conducted, although the simulations were used in real conditions, they were considered in static conditions. In [22], to describe the water extracted from offshore oil wells, the detection of transmitted and scattered gamma radiation was used, and its possibility was investigated. They determined the salinity and even the type of salt in the extracted water by measuring the gamma rays scattered, gamma rays transmitted, and calibration

Figure 3 show the amount of energy received by the detector in terms of count per source particle. At two energies, 0.662 MeV and 0.356 MeV, this graph peaked, which is due to the energy of the dual-energy source of cesium-137 and barium-133. The rest of the spectrum received by the detector is due to the interaction of photons sent by the source with the environment, resulting in the loss of energy and ultimately received by the detector.

3. Discrete Wavelet Transform

The received signal can be broken down into several sets by discrete wavelet transform (DWT), and each set is a time series of coefficients that describe the temporal evolution of the signal in the corresponding frequency band. One of the most common methods of time-frequency filtering is the use of discrete wavelet transform (DWT) [23,24]. The multi-resolution analysis is possible by decomposing the discrete signal x (n) into low and high-frequency components using the DWT method. An iterative Mallat algorithm is required to determine DWT. This method works based on a mother wavelet function and a corresponding scaling function to determine the high and low band filters. The signal x (n) is decomposed into low aj, k (approximately) and high dj, k (in detail) frequency components (Figure 4) with multilevel filter banks:

$$a_{j,k}={{\displaystyle \sum }}_{l}h\left(l-2k\right)a_{j-1,m}$$

(2)

$$d_{j,k}={{\displaystyle \sum }}_{l}g\left(l-2k\right)a_{j-1,m}$$

(3)

where k is related to the translation at each level of the wavelet function. l is the number of levels and is an integer scale. j is a parameter that affects the DWT scaling. h (l) and g (l) are low-pass and high-pass quadrature filters, respectively. m is used in the scaling function as a translation of the j scale. Wavelet transform includes several families of wavelet functions such as Daubechies, Haar, and so on. The Daubechies 2 (db2) wavelet was selected to analyze the signals received from the scintillator detector.

As can be seen in Figure 4, performing the wavelet transform operation from step 5 onwards no longer provides acceptable high-frequency information, so to reduce the computational volume, the wavelet operation is performed up to the fourth step. The approximation signals of step 4 (a4) and details of step 1 to 4 (d4, d3, d2, and d1) were averaged, and these characteristics were used as the input of the GMDH Neural Network for training.

4. Artificial Neural Network

In 1968, a Ukrainian mathematician developed a method for learning inductive statistics called the Group Method of Data Handling (GMDH), which later made him famous [25]. A self-control model was developed with the power to monitor the synthesis and related system problems and to solve predictions and classifications. It is worth mentioning that, in the recent years, various mathematical approaches have been used in different research fields such as electrical and computer engineering [26,27,28,29,30], mechanical engineering [31,32,33,34], civil and urban engineering [35,36,37], biomedical engineering [38,39], industrial engineering [40,41,42,43], and physics [44,45], but among them, ANN is the most well-known and powerful numerical tool for prediction and classification [46,47,48]. Neuron values, invisible layer, effective input profile, and efficient network fabrication were determined independently in the GMDH operation. It is assumed that the input–output relationship of the system is characterized as a significant order polynomial, which is shown below as the Kolmogorov–Gabor polynomial.

$$y=a_0+{\displaystyle \sum }_{i=1}^m{a}_i{x}_i+{\displaystyle \sum }_{i=1}^m{\displaystyle \sum }_{j=1}^m{a}_{ij}{x}_i{x}_j+{\displaystyle \sum }_{i=1}^m{\displaystyle \sum }_{j=1}^m{\displaystyle \sum }_{k=1}^m{a}_{ijk}{x}_i{x}_j{x}_k+\dots$$

(4)

where a (a₁, a₂,…, a_m) are weights or coefficients of vector, x (x₁, x₂,…, x_m) are also vector inputs or the same extracted features, and y is the output of the network. The steps of the GMDH algorithm are as follows:

Step A: Generating novel variants $z_1$, $z_2$, …, $z_{\left(\underset{2}{m}\right)}$. In this part, for the total non-dependent variables (characteristics) (x₁, x₂,…, x_m), two synchronically and for any $\left(\underset{2}{m}\right)$ admixture, the quadratic regression polynomials are computed by considering Equation (5).

$$Z=c_1+c_2{x}_i+c_3{x}_j+c_4{x}_i^2+c_5{x}_j^2+c_6{x}_i{x}_j$$

(5)

This step aims to achieve the $c_i$ coefficients. The least-squares algorithm was utilized to obtain the desired coefficients. Each obtaining $\left(\underset{2}{m}\right)$ compiled quadratic regression polynomial approximates the insignificant output.

Step B: Screening of non-significant z’s in such a way that the error of each output in the given neurons (each neuron must approximate the quadratic regression polynomial) is calculated with the desired output, and the outputs (neurons) with the maximum error rates are not based on a scale of options. Another is applied to build the following layer. Here, the first latent layer is produced, and the affected neurons are systematically selected.

Step C: Applying modern variables ($z_1$, $z_2$, …, $z_{\left(\underset{2}{m}\right)}$) as the quadratic regression polynomial inputs to generate modern variables. It means that the novel polynomial is obtained from a bygone polynomial ($z_1$, $z_2$, …, $z_{\left(\underset{2}{m}\right)}$) by making polynomials of polynomials; the high-order polynomial was preserved, solving intricate and nonlinear issues. Then, step B was repeated, and the outputs were considered with the best estimate of the desired outputs. After the creation of hidden layer number 2, the production of new polynomials and their best approximations takes enough time to obtain the best input–output relationships and eventually to become Kolmogorov–Gabor polynomials.

Step D: Checking the GMDH neural network. At this stage, the evaluation of the final model against the experimental data set is performed to determine that the neural network has specifically determined the output–input relevance. In the present study, the sample percentage for GMDH neural network training is approximately 70% (88 samples), and the sample percentage for neural network testing is 30% (38 samples). The GMDH neural network training flowchart is shown in Figure 5.

To estimate the volume fraction of each phase in this investigation, a GMDH network was used, and the derived features (as discussed in the previous step) were considered as inputs of the GMDH neural network for testing and training.

5. Result and Discussion

In this research, a network structure of GMDH was taught with the mean signals of the fourth stage approximation and the mean signals of the details of the first to fourth stages of the wavelet transform. The output of this network is the percentage of empty volume in the pipe. The structure of this network is shown in Figure 6. To show the accuracy of the designed network, the regression diagram and the error diagram for both the training and test data sets can be seen in Figure 7. It should be noted that three error criteria with the names of mean relative error percentage (MRE%), mean square error (MSE), and root mean square error (RMSE) are calculated and shown in

Table 1. Calculated errors.

Data Set	MRE%	MSE	RMSE
Train	1.22	0.19	0.44
Test	0.97	0.12	0.35

to determine the accuracy of the network according to the following equations.

$$MRE\%=100\times \frac{1}{N}{{\displaystyle \sum }}_{j=1}^N\left|\frac{X_j\left(Exp\right)-X_j\left(Pred\right)}{X_j\left(Pred\right)}\right|$$

(6)

$$MSE=\frac{{{\displaystyle \sum }}_{j=1}^N{\left(X_j\left(Exp\right)-X_j\left(Pred\right)\right)}^2}{N}$$

(7)

$$RMSE={\left[\frac{{{\displaystyle \sum }}_{j=1}^N{\left(X_j\left(Exp\right)-X_j\left(Pred\right)\right)}^2}{N}\right]}^{0.5}$$

(8)

where N is the number of data, ‘X (Exp)’ and ‘X (Pred)’ stands for the experimental and predicted (ANN) values, respectively.

Wavelet transform is the technique used to extract the characteristics in this research. Advances to the fourth stage of wavelet transform led to the extraction of very suitable characteristics as neural network inputs. The comparison of this detection system with the others is shown in

Table 2. A comparison of the accuracy of the proposed detection system and previous studies.

Ref.	Extracted Features	Type of Neural Network	MSE		RMSE
			Training	Testing	Training	Testing
[5]	Time-domain	MLP	0.21	0.036	0.46	0.6
[6]	Time-domain	GMDH	1.24	1.20	1.11	1.09
[7]	Lack of feature extraction	GMDH	7.34	4.92	2.71	2.21
[8]	Frequency-domain	MLP	0.17	0.67	0.42	0.82
[49]	Lack of feature extraction	MLP	17.05	9.85	4.13	3.14
[50]	Lack of feature extraction	MLP	2.56	2.56	1.6	1.6
[current study]	Wavelet feature	GMDH	0.19	0.12	0.44	0.35

. It is clear that by extracting the convenient characteristics, the accuracy of the system can be outstandingly increased. In operating conditions, petroleum products are mixed in different types based on the pressure, temperature, and velocity of the products. Additionally, over time, the scale settles inside the oil pipes. In this study, in order for the proposed system to work properly in operating conditions, different conditions were simulated, including different flow regimes and different thicknesses of scales in different volume percentages. These simulations were considered primary data for system implementation. Finally, the detection of volume percentages independent of the type of flow regimes and the amount of scale inside the pipe with very high accuracy were considered as the advantages of this research. The study of three-phase flows with the method discussed in this article can be a good research topic for the subsequent study of researchers. The use of deep neural networks to determine the parameters of multiphase flows can also be evaluated for subsequent work. Requiring employees to use protective equipment when working with this device is a limitation of this research. The reason for this limitation is the inability to turn off the device and the device always being on.

6. Conclusions

Determining the volume percentage in scaled oil pipelines was the goal of this scrutiny. The Monte Carlo code became the basis for structural simulation in which the scale thickness was simulated at different volume percentages. The prementioned structure consists of a gamma energy source on one side of the pipe and a detector on the other side of the pipe. In this structure, all that is needed is radiation from the source to the detector. Radiation through the pipe is the main source of data collection. After collecting these data, the wavelet feature extraction technique was applied to access the high- and low-frequency information of the received signal. The average values of a4, d4, d3, d2, and d1 were given as inputs to the neural network to predict the volume percentage with an RMSE of less than 0.44. The superiority of this scrutiny over previous studies is the use of one detector. This reduction in the number of detectors is due to the wavelet feature extraction techniques and GMDH neural network. In addition to increasing the simplicity of the system, reducing the final manufacturing cost are advantages. According to the growing needs of the oil industry in the use of highly accurate and non-invasive devices to determine the parameters of multiphase flows, using the proposed methodology due to the high accuracy and low cost of the proposed system compared to previous ones is highly recommended.