Integrity assessment of shale gas wells in Changning Block based on hierarchical analysis method

Abstract

The integrity of shale gas wells is crucial in ensuring safety and efficiency throughout the development process. Such integrity spans the entire process of drilling and fracturing horizontal wells and is an essential indicator for ensuring safe and stable production throughout the lifespan of the well. This study investigates methods for assessing the integrity of shale gas wells by employing the analytic hierarchy process combined with experimental data to establish evaluation criteria and weights. The assessment is carried out specifically on shale gas wells in Changning Block. Results indicate that the integrity of these shale gas wells is influenced by various factors, such as drilling and fracturing processes. Moreover, the integrity assessment of indicators such as oil layer casing/technical casing, liquid carrying capacity, and tube column deformation is relatively low, indicating a need for enhanced monitoring and management. The comprehensive evaluation results indicate that, overall, the integrity rating of shale gas wells is generally considered “common,” but some potential safety hazards still remain that require timely attention and resolution. Case analysis reveals varying levels of integrity risks in shale gas wells. Case 1’s score of 93.51 warrants attention but is still deemed generally safe. However, Case 2’s score of 73.89 indicates a disaster level, emphasizing urgent intervention needs. Critical factors such as pressure, cementation quality, and corrosion demand proactive management for safe, sustainable operations.

Introduction

In shale gas development, drilling and fracturing are two very important links that can affect the integrity of shale gas wells. During drilling, encounters with complex formations, abnormal pressure, and other circumstances may lead to structural damage to the wellbore. During fracturing, injecting high-pressure liquids and proppants can also affect the integrity of the wellbore. To ensure the integrity of shale gas wells, a series of measures need to be taken during drilling and fracturing. For example, in the drilling process, it is necessary to select suitable drill bits, optimize drilling parameters, and avoid drill string fatigue. In the fracturing process, selecting suitable fracturing fluids, proppants, and fracturing parameters while also monitoring and controlling the fracturing process is crucial. In summary, the integrity of shale gas wells is an engineering guarantee for improving the single-well production of shale gas, which is highly valued. Thus, corresponding measures must be taken to ensure the integrity of shale gas wells.

Development of unconventional oil and gas resources, such as shale and tight gas: Unconventional oil and gas resources, such as shale and tight gas, have attracted significant domestic and international attention. Since the beginning of the twenty-first century, the widespread application of horizontal well drilling and hydraulic fracturing technologies in the efficient development of shale gas has turned shale gas exploitation into a reality, propelling North America into the era of the “Shale Gas Revolution.” The success of the North American shale gas revolution has garnered global interest, prompting governments and enterprises worldwide to invest substantial human, material, and financial resources into the exploration and development of shale gas, thereby altering the global energy landscape to a certain extent. In Nelson et al. (2007) pointed out that the complex characteristics of the fracturing process, including large fracture volumes, numerous transformation stages, and significant pumping volumes, can lead to intricate mechanical behaviors and changes in the stress field around horizontal well casings, ultimately resulting in casing failure. In Gray et al. (2009) established a finite element model of wellbore mechanics that considered the variations in load during cementing. The model detects stress conditions near the wellbore under in-situ stress, overburden pressure, cement setting and shrinkage, interface separation, and plastic deformation of cement and reservoir rocks (Gray et al. 2009). In Nabipour et al. (2010) developed a 2-D finite element model for analyzing stress in the cement sheath of deep gas wells. Mechanically induced failure of the cement sheath, primarily caused by elevated Von-Mises stresses, was identified as the main reason for cement sheath seal failure. Radial cracks in the cement are most likely to occur on the inner surface perpendicular to the direction of maximum horizontal stress. The eccentricity of the casing alters the stress state of the cement. Casing eccentricity-induced uneven thickness of the cement sheath would impact the forces acting on the cement sheath, with the maximum Von-Mises stress occurring when the inner surface of the thicker portion of the cement is at a 45° angle to the direction of horizontal stress (Nabipour et al. 2010). In Bois et al. (2011) investigated ways to enhance the sealing integrity of cement sheath and proposed that variations in downhole pressure, temperature, and cement hydration are the primary factors leading to cement sheath failure. In Axel-Pierre Bois et al. (2012) suggested that the cement sheath, bonded with reservoir rocks, might take several days or weeks to equalize pore pressure with formation pressure and might require weeks–months to achieve sufficient strength to isolate the reservoir. De Andrade and Sangesland (2016) utilized finite element methods to study the effects of casing pressure testing, wellbore temperature changes, and casing eccentricity on the stress and failure of the cement sheath. Their results indicated that using cement with a low elastic modulus effectively reduces radial cracks in the cement sheath. In oil and gas wells with poor cementing quality, casing eccentricity increases the risk of failure in the thinner portions of the cement sheath (De Andrade and Sangesland 2016; De Andrade et al. 2014, 2016).

Shale gas well integrity: The main problems affecting shale gas well integrity include wellbore corrosion, annular pressure, cross-flow between production and injection wells, wellhead valve leakage, and wellhead valve failure. Among these, research on casing corrosion has become a very popular topic. The main types of corrosion are scaling caused by salt-type substances, electrochemical corrosion, SRB corrosion, H2S corrosion, and CO₂ corrosion (Li et al. 2023). Nesic (2012) studied the influence of CO₂ corrosion rate on low-carbon steel under multiphase flow. The study found that media containing sediment, shear stress, and ion concentration can all have a certain impact on CO₂ corrosion. Cementing failure may also occur during completion, pressure testing, fracturing modification, and production processes, which may lead to seal failure of the cement sheath (Niu et al. 2022). Seal failure of the cement sheath may cause serious environmental pollution, such as fluid leakage into water-producing layers and pollution of drinking water. In addition, if the fluid is high-pressure gas, when it reaches the top of the liner or the surface of the surface casing, due to low pressure, the gas will expand rapidly, which may cause damage to the wellbore and surface facilities (Nasvi et al. 2016).

In summary, current research on shale gas well integrity remains at a single factor level and cannot comprehensively identify the interactions between various factors and their influence weights. Therefore, this article uses hierarchical analysis methods and experimental data to establish an evaluation index for shale gas well integrity. Taking the example of Changning Block’s wells, the developed index evaluates their integrity. It identifies the main factors affecting it and proposes corresponding improvement measures to provide theoretical support and practical guidance for ensuring the integrity of shale gas wells.

Theoretical analysis

Well integrity evaluation process

The main problems of well integrity include wellbore corrosion, ring air belt pressure, square well channel gas problem, wellhead valve leakage, and well safety valve fault.

Analysis of shaft corrosion causes

The causes of wellbore corrosion are as follows: typical bacterial corrosion products are present in the corrosion products of the downhole tubing string, and bacterial corrosion is the main cause of corrosion perforation. Carbon dioxide also participates in the corrosion (the produced gas in the Changning Block contains 0.5% CO₂). Formation temperature of the perforated tubing is concentrated in the range of 20–70 °C, within the active temperature range of bacteria. Bacteria lose their activity at temperatures above 80 °C, and deep-seated tubing corrosion is dominated by CO₂ corrosion, which is relatively mild (Li et al. 2018; Jung and Kim 2011; Loganathan et al. 2010) (Fig. 1).

Fig. 1

Analysis of underground corrosion products in Changning block

Analysis of annular casing pressure

The four main reasons for annular casing pressure in shale gas well are tubing and casing leakage, low replacement efficiency during cementing, unreasonable cement slurry system selection or formulation design, and changes in fracturing and production parameters. Take the present project, 101H10-3, as an example (Fig. 2) (Liu et al. 2015).

Fig. 2

Cannular casing pressure diagnostic test curve of 101H10-3 well

The release test on annular casing pressure resulted in pressure relief down to 2.66 MPa with liquid discharge. When pressure relief was stopped for the pressure recovery test, annular casing pressure recovered from 2.66 to 3.66 MPa, which was higher than the level before pressure relief. The temperament nature of the C ring should be further tested. If the gas is non-producing, then the second well barrier is damaged; if gas is present, then the second well barrier fails.

Analysis of gas blowby

Shale gas migration within wells occurs for two reasons. First, the inter-well pressure has an impact on the production dynamics of the production well (mother well), thereby reducing its production capacity. Second, the artificial fracture communication with low-pressure areas is detrimental to the net pressure of the fracturing well (subwell), which affects the transformation effect.

Analysis of internal leakage in wellhead valve

The internal leakage of shale gas wellhead valves occurs for several reasons: improper transportation and lifting may cause overall damage to the valve, failure to dry and prevent corrosion after water pressure is applied, inadequate protection at the construction site, failure to inject lubricating grease into the valve seat, and failure to install the valve in the fully open position (Huang and Gao 2015).

Analysis of well safety valve failure

Various reasons may cause the failure of the well safety valve in shale gas wells. Possible reasons for such failure include improper valve design, manufacturing quality issues, improper installation, fluid characteristics issues, improper maintenance, human factors, and natural disasters such as earthquakes (Liang et al. 2020).

Analytic hierarchy process

Introduction of the hierarchical analysis method

The analytic hierarchy process (AHP) is a combination of qualitative and the quantitative methods, which have the advantages of being systematic and hierarchical. Owing to its practicality and effectiveness in dealing with complex decision-making problems, AHP has quickly gained attention worldwide. Its applications have spread to economic planning and monitoring, energy policy and distribution, behavioral science, military command, transportation, agriculture, education, talent, medical care, and the environment (Champion et al. 2011; Sipahi and Timor 2010; Darko et al. 2019).

Step of AHP

• (1) Establish a hierarchical structure model

The principle of AHP is to treat the problem as a large system and, through analyzing multiple factors in each system, identify the ordered hierarchy of interrelated factors. After experts objectively judge each factor at each level, they give relative quantitative representations of these factor’s relative importance. Then, a mathematical model is established to calculate the relative importance of all factors at each level, and the order is ranked. Finally, planning, decision-making, and problem-solving measures are implemented based on the ranking results.

• (2) Construct the judgment (pairwise comparison) matrix

The principle of the AHP method stipulates that the evaluation index at each level requires each expert participating in the evaluation to provide a relative and important judgment based on their own experience. The form of the Judgment matrix is as follows:

$$d = \left| {\begin{array}{*{20}c} {d_{11} } & {d_{12} } & {d_{13} } & {...} & {d_{1m} } \\ {d_{21} } & {d_{22} } & {d_{23} } & {...} & {d_{2m} } \\ {d_{31} } & {d_{32} } & {d_{33} } & {...} & {d_{3m} } \\ {d_{n1} } & {d_{n2} } & {d_{n3} } & {...} & {d_{nm} } \\ \end{array} } \right|$$

(1)

where $d_{ij}$ represents the importance of i to j.

According to the degree of relative importance, the relative weight of the evaluation index in the same layer is made as the ratio. The specific ratio calculation method adopts the 1–9 scale method, as shown in Table 1.

Table 1 1–9 scale method

• (3) Conformity test

In this article, due to the different judgments of experts, various interpretations about the same indicator may arise. Some experts are only familiar with their industry fields and may need to become more familiar with content that slightly deviates from their expertise, leading to certain deviations from the actual evaluation results and inconsistencies in evaluation. Therefore, conducting a consistency test on the results after expert judgment is necessary to detect whether they meet the standard consistency requirements. The calculation method of the consistency test is as follows:

$${\text{C}}.{\text{I}} = \frac{{\lambda_{\text {MAX}} - n}}{n - 1}$$

(2)

where $\lambda_{\text {MAX}}$ is the largest feature root of the matrix. $n$ is the number of rows of the matrix. ${\text{C}}.{\text{I}}$ is the consistency index.

The magnitude of the ${\text{C}}.{\text{I}}$ value is meaningful. Its value is larger when the constructed matrix does not meet the full consistency requirement, smaller when the constructed matrix is close to meeting the consistency requirement, and 0 when the Judgment matrix fully meets the consistency requirement.

The Judgment matrix is determined by subjective experience, with the understanding and thinking of each expert being its influence conditions. Therefore, it is impossible to get completely consistent results from the subjective method. To determine whether the actual Judgment matrix meets the consistency, we only need to check whether the matrix meets the satisfactory consistency. The average random consistency index ${\text{R}}.{\text{I}}$ is used to determine whether a matrix meets the satisfactory consistency. The values of the average random consistency ${\text{R}}.{\text{I}}$ index are shown in Table 2.

$${\text{C}}.{\text{R}} = \frac{{\text{C}}.{\text{I}}}{{{\text{R}}.{\text{I}}}}$$

(3)

where ${\text{C}}.{\text{R}}$ is the new average random agreement index.

Table 2 Average random consistency indicator

When A < 0.10, we stipulate that the matrix meets the requirements of satisfactory consistency, otherwise the matrix needs to be improved and Judgment matrix constructed and analyzed again.

Results and discussion

Design the calculation process

The integrity index of shale gas wells in this study is calculated through a secondary fuzzy comprehensive assessment using the AHP.

Well tube safety

The integrity assessment index system for shale gas wells is divided into two categories: wellbore safety and production efficiency. Wellbore safety consists of three primary indicators: abnormal ring air pressure, divulge, and corrosion erosion.

• (1) Abnormal ring air pressure

Abnormal ring air pressure refers to the abnormal increase or decrease in pressure inside the wellbore, indicating potential issues such as fluid leakage or formation fractures. Elevated abnormal ring air pressure may damage or fail equipment, compromising well safety. Therefore, the proper monitoring and assessment of abnormal ring air pressure are crucial for ensuring wellbore safety.

The primary indicator of abnormal ring air pressure is divided into four secondary indicators: pressure magnitude, bottom integrity, well cementation quality, and hydrogen sulfide content (non-reservoir section).

Pressure magnitude: This indicator refers to the pressure level within the abnormal annulus (area around the wellbore). Abnormal ring air pressure is often related to downhole formation pressure, wellbore fluid height, and rock properties. Monitoring and managing pressure within the abnormal annulus are essential to prevent wellbore wall failure or equipment malfunction.

Bottom integrity: This indicates the integrity of the well’s bottom by assessing the presence of leaks, damage, or penetration points. Issues with bottom integrity may lead to fluid leakage into the subsurface, causing environmental contamination and wellbore instability.

Well cementation quality: This involves the quality and integrity of the wellbore’s internal cementing material, usually cement. Proper cementation is crucial to prevent fluid leakage into the subsurface or surface. Monitoring and ensuring that well cementation quality meets standards are essential for effective wellbore sealing.

Hydrogen sulfide content (non-reservoir section): An additional risk coefficient is applied if hydrogen sulfide is detected in the annular pressure. Hydrogen sulfide is a toxic gas that may be present in oil and gas wells, posing hazards to the working environment and equipment and corroding wellbore walls and equipment.

• (2) Divulge

Divulge may occur inside the wellbore or around the wellhead, potentially leading to natural gas leakage, environmental pollution, and even fire or explosion. Therefore, detecting and promptly addressing leakage issues are crucial for ensuring wellbore safety.

The primary indicator of divulge is further divided into two secondary indicators: gas recovery tree/casing head divulge and hydrogen sulfide content (non-reservoir section).

Gas recovery tree/casing head divulge: The Christmas tree and casing head are critical components at the wellhead, controlling the flow of fluids, pressure, and temperature. Their integrity is essential for good safety and environmental protection.

Hydrogen sulfide content (non-reservoir section): An additional risk coefficient is applied if hydrogen sulfide is present in the annular pressure. Monitoring and controlling hydrogen sulfide concentration are necessary to reduce safety risks.

• (3) Corrosion erosion

Corrosion refers to the gradual damage of wellbore materials when exposed to acidic or corrosive substances over an extended period, while erosion involves material wear under the impact of high-speed fluids. Both corrosion and erosion may lead to equipment damage, increased maintenance costs, and reduced wellbore lifespan.

The primary indicator of corrosion erosion is divided into three secondary indicators: Christmas tree, oil layer casing/technical casing, and material quality.

Christmas tree: The Christmas tree is a crucial device at the wellhead, controlling the production fluid flow, pressure, and temperature. Its material quality and surface condition are critical to resist corrosion and erosion from wellbore fluids.

Oil layer casing/technical casing: These pipes inside the wellbore are used for transporting oil and gas. Their material quality and strength are crucial to withstand corrosion or erosion challenges from wellbore fluids.

Material quality: This refers to the material quality selection for various components inside the wellbore, such as casing, valves, and pipes. Proper selection reduces the risk of corrosion or erosion. Material quality choice depends on factors such as fluid properties, temperature, pressure, and other environmental conditions.

The evaluation criteria for each indicator are provided, considering factors such as pressure levels, leakage severity, corrosion rates, and material quality. The translated content adheres to the requirements for publication in the field of petroleum engineering.

Productive efficiency

The integrity assessment index system of shale gas wells comprises wellbore safety and production efficiency. Production efficiency is divided into two primary indicators: tubing state and drivepipe state.

• (1) Tubing state

Tubing state evaluates the health of the pipeline equipment transporting oil and natural gas within the wellbore. Oil tubes play a critical role in shale gas well production by conveying natural gas and liquid hydrocarbons, requiring them to be in good condition to ensure production efficiency.

Under the primary indicator tubing state, there are four secondary indicators: liquid carrying capacity, tubing blockage/scaling, tube column deformation, and P-string corrosion/erosion.

Liquid carrying capacity assesses the efficiency and capability of the oil tube in transporting liquids. In shale gas well production, oil tubes may need to convey liquid products (e.g., oil–water mixture) and handle wastewater. Thus, liquid carrying capacity is crucial, as it impacts production and efficiency.

Tubing blockage/scaling refers to the potential obstruction or scaling within the oil tube, leading to production interruptions and fluid transport difficulties. Regular cleaning and maintenance are vital to prevent blockages.

Tube column deformation addresses potential shape or structural changes in the oil tube or column during production, which may result from downhole conditions or abnormal operational situations.

P-string corrosion/erosion indicates the surface corrosion or wear of the oil tube, which may reduce its strength and integrity and increase the risk of leaks and wellbore damage.

• (2) Drivepipe state

Drivepipe state evaluates the health of various casings within the wellbore by isolating different formations and protecting the wellbore’s integrity.

Under the primary indicator drivepipe state, there are two secondary indicators: deformation extent and influence fracturing segment.

Deformation extent assesses whether casings have undergone shape or structural changes due to external factors, potentially causing internal issues.

Influence fracturing segment examines whether the drivepipe state affects the number of fracturing segments in the well. The condition of the casings may impact the efficiency and effectiveness of fracturing operations.

The conditions for evaluating each indicator are detailed, considering factors such as maximum deformation extent, scaling severity, and influence on fracturing segments. The corresponding evaluations range from slight to severe, comprehensively assessing wellbore integrity in shale gas production.

Process of well integrity evaluation

Selection and determination of the evaluation index

After repeated discussions, research, and expert summaries, combined with the topic of this article, it was agreed to use “well integrity” as the first-level indicator. From the specific aspects of well integrity evaluation, five Level 2 indicators were derived. The screening and determination process for each Level 2 indicator was repeated, with experts obtaining 15 specific indicators as Level 3 indicators for each Level 2 indicator. The specific evaluation system is shown in Table 3.

Table 3 Framework of the well integrity evaluation inde system

The well integrity evaluation system is shown in Table 3. In order to meet the operation of the fuzzy evaluation method, the mathematical set should be represented as follows:

• $X =$(Well integrity)

• $X = (X_{1} ,X_{2} ,X_{3} ,X_{4} ,X_{5} )$ = (Abnormal ring air pressure, divulge, Corrosion erosion, Tubing state, drivepipe state)

• $X_{1}$ = (Pressure, Formation integrity, Well cementation quality)

• $X_{2}$ = (Gas recovery tree/casing head divulge, Hydrogen sulfide content (non-reservoir section))

• $X_{3}$ = (christmas tree, Oil layer casing/technical casing, Material quality)

• $X_{4}$ = (Liquid carrying capacity, Tubing blockage/scaling, Tube column deformation, Pstring corrosion/erosion)

• $X_{5}$ = (Deformation extent, Influence fracturing segment)

Determination of weights

(1) Establish the Judgment matrix of the index system

Experts from Changning Block are requested to fill in the weighted questionnaire and determine the Judgment matrix by scoring the above well integrity index according to the influence level and 1–9 scale method listed in Tables 1 and 2, respectively. Through the assessments of 20 experts holding titles ranging from associate senior to junior levels and above, each with more than 5 years of industry experience, the weight of each index is determined, and the Judgment matrix at all levels is established as follows (Table 4):

Table 4 Judgement matrix

(2) Eigenvalues and feature vectors

The maximum eigenvalues of the corresponding eigenvectors using Matlab software.

• $\lambda_{1}$ = 3.0037, the corresponding eigenvector is (0.1640, 0.4629, 0.8571).

• $\lambda_{2}$ = 2.0000, the corresponding eigenvector is (0.8944, 0.4472).

• $\lambda_{3}$ = 3.1078, the corresponding eigenvector is (0.2215, 0.9214, 0.3194).

• $\lambda_{4}$ = 4.1431, the corresponding eigenvector is (0.7159, 0.1995, 0.4938, 0.3886).

• $\lambda_{5}$ = 2.0000, the corresponding eigenvector is (0.9701, 0.2425).

• $\lambda$ = 5.9942, the corresponding eigenvector is (0.5501, 0.2173, 0.0988, 0.1519, 0.3865).

(3) Conformity test.

According to formula (1)–(3):

• ${\text {C}}.{\text {R}}_{1}$ = 0.0036 < 0.1.

• ${\text {C}}.{\text {R}}_{2}$ = 0.0430 < 0.1.

• ${\text {C}}.{\text {R}}_{3}$ = 0.0432 < 0.1.

• ${\text {C}}.{\text {R}}_{4}$ = 0.0536 < 0.1.

• ${\text {C}}.{\text {R}}_{5}$ = 0.0295 < 0.1.

• ${\text {C}}.{\text {R}}$ = 0.0975 < 0.1.

Obviously, each Judgment matrix is less than 0.1, which has passed the consistency test and shows that the calculated each eigenvector is valid.

(4) Normalization treatment

The feature vectors were normalized to obtain the weight of each index:

• $w_{1}$ = (0.1095, 0.3090, 0.5815).

• $w_{2}$ = (0.6667, 0.3333).

• $w_{3}$ = (0.1514, 0.6711, 0.1775).

• $w_{4}$ = (0.3982, 0.1110, 0.2747, 0.2162).

• $w_{5}$ = (0.8080, 0.1920).

• $w$ = (0.2664, 0.1789, 0.3041, 0.0634, 0.1872).

Acquisition of the data

According to the evaluation index system established according to Table 3, this paper carries out a survey (Table 5) on the effectiveness of well integrity and finds many experienced experts in the Changning oil and gas field to evaluate each index.

Table 5 Attribute indicator evaluation result

The evaluation values of experts for each indicator are analyzed and calculated through understanding the integrity of the engineering testing organization, testing the information within the organization, and quantifying the influence of these indicators using fuzzy mathematics methods. For example, assume that we have selected 20 testing personnel, technical engineers, and ordinary employees for a questionnaire survey, and 11 of them agree with the evaluation level “B” for one of the indicators of good integrity. This number indicates that 11/20 people agree with this indicator being at level “B” or above. Therefore, we obtain its evaluation value as 0.55. By analogy, we can obtain the fuzzy evaluation matrix $R_{i}$($i$ = 1, 2, 3, 4, 5, 6) for each Level 2 indicator $X_{i}$($i$ = 1, 2, 3, 4, 5, 6).

Take an oil and gas field project of our company as an example. A questionnaire survey is conducted among all 46 employees of the company. The respondents include all the senior management personnel, department managers, technical engineers, and ordinary employees involved in testing. They are all very familiar with the company or the testing industry and have rich experience, solid professional foundation, and accurate judgments on all aspects of the testing work. They also have unique insights into various company affairs.

Owing to the support of the company leaders, the questionnaire’s recovery rate is close to 100%. After screening the questionnaire, 41 valid questionnaires are obtained. Data collected from the statistics of the 41 valid questionnaires are shown in Table 5.

The membership of each attribute index at a certain level can be calculated according to the calculation method of membership. At the same time, the membership levels of “A, B, C, D, and E” are calculated, and the fuzzy evaluation vector of A certain attribute index is obtained. The influence degree of these indicators is quantified according to the fuzzy mathematical method. Finally, the attribute indexes of the same sub-target are gathered to obtain the fuzzy evaluation matrix of the sub-target as follows:

$$R_{1} = \left| { \, \begin{array}{*{20}c} {{0}{\text{.3415}}} & {0.2439} & {{0}{\text{.1463}}} & {{0}{\text{.1707}}} & {{0}{\text{.0976}}} \\ {{0}{\text{.3171}}} & {0.1951} & {{0}{\text{.1951}}} & {{0}{\text{.1951}}} & {{0}{\text{.0976}}} \\ {{0}{\text{.2927}}} & {{0}{\text{.2683}}} & {{0}{\text{.2439}}} & {{0}{\text{.1463}}} & {{0}{\text{.0488}}} \\ \end{array} } \right|$$

$$R_{2} = \left| { \, \begin{array}{*{20}c} {{0}{\text{.2439}}} & {{0}{\text{.3659}}} & {{0}{\text{.1951}}} & {{0}{\text{.1707}}} & {{0}{\text{.0244}}} \\ {{0}{\text{.3171}}} & {{0}{\text{.1951}}} & {{02683}} & {{0}{\text{.1951}}} & {{0}{\text{.0244}}} \\ \end{array} } \right|$$

$$R_{3} = \left| { \, \begin{array}{*{20}c} {{0}{\text{.2927}}} & {{0}{\text{.2439}}} & {{0}{\text{.2195}}} & {{0}{\text{.1951}}} & {{0}{\text{.0488}}} \\ {0.2927} & {0.3659} & {{0}{\text{.1951}}} & {{0}{\text{.0976}}} & {{0}{\text{.0488}}} \\ {0.0976} & {0.3415} & {0.4146} & {{0}{\text{.0488}}} & {{0}{\text{.0976}}} \\ \end{array} } \right|$$

$$R_{4} = \left| {\begin{array}{*{20}c} {{0}{\text{.3415}}} & {0.2927} & {0.0976} & {0.1463} & {0.1220} \\ {0.3659} & {0.3171} & {0.1707} & {0.0488} & {0.0976} \\ {0.2195} & {0.6098} & {0.1220} & {0.0244} & {0.0244} \\ {0.1707} & {0.4878} & {0.1707} & {0.1463} & {0.0244} \\ \end{array} } \right|$$

$$R_{5} = \left| { \, \begin{array}{*{20}c} {{0}{\text{.2195}}} & {{0}{\text{.3659}}} & {{0}{\text{.1463}}} & {0.1463} & {0.1220} \\ {{0}{\text{.2927}}} & {{0}{\text{.4634}}} & {0.0976} & {0.0488} & {0.0976} \\ \end{array} } \right|$$

Union operation

Starting from the attribute index layer, the fuzzy evaluation matrix $R_{k}$ of the sub-target $X_{k}$ is, and the weight vector $w_{k}$ and the fuzzy evaluation matrix are combined to obtain the comprehensive evaluation vector $b_{k}$ of the sub-target $X_{k}$:

• $b_{1} = w_{1} \times R_{1}$ = (0.3056, 0.2430, 0.2181, 0.1641, 0.0692)

• $b_{2} = w_{2} \times R_{2}$ = (0.2683, 0.3090, 0.2195, 0.1788, 0.0244)

• $b_{3} = w_{3} \times R_{3}$ = (0.2581, 0.3431, 0.2378, 0.1037, 0.0575)

• $b_{4} = w_{4} \times R_{4}$ = (0.2738, 0.4247, 0.1282, 0.1020, 0.0714)

• $b_{5} = w_{5} \times R_{5}$ = (0.2336, 0.3846, 0.1369, 0.1276, 0.1173)

Construct the fuzzy evaluation matrix $R$ from the subobjective vector $b_{k}$.

$$R = \left| { \, \begin{array}{*{20}c} {{0}{\text{.3056}}} & {{0}{\text{.2430}}} & {{0}{\text{.2181}}} & {0.1641} & {{0}{\text{.0691}}} \\ {{0}{\text{.2683}}} & {{0}{\text{.3090}}} & {{0}{\text{.2195}}} & {0.1788} & {{0}{\text{.0244}}} \\ {{0}{\text{.2581}}} & {{0}{\text{.3431}}} & {{0}{\text{.2378}}} & {0.1037} & {{0}{\text{.0575}}} \\ {{0}{\text{.2738}}} & {{0}{\text{.4247}}} & {{0}{\text{.1282}}} & {{0}{\text{.1020}}} & {{0}{\text{.0714}}} \\ {{0}{\text{.2336}}} & {{0}{\text{.3846}}} & {{0}{\text{.1369}}} & {{0}{\text{.1276}}} & {{0}{\text{.1173}}} \\ \end{array} } \right|$$

Using the weight vector of the subtarget layer, the evaluation vector of the total target layer is obtained:

$b = w \times R =$(0.2680, 0.3251, 0.2048, 0.1378, 0.0644).

To normalize the above equation:

$$b^{\prime } {\text{ = (0}}{\text{.2679, 0}}{\text{.3251, 0}}{\text{.2048, 0}}{\text{.1378, 0}}{\text{.0644)}}$$

According to the maximum degree of membership principle, the overall evaluation of Changning Block:

$$F = \max (b^{\prime}) = 0.3251$$

Therefore, the corresponding well integrity evaluation grade is "B".

According to the principle of maximum membership degree, the subtargets are analyzed, and the Level 2 indicators results such as Table 6.

Table 6 Secondary evaluation index results

Case analysis

After the integrity assessment index system for shale gas wells was established using the fuzzy comprehensive two-level AHP, two scenarios were obtained by testing two wells in the western Sichuan region. By comparing these scenarios with the on-site conditions, the reliability and rationality of the shale gas well integrity assessment were validated.

Protocol (basic parameters)

In the first-level index scheme, a hierarchical comparison scoring was conducted for the static evaluation, including abnormal ring air pressure, leakage, corrosion erosion, tubing state, and drivepipe state. The maximum eigenvalue obtained was λ = 5.0254, and both the consistency index (CI) and random consistency index (CR) passed the consistency test. The specific numerical values are shown in the Table 7 below.

Table 7 First-level index scheme

In the second-level index scheme (abnormal ring air pressure), a hierarchical comparison scoring was conducted for pressure size, formation integrity, well cementation quality, and hydrogen sulfide content (non-reservoir section). The maximum eigenvalue obtained was λ = 4.0311, and both the CI and CR passed the consistency test. The specific numerical values are shown in Table 8.

Table 8 Secondary index (abnormal ring air pressure) scheme

In the second-level index scheme (corrosion erosion), a hierarchical comparison scoring was conducted for Christmas tree, oil layer casing/technical casing, and material quality within corrosion erosion. The maximum eigenvalue obtained was λ = 3.0034, and both the CI and CR passed the consistency test. The specific numerical values are shown in Table 9.

Table 9 Secondary index (corrosion erosion) scheme

In the secondary indicators (tubing state) scheme, a hierarchical comparison scoring was conducted for liquid carrying capacity, tubing blockage/scaling, tube column deformation, and p-string corrosion/erosion within tubing state. The maximum eigenvalue obtained was λ = 4.1541, and both the CI and CR passed the consistency test. The specific numerical values are shown in Table 10.

Table 10 Secondary indicators (tubing state) scheme

To enhance the reliability and logical coherence of the consistency tests for all indicators, a validation of the overall random consistency test was performed:

$${\text{CR}}\_{\text{total}} = 0.0{26} < 0.{1}$$

Thus, it is confirmed that the overall consistency test for the hierarchy is satisfactory.

Case analysis result 1

The membership matrix shown in Table 11 is obtained by importing the data from the first well into the scheme, and the specific values are shown in the Table 11:

Table 11 Example Data 1

Integrating the evaluation set and the initial weights provides further normalized weights, as shown in Table 12:

Table 12 Adaptive weights

Case analysis result 2

The membership matrix shown in Table 13 can be obtained by importing the data from the second well into the scheme. The specific values are shown in the following table:

Table 13 Example data 2

Integrating the evaluation set and initial weights provides further normalized weights, as shown in Table 14:

Table 14 Adaptive weight

Evaluation results

Taking the field example data in 6.1 scheme into the evaluation system of shale gas well established in this paper can obtain the evaluation matrix of two Wells, and then get the comprehensive evaluation score. The specific values are shown in Tables 15 and 16.

Table 15 Case 1 evaluation results

Table 16 Evaluation results of Case II

Conclusion

This article introduces an integrity assessment method for shale gas wells based on the analytic hierarchy process, including establishing an evaluation index system, determining indicator weights, calculating comprehensive scores, developing evaluation standards, and implementing evaluation plans. The main conclusions are summarized as follows:

• The weight was determined through the AHP method, and fuzzy evaluation was conducted. The well integrity assessment system includes five secondary indicators: abnormal annular pressure, leakage, corrosion erosion, tubing state, and casing state. A total of 41 valid questionnaires were collected for fuzzy evaluation of each attribute indicator. According to the principle of maximum membership degree, the overall evaluation of well integrity in Changning Company is Grade B, with abnormal annular pressure, leakage, and tubing state evaluated as Grade B, corrosion erosion as Grade C, and casing state as Grade A.

• The well integrity evaluation system was established, comprising one primary indicator, five secondary indicators, and fifteen tertiary indicators. Through weight determination and data acquisition, a comprehensive assessment of well integrity in Changning Block was conducted, resulting in a grade of 'B'. This evaluation provides valuable insights for enhancing well safety and reliability, guiding pertinent improvement efforts.

• The test results from two wells in western Sichuan region indicate that the comprehensive scores for the two cases are 93.51 and 73.89, respectively. The first case has a warning level classified as common, whereas the second case has a warning level classified as catastrophic. This suggests that the first case exhibits a higher overall integrity level compared to the second case. Additionally, differences in the impact weights and normalized weights of various factors are observed between the two cases, reflecting varying contributions of each factor to the well integrity assessment. These evaluation results provide vital references for subsequent management and maintenance efforts, aiding in the timely identification and resolution of safety hazards in wells to ensure smooth production and operations.