Applying Data Mining and Artificial Intelligence Techniques for High Precision Measuring of the Two-Phase Flow’s Characteristics Independent of the Pipe’s Scale Layer

Abstract

Scale formation inside oil and gas pipelines is always one of the main threats to the efficiency of equipment and their depreciation. In this study, an artificial intelligence method method is presented to provide the flow regime and volume percentage of a two-phase flow while considering the presence of scale inside the test pipe. In this non-invasive method, a dual-energy source of barium-133 and cesium-137 isotopes is irradiated, and the photons are absorbed by a detector as they pass through the test pipe on the other side of the pipe. The Monte Carlo N Particle Code (MCNP) simulates the structure and frequency features, such as the amplitudes of the first, second, third, and fourth dominant frequencies, which are extracted from the data recorded by the detector. These features use radial basis function neural network (RBFNN) inputs, where two neural networks are also trained to accurately determine the volume percentage and correctly classify all flow patterns, independent of scale thickness in the pipe. The advantage of the proposed system in this study compared to the conventional systems is that it has a better measuring precision as well as a simpler structure (using one detector instead of two).

1. Introduction

The need to continue drilling or stopping, optimizing the separation process, how the extracted material is transported, and many other things depend on recognizing the flow pattern and volume fraction of each component. Gamma radiation is used for the detection, although hydrostatic, ultrasonic, and hydrometric techniques can also be used to detect the flow pattern and volume fraction of the multiphase flow. In 1999, Abro et al. conducted one of the first studies in this field to determine the volume percentage [1]. The use of the low-energy gamma-ray of americium-241 instead of the traditional source of caesium-137, and the use of three detectors at 140°, −154°, and 180° relative to the source to find the optimal position of the detector, were the most positive and creative points of the study. Sattari et al. presented a study in 2020 by decreasing the number of detectors to one and using two independent GMDH neural networks to determine the percentage of volume fraction and flow regime [2]. The simulation of three common flow patterns, namely annular, homogeneous, and stratified, in void fractions of 5% to 90% was done by removing the noise of the extracted photon spectrum using a Savitzky−Golay filter and providing the filter output as the input of the neural network. The approach in the study of Sattari et al. ultimately predicted the volume percentage and type of flow regime with a root mean square error (RMSE) less than 1.11; however, oil and gas transmission pipes sometimes deposit scale after a period of use, which was not investigated in this study. Studies have been conducted in recent years to identify these scales and to make the mentioned predictions. In 2015, Oliveira et al. conducted a pipeline survey using a structure that was included a detector and a cesium-137 energy source [3]. The process was such that the source and the detector were continuously shifted 5 mm at the same time, and the detector received radiation emitted from the source for 60 s. The results proved that the presence or absence of scales, as well as their thickness, can be predicted with good accuracy. In [4], the researchers were able to model flow patterns in different volume percentages and thickness scales using the SVM network, and to classify the flow regimes with a not so high accuracy. The volume percentage was also calculated with an RMSE of less than 3.67. Alamoudi et al. attempted to develop a gamma attenuation technique using RBFNN to determine the scale thickness of oil pipelines where two-phase flow with various symmetric patterns and volume fractions exist [5]. The applications of artificial intelligence in multiphase flowmeters have been discussed in many studies to date, some of which can be found in [6,7,8,9,10,11,12,13,14,15]. In pipelines, valves, and pumps used in the production and processing of oil, scales may form over time. The formation of scales leads to the blockage and obstruction of the flow of fluid. At this time, the oilfield scale inhibition process becomes important. These deposits lead to a reduction in the inner diameter of the pipe and consequently cause a reduction in the life of the equipment, reducing efficiency, and ultimately increasing costs [16]. In [17], the researchers implemented a structure consisting of a dual- energy gamma source to detect the type of flow regimes independent of scale thickness. Although these important parameters were predicted with an acceptable accuracy, the use of two detectors increased the cost and complexity of the detection system. An example of scale deposition in the oil pipe is shown in Figure 1.

2. Simulation Setup

The modeling of the detection system in this study was performed using version X of the Monte Carlo N-Particle Code (MCNPX) [18]. The schematic configuration of the above-mentioned detection system is demonstrated in Figure 2. As is apparent, this schematic diagram uses the stratified flow as an example. The dual-energy source is on the left, a pipe in which two-phase flows and scales are formed in it is on the middle, and an NaI detector to receive the transmitted photons is on the right.

The disk source defined for modeling the radiation source. It was located inside a shield to move the beams toward the transmission detector. The source includes two radioisotopes of cesium-137 and barium-133, which acted at 0.662 MeV and 0.356 MeV, respectively. In the proposed structure, just in front of the photon emission source, a 25.4 mm NaI detector was placed to receive the passing photons. Three annular, stratified, and homogeneous flow regimes were simulated by 15% steps in 10% to 85% volumetric percentages with 7 different scale thicknesses (0, 0.5, 1, 1.5, 2, 2.5, and 3 cm). These three regimes are illustrated in Figure 3.

In this study, a steel pipe with inner diameter of 20 cm was selected. The scale inside the pipe was a symmetrical circular layer of BaSO₄ with different thicknesses. The depiction of the recorded spectra for three flow patterns and different gas volume percentages is apparent in Figure 4.

3. Feature Extraction

Elimination of useless data, reduction of size, facilitation of the training process, and generalization of data can be considered as goals of feature extraction. Using these extracted features has a better result on the raw data than using machine learning directly, and makes the interpretation of data simpler. The schematic diagram of this procedure can be seen in Figure 5.

Data analysis may be very difficult when the amount of data is huge. Feature extraction in the domain of time, frequency, and time−frequency are among the various methods of feature extraction. Of course, these are not the only methods, and there are several methods that could be implemented to decrease the dimensionality of the data. In the present study, frequency domain feature extraction was performed, and the received signal was converted to the frequency domain using FTT (Equation (1) [19]). Then, the first to fourth dominant frequencies were extracted.

$$Y\left(k\right)={\displaystyle \sum }_{J=1}^{n}x\left(J\right)w_n^{\left(y-1\right)\left(k-1\right)}$$

(1)

where Y(k) = FFT(X) and w_n = e^((−2πi)∕n) is one of n roots of unity.

As mentioned earlier, one detector was utilized in present investigation and four features were extracted from it. So, these four features were utilized to train NNs. The converted signals of all three flow regimes to the frequency domain at a 1 cm scale thickness are shown in Figure 6.

4. RBF Neural Network

In recent years, different advanced computational approaches have been applied in various fields of study, such as fluid mechanic engineering [20,21,22,23,24,25,26,27,28], chemical engineering [29,30,31,32,33], electrical engineering [34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59], computer engineering [60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76], civil engineering [77,78,79], petroleum engineering [80,81,82,83,84,85,86,87,88,89,90,91,92,93,94], energy engineering [95,96,97,98,99,100,101], mathematics [102,103,104,105,106,107,108,109,110], medical and pharmaceutical [111,112,113,114,115,116]. It has been proved that ANN is one of the most powerful computational approaches. In addition, RBF has become one of the most widely used types of neural networks due to the various applications that have been developed for it; therefore, it is the most important competitor for multilayer perceptron. The main architecture of RBF consists of three layers. The input layer is a puller layer and with no calculation occurring in it. The second layer (hidden layer) establishes a nonlinear conformity between the input space and another space with a larger dimension. Finally, third layer generates a weighted sum along with a linear output. Such an output would be useful if RBF was used to approximate the function. An exclusive trait of RBF is processing that is done in the hidden layer. Making clusters from input space patterns is a basic idea of this process. In addition, this distance measurement is done nonlinearly, so if a pattern is located in an area adjacent to the center of a cluster, the generated value will be close to 1. The value obtained outside this area is significantly reduced. The important point is that this region is radially symmetric around the center of the cluster, so the nonlinear function becomes a known function of the radial base. The most common form of the radial base function is as follows [117]:

$$\phi \left(r\right)=\exp \left[-\frac{r^2}{2{\sigma }^2}\right]$$

(2)

In RBF, r is the numerical value of the distance from the center of the cluster. Equation (2) shows a normal bell-shaped curve. Usually, the measured distance to the center of the cluster is the Euclidean distance. For each neuron in the hidden layer, the weights show the coordinates of the center of the cluster. Therefore, once a neuron receives an X input pattern, the distance is obtained using the following equation [55]:

$$r_j=\sqrt{{\displaystyle \sum }_{i=1}^n{\left(x_i-w_{ij}\right)}^2}$$

(3)

Therefore, the output of jth neuron in the hidden layer is as follows:

$${\varnothing }_j=\exp [-\frac{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-w_{ij}\right)}^2}{2{\sigma }^2}]$$

(4)

The variable σ is defined as the width or radius of the bell curve, and is sometimes necessarily determined experimentally. When the distance from the center of the normal curve reaches σ, the output decreases from 1 to 0.6.

The hidden layer includes some units which are weighted, and these weights are related to the vector that represents the center of the cluster. Weights can be obtained using traditional methods like the K-Mean or methods based on the Kohonen algorithm. In any case, the training is done non-supervised, but the number of expected clusters (k) is pre-selected, and then these algorithms obtain the best fit for these clusters. In this research, MATLAB 2018b software was used to extract the mentioned characteristics and design the RBF neural network. In MATLAB software, there are many different toolboxes for neural network training, but in designing this network, no pre-designed toolbax was used for designing the RBF network in order for more freedom of action, and all steps of neural network training were programmed. It is necessary to say that the preset function of newrb (available in the MATLAB software) was used to train the network.

Training dataset: The sample of data utilized to fit the model. The dataset that is used to train the model. The model sees and learns from this data.

Testing dataset: The sample of data utilized to provide an unbiased evaluation of a final model fit on the training dataset.

5. Results and Discussion

Two neural networks of RBF were designed in this study, with the aim of determining the type of flow patterns and estimating the gas volume percentages independent of the thickness of scale in the pipe. The structure of these networks is shown in Figure 7. The inputs of these networks were the amplitude of the first to fourth dominant frequencies of the received signal, and their outputs were the void fraction and type of flow patterns. The type of flow regimes in the classifier network were shown with numbers 1, 2, and 3. In addition, the numerical ranges for each of the regimes were defined as follows. Numbers between 0.5 and 1.5 returned to 1. Numbers between 1.5 and 2.5 indicated a homogeneous regime, and numbers in the range 2.5 to 3.5 indicated a stratified regime.

A confusion matrix was implemented to represent the performance of the classifier network. This matrix can be seen for both the training and testing datasets in Figure 8, which shows 100% accuracy of the trained network.

The predictor network performance for training and testing data can be seen in Figure 9. This figure displays four graphs fir the f fitting, regression, error, and error histogram. In the fitting diagram, the optimal output and the output predicted by the neural network are plotted on a diagram (obviously, the greater the compatibility of these two graphs, the higher the accuracy of the network). In the regression diagram, the network output is displayed as black circles and the desired output is displayed as a blue line. The error diagram shows the difference between the network output data and the desired data. In addition, the error histogram shows the error scatter. In addition, four error criteria, namely mean square error (MSE), RMSE, mean absolute error (MAE), and mean relative error (MRE), were calculated to calculate the error rate of this network as follows:

The specifications and accuracy of the trained networks can be seen in

Table 1. Specifications of the designed networks.

	Predictor Network		Classifier Network
Goal of MSE	0		0
RBF spread	5		4
Number of neuron in hidden layer	38		43
CalculCalculated MSE	Train data	Test data	Train data	Test data
	3.36	6.015	0	0
Calculated RMSE	1.83	2.45	0	0
Calculated MAE	1.57	1.72	0	0
Calculated MRE%	5.86	5.16	0	0

.

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

(5)

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

(6)

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

(7)

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

(8)

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

6. Conclusions

In the present investigation, an attempt was made to present a manner for predicting the volume percentage and flow pattern in scaled oil pipelines based on a non-invasive method with a creative structure based on gamma radiation. In this regard, using the Monte Carlo code, a dual-energy source was simulated on one side of the oil transfer pipe and a detector on the other side. This process was performed to simulate different flow regimes in different volume percentages, as well as to model the thickness of the scale inside the tube. The feature extraction routine in the frequency domain, after all the simulations and data collection, was used to better decipher the collected data. The extracted features, which included the amplitude of the first to fourth dominant frequencies, were considered as neural network inputs. The prediction of volume percentage with RMSE less than 1.83 and fully classifying flow regimes were the results of the two designed neural networks. The number of detectors was decreased to one, resulting in a simplified system and reduced costs. This reduction was due to feature extraction method, which is an advantage over previous works. The results of this investigation show that the proposed process can be used in oil and petrochemical industries to measure the volume percentages and detect the fluid flow regimes.