Risk analysis and Assessment of Wellbore Integrity Failure in Underground Gas Storage Based on Bayesian Network

Well integrity assessment plays vital role in the risk management of gas storage wells, which has emerged as a key topic of political and scientific discussion in the gas industry. However, the current research did not provide quantized assessment of failure probability of well integrity. To quantitatively evaluate the failure risk of gas storage well integrity, the probability model based on Bayesian network is established and calculated incorporating the relevant historical statistical data of gas storage well integrity failure and Leaky Noise or Gate extended model. Besides, the risk priority evaluation criteria of well integrity are set up, combining with the analytic hierarchy process. And the risk judgment matrix is constructed to quantitatively evaluate the risk of wellbore integrity failure in gas storage. Practical guidelines and solutions derived from the results of the current study can be used for the design of the gas storage wellbores.


Introduction
The underground gas storage is a large artificial gas field or natural gas storage facility, typically developed from mature or abandoned oil and gas fields.Its primary purpose is to re-inject natural gas into underground reservoirs during periods of low consumption for sealed storage and extract gas during periods of high demand to meet human production needs [1,2] .The underground gas storage serves as a critical component of the Chinese natural gas "production-supply-storagedistribution" industry chain.It has three core functions including emergency secure gas supply, seasonal gas demand regulation and national strategic energy reserves.Wellbore integrity protection involves the use of management, operational and technological measures to reduce potential risks throughout the entire life of wells [3] .In the production process of underground gas storage wells, failure wellbore integrity is the key issue that needs to be addressed.It can lead to accidents such as well leakage and pressure in the annulus and contribute to threaten the safety of personnel, environment and itself [4][5][6][7] .To improve the reliability of wellbore integrity and ensure the safe operation of oil and gas wells, it is necessary to assess the of wellbore integrity failure risk and take preventive measures in advance.This paper first identifies the risk factors of wellbore integrity failure and establishes an accident tree model according to the logical relationship between the risk factors.Through statistical analysis of historical data, the conditional probability of Bayesian network is calculated based on the Leaky Noise or Gate extended model.The failure probability result is combined with the analytic hierarchy process to construct a risk judgment matrix to quantitatively evaluate the wellbore integrity failure risk, which lays a theoretical foundation for the optimization and protection of gas storage wellbore integrity in the later stage.

Identification of risk factors for gas storage well integrity failure
It is necessary to first identify potential risk factors that may exist in the wellbore system and establish corresponding risk barrier units.Five risk barrier units for wellbore integrity failure in gas storage facilities are identified [8] and the accident tree model of risk factor accident of wellbore integrity failure of gas storage as shown in Figure 1.From a subdivision point of view, there are 13 risk factors that lead to the occurrence of 5 intermediate accidents, respectively expressed by X1~X13.Table 1 shows the specific events corresponding to each symbol in the wellbore integrity failure tree mod el  Based on the established gas storage well integrity failure accident tree model, the gas storage well integrity failure is taken as the child node A, five risk barrier units (wellhead instability, casing failure, tubing failure, cement failure, cement interface failure) are taken as parent nodes, and other risk factors affecting wellbore integrity failure are taken as root nodes.After analysing the influencing factors and development process of the gas storage well integrity failure, the Bayesian network model of the gas storage well integrity failure is established, as shown in Figure 2. The arrow indicates the connection between nodes, and the parent node points to the child node.

Calculation model of wellbore integrity failure probability
Each risk factor can independently or jointly cause the wellbore integrity failure of gas storage, which meets the use conditions of the Noisy-or Gate model: Where, Pij is the probability of A occurring only if Ai takes the true value, also known as the connection probability of Ai; Ai and Aij represents the risk barrier unit i and j that causes the occurrence of a child node; ‫‬൫ ‫ܣ‬ | | ‫ܣ‬ ൯ represents the probability of occurrence of Ai risk barrier units in the event of Aij risk factors occurring; ‫‬൫ ‫ܣ‬ | | ‫ܣ‬ ൯ represents the probability of the occurrence of Ai risk barrier units in the absence of Aij risk factors.The Leaky Noisy or Gate formula is shown as follow: Where, Aisub represents a subset of events that occur at the root node; AL is the set of unknown risk factors that lead to wellbore integrity failure; p L is the probability of omission, and this evaluation model takes 0.05.

Risk assessment model for wellbore integrity failure
To conduct risk assessment on wellbore integrity and obtain its failure risk level, this section combines the Analytic Hierarchy Process and Bayesian network analysis to construct a risk judgment matrix and establishes a quantitative evaluation method for wellbore integrity risk.The risk value of risk factors is defined as: Where, Li is the risk value of the risk factor i; pi is the probability of occurrence of the risk factor; Ci is the severity of the risk factor.The severity of wellbore integrity risk barrier unit failure is divided into 5 levels [9] .The specific classification results of risk severity levels are shown below.
Table 2. Severity levels for different events [9] Number The wellbore integrity failure risk degree R [10] can be calculated according to equation : Where, R is the risk level of wellbore integrity failure; Li represents the risk value of the risk factor i; ߱ represents the weight of the risk factor i, which can be obtained by establishing a risk judgment matrix and calculating the eigenvector.If the importance ratio of event i to j is aij, then the importance ratio of event j to i is 1/aij.

Table 3. Risk factor scale value
Importance level Scale value equally important 1 slightly more important 3 significantly more important 5 more important 7 According to the application requirements of Analytic Hierarchy Process, the consistency ratio parameter C R of the risk judgment matrix needs to be less than 0.1 to meet the consistency requirements, where C R can be expressed as: Where, C R is the consistency ratio; ߣ ௫ represents the maximum eigenvalue of the risk judgment matrix; n is the order of this risk judgment matrix; R 1 represents the proportional coefficient of this risk judgment matrix, which is related to the order of the risk matrix.When n equals 5, its value is 1.12.

Calculation of wellbore integrity failure probability
After consulting relevant references on gas storage wellbore integrity and collecting and organizing relevant on-site accident statistical data, the conditional probability of a node can be reached by bringing the data from the table into the Leaky Noisy or Gate extended model.The data is then fed into Bayesian software GeNIe 2.0.Under the condition of Prior probability, the failure probability of gas storage wellbore integrity is 27%.The risk of cement failure in this gas storage is the highest (44%), followed by the risk of wellhead instability failure (33%), cement interface failure (24%), casing failure (19%) and tubing failure (17%).

Risk assessment of wellbore integrity failure in gas storage facilities
Based on expert knowledge and the risk consequences, the severity of each risk unit is assigned as Wellhead instability (95), Casing failure (90), Tubing failure (80), Cement failure (75), Cement interface failure (60).The risk values for each risk unit of wellbore integrity failure in gas storage can be calculated by substituting the severity of each factor into equ ation (3).The results are shown in Table 4. 14.4By using the MATLAB software to solve the constructed risk judgment matrix and obtain its maximum eigenvalue λ max =5.0556, C R =0.0124, which meet the consistency requirements.And the normalized weight of the maximum eigenvalue is obtained as: ω=(0.3430.343 0.129 0.129 0.055) T .The risk of wellbore integrity failure in gas storage is calculated using equation (4), with R=23.42.Due to the calculated risk degree R=23.42, it can be determined that the risk of gas storage integrity failure is at level 2 (medium risk).Therefore, it is necessary to strengthen the prediction work of annular pressure to reduce the threat of wellbore integrity failure risk.

Conclusions
In this study, various risk assessment methods were comprehensively utilized with historical data of gas storage wellbore integrity failure to quantitatively evaluate the failure risk of gas storage wellbore integrity.The specific research conclusions of this paper are as follow: z Using the Leaky Noise or Gate extended model combined with Bayesian network method, the probability of gas storage wellbore failure is calculated to be 27% based on the collected historical statistical data.And the failure risk probabilities of cement, wellhead, cement interface, casing, and tubing are 44%, 33%, 24%, 19%, and 17%, respectively.z The risk value of wellbore integrity failure risk factors is obtained through data statistics and theoretical calculations.And the risk weights is calculated using the Analytic Hierarchy Process ω=(0.3430.343 0.129 0.129 0.055) T .The risk degree R of gas storage wellbore integrity failure is calculated as 23.42 by combining the two results, which belongs to level 2 medium risk and requires strengthening the prediction works.

Figure 1 .
Figure 1.Wellbore integrity failure risk factors accident tree model

Figure 2 .
Figure 2. Bayesian network model of wellbore integrity failure of gas storage

Table 1 .
Specific name of Wellbore integrity failure accident tree events

. Risk assessment of wellbore integrity failure in gas storage 3
.1 Establishment of Bayesian network for integrity failure of gas storage

Table 4 .
Risk values of each risk unit

Table 5 .
Wellbore integrity risk priorities of gas storage