Introduction

The salt cavern gas storage is created by drilling deep into the salt rock layer. Water is injected through a cavity-making pipe string to erode and dissolve the salt. The resulting brine is then discharged, leaving behind a cavern for gas storage1. This system consists of three main parts: ground engineering, well structure, and the salt cavern. Typically, a certain thickness of the salt layer is reserved between the top of the salt cavity, which is connected to the wellbore, and the overlying mudstone caprock. This reserved salt layer is referred to as the top plate of the gas storage. The well structure extends to the surface through the top plate, serving as the channel for injecting natural gas into the salt cavity, which is the main site for natural gas storage. The construction of the top plate of the gas storage reservoir is shown in Fig. 1. Salt caverns are currently widely used for storing natural gas, crude oil, hydrogen, compressed air, and other forms of energy. This review covers the history, current status, and future development trends of salt cavern energy storage (SCES) technology. Salt caverns are expected to play a crucial role in the future development of the energy sector2. The challenge of balancing unfavorable geological characteristics—such as thin salt layers, high impurity content, and numerous interlayers—with the increasing demand for natural gas presents significant theoretical and technical difficulties for implementing large-scale energy storage in layered salt rock formations in China3. Based on existing design experience4, the thickness of the top plate of the gas storage typically ranges from 30 to 35 m. The casing shoes (the floating shoes at the bottom of the casing) divide the section into the bare wells and the cementing section5. The height from the casing shoes to the top of the cavity is reerred to as the bare wells section, usually ranging from 10 to 15 m, while the portion above this is the cementing section. However, due to layered formation conditions in China, finding a sufficiently thick salt layer for constructing a large gas storage cavern remains challenging6,7. Considering the limited thickness of the salt layer, reducing the thickness of the top plate can result in a larger cavity volume. Based on international experience, the recommended ratio of the long to short axis of the elliptical cavity ranges from 1.53 to 2.7. If the cavity height of the gas storage increases by 1 m, the cavity volume can theoretically increase by 2%8. However, reducing the thickness of the top plate may introduce safety concerns and affect the stability of the gas storage. This is because the casing will continue to expand and contract during periodic injection and production operations while being compressed and subjected to creep by the formation. These conditions can potentially lead to safety issues such as cement sheath rupture and gas leakage. Therefore, it is essential to investigate the impact of top plate thickness on the stability of the well structure and to further optimize the top plate thickness for gas storage design.

Fig. 1
figure 1

Gas storage roof structure diagram.

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The casing and cement sheath are critical components of the gas storage’s top plate. Because the cement sheath can easily reach its yield strength and experience plastic damage, there is a risk of instability in the casing-cement sheath structure of the gas storage salt roof, which directly affects the stability of the top plate of the gas storage. Therefore, many scholars have analyzed and investigated the stress state and stability of the casing, cement sheath, and surrounding rock using simplified models. Zinkham et al.9 studied the mechanical model of the downhole casing-cement sheath-surrounding rock structure and noted that the cement sheath provides protective and buffering effects on the casing. Jackson et al.10 developed a simulation experiment apparatus for the casing-cement sheath and found a small gap at the cementing interface during the modeling of injection-production internal pressure. Bosma et al.11 established a two-dimensional model of the casing-cement sheath-surrounding rock using finite element software and simulated how different cement sheath materials affect the integrity of the wellbore structure. Haider et al.12 created a multi-layer combined wellbore model to explain both the wellbore structure and the stress distribution in the surrounding rock. Reza Taheri13 highlighted the importance of setting appropriate cement sheath parameters to prevent casing failure and emphasized the protective role of the cement sheath in the top plate of the gas storage. He et al.14 incorporated the damage constitutive equation into the casing-cement sheath-formation numerical model to study the damage characteristics of the cement sheath. Li et al.15 established an elastic–plastic mechanical model for the casing-cement sheath-formation of gas storage. They combined factors such as the elastic modulus of the cement sheath and formation to simulate and analyze how the matching relationship between the casing, cement sheath, and formation varies under alternating internal pressure in gas storage. Zhang et al.16 developed a finite element model to analyze the effects of formation type, internal pressure, and burial depth on the interface stress of the cement sheath and determined the mechanical properties of the cement sheath. Wang et al.17 conducted a wellbore integrity test using an equivalent design for injection-production loads and durations. They analyzed the impact of these loads on wellbore integrity. Additionally, Wang et al.18 studied the fatigue damage of the wellbore cement sheath under cyclic loading. They established a numerical model and revealed the damage characteristics of the cement sheath. To address the problem of roof stability in salt cavern gas storage, Devries et al.19 investigated the effects of span, buried depth of the cavity top, and cyclic gas recovery on the stability of the top plate of gas storage. Bauer20 used the classical beam and plate model to simulate the roof of layered salt rock gas storage and analyzed how interlayer type and caprock lithology affect roof stability. Jiang et al.21 applied the fixed large deformation circular plate catastrophe model to study roof stability after dissolving the single well in the salt top. They found that reducing the thickness of the salt top adversely affects roof stability. Based on the Mohr–Coulomb damage criterion, Hao et al.22 established the damage strength condition at the junction of salt rock and mudstone, concluding that a thicker salt top is more favorable for roof stability. Liu et al.23 used numerical simulations to show that roof failure significantly increases the range of gas penetration. Wang et al.24 established a three-dimensional geomechanical model of gas storage and investigated roof stability, finding that roof collapse is related to the lower limit of internal pressure and gas recovery rate. Zhang et al.25 determined that the lower limit of injection-production internal pressure is crucial for roof stability. Increasing the thickness of the salt layer reduces deformation and the volume of the plastic zone but also decreases energy storage efficiency. Zhang et al.26 examined the effects of various long-term injection-production cycles, minimum gas injection pressure, minimum gas injection interval, and residence duration on the stability of the surrounding rock.

The purpose of this study is to investigate how to enhance the energy storage capacity of salt cavern gas storage by appropriately reducing the thickness of the top plate of the gas storage while ensuring the stability of the top plate. Many previous studies have overlooked the influence of salt layer thickness, casing, and cement sheath, often using the reserved salt layer as a simplified mechanical model for the top plate. This approach does not accurately reflect the true conditions of the gas storage roof. Specifically, during gas injection and production, there is a significant risk of the cement sheath cracking, which could lead to gas leakage. Currently, there is a lack of systematic theoretical verification regarding the impact of the casing-cement sheath-surrounding rock system on roof stability. According to existing engineering experience, the thickness of the top plate is typically between 30 and 35 m, which does not fully utilize the energy storage capacity of the gas storage cavern. In this study, an elastic–plastic mechanical model of the casing-cement sheath-surrounding rock system was developed based on actual formation conditions, and a three-dimensional numerical model was constructed. The feasibility of using numerical simulation to investigate the deformation behavior of the surrounding rock of the shaft wall was validated through elastic–plastic mechanics theory. Three methods for reducing the thickness of the top plate salt deposit were designed. The effects of these methods on the stress and deformation distribution of the surrounding rock in the roof shaft wall were analyzed through numerical modeling. After a comparative analysis, the optimal technique was identified, offering new insights for enhancing energy storage efficiency and optimizing the top plate of the gas storage design in practical engineering applications.

Elastic–plastic modeling of casing-cement sheath-surrounding rock assemblage in the salt roof of the gas storage

The construction of the top plate of the gas storage primarily consists of three components: casing, cement sheath, and surrounding rock. These components interact in complex and dynamic ways during the formation and injection-production cycles of gas storage. The casing-cement sheath structure is particularly sensitive to various factors, including internal pressure, in-situ stress, and the creep behavior of both salt rock and mudstone. These factors can result in the failure of the injection-production string and cement sheath, leading to instability in the top plate of the gas storage. This instability can cause gas leakage and significant economic losses. Therefore, studying the displacement and stress distribution patterns of the casing, cement sheath, and surrounding rock structure of the gas storage is essential. The system can be simplified as a two-dimensional plane problem and analyzed using elastic–plastic theory. Based on this, an elastic mechanics model of the casing-cement sheath-surrounding rock composite system is constructed, and stress components and displacements are analyzed using plane strain theory. Additionally, the elastic–plastic theoretical formula for the casing-cement sheath-surrounding rock structure is derived. Given that the cement sheath in the structure is prone to plastic deformation, the theoretical stress distribution model of the casing-cement sheath-surrounding rock system in a two-dimensional plane is established using elastic–plastic mechanics theory. This provides a theoretical foundation for the three-dimensional numerical simulation of the top plate of the gas storage.

Elasticity analysis

Due to the elastic–plastic characteristics of the cement sheath under formation stress, it is common practice in geotechnical mechanics and petroleum engineering to simplify the complex behavior of the casing and formation by assuming that both are isotropic and homogeneous elastic materials27,28, the following assumptions have been made: (i) The wellbore is assumed to be a regular geometric circle, with the casing filled with cement slurry forming a stable cement sheath between the casing and the surrounding rock; (ii) The casing and formation are considered isotropic, homogeneous, and elastic materials; (iii) It is assumed that plane strain and axisymmetric conditions are satisfied; and (iv) The casing, cement sheath, and surrounding rock are assumed to be in continuous contact at the interface with no relative sliding. An elastic–plastic mechanical model of the salt roof casing-cement sheath-surrounding rock structure has been constructed, as illustrated in Fig. 2. In Fig. 2, different colors are used to represent various layers. This color coding helps ensure that, when plotting subsequent curve graphs, the background color of each curve will match the hues of the corresponding strata. This approach enhances the clarity of the visual representation, making it easier to emphasize and differentiate the changes in the curves across the different strata.

Fig. 2
figure 2

Casing-cement sheath-surrounding rock composite structure diagram.

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The salt roof casing-cement sheath-surrounding rock structure can be seen as a combination of multiple sets of thick-walled cylinders. According to the theory of thick-walled cylinders, the polar coordinate equilibrium equation can be obtained:

$$\frac{{d\sigma_{r} }}{dr} + \frac{{\sigma_{r} - \sigma_{\theta } }}{r} = 0$$
(1)

where,\(\sigma_{r}\) is radial stress, MPa;\(\sigma_{\theta }\) is annular stress, MPa;

Elastic constitutive equation, geometric equation:

$$\left\{ \begin{gathered} \varepsilon_{r} = \frac{{1 - \mu^{2} }}{E}(\sigma_{r} - \frac{\mu }{1 - \mu }\sigma_{\theta } ) \hfill \\ \varepsilon_{\theta } = \frac{{1 - \mu^{2} }}{E}(\sigma_{\theta } - \frac{\mu }{1 - \mu }\sigma_{r} ) \hfill \\ \end{gathered} \right.$$
(2)
$$\left\{ \begin{gathered} \varepsilon_{r} = \frac{\partial u}{{\partial r}} \hfill \\ \varepsilon_{\theta } = \frac{u}{r} \hfill \\ \end{gathered} \right.$$
(3)

where \(\varepsilon_{r}\) is the radial strain;\(\varepsilon_{\theta }\) is the hoop strain;\(u\) is the radial displacement.

Equations (1), (2), and (3) can be solved for the general solution of radial stress, annular stress, and displacement:

$$\left\{ \begin{gathered} \sigma_{r} = \frac{A}{{r^{2} }} + C \hfill \\ \sigma_{\theta } = - \frac{A}{{r^{2} }} + C \hfill \\ u = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{A}{r} + 2C\frac{1 - 2\mu }{{1 - \mu }}r} \right] \hfill \\ \end{gathered} \right.$$
(4)

The boundary conditions satisfy that the radial stress and displacement are continuous on the four sets of interfaces of the inner diameter of the casing, the outer diameter of the casing and the inner diameter of the cement sheath, the outer diameter of the cement sheath and the inner diameter of the formation, and the outer diameter of the formation:

$$\left\{ \begin{gathered} (\sigma_{r} )_{{r = r_{1} }} = - p_{i} \hfill \\ (\sigma_{r} )_{{r = r_{2} }}^{ca} = (\sigma_{r} )_{{r = r_{2} }}^{ce} \hfill \\ (u)_{{r = r_{2} }}^{ca} = (u)_{{r = r_{2} }}^{ce} \hfill \\ (\sigma_{r} )_{{r = r_{3} }}^{ce} = (\sigma_{r} )_{{r = r_{3} }}^{s} \hfill \\ (u)_{{r = r_{3} }}^{ce} = (u)_{{r = r_{3} }}^{s} \hfill \\ (\sigma_{r} )_{{r = r_{4} }} = - p_{0} \hfill \\ \end{gathered} \right.$$
(5)

where \(ca\) it is labeled as casing,\(ce\) is labeled as cement sheath, and \(s\) is labeled as stratum; \(P_{i}\) is internal casing pressure;\(P_{0}\) is uniform formation confining pressure.

Then according to Eq. (4) and Eq. (5), a set of equations for radial stress, circumferential stress, and displacement can be obtained for the casing, cement sheath, and stratum in an elastic state.

$$\left\{ {\begin{array}{*{20}l} {\frac{{A_{1} }}{{r_{1}^{2} }} + C_{1} = - p_{i} } \hfill \\ {\frac{{A_{2} }}{{r_{2}^{2} }} + C_{2} = \frac{{A_{1} }}{{r_{2}^{2} }} + C_{1} } \hfill \\ {\frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{2} }}{{r_{2} }} + 2C_{2} \frac{1 - 2\mu }{{1 - \mu }}r_{2} } \right] = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{1} }}{{r_{2} }} + 2C_{1} \frac{1 - 2\mu }{{1 - \mu }}r_{2} } \right]} \hfill \\ {\frac{{A_{3} }}{{r_{3}^{2} }} + C_{3} = \frac{{A_{2} }}{{r_{3}^{2} }} + C_{2} } \hfill \\ {\frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{3} }}{{r_{3} }} + 2C_{3} \frac{1 - 2\mu }{{1 - \mu }}r_{3} } \right] = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{2} }}{{r_{3} }} + 2C_{2} \frac{1 - 2\mu }{{1 - \mu }}r_{3} } \right]} \hfill \\ {\frac{{A_{3} }}{{r_{4}^{2} }} + C_{3} = - p_{0} } \hfill \\ \end{array} } \right.$$
(6a)

According to Eq. (6a), the six coefficients \(A_{1} ,A_{2} ,A_{3} ,C_{1} ,C_{2} ,C_{3}\) can be determined, and then substituted into Eq. (4) to obtain the analytical solutions of radial stress, annular stress, and displacement for the casing, cement sheath, and stratum in an elastic state.

To facilitate the calculation, the system of Eqs. (6a) is simplified by assuming the following variables \(d_{1}\)\(d_{2}\),\(b_{1}\) and \(b_{2}\) respectively:

$$\left\{ \begin{gathered} d_{1} = 2(1 - \mu )r_{2}^{2} \hfill \\ d_{2} = r_{3}^{2} + (1 - 2\mu )r_{3}^{2} \hfill \\ b_{1} = \frac{{2(1 - \mu )r_{2}^{2} b_{2} }}{{d_{1} }} \hfill \\ b_{{_{2} }} = \frac{{2(1 - \mu )R_{3}^{2} }}{{d_{2} }} \hfill \\ \end{gathered} \right.$$
(6b)

where \(d_{i}\) is the variable of radial displacement function between the boundaries of the system;\(b_{i}\) is the variable of boundary conditions of the system.

The solution \(A_{1} ,A_{2} ,A_{3} ,C_{1} ,C_{2} ,C_{3}\) is calculated as follows:

$$\left\{ \begin{gathered} A_{1} = - r_{1}^{2} p_{i} \hfill \\ A_{2} = - r_{1}^{2} p_{i} + \left[ {b_{2} r_{2}^{2} - b_{1} (r_{2}^{2} - r_{1}^{2} )} \right]p_{0} \hfill \\ A_{3} = - r_{1}^{2} p_{i} + \left[ {r_{3}^{2} - b_{1} (r_{2}^{2} - r_{1}^{2} ) - b_{2} (r_{3}^{2} - r_{2}^{2} )} \right]p_{0} \hfill \\ C_{1} = - b_{1} p_{0} \hfill \\ C_{2} = - b_{2} p_{0} \hfill \\ C_{3} = - p_{0} \hfill \\ \end{gathered} \right.$$
(6c)

Elastic-plasticity analysis

With the increase of internal pressure in the operation of gas storage, the stress of casing and cement sheath increases, which may cause the cement sheath to enter the plastic state first, and fracture sprouting and expansion occurs, then the stress–strain relationship of the cement sheath conforms to the elastic–plastic material. The dotted line in the structure of the cement sheath in Fig. 2 is the demarcation line between the elastic and plastic zones \(r = r_{2p}\). At this time, the elastic zone of the cement sheath can still be calculated according to Eq. (4), and the calculation range is \(r_{2p} \le r \le r_{3}\). In the plastic zone of the cement sheath, according to the Mohr–Coulomb failure criterion, the yield condition of plastic failure of the cement sheath can be obtained as (positive pressure):

$$(\sigma_{r} - \sigma_{\theta } ) + (\sigma_{r} + \sigma_{\theta } )\sin \phi = 2c\cos \phi$$
(7)

where,\(\sigma_{r}\) is radial stress, MPa;\(\sigma_{\theta }\) is annular stress, MPa; \(c\) is cohesive force, MPa;\(\phi\) is internal friction angle.

The radial and annular stresses within the plastic zone of the cement sheath are solved by substituting Eq. (7) into Eq. (1):

$$\left\{ {\begin{array}{*{20}l} {\sigma_{r} (r) = \frac{{B \cdot r^{{\frac{2\sin \phi }{{1 + \sin \phi }}}} - 2c \cdot \cos \phi }}{2\sin \phi }} \hfill \\ {\sigma_{\theta } (r) = \frac{{B \cdot r^{{\frac{2\sin \phi }{{1 + \sin \phi }}}} - 2c \cdot \cos \phi }}{2\sin \phi }(\frac{1 - \sin \phi }{{1 + \sin \phi }}) + \frac{2c \cdot \cos \phi }{{1 + \sin \phi }}} \hfill \\ \end{array} } \right.$$
(8)

According to the plane strain assumption, εz = 0 and without considering the volume change, it can be obtained:

$$\varepsilon_{r} + \varepsilon_{\theta } = 0$$
(9)

The displacement of the plastic zone of the cement sheath can be obtained by substituting the geometric Eq. (3) into Eq. (9):

$$u(r) = \frac{D}{r}$$
(10)

From the cement sheath plastic zone and elastic zone interface radial, annular stress, and displacement are equal, and the boundary conditions to meet the formula (11):

$$\left\{ {\begin{array}{*{20}c} \begin{gathered} (\sigma^{e}_{r} )_{{r = r_{2p} }}^{ce} = (\sigma^{p}_{r} )_{{r = r_{2p} }}^{ce} \hfill \\ (\sigma^{e}_{\theta } )_{{r = r_{2p} }}^{ce} = (\sigma^{p}_{\theta } )_{{r = r_{2p} }}^{ce} \hfill \\ \end{gathered} \\ {(u^{e} )_{{r = r_{2p} }}^{ce} = (u^{p} )_{{r = r_{2p} }}^{ce} } \\ \end{array} } \right.$$
(11)

Where e is labelled as the elastic zone of the cement sheath and \(p\) is labelled as the plastic zone of the cement sheath; sp is the radial stress at the interface between the plastic and elastic zones of the cement sheath.

By combining Eqs. (4), (5), (8), (10), and (11), the system of equations for radial stress, hoop stress, and displacement in the cement sheath under elastic–plastic conditions can be obtained:

$$\left\{ {\begin{array}{*{20}l} \begin{gathered} \frac{{A_{1} }}{{r_{1}^{2} }} + C_{1} = - p_{i} \hfill \\ \frac{{B \cdot r_{2p}^{{\frac{2\sin \varphi }{{1 + sin\varphi }}}} - 2c \cdot \cos \varphi }}{2\sin \varphi }(\frac{1 - \sin \varphi }{{1 + \sin \varphi }}) + \frac{2c \cdot \cos \varphi }{{1 + \sin \varphi }} = - \frac{{A_{2} }}{{r_{2p}^{2} }} + C_{2} \hfill \\ \end{gathered} \hfill \\ {\frac{{B \cdot r_{2}^{{\frac{2\sin \phi }{{1 + \sin \phi }}}} - 2c \cdot \cos \phi }}{2\sin \phi } = \frac{{A_{1} }}{{r_{2}^{2} }} + C_{1} } \hfill \\ {\frac{D}{{r_{2} }} = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{1} }}{{r_{2} }} + 2C_{1} \frac{1 - 2\mu }{{1 - \mu }}r_{2} } \right]} \hfill \\ {\frac{{B \cdot r_{2p}^{{\frac{2\sin \phi }{{1 + \sin \phi }}}} - 2c \cdot \cos \phi }}{2\sin \phi } = \frac{{A_{2} }}{{r_{2p}^{2} }} + C_{2} } \hfill \\ {\frac{D}{{r_{2p} }} = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{2} }}{{r_{2p} }} + 2C_{2} \frac{1 - 2\mu }{{1 - \mu }}r_{2p} } \right]} \hfill \\ {\frac{{A_{3} }}{{r_{3}^{2} }} + C_{3} = \frac{{A_{2} }}{{r_{3}^{2} }} + C_{2} } \hfill \\ {\frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{3} }}{{r_{3} }} + 2C_{3} \frac{1 - 2\mu }{{1 - \mu }}r_{3} } \right] = \frac{{1 - \mu^{2} }}{E}\left[ { - \frac{1}{1 - \mu }\frac{{A_{2} }}{{r_{3} }} + 2C_{2} \frac{1 - 2\mu }{{1 - \mu }}r_{3} } \right]} \hfill \\ {\frac{{A_{3} }}{{r_{4}^{2} }} + C_{3} = - p_{0} } \hfill \\ \end{array} } \right.$$
(12)

According to Eq. (12), the 9 coefficients of \(A_{1} ,A_{2} ,A_{3} ,C_{1} ,C_{2} ,C_{3} ,B,D,r_{2p}\). By substituting these coefficients into Eqs. (4), (8), and (10), we can derive the analytical solutions for radial stress, circumferential stress, and displacement for the casing, cement sheath, and surrounding rock under the elastic–plastic state of the cement sheath.

A simplification of Eq. (12) for ease of calculation assumes that \(x_{1} ,x_{2} ,x_{3} ,y_{1} ,y_{2} ,y_{3} ,a_{1} ,a_{2} ,a_{3} ,z_{1}\)

$$\left\{ \begin{gathered} x_{1} = c\cot \varphi ,x_{2} = - \left( {p_{i} + c\cot \varphi } \right) \hfill \\ x_{3} = 1 + \sin \varphi ,y_{1} = \frac{{\left( {p_{0} + x_{1} } \right)x_{3} }}{{x_{1} + p_{i} }} \hfill \\ f_{1} = 2n_{2} r_{2}^{2} y_{1}^{{\frac{2}{{a_{1} }}}} ,f_{2} = b_{1} + r_{1}^{2} p_{i} \hfill \\ a_{1} = - \frac{2\sin \varphi }{{1 + \sin \varphi }},b_{1} = \frac{1}{2}r_{2}^{2} y_{1}^{{\frac{{2 + a_{1} }}{{a_{1} }}}} x_{2} (1 - a_{2} ) \hfill \\ a_{2} = \frac{1 - \sin \varphi }{{1 + \sin \varphi }},b_{2} = \frac{1}{2}r_{3}^{3} x_{2} y_{1} (1 + a_{2} ) \hfill \\ z_{1} = x_{1} + \frac{{b_{1} }}{{r_{3}^{3} }}, \hfill \\ \end{gathered} \right.$$
(13)

The solution of \(A_{1} ,A_{2} ,A_{3} ,C_{1} ,C_{2} ,C_{3}\) is obtained.

Verification of the accuracy of numerical simulation

To verify the accuracy of the numerical simulation results, the three-dimensional model of the casing-cement sheath-surrounding rock is simplified to a two-dimensional plane model for calculation and compared with the theoretical solution. The dimensions of the section for the casing-cement sheath-surrounding rock are shown in Fig. 3. According to the casing dimension specifications for gas storage, the fundamental mechanical parameters of the casing, cement sheath, and surrounding rock are presented in Table 1. The casing-cement sheath structure requirements are as follows: The casing is N80 steel grade, with a size of 9–5/8 inches, an outer diameter of 244.48 mm, and a thickness of 11.99 mm. The cement sheath is made of G-grade cement, manufactured and solidified in strict accordance with API standards, and has a thickness of 48.5 mm. Considering the actual stress field of the surrounding rock in the inner shell pipe-cement sheath of the top plate of the gas storage, the wellbore pressure is determined to be 7 MPa, and the calculated surrounding rock pressure is 26.275 MPa. By substituting the mechanical parameters listed in Table 1 and following the approach outlined in “Elasticity analysis”, the radial stress, axial stress, and displacement at radii of 0.122 m, 0.134 m, 0.14 m, 0.158 m, and 0.17 m are analytically computed.

Fig. 3
figure 3

The cross-sectional schematic diagram of the casing-cement sheath-surrounding rock.

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Table 1 The calculation parameters for casing-cement sheath-surrounding rock.
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The two-dimensional mechanical grid model of the casing-cement sheath-surrounding rock composite system was constructed using FLAC3D numerical simulation software. The model utilizes an elastic–plastic approach, with boundary conditions and mechanical parameters matching those of the theoretical model. Table 2 presents a comparison between the theoretical elastic analytical solutions for axial stress, radial stress, and displacement and the numerical simulation results. Figure 4 illustrates the comparison between the theoretical elastic analytical solution and the numerical simulation results for axial stress, radial stress, and displacement in the middle section of the wellbore (25 m above the lower limit of the model). Figure 4 shows that the axial stress, radial stress, and displacement trends for the casing-cement sheath-surrounding rock are consistent between the theoretical and numerical simulation results, with the maximum error being less than 3%. This indicates that although there are some differences between the numerical simulation and the theoretical values in the two-dimensional plane model, the results are still within an acceptable range. Therefore, numerical modeling can be effectively used to examine the impact of varying salt layer thicknesses on the integrity of the casing, cement sheath, and surrounding rock in the gas storage roof’s cementing section and bare wells. The mechanical and numerical models in the theoretical analysis are based on real formation conditions, ensuring the practical application and wide applicability of the research results. The theoretical solution aids in optimizing the design and verifying the numerical simulation results. In contrast, the numerical model provides detailed insights into the stress and deformation of the roof under complex working conditions, offering an accurate basis for roof design and construction. Through three-dimensional numerical simulation, the influence of changes in salt layer thickness on the surrounding rock under long-term injection and production conditions can be predicted, aiding in the evaluation of roof stability and reducing engineering risks. By combining the theoretical solution with the numerical model, a comprehensive study of the deformation and damage behavior of the surrounding rock in salt cavern gas storage roofs is achieved, providing a scientific basis and technical support for engineering design, optimization, and safety management.

Table 2 Theoretical and simulated values of stress and displacement at the wellbore radius of gas storage.
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Fig. 4
figure 4

Comparison of wellbore stresses and displacements of gas storage.

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Numerical model and mechanical parameters

Numerical model and boundary conditions

To gain further insight into the impact of reducing the thickness of the salt layer on the top plate, with a particular focus on the stress and deformation at the casing shoes (the interface between the cementing section and the bare wells), a 3D geomechanical model of the gas storage top plate structure was constructed based on the actual working conditions of the storage. As indicated in Fig. 5, the model is a 40-m-long, 40-m-wide, and 47-m-high cuboid reflecting the surrounding rock of the gas storage facility. The casing-cement sheath composite structure is embedded within the surrounding rock formation. The impact of modulating the height of the cementing section and bare wells of the casing-cement sheath composite structure on the stability of the model is investigated by modifying the top plate thickness. To restrict horizontal movement, horizontal constraints are applied to the four vertical faces of the model. Similarly, defined constraints are imposed at the bottom of the model to restrict both horizontal and vertical movement. The 3D geomechanical model is subjected to initial ground stress and stress gradient, with the value being the average gravity of the overlying strata:

$$\sigma_{z} = \rho gh$$
(14)
Fig. 5
figure 5

Numerical model of the salt roof structure.

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Here, \(\rho\) represents the thickness of the overlying strata, g is the gravitational acceleration, and h is the burial depth of the top surface of the model. Based on actual geological conditions, it is calculated that the vertical load component at the top boundary of the model (at a burial depth of 970 m) is 25.8 MPa.

Constitutive model and parameter selection

Following the importation of the model into FLAC3D, the Mohr–Coulomb elastic–plastic constitutive model is selected for the casing-cement sheath structure. Given the substantial creep characteristics of salt rock, the C-power creep constitutive model is employed for this material, which incorporates both the Norton power law function and the Mohr–Coulomb model. By the casing dimensions specification for gas storage29, the fundamental mechanical parameters of the casing, cement sheath, and surrounding rock are depicted in Table 3. The design specifications of the casing-cement sheath structure are consistent with the design specifications in “Verification of the accuracy of numerical simulation”.

Table 3 Mechanical parameters of materials.
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The primary function of natural gas storage is to accommodate the seasonal fluctuations in natural gas demand, which typically occur on an annual basis. A typical cycle comprises four distinct phases: the gas injection period, the high-pressure shut-in, the gas production period, and the low-pressure shut-in. Salt cavern reservoir working pressure is usually cyclical, with the internal pressure gradually hitting the upper-pressure limit \(P_{\max }\) during gas injection and dropping to the lower pressure limit \(P_{\min }\) during gas extraction. In the determination of the operating pressure limit, four methods are often used, such as hydrostatic column pressure conversion algorithm, German salt layer cavity operation internal pressure design experience, cavity top burial depth conversion method, and overlying strata pressure conversion method. The specific upper limit pressure can be 1.5–2.0 times the hydrostatic column pressure, or the Canadian upper limit pressure does not exceed 80% of the rupture pressure. Domestic more reference to Jintan gas storage experience, according to the pressure gradient 1.7 MPa/100 m to determine the maximum pressure, and the minimum pressure should be 0.007 MPa/m, there is also foreign experience of the maximum pressure and minimum pressure ratio of the empirical value of the general 2:1–6:1. Comprehensive existing design experience and related theories, presuming that according to the casing, shoe buried depth of 1000 m, the preliminary design pressure of the gas storage roof structure is set at 17 MPa during injection and Pmin is set at 7 MPa during withdrawal. The time of gas injection and gas production is 120 days, and the time of shut-in is 30 days, which makes 300 days as an injection-production cycle and 30 years of continuous operation, as shown in Fig. 6.

Fig. 6
figure 6

Injection-production pressure variation diagram of an injection-production cycle.

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Simulation scheme design and results analysis

Salt roof deformation and stress distribution

Firstly, considering that the thickness of the gas storage roof is generally between 30 and 35 m based on existing engineering experience, the thickness of the salt layer cannot be excessively reduced4,5. Secondly, the stability of the roof is closely related to the integrity of the wellbore structure, which is composed of the cementing section and the bare wells30. Therefore, the stress and strain changes in the bare wells and the cementing section will affect the roof’s stability. Finally, in order to study the different methods of reducing the thickness of the cementing section and the bare wells to determine which method has the least impact on roof stability. Seven Schemes, designated a, b, c, d, e, f, and g, are formulated accordingly. Table 4 shows the heights of the bare wells, the height of the cementing section, and the thickness of the salt roof for each situation. In Schemes a and b, the cementing section remains unaltered, with the thickness of the salt layer in the bare wells specified at 5 m and 10 m, respectively. Scheme c is used as the benchmark scheme. In Schemes d and e, the bare wells remain unaltered, with the thickness of the salt layer in the cementing section set at 15 m and 10 m, respectively. Finally, in Schemes f and g, the thickness of both the cementing section and the bare wells is reduced simultaneously, with the new thicknesses set at 17.5 m/12.5 m and 15 m/10 m, respectively. Therefore, there are three cases of the total thickness of the salt layer roof under seven operating conditions, which are 35 m, 30 m, and 25 m, respectively, as shown in Fig. 7. The top plate structure within 0.5 m from the casing shoes is shown in Fig. 8. The difference between the inner and outer diameters of the casing is 11.99 mm, the difference between the inner and outer diameters of the cement sheath is 48.5 mm, and the internal pressure of the wellbore is the far-field formation pressure.

Table 4 The heights of the cementing section and bare section of different schemes.
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Fig. 7
figure 7

Schematic diagram of different comparison schemes.

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Fig. 8
figure 8

Model diagram of 0.5 m up and down casing shoes.

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Salt roof deformation and stress distribution

Vertical displacement and radial displacement of the surrounding rock can reflect the deformation characteristics of the salt layer at each location, which is an important indicator to reflect the stability of the gas storage. At the same time, according to whether the equivalent strain (ES) exceeds the permitted value, it can reflect the creep damage caused by long-term operation30,31.

$$\overline{\varepsilon } = \sqrt {\frac{2}{3}\varepsilon^{\prime}_{ij} = \frac{2}{3}\sqrt {I_{1}^{2} - 3I_{2}^{2} } = \frac{2}{\sqrt 3 }\sqrt {J^{\prime}_{2} } }$$
(15)

where:\(\varepsilon^{\prime}_{ij}\) is the strain bias;\(I^{\prime}_{1}\)\(I^{\prime}_{2}\)\(J^{\prime}\) are the first and second invariants of the strain tensor and the second invariant of the strain bias, respectively.

Taking scheme c as the benchmark scheme. The roof structure within 0.5 m from the casing shoes is shown in Fig. 8. The difference between the inner and outer diameters of the casing is 11.99 mm, while the difference between the inner and outer diameters of the cement sheath is 48.5 mm. The internal pressure of the wellbore is equal to the far-field formation pressure.

Figure 9 shows the vertical displacement, radial displacement, and effective strain curves of scheme c with the change of position. From Fig. 9a, it can be seen that the vertical displacement of the inner wall of the casing and the inner wall of the cement sheath is the same, and the maximum difference in the vertical displacement between the inner wall of the surrounding rock and the inner wall of the casing and the inner wall of the cement sheath is greater than 1 mm at the casing shoes. In the bare wells, the vertical displacement of the casing and the cement sheath is progressively approaching, and the difference between the two is only 0.15 mm at a height of 14.7 m. However, in the cementing section, the disparity between the two is still very substantial. At 0.5 m below the casing shoes, the difference between the two approaches is 1.75 mm. This shows that the deformation ability of various sections of the casing shoes is different due to the change of structure and material. The material qualities of the casing, cement sheath, and surrounding rock are quite varied; notably, the elastic modulus and plastic characteristics are distinct. The casing material is steel and has a high elastic modulus, while the elastic modulus of the cement sheath and surrounding rock is relatively low, so the deformation difference is significant under the same load. The influence of the structural position is also very significant. The casing shoes are the transition region between the cementing section and the bare walls. It is not only affected by the vertical stress but also by the radial stress, which makes the deformation more complicated. Figure 9b shows the curve of radial displacement and equivalent strain varying with the distance from a cementing section in the plane 0.1 m away from the casing shoes. It can be seen that in the cement sheath, as the distance from the interior wall of the casing increases, the radial displacement and equivalent strain fluctuate significantly. The radial displacement increases notably, from 23.9 mm to 25.3 mm from the inner wall of the casing, and it is greater than the casing displacement. This indicates that the deformation of the cement sheath under external load is significant, primarily due to the lower rigidity of the cement sheath compared to the casing. In the cementing section, the increase in radial displacement reflects the compressive effect of the surrounding rock mass on the cement sheath. This compressive effect creates a large strain gradient at the interface between the casing and the cement sheath, which further increases radial displacement within the cementing section. Such conditions may lead to stress concentration at the interface and pose a risk of failure. The effective strain increases first and then decreases. Among them, the mutation of effective strain in the inner wall of the cement sheath is the most evident, from 3.0 to 6.6%. This sudden change indicates that the stress is redistributed within the cement sheath, resulting in increased strain concentration. In the strain concentration area, the material may undergo plastic deformation or even micro-crack propagation, which reduces the stability of the overall structure. The radial displacement of the surrounding rock increases slightly at first, then gradually decreases and tends to stabilize. The difference between the maximum and the minimum is 0.3 mm, which is due to the large difference in stiffness between the surrounding rock and the cement sheath. The effective strain of the surrounding rock decreases gradually. In the surrounding rock area far from the casing, the stress on the surrounding rock weakens, and deformation is reduced. This indicates that the presence of different materials, such as casing and cement sheath, in the cementing section makes the interface between the casing and cement sheath prone to abrupt changes, which is not conducive to the stability of the salt top structure.

Fig. 9
figure 9

Vertical displacement, radial displacement, and equivalent strain versus position curves for Scheme c.

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Therefore, retaining a certain height of the bare wells at the top of the gas storage cavity can more evenly distribute the stress, avoid stress concentration damage to the casing shoes and the cementing section, and improve the long-term stability of the top plate of the gas storage.

Analysis of the effect of different salt roof thicknesses

Vertical displacement

Figure 10 shows the relationship between the vertical displacement of the inner wall of the cement sheath and the surrounding rock under different schemes. Figure 10a illustrates the change in vertical displacement between the cement sheath and the surrounding rock with the adjusted bare well height (schemes a, b, and c). Figure 10a reveals a significant difference in vertical displacement between Scheme a and Scheme c, particularly in the bare well section. At 14.5 m in the bare well section, the vertical displacement of the cement sheath and surrounding rock in Scheme a is six times higher than that in Scheme c. This indicates that a decrease in the height of the bare wells results in increased stress in the bare wells, leading to a higher vertical displacement of the cement sheath and the surrounding rock. In other words, the vertical displacement increases as the height of the bare well section decreases, and since the bare well section is relatively soft, it is more prone to deformation under larger stress.

Fig. 10
figure 10

Vertical displacement relationship curves for different schemes.

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Figure 10b shows that adjusting the height of the cementing section (schemes c, d, and e) affects the vertical displacement of the cement sheath and the surrounding rock. As the thickness of the salt layer in the cementing section decreases, the displacement of the cement sheath exhibits different trends above and below the casing shoe. The cementing section’s vertical displacement above the casing shoe decreases by 1%, but the trend is not significant. In contrast, the vertical displacement of the bare wells below the casing shoes increases, but the maximum increase is only 0.4%. Additionally, the vertical displacement of the surrounding rock in both the cementing section and the bare wells shows an upward trend, with a maximum increase of 0.8%. This occurs because decreasing the thickness of the salt layer in the cementing section increases the stiffness above the casing shoes, thereby reducing vertical displacement deformation. However, the relatively low stiffness of the bare wells below the casing shoes results in a small increase in vertical displacement, indicating that the influence of the cementing section height on the bare wells is limited.

Figure 10c shows the change in vertical displacement with height after reducing the thickness of the salt layer in both directions. The figure indicates that the vertical displacement deformation of the cement sheath and surrounding rock differs between schemes f and g, but both show an increasing trend. The vertical displacement in Scheme g increases the most, reaching up to 1.7 times that of Scheme c. In Scheme f, the vertical displacement of the surrounding rock increases the most, up to 1.8 times that of Scheme c. This is due to a two-way reduction in the salt layer’s thickness, which causes stress concentration in the cement sheath and surrounding rock, resulting in increased vertical displacement deformation.

In summary, when the thickness of the salt layer in the cementing section decreases, the vertical deformation of the cement sheath and surrounding rock is minimized, which helps control the deformation of the salt top. However, when the salt layer thickness decreases in both directions, the vertical displacement of the cement sheath and surrounding rock increases significantly. For instance, when the thickness of the salt top is reduced by 5 m and 10 m, the deformation of the cement sheath and surrounding rock in schemes a and b increases by 6 times and 1.7 times, respectively. In contrast, the deformation in schemes f and g increases by 1.2 times and 1.7 times, respectively. These large deformations are detrimental to controlling the deformation of the salt top in gas storage. Therefore, reducing the thickness of the salt layer in the cementing section can effectively control the deformation of the cement sheath and the surrounding rock, which is important for the stability of the gas storage roof structure.

Radial displacement

Figure 11 shows the variation of plane radial displacement with the distance from the shaft wall under different schemes. As depicted in the figure, the trend of radial displacement for each scheme is consistent with the increasing distance from the shaft wall. From Fig. 11a, it is evident that reducing the height of the salt layer in the bare wells results in significant changes in radial displacement. Notably, the radial displacement in Scheme a is four times that of Scheme c. This is because reducing the height of the salt layer increases the flexibility of the bare wells, leading to greater radial displacement under external stress. Therefore, decreasing the thickness of the salt layer in the bare wells is detrimental to the stability of the salt top structure.

Fig. 11
figure 11

Relation curve of water radial movement for different schemes.

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Figure 11b illustrates the radial displacement curve for reducing the thickness of the salt layer in the cementing section. In this figure, the radial displacement of Schemes d and e is less than that of Scheme c within the casing range. However, in the cement sheath and surrounding rock ranges, the radial displacement of Schemes d and e is higher than that of Scheme c, with an increase of only 2% compared to Scheme c. The smaller radial displacement after reducing the thickness of the cementing section is due to its increased stiffness, which better resists external stress. However, the increase in radial displacement in the cement sheath and surrounding rock areas indicates that reducing the thickness of the salt layer in the cementing section leads to stress concentration and increased deformation in these areas.

From Fig. 11c, it can be seen that the radial displacement in schemes f and g increases significantly after the two-way reduction of salt layer thickness. This increase occurs because reducing the salt layer thickness in both directions enhances the flexibility of the salt top structure, leading to a substantial rise in radial displacement under external stress. Consequently, these schemes have a greater impact on the stability of the salt top structure compared to the scheme that reduces the salt layer thickness only in the cementing section.

In summary, appropriately reducing the thickness of the salt layer in the cementing section optimizes radial displacement within the wellbore structure, reduces deformation, and improves stability. This approach improves the use of the salt layer in the construction section and increases the gas storage capacity.

Principal stresses

Figure 12 shows the variation in the principal stress in the plane with the distance from the borehole wall under different schemes. As illustrated in Fig. 12a, the minimum principal stress (absolute value) decreases progressively with increasing distance from the borehole wall, exhibiting fluctuations at each junction, particularly in scheme a. These fluctuations are more pronounced in scheme a, primarily due to the height of the bare wells being only 5 m, making it more susceptible to the influence of the top of the gas storage cavity. Consequently, a lower height of the bare wells leads to more significant stress fluctuations caused by the top of the gas storage cavity. As the horizontal distance increases, the minimum principal stress in the surrounding rock tends to stabilize, indicating that the stress state becomes more balanced with increasing distance from the cavity top. Based on the data in Fig. 12b, it is evident that the maximum principal stress within the casing starts high but decreases rapidly and stabilizes at the far-field stress level upon entering the cement sheath. Scheme b shows a significant reduction in the maximum principal stress from 271 to 153 MPa, representing a 43% decrease. This reduction is attributed to the decrease in the thickness of the salt layer in the cementing section, resulting in a rapid decline in stress within the casing and stabilization after entering the cement sheath. The presence of the cement sheath effectively buffers the stress, causing it to quickly return to the far-field stress. These findings demonstrate that modifying the height of the cementing section can effectively control the stress state and mitigate stress concentration, ultimately enhancing the structural stability of the gas storage top. Therefore, reducing the thickness of the salt layer in the cementing section is an effective strategy to reduce the stress fluctuation and stress concentration in the casing and cement sheath area.

Fig. 12
figure 12

Variation of minimum and maximum principal stresses with horizontal distance for different schemes.

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Comparative analysis of different programs

The junction between the casing and the cement sheath in the salt roof structure is a critical area prone to deformation. Therefore, this junction is the focus of analysis in each scheme, with Scheme c used as the reference. The displacement and principal stress ratios at this junction are compared across different schemes, as shown in Fig. 13.

Fig. 13
figure 13

Displacement and stress variation curves at casing-cement sheath junction for each scheme.

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From Fig. 13a, it is evident that the displacement ratio curve first decreases and then gradually increases, forming a concave shape. This indicates that as the thickness of the bare wells increases, the displacement ratio decreases rapidly, while changes in the thickness of the cementing section have minimal impact on the displacement ratio. A reduction in thickness in both directions results in a gradual increase in the displacement ratio. Specifically, in Schemes a and b, reducing the thickness of the bare wells by 10 m and 5 m increases the displacement ratio by 5.6 times and 1.8 times, respectively. In Schemes d and e, altering the thickness of the cementing section has little effect on the displacement ratio. Therefore, reducing the thickness of the bare wells significantly increases the displacement ratio, leading to greater structural deformation and decreased roof stability. Conversely, reducing the thickness of the cementing section has minimal impact on the displacement ratio, which helps control roof deformation and maintain structural stability.

Figure 13b shows the principal stress ratio curve at the junction of the casing and cement sheath for each scheme compared to the reference scheme. The maximum principal stress ratio curve exhibits a trend of initially decreasing and then gradually increasing, forming a concave shape. This indicates that with an increase in the thickness of the bare wells, the stress ratio decreases. Conversely, a decrease in the thickness of the cementing section also leads to a decrease in the stress ratio, while a reduction in thickness in both directions causes a slow increase in the ratio. In particular, when the thickness of the bare wells is reduced by 10 m and 5 m, the maximum principal stress ratio in Schemes a and b increases by 1.48 and 1.28 times, respectively. This suggests that reducing the thickness of the bare wells leads to increased stress concentration, increasing the maximum principal stress ratio, and negatively affecting structural stability. On the other hand, in Schemes d and e, reducing the thickness of the cementing section by 5 m and 10 m results in a decrease in the maximum principal stress ratio by 0.79 and 0.69 times, respectively. This indicates that reducing the thickness of the cementing section helps to alleviate stress concentration, control the principal stress ratio, and maintain structural stability. The maximum principal stress ratios of schemes f and g increase by 0.84 and 0.96 times, respectively, with a two-way decrease of 5 m and 10 m in the bare wells and cementing section. This suggests that reducing the salt layer thickness in both directions has a significant impact on the principal stress ratio, which is detrimental to the roof structure’s stability. Comparing the maximum principal stress ratios of all schemes, Schemes d and e show the lowest values. To enhance the stability of the gas storage roof, it is recommended to optimize the reduction of the cementing section thickness. This approach helps control the displacement ratio and the maximum principal stress ratio, reducing deformation and stress concentration, and thereby maintaining structural stability. It is advisable to avoid reducing the thickness of the bare wells, as this could lead to a significant increase in both the displacement ratio and the maximum principal stress ratio, adversely affecting roof stability.

The minimum principal stress ratio curve initially decreases, then increases, and subsequently decreases again. This pattern indicates that the ratio decreases as the thickness of the bare wells increases, and increases as the thickness of the cementing section decreases. A reduction in thickness in both directions leads to a decrease in the ratio. Specifically, when the thickness of the bare wells decreases by 10 m and 5 m, the minimum principal stress ratio in schemes a and b increases by 0.998 and 0.774 times, respectively. This suggests that reducing the thickness of the bare wells significantly increases stress concentration, raising the risk of shear failure, particularly at the junction of the casing and cement sheath. Additionally, shorter bare wells result in more concentrated structural deformation and uneven stress distribution. In contrast, the minimum principal stress ratios of schemes d and e increase by 1.031 and 1.079 times, respectively, when the thickness of the cementing section is reduced from 5 to 10 m. This shows that while reducing the thickness of the cementing section also increases stress concentration, the effect is relatively minor. This indicates that while reducing the thickness of the cementing section also increases stress concentration, the effect is relatively minor. This is because the greater stiffness of the cementing section helps disperse stress more effectively and reduces the area of concentrated stress. The minimum principal stress ratio for Schemes f and g is reduced by 1.04 and 0.835 times, respectively. Although this reduction can decrease stress concentration, it is critical to consider the overall stability of the structure to ensure the gas storage roof’s long-term safety and stability.

In summary, changes to the thickness of the bare wells and the cementing section have a significant impact on the roof structure’s stability. Reducing the thickness of the bare wells significantly increases stress concentration, leading to a higher risk of shear failure, whereas reducing the thickness of the cementing section has a relatively smaller effect on stress concentration. Therefore, appropriately reducing the thickness of the cementing section can improve the energy storage efficiency of the gas storage while also ensuring the stability and safety of the roof structure during long-term injection and production.

Conclusion

This study aims to investigate the impact of reducing the thickness of the top salt layer on the deformation and failure behaviors of surrounding rock in salt cavern gas storage. The developed elastic–plastic mechanical model, based on real geological conditions, ensures the broad applicability of the research findings and validates the feasibility of the numerical model. The numerical model effectively analyzed three methods for reducing the top salt layer thickness. The results indicate that reducing the thickness of the salt layer in the cementing section has the least impact on the stability of the gas storage cavern. Both the theoretical and numerical models are based on real geological conditions, ensuring the relevance and applicability of the results to actual engineering practices.

  1. 1.

    The three-dimensional numerical model of the gas storage top plate cementing section aligns closely with the theoretical model solution for the salt roof casing-cement sheath-surrounding rock elastic–plastic model. This consistency verifies the reliability of the numerical model. With this validated numerical model, the stress and deformation states of the salt roof casing-cement sheath-surrounding rock system can be further examined by considering the effects of varying the heights of the cementing section and bare wells.

  2. 2.

    At the junction of the casing and the cement sheath, significant changes in displacement, equivalent strain, and maximum principal stress are observed. In contrast, at the interface between the cement sheath and the surrounding rock, these changes are relatively minor. Consequently, the deformation and stress states at the junction of the casing and cement sheath in the cementing section require closer examination.

  3. 3.

    The influence of different thicknesses of the salt roof on radial displacement, horizontal displacement, and principal stress is essentially similar. However, the degree of influence varies considerably, particularly in the regions above and below the casing shoes. The displacement change in the bare wells of the salt roof shows significant variation at the casing shoes. Furthermore, the displacement change in the cementing section is more pronounced compared to the bare wells. Therefore, maintaining a certain height for the bare wells is advantageous for ensuring the stability of the salt roof structure.

  4. 4.

    The thickness of the salt roof is not a uniform variable; it exhibits a range of values. Among these, the thickness of the bare wells exerts the greatest influence on the stress and deformation of the salt roof structure. This is followed by bidirectional changes in both the cementing section and bare wells, while the thickness of the cementing section has the least effect. Therefore, it is recommended to enhance the safety and stability of the gas storage by primarily reducing the thickness of the salt roof from the cementing section.