Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 3, No. 3, 2022 85 Prediction of Gas Well Annulus Pressure Based on Neural Network Man Pu1, Jialong Xie2, Miaomiao Cheng3, Xin Yi3 1School of Electrical and Information, Southwest Petroleum University, China 2School of Science, Southwest Petroleum University, China 3School of Mechanical and Electrical Engineering, Southwest Petroleum University, China Abstract: Abnormal pressure in the annulus is one of the main risks that threaten the safe production of gas wells and affect their production efficiency. To further improve the gas well annulus pressure management level based on the gray system theory and new information priority ideology, this study introduced a new perspective. First, we considered the influence of various factors related to the change of the gas well annulus pressure and performed a grey correlation analysis. Next, we established a multivariable grey prediction model of gas well annular pressure with the associated metabolic function. The measured data of high-pressure and high-yield gas wells in Northwestern Sichuan for 12 consecutive hours in a day, was used as a case study. The effectiveness of this proposed model was verified by comparing the predicted results with the measured data. The research results verify the feasibility of the gray system theory for the dynamic prediction of gas well annulus pressure and provide theoretical support for the early diagnosis and active prevention of continuous annulus pressure. Keywords: Production safety, Annulus pressure, Grey system theory, Multivariate grey model. 1. Introduction In recent years, with the large-scale development of high temperatures and high pressure, annulus pressure has become a common problem and safety problem faced by the world's petroleum industry[1]. Many scholars have made an extensive exploration of the formation mechanism and indirect calculation method of annular pressure, but there is still little research on real-time prediction of annular pressure in gas wells. After the oil casing of the sour gas, well is channeled, the manual pressure relief of annular air needs to be led to the combustion pool by the blowout pipeline for ignition and pressure relief, and the crowd evacuation needs to be carried out in advance, so it is necessary to further improve the management level of annular pressure. According to the existing understanding, the annular pressure of gas wells in northwest Sichuan is not simply caused by heat, but mainly caused by abnormal sustained casing pressure., with complex and diverse pressure sources. Since Deng Julong first proposed the "grey system" in 1982[2], it has rapidly developed into a new discipline to study the uncertainty of "small data, poor information", in which the grey correlation analysis is an important part of the grey system theory[3]. Aiming at the deficiency of the structure of grey GM (1,1) model, Su Bianping [4]and Chen Xiangdong[5] successively combined the GM (1,1) model, discrete grey prediction model, and the traditional multiple linear regression model in mathematical statistics, and proposed a multivariable grey prediction model. In conclusion, according to the characteristics of the gas well annulus system, based on existing knowledge, the grey correlational analysis is considered to analyze the main related variables that affect the change of gas well annulus pressure, and on this basis, a multivariable grey prediction model of gas well annulus pressure is established to realize the early diagnosis and active prevention of abnormal annulus pressure, thus providing a new research idea and method for the management of gas well annulus pressure. 2. Grey Correlation Analysis Mechanism The system characteristic sequence and the correlation factor sequence together constitute the modeling object of the multivariable gray prediction model, so the gray correlation analysis is the basis of establishing the multivariable gray prediction model. The general calculation steps of Deng's grey relational analysis are as follows: (1) Select the system feature sequence and related factor sequence, and conduct dimensionless processing on the data; (2) Find the absolute value sequence of the difference between the corresponding components of the initial value image of the system feature sequence and the correlation factor sequence, and calculate the maximum and minimum values; (3) Calculate the correlation coefficient and average it. On this basis, Liu Sifeng et al[6]. explored the structure and nature of Deng's grey relational analysis model and proposed some improved grey relational analysis methods. The algorithm of grey comprehensive relational degree combines the characteristics of grey relative relational degree and grey absolute relational degree, which can not only reflect the similarity of two-time series but also reflect their change rate relative to the starting point, It indicates whether the sequences are closely related. 3. Multivariable Grey Prediction Mechanism The modeling object of the multivariable grey prediction model is composed of a system feature sequence and several related factor sequences. The influence of related factors on the development trend of the system is fully considered, which makes up for the shortcomings of the GM (1,1) model with a single structure and limited simulation ability[7]. The steps of establishing a multivariable grey prediction model for the system are as follows: (1) grey accumulation generation and adjacent mean generation for the original sequence; (2) The GM (1,1) model is established for the sequence of 86 relevant factors respectively, and the prediction value of the subsequent time of each relevant factor is obtained; (3) The average relative error is used to test the prediction accuracy of GM (1,1) model. The accuracy inspection level is shown in Table 1. When the accuracy inspection level reaches Level I or Level II, subsequent prediction can be made; (4) The grey multivariable prediction model is established for the system characteristic sequence and the related factor sequence, and the prediction value of the subsequent time of the system is obtained. Table 1. Reference Table of Average Relative Error Accuracy Test Grade Accuracy class One-level Two-level Three-level Four-level Average relative error α 1% 5% 10% 20% 4. Multivariate Grey Prediction of Annular Pressure in Gas Wells The principle of new information priority is one of the basic principles of grey system theory, that is, new information plays a greater role in cognition than old information[8]. Based on the grey correlation analysis and the principle of new information priority, this paper establishes a multivariable grey prediction model of gas well annular pressure with metabolic function. The calculation flow chart is shown in Figure 1:Fig. 1 Multivariate Grey Prediction Calculation Flow Chart of Annular Pressure of Gas Well. Start Obtain the sequence values of annular pressure and related factors from time t=i to time t=j. Set time parametersi,j,k. (i3,k-j>1) Calculate the gray correlation degree ρ of the annular pressure and the sequence values of related factors from time t=i to time t=j. ρ≥0.5？ Establish multivariate grey prediction model. Calculate the predicted value of annular pressure from time t=j+1 to time t=k. End to predict？ i+1,j+1,k+1 End Yes Yes Figure 1. Multivariate Grey Prediction Calculation Flow Chart of Annular Pressure of Gas Well 4.1. Grey correlation experiment The measured values of annulus A pressure and tubing pressure, wellhead temperature, and gas production for 12 consecutive hours in a day in a high-pressure and high-yield gas well in northwest Sichuan are selected as the experimental data. The interval between each time is 1 hour. The calculation results of the grey relative correlation degree 0ir , grey absolute correlation degree 0i , and grey comprehensive correlation degree 0i ( 1, 2,3)i  between annulus A pressure and tubing pressure, wellhead temperature, and gas production during the 00:00-06:00 period are shown in Table 2: Table 2. Calculation Results of Grey Incidence Parameter Oil pressure Wellhead temperature Gas production Association degree type r01 ε01 ρ01 r02 ε02 ρ02 r03 ε03 ρ03 Relevancy 0.947 0.716 0.832 0.946 0.890 0.918 0.889 0.500 0.694 It can be seen from the above table that the calculated value of each gray comprehensive correlation degree is greater than 0.5, indicating that these three factors are the interpretation variable sequences with high correlation with the annular pressure of gas well A during the period 00:00-06:00. 87 4.2. Multivariable Grey Prediction Experiment Firstly, GM (1,1) model is established for oil pressure, wellhead temperature, and gas production sequence in the period of 00:00-06:00, and precision inspection is carried out. Through inspection, the precision grade of average relative percentage error of grey GM (1,1) prediction of oil pressure and wellhead temperature in the period of 00:00-06:00 reaches Grade I, and the precision grade of average relative percentage error of grey GM (1,1) prediction of gas production reaches Grade II, so it can be used for short-term prediction. Therefore, the prediction values of various factors at 07:00-11:00 can be obtained through the established grey GM (1,1) model. The calculation results are shown in Table 3: Table 3. Prediction Values of Relevant Factors 07:00-11:00 Time Oil pressure (MPa) Wellhead temperature(℃) Gas production(m3) 07:00 55.674 33.894 202095.417 08:00 55.178 34.182 204973.519 09:00 54.688 34.471 207892.608 10:00 54.201 34.764 210853.269 11:00 53.719 35.058 213856.094 The multivariable grey prediction model is established for the A annulus pressure sequence and the relevant factor sequence. The data from 00:00-06:00 is used as the basis for the least squares estimation of the model parameters, and the data from 07:00-11:00 is used as the basis for testing the prediction effect of the model. The prediction results of the A annulus pressure from 07:00-11:00 are shown in Table 4, which are compared with the measured values and plotted as shown in Figure 2. Table 4. Prediction Results of A Annular Pressure 07:00-11:00 Time A predicted value of annulus pressure (Mpa) An actual value of annular pressure (Mpa) Error (%) 07:00 40.429 40.401 0.07% 08:00 40.634 40.565 0.17% 09:00 40.837 40.723 0.28% 10:00 41.039 40.853 0.46% 11:00 41.241 40.975 0.65% Figure 2. A Comparison Chart of Annular Pressure Prediction Results 5. Conclusion Real-time prediction of annular pressure in gas wells is of great significance to ensure safe production and improve production efficiency. Based on the grey system theory and the idea of new information priority, a multivariable grey prediction model for the annular pressure of gas wells with metabolic function is proposed by considering the influence of various related factors on the changing trend of annular pressure of gas wells and combining the results of grey correlation analysis. Taking the 12-hour measured data of A annulus pressure, oil pressure, wellhead temperature, and gas production of a high-pressure and high-yield gas well in northwest Sichuan as an example, the maximum prediction error is 0.65% through comparison and analysis of the model prediction results and the measured data, which verifies the 88 effectiveness of the prediction model. The research results verify the feasibility of applying grey system theory to the dynamic prediction of annular pressure in gas wells and provide a new research idea and method for the management of continuous annular pressure. Acknowledgment The study is support by 2022 Innovation and Entrepreneurship Training for College Students in Sichuan Province (S202210615216) and Extracurricular Opening Experiment of Southwest Petroleum University (2021KSZ09014) References [1] Zhu Dajiang. Study on Annular Pressure Mechanism of Gas Wells [D]. Southwest Petroleum University, 2014. [2] Zhang Ke. Research on Matrix Grey Correlation Analysis Modeling Technology [D]. Nanjing University of Aeronautics and Astronautics, 2010. [3] Deng Ju-Long.Control problems of grey systems[J].Systems and Control Letters,1982,Vol.1: 288-294. [4] Su Bianping, Cao Yanping, Wang Ting. Grey prediction model of multi factor time series [J]. Journal of Xi'an University of Architecture and Technology (Natural Science Edition), 2007, Volume 39 (2): 289-292. [5] Chen Xiangdong, Wang Bin. Multi factor Grey Prediction Model and Its Application [J]. Mathematical Practice and Understanding, 2012, (1): 80-83. [6] Liu Sifeng, Guo Tianbang. Grey system theory and its application [M]. Kaifeng: Henan University Press, 1991. [7] Zeng Bo, Yin Xiaoyong, Meng Wei. Practical Grey Prediction Modeling Method and Its MATLAB Program Implementation [M]. Beijing: Science Press, 2018. [8] Liu Sifeng, et al. Grey System Theory and Its Application 8th Edition [M]. Beijing: Science Press, 2017.