Optimizing the Gamma Ray-Based Detection System to Measure the Scale Thickness in Three-Phase Flow through Oil and Petrochemical Pipelines in View of Stratified Regime

Abstract

As the oil and petrochemical products pass through the oil pipeline, the sediment scale settles, which can cause many problems in the oil fields. Timely detection of the scale inside the pipes and taking action to solve it prevents problems such as a decrease in the efficiency of oil equipment, the wastage of energy, and the increase in repair costs. In this research, an accurate detection system of the scale thickness has been introduced, which its performance is based on the attenuation of gamma rays. The detection system consists of a dual-energy gamma source (²⁴¹ Am and ¹³³ Ba radioisotopes) and a sodium iodide detector. This detection system is placed on both sides of a test pipe, which is used to simulate a three-phase flow in the stratified regime. The three-phase flow includes water, gas, and oil, which have been investigated in different volume percentages. An asymmetrical scale inside the pipe, made of barium sulfate, is simulated in different thicknesses. After irradiating the gamma-ray to the test pipe and receiving the intensity of the photons by the detector, time characteristics with the names of sample SSR, sample mean, sample skewness, and sample kurtosis were extracted from the received signal, and they were introduced as the inputs of a GMDH neural network. The neural network was able to predict the scale thickness value with an RMSE of less than 0.2, which is a very low error compared to previous research. In addition, the feature extraction technique made it possible to predict the scale value with high accuracy using only one detector.

1. Introduction

The presence of scale inside oil pipes causes problems such as reducing the cross-section of oil pipes, disrupting the performance of oil equipment, increasing the cost and time of repairs, and even emergency shutdown of the oil field. Using an accurate and non-invasive diagnostic system to diagnose this problem and take action to fix it can prevent the above-mentioned problems. In recent years, systems based on gamma-ray attenuation to determine the parameters of the type of flow regime and volume percentages in three-phase [1,2,3] and two-phase [4,5,6] fluids have received much attention from researchers. In these researches, different gamma sources have been investigated. Still, the big problem of these researches is the use of two or more detectors, which has increased the cost and complexity of the detection structure. In study [7], researchers proposed a system based on gamma rays to determine volume percentages and type of flow regimes, whose detection structure consisted of a cesium source and two sodium iodide detectors. They simulated a two-phase flow in different volume percentages and three regimes of annular, stratified, and homogeneous using Monte Carlo N Particle (MCNP) code. In order to increase the accuracy, they examined several time characteristics and introduced the best time characteristic with an innovative method. The use of two detectors is the most fundamental gap of this research, which, in addition to imposing a high cost on system design, has increased the complexity of the detection system. In [8], researchers investigated the performance of the GMDH neural network, but the lack of characteristic extraction and the use of raw signals as inputs of the neural network prevented access to high accuracy. In the following research [9], the researchers put the temporal characteristics as the inputs of the GMDH neural network. This neural network has the ability to self-organize and can recognize the network structure and appropriate inputs automatically. They predicted the type of flow regimes and volume percentages with high accuracy. Alamoudi et al. [10] proposed an in-pipe scale value detection system. The proposed detection structure consisted of a dual-energy gamma source and two detectors placed opposite each other on either side of a test pipe. In the test pipe, a two-phase flow of oil and gas in different volume percentages was simulated. They did not check the characteristics of the received signals, which made not only the accuracy of their proposed system not high, but also the structure of the introduced system was complex and expensive. The use of radioisotope devices has problems such as the need to use protective clothing, difficult transportation, inability to turn off, etc.; for this reason, in recent years, the use of X-ray tubes to determine various parameters of Multiphase flows has been studied by researchers. In [11], to determine the type of flow regime and volume percentages in two-phase flows, a system consisting of an X-ray tube and a detector was introduced. They extracted temporal characteristics from the signals received by the detector and considered them as inputs of the MLP neural network. Two neural networks were designed that were responsible for determining the type of flow regimes and the percentage of void fraction separately. In [12], a three-phase flow was simulated in three different regimes and different volume percentages. The simulated structure consisted of an X-ray tube and two sodium iodide detectors. The received signals were processed in the frequency domain, and four frequency characteristics were considered as the inputs of the RBF neural network. Three RBF neural networks were trained, two of which had the task of determining volume percentages, and the other one had the task of determining the type of flow regimes. The X-ray tube has also been used to determine the type and amount of product passing through oil pipelines [13,14]. In [13], four petroleum products were simulated in a two-by-two combination in a test pipe. An X-ray tube was placed on one side of the pipe, and a sodium iodide detector was placed on the other side of the pipe directly in front of the source. The signals received from each simulation without any processing were simultaneously considered as the input of three MLP neural networks, and the volume ratio of each product was predicted with a mean absolute error of less than 2.72. In the next research [14], in order to increase the accuracy of the proposed system in research [14], the received signals were processed using wavelet transform, and the characteristics of approximate and detailed signals were extracted. They increased the accuracy of the detection system by about two times.

Inspired by previous researches, in current research, an attempt has been made to implement a system for detecting the amount of scale inside an oil pipe while a three-phase regime is passing through it. This research has tried to improve two important parameters, such as increasing accuracy and simplifying the detected system, using time characteristic extraction techniques. These are the contributions made by this study:

• Extracting signal features by the use of statistical formulas.
• Utilizing a single detector reduces expenses and the complexity of the detection system’s structure.
• Improving scale thickness determination accuracy by the extraction of valuable properties from received signals
• Determining scale thickness using the GMDH neural network as a self-organizing network.

2. MCNP Simulation Setup

MCNP code has been used to simulate the detection structure. In this simulation, a dual-energy gamma source, a steel pipe, with an inner diameter of 10 cm and a thickness of 0.5 cm, and a sodium iodide detector are used. The simulated structure is shown in Figure 1. The dual-energy source consists of ²⁴¹ Am and ¹³³ Ba, are capable of emitting photons with energies of 59 and 356 KeV, respectively. In the test pipe, a three-phase flow consisting of water, oil, and gas was simulated in a stratified flow regime. Different volume percentages in the range of 10% to 80% were investigated for each phase. The considered scale was made of barium sulfate (BaSO₄) with a density of 4.5 g · cm⁻³. Seven different scale thicknesses, including 0, 0.05, 1, 1.5, 2, 2.5, and 3 cm, were simulated inside the pipe. The sodium iodide detector with dimensions of 2.54 cm × 2.54 cm was placed at a distance of 30 cm and directly in front of the gamma source. 252 different simulations were performed, and all the collected data were labeled for use in the next step. The graph of the spectrum received by the detector for two scale thicknesses of 0 cm and 1.5 cm is shown in Figure 2.

LamberteBeer’s law is used to determine the attenuation rate when a narrow gamma ray strikes an object.

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

(1)

$I$, $I_0$, $\mu$ and $\rho$ denote the intensity of un-collided, the original photons, the mass attenuation coefficient, and the material density of the absorber, respectively. X denotes how far the beam travels through the absorber. Equation (1) states that different objects respond to gamma radiation in different ways. This variation in behavior determines the kind and amount of a substance in the environment. A 2.54 cm × 2.54 cm NaI detector was used in this research to capture the photons that were transmitted. The detector was used to record photon energy spectra using pulse height tally (Tally F8). Previous analyses have supported the study’s reproductive outcomes [6]. Several research laboratory structures were used in this review, and the results from the MCNP code were compared with them. Both were normalized to units to examine exploratory and reenactment data because the Tally output in the MCNP procedure is per source particle. The disparity between the simulation results and the lab setup represented the largest relative error at 2.2%.

3. Time-Domain Feature Extraction

The signals collected in the previous section had many dimensions, and their interpretation was a very complicated and time-consuming task. For this purpose, to simplify and separate the available data, an attempt was made to extract time characteristics. Four time-characteristics with the names of sample mean, sample of summation of square root (SSR), sample skewness, and sample kurtosis were extracted from the signals recorded by the NaI detector. These features have been used to improve the accuracy and structure of the scale thickness detection system since they were first introduced as helpful characteristics in earlier study [7,9,11]. The equations of these features are given below:

• Sample mean:

  $$m=\frac{1}{N}{\displaystyle \sum }_{n=1}^{N}x\left(n\right)$$

  (2)

• Sample of summation of square root (SSR):

  $$SSR={\displaystyle \sum }_{n=1}^N{\left(x\left(n\right)\right)}^{0.5}$$

  (3)

• Sample skewness:

  $$Skewness=\frac{m_3}{{\sigma }^3} , m_3=\frac{1}{N}{\displaystyle \sum }_{n=1}^N{\left[x\left(n\right)-m\right]}^3$$

  (4)

• Sample kurtosis:

  $$Kurtosis=\frac{m_4}{{\sigma }^4}, m_4=\frac{1}{N}{\displaystyle \sum }_{n=1}^N{\left[x\left(n\right)-m\right]}^4$$

  (5)

Here $n$ is the dataset’s values, $N$ denotes the total data number, and x(n) represents the principal signal in the time domain.

The diagram of these four characteristics in terms of volume percentage of gas and oil is shown in Figure 3. As it is clear from this figure, the amount of scale thickness can be separated into different volume percentages. These characteristics have been used to train the GMDH neural network. As mentioned in the previous section, 252 different simulations have been performed, and four time characteristics have been extracted from the signal received from each simulation. Therefore, the available matrix contains 4 rows and 252 columns. The output of the neural network is also the value of the thickness of the scale inside the pipe in centimeters.

4. GMDH Neural Network

In 1968, a Ukrainian mathematician named M.G. Ivakhnenko presented a mathematical model to solve prediction and classification problems and called it Group Method of Data Handling (GMDH) [15]. The model proposed by Ivakhnenko has self-organization capability so that the network structure, effective inputs, number of hidden layers, and number of neurons of hidden layers are automatically selected. In this neural network, the relationship between input and output is described by the Kolmogorov-Gabor polynomial, which is described below.

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

(6)

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. GMDH neural network is implemented in 5 steps, which are as follows.

1.

All neural network inputs (extracted characteristics) two at the time and for each $\left(\begin{array}{c}m\\ 2\end{array}\right)$ admixture are fitted to the quadratic polynomial given in Equation (7). The purpose of this step is to calculate the C coefficients that are obtained with the least squares algorithm. The output of each quadratic polynomial predicts the desired output value. The task of calculating these polynomials is assigned to the neurons of the neural network.

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

(7)

2.

The neurons with the most error in predicting the desired output are removed.

3.

The neurons selected in the previous step are considered quadratic polynomial inputs described in step one. In this step, polynomials are produced from polynomials, producing a polynomial with a higher order.

4.

The second step is repeated, and neurons with high errors are removed. This repetition of the steps and generation of polynomials from polynomials are repeated until the desired error value is obtained.

5.

Checking network performance with test data. In the design of neural networks, the major of the data (about 70%) are used for training the neural network, and the rest of the data are used for the final test of the network. The correct performance of the neural network against these data sets ensures that the designed network can show acceptable performance in operational conditions. In order to identify various characteristics in many scientific domains, several studies have employed intelligent computer systems [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37].

5. Results

A GMDH neural network with four inputs and one output was trained. The inputs of this network were the extracted temporal characteristics, and the network’s output was the value of the scale thickness inside the pipe in centimeters. 252 samples were available for the implementation of this network, of which 176 samples were assigned to the training data, and the remaining samples were used for the final test of the neural network. The selection of these samples was done randomly so that the neural network could be trained with all the range of data. According to the self-organizing capability of the GMDH neural network, the structure that had the best accuracy is shown in Figure 4. This network has 3 hidden layers, and the number of selected neurons in these layers was 4, 4, and 2, respectively. A regression diagram and error diagram have been used to show the performance of the designed neural network. In the regression diagram, the yellow line shows the desired output, and the green circles represent the output of the neural network. The closer the yellow line and the green circle are to each other, the more accurate the designed neural network is. The error diagram shows the difference between the network output and the desired output for each sample. The regression and error graphs for the training and testing datasets are shown in Figure 5. In order to obtain the error value, two widely used criteria named Mean Square Error (MSE) and Root Mean Square Error (RMSE) were calculated with the following equations:

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

(8)

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

(9)

In which N indicates data number, ‘X (Exp)’, and ‘X (Pred)’ illustrate the experimental and predicted (ANN) values, respectively.

The comparison table of the output of the neural network with the desired output is given in

Table 1. Comparison of target values with neural network outputs.

Data Number	Train Targets	Train Outputs	Test Targets	Test Outputs
1	0.5000	0.8364	1.5000	1.3493
2	1.0000	1.2139	2.5000	2.6387
3	1.0000	1.0764	1.0000	0.9995
4	3.0000	2.8872	2.0000	1.8995
5	1.5000	1.7345	0	−0.1932
6	1.0000	0.7840	0.5000	0.5605
7	0	0.1079	0.5000	0.6024
8	0	0.0893	2.5000	2.3590
9	2.5000	2.3907	2.0000	1.9970
10	1.0000	0.8268	2.0000	1.5573
11	0	0.0608	2.0000	2.1318
12	1.0000	1.2595	2.5000	2.5019
13	1.0000	1.1938	0	0.2556
14	2.5000	2.4362	2.5000	2.5553
15	0.5000	0.6588	0	0.0966
16	2.5000	2.6227	1.5000	1.4977
17	3.0000	2.8169	3.0000	2.9088
18	3.0000	2.9739	1.0000	1.2369
19	2.5000	2.6138	2.0000	1.7970
20	2.0000	2.3813	2.5000	2.2073
21	2.0000	2.2872	3.0000	2.9807
22	0	0.0054	3.0000	3.0354
23	0.5000	0.5838	1.5000	1.0813
24	1.5000	1.7266	0.5000	0.8614
25	0	0.1918	3.0000	3.0631
26	2.0000	1.7102	0	0.3922
27	0	0.0498	0	0.1574
28	1.5000	1.8249	1.0000	1.0251
29	2.5000	2.0919	0	0.0212
30	2.5000	2.3027	2.0000	2.1242
31	0	−0.1304	2.5000	2.2996
32	2.5000	2.6107	3.0000	3.0133
33	0.5000	0.6473	1.0000	0.8878
34	3.0000	3.0209	1.0000	0.9709
35	0.5000	0.8172	2.0000	1.8204
36	0	0.0083	1.5000	1.7240
37	0.5000	0.5213	0.5000	0.6903
38	1.5000	1.2158	2.5000	2.3593
39	1.5000	1.8909	0	0.0223
40	2.0000	2.0860	1.5000	1.3002
41	2.0000	2.2205	1.5000	1.5859
42	1.0000	0.9735	3.0000	3.0234
43	0	0.1812	1.5000	1.1938
44	0.5000	0.9019	2.0000	2.0133
45	2.0000	2.0582	1.5000	1.2607
46	0	0.2109	3.0000	3.0214
47	1.5000	1.6819	1.0000	1.1423
48	2.0000	2.3901	0	−0.1317
49	0	0.0807	1.0000	0.9227
50	2.0000	1.3950	3.0000	2.6769
51	2.5000	2.6330	3.0000	2.9334
52	2.5000	2.3719	2.5000	2.1041
53	1.5000	1.3983	2.0000	1.8912
54	1.0000	1.1618	1.5000	1.4685
55	0.5000	0.4591	2.0000	1.5945
56	2.5000	2.3568	2.0000	1.7184
57	2.5000	2.5199	3.0000	2.8049
58	3.0000	2.7633	3.0000	2.7848
59	1.0000	1.1078	0.5000	0.2380
60	0	0.1705	3.0000	2.9187
61	1.0000	0.8614	2.5000	2.3903
62	1.0000	0.9309	3.0000	3.0254
63	1.5000	1.4250	1.0000	0.9684
64	0.5000	0.8160	2.0000	2.2965
65	2.0000	2.4583	2.0000	2.3671
66	0.5000	0.5069	0	0.0096
67	0.5000	0.7269	1.0000	0.9977
68	2.5000	2.3730	2.0000	2.1213
69	1.5000	1.3851	0.5000	0.7948
70	3.0000	3.0613	1.5000	1.5571
71	1.0000	1.0067	2.0000	2.0093
72	1.0000	0.6657	1.5000	1.2935
73	1.0000	0.7362	0	0.0936
74	1.0000	1.0683	0.5000	0.6893
75	0	0.1252	2.0000	1.5044
76	1.5000	1.2048	3.0000	2.7268
77	2.0000	2.1610	-	-
78	0.5000	0.3873	-	-
79	0.5000	0.6288	-	-
80	1.5000	1.2658	-	-
81	1.5000	1.3239	-	-
82	0.5000	0.3186	-	-
83	1.0000	0.9420	-	-
84	1.5000	1.4139	-	-
85	3.0000	3.0394	-	-
86	3.0000	2.9834	-	-
87	0	0.0517	-	-
88	3.0000	2.6107	-	-
89	1.0000	0.9446	-	-
90	0.5000	0.5613	-	-
91	0	−0.0763	-	-
92	0	−0.1754	-	-
93	3.0000	3.0456	-	-
94	3.0000	2.7840	-	-
95	2.5000	2.3713	-	-
96	0.5000	0.7758	-	-
97	2.0000	2.4267	-	-
98	2.0000	1.8703	-	-
99	1.0000	1.1189	-	-
100	1.0000	1.2409	-	-
101	1.0000	1.0213	-	-
102	2.0000	2.0038	-	-
103	0	−0.1516	-	-
104	1.5000	1.5227	-	-
105	3.0000	2.7891	-	-
106	1.5000	1.4973	-	-
107	2.0000	2.3414	-	-
108	3.0000	2.9899	-	-
109	2.0000	1.7173	-	-
110	0.5000	0.8231	-	-
111	1.5000	1.6692	-	-
112	0.5000	0.6473	-	-
113	0	−0.0318	-	-
114	1.0000	1.1917	-	-
115	0.5000	0.3629	-	-
116	0.5000	0.4943	-	-
117	0	−0.1362	-	-
118	3.0000	3.0185	-	-
119	2.5000	2.1735	-	-
120	2.5000	2.1380	-	-
121	0	0.0072	-	-
122	2.0000	1.9919	-	-
123	2.5000	2.3027	-	-
124	0	0.0226	-	-
125	1.5000	1.6830	-	-
126	0	−0.0423	-	-
127	0.5000	0.7433	-	-
128	0.5000	0.7383	-	-
129	0	0.1972	-	-
130	3.0000	3.0329	-	-
131	2.5000	2.4056	-	-
132	3.0000	3.0404	-	-
133	2.5000	2.4958	-	-
134	3.0000	3.0254	-	-
135	0	0.0398	-	-
136	3.0000	2.8249	-	-
137	2.5000	2.6042	-	-
138	2.5000	2.4641	-	-
139	0.5000	0.7573	-	-
140	2.0000	1.4576	-	-
141	1.5000	1.7930	-	-
142	2.5000	2.5810	-	-
143	1.5000	1.1687	-	-
144	1.0000	1.1215	-	-
145	3.0000	3.0252	-	-
146	0.5000	0.4367	-	-
147	2.5000	2.2581	-	-
148	0.5000	0.6105	-	-
149	2.5000	2.5026	-	-
150	2.0000	1.5837	-	-
151	3.0000	2.9770	-	-
152	1.5000	1.3390	-	-
153	2.0000	1.9029	-	-
154	1.0000	0.9743	-	-
155	1.5000	1.2099	-	-
156	1.5000	1.2457	-	-
157	2.5000	2.6815	-	-
158	2.5000	1.9872	-	-
159	2.0000	2.1030	-	-
160	0	−0.0921	-	-
161	1.0000	1.3085	-	-
162	1.5000	1.1887	-	-
163	1.5000	1.5302	-	-
164	0.5000	0.2263	-	-
165	0.5000	0.6759	-	-
166	2.5000	2.2218	-	-
167	1.5000	1.4478	-	-
168	2.5000	2.2561	-	-
169	1.0000	1.2136	-	-
170	0.5000	0.6492	-	-
171	0	−0.1685	-	-
172	1.0000	1.0860	-	-
173	1.0000	0.8985	-	-
174	0.5000	0.6025	-	-
175	3.0000	3.0462	-	-
176	3.0000	2.9525	-	-

. To show the accuracy of the implemented system,

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

Ref	Number of Detectors	Source Type	Type of Neural Network	Maximum MSE	Maximum RMSE
[9]	1	137Cs	GMDH	1.24	1.11
[7]	2	137Cs	MLP	0.21	0.46
[8]	1	60Co	GMDH	7.34	2.71
[38]	2	137Cs	MLP	0.67	0.82
[39]	1	X-Ray tube	MLP	17.05	4.13
[40]	1	137Cs	MLP	2.56	1.6
[41]	1	60Co	RBF	37.45	6.12
[42]	2	137Cs	MLP	1.08	1.04
[current study]	1	Dual-energy gamma source	GMDH	0.04	0.2

shows a comparison between the accuracy of current research and previous research. Extracting the appropriate features from the received signals has not only improved the accuracy of the presented system, but also reduced the number of detectors. Reducing the number of detectors, along with reducing the complexity of the system, will significantly reduce the implementation cost of the detection system.

6. Conclusions

The presence of scale inside the oil pipes will cause significant problems such as reducing the effective diameter of the oil pipes, increasing the energy consumed by the oil pumps, reducing the efficiency, and increasing the repair costs. Therefore, timely detection of the amount of scale inside the oil pipes helps to reduce the mentioned damages. In this research, a non-invasive system based on gamma-ray attenuation was introduced. The introduced system consisted of a dual-energy source of ²⁴¹Am and ¹³³Ba, a NaI detector, and a steel pipe. A three-phase flow was simulated in a stratified regime consisting of oil, water, and gas in different volume percentages. In all these simulations, the value of different scales in the range of 0 to 3 cm were examined. All these structures and flows passing through the test pipe were simulated by MCNP code. After collecting the received signals from the detector, the feature extraction operation started in the time domain, and four time features with the names of sample mean, sample SSR, sample skewness, and sample kurtosis were extracted from the signals and introduced as the inputs of the GMDH neural network. The trained neural network predicted the thickness of the scale inside the pipe with an RMSE of less than 0.2, which is a very low error compared to previous studies. In addition, the use of feature extraction techniques made it unnecessary to have multiple detectors, and only one detector is enough to determine the thickness of the scale, which has significantly saved the implementation costs. One of the major limitations of this research is that working with radioisotope devices requires the use of protective clothing, and the transportation of these devices is challenging. The use of feature extraction techniques in the frequency domain, time-frequency domain, and the investigation of the performance of other neural networks such as MLP, RBF, and even deep neural networks are highly recommended to the researchers in this field.