Allowable Pillar Width for Salt Cavern Gas Storage Based on Triangular Well Layout: A Case Study in China

Abstract

Salt rock, renowned for its remarkable energy storage capabilities, exists in deep underground environments characterized by high temperature and pressure. It possesses advantageous properties such as high deformability, low permeability, and self-healing from damage. When establishing a cluster of salt cavern gas storage facilities, the careful selection of ore column widths between these reservoirs is crucial for minimizing the risk of structural failure, optimizing salt rock resource utilization, and enhancing the construction and operation of gas storage reservoirs. In current practices, square triangular arrangements are commonly used in designing well layouts for reservoir groups to balance stability and economic considerations. This study, conducted in the context of the Jintan salt cavern gas storage project in Jiangsu Province, employed FLAC^3D to create a finite element model for proposed gas storage configurations. A comprehensive analysis of the long-term operational safety of salt cavern gas storage with triangular well layouts was carried out. Various indices were examined, covering aspects such as cavern wall displacement, characteristics of the plastic zone, volume shrinkage, safety coefficients, seepage range, pore pressure fluctuations, and seepage volume. The study also considered the mechanical behavior of hexagonal columns within the surrounding rock during extended storage operations, leading to the optimization of allowable widths for these columns. The results indicate that, at operating pressures ranging from 6.5 to 17 MPa, the permissible column width should exceed 1.67 times the maximum cavern diameter to ensure compliance with criteria for long-term stability and containment within a square triangular layout. These findings provide valuable insights into determining the optimal allowable widths of salt cavern columns for positive triangular layouts.

1. Introduction

Energy reserves play a pivotal role in ensuring the sustainable development of a nation’s economy and society. In the future, China’s energy strategy will prominently feature both strategic energy reserves and commercial storage. Salt rock, characterized by its extremely low permeability and excellent creep behavior, provides a robust containment medium for these reservoirs. Moreover, it exhibits stable mechanical properties, including high deformation capacity and self-recovery from damage, making it adaptable to variations in storage pressure [1]. Additionally, the water-soluble nature of salt rock simplifies its construction and excavation, rendering it a more cost-effective choice for storage solutions. Consequently, salt rock has gained international acclaim as an ideal medium for energy storage and has seen extensive utilization in Europe, the United States, and other developed nations. Diverging from Europe and the United States [2], where storage reservoirs are primarily built within thick salt mounds, Chinese salt mines are predominantly layered with thin individual strata, often containing insoluble interlayers. To enhance the safety and utilization of energy storage spaces, reservoirs in China are typically arranged in compact clusters of small cavities [3].

The design of reservoir spacing, specifically the determination of the minimum width of the pillar, is a critical aspect of organizing a reservoir group. Optimal pillar width is a delicate balance, as a pillar that is excessively wide leads to inefficient use of space, while a pillar that is excessively narrow jeopardizes the stability of the entire reservoir group. Achieving the right balance is essential to ensure the economic and structural viability of the gas storage facility [4]. In 1978, Germany took a pioneering step by commissioning the world’s first commercial salt cavern compressed air energy storage facility, the Huntorf power station. This station boasts an output capacity of 321 MW, with an operational efficiency of 29%. The salt cavern utilized in this facility has a maximum diameter of 60 m, an inter-well spacing of 220 m, and a pillar-to-cavern ratio of 2.67 times the maximum cavern diameter [5]. In prior studies concerning pillar research in China, taking into account the results of single-cavern stability analysis and double-cavern stability analysis, along with the inclusion of a certain safety margin, it has been recommended that, under conditions where the cavern diameter falls within the range of 80–90 m, the safety factor P/D (pillar width-to-cavern diameter ratio) should exceed 1.75. For practical engineering purposes, it is suggested that an initial design of well positioning adopts a P/D value of 2.0, with subsequent gradual reduction of the P/D value as part of ongoing safety monitoring and adjustments in the project’s development [4]. In the United States, underground salt cavern storage is the primary method employed for petroleum reserves. Strategic petroleum reserves in the U.S. are stored within vast underground salt caverns at depths ranging from 610 to 1200 m. These caverns typically have a cavern height of approximately 250 m, a diameter of approximately 70 m, and an inter-cavern spacing of 1.5 to 2 times the cavern diameter. Jarosław Slizowski et al. found that the Zatoka Gdanska area in Poland has a stratigraphy similar to that in China and is a stratified salt deposit. In this area, a salt cavern gas storage reservoir is triangularly laid out to achieve the best gas storage capacity. As shown in Figure 1, the main part of the cavern is a cylindrical truncated cone with diameter D (or a), and L is distance between the axes of neighboring caverns (m). According to SMRI (Solution Mining Research Institute), the salt cavern arrangement (L/D) should depend on the depth of the rock salt formation as follows [6].

• For shallow caves (top of the rock salt layer at a depth of 600 m), the grid spacing should be at least 3.5 D.
• For caves located at moderate depths (top of rock salt layer at 1000 m depth), the grid spacing should be at least 4.0 D.

Cheng Lijuan [7] from Tsinghua University introduced a method for assessing the stability of underground cavern clusters based on unbalanced forces and the minimum plastic residual energy parameterization, which was incorporated into FLAC^3D. They derived its equivalent representation in FLAC^3D and demonstrated that the stability of the reservoir cluster can be evaluated by considering the maximum unbalance force and the extent of the plastic zone. Additionally, they characterized the damage location and expansion path of the reservoir cluster by analyzing the distribution of unbalanced forces and the adjustment process within FLAC^3D. The optimization of densely arranged reservoir groups involves two primary considerations: determining the appropriate spacing between reservoirs and establishing an optimal planar arrangement for the reservoir group. It is worth noting that an economically safe spacing is approximately 1.5 times the hole spacing. Among planar arrangements, the square triangular layout stands out as the most optimized configuration for reservoir groups [4]. Three types of arrangement forms are shown in Figure 2.

Li [8] used numerical simulations to analyze the influence of salt cavern diameter, column width, intra-cavern pressure, cavern depth, and well placement method on the stability of the column and found that the critical salt cavern spacings were 0.85 D and 1.15 D for rectangular and triangular layouts, respectively. This conclusion is far from the commonly held view that the triangular layout provides greater utilization of the mine site. When the neighboring cavities are equally spaced, the safety margin is greater for the rectangular layout. This requires the width of the inter-reservoir pillar to meet the requirements of both reservoir stability and tightness and to maximize the utilization of the salt rock resources.

Hence, the determination of the minimum allowable column width for a cluster of layered salt cavern gas storage reservoirs, which guarantees long-term operational safety while adhering to the demands for both safety and utilization in a triangular layout, remains a subject that has yet to be thoroughly investigated and studied. This area of research holds significant importance in optimizing the design and operation of such gas storage facilities.

Wu et al. [9] conducted a systematic study on the criteria for evaluating the stability aspects of energy repositories in salt rocks. He and his team concluded that the criteria for evaluating the stability of energy repositories in salt rocks involve a wide range of many elements, which are summarized in the following three aspects: (1) stability of the repository; (2) sealing of the repository; and (3) serviceability of the repository. Figure 3 shows the main components of the stability evaluation of oil and gas underground storage in salt rock. Stability mainly includes the minimum internal pressure inside the repository (⑪, ⑫); the distance between the repositories ⑬; the distance from the repository floor to the salt formation floor and the floor rise ⑯; the distance from the repository perimeter to the salt formation side boundary ⑭; the thickness of the salt formation from the repository roof to the salt formation roof ⑲; the rate of change of the internal pressure; and the surface settlement (⑳–㉓) related to the height ⑮, diameter ⑱, and depth of the repository ④, including the lithological properties of the overlying rock layer of the repository ⑤. Confinement mainly includes the maximum internal pressure, the repository perimeter, and the maximum internal pressure, including the maximum internal pressure, and the permeability of the reservoir envelope (⑥–⑧, ①–③), and serviceability mainly includes the convergence of the reservoir envelope (⑨, ⑩, ⑰).

This study advances the current methodology by introducing a set of evaluation criteria encompassing various factors, including cavern wall displacement, plastic zone characteristics, volume reduction, safety coefficients, seepage range, variations in pore pressure, and seepage volume, among others. It leverages the Jiangsu Jintan salt cavern gas storage reservoir as a practical engineering case, using FLAC^3D to construct a finite element model for evaluating the proposed reservoir configuration. The research delves into the long-term operational safety analysis of the salt cavern gas storage reservoir with a triangular well layout. It explores the mechanical behavior of the surrounding rock and pillars throughout extended reservoir operation and optimizes the allowable width of these pillars to enhance the safety and efficiency of the gas storage facility.

2. Background of Jintan Salt Mine

Jintan Salt Mine was among the pioneers in China to initiate the construction and operation of salt cavern gas storage facilities. The China National Salt Jintan Ganghua Gas Storage, located in the Jintan District of Changzhou City, Jiangsu Province, comprises the first-phase project featuring 10 wells, with some already operational for gas storage, while the rest are in the process of cavity construction. The inter-well spacing employed is approximately 200 m. The second-phase project, consisting of 12 wells, has not yet commenced drilling.

The authors collected information from six boreholes, namely Well No. 1, representing the second-phase reservoir area; Well No. 1 in the Maoling area (Mao 16 well); Well No. 2 in the Maoling area (Mao 15 well); Well No. 3 in the Maoling area (Mao 10 well); Well No. 4 in the Maoling area (Mao 19 well); and Well No. 17 in the Maoxing area. These boreholes provide a comprehensive overview of the salt and interbedded formations in the Maoxing well area of the Jintan salt mine.

The salt rock layers comprise up to 19 salt beds (Well No. 1 in the second-phase reservoir area). The thickness of individual salt beds ranges from 0.30 to 49.75 m, generally a few meters thick. The cumulative thickness of salt rock layers in a single borehole ranges from 100.52 to 214.55 m. Interbedded layers in the salt rock formations primarily include mudstone, clayey mudstone, clayey salt rock, and salt-bearing mudstone.

This study is conducted against the backdrop of the second-phase project at Jintan Salt Mine, where a triangular well layout is used to optimize the spacing of newly constructed solution-mining pillars. This approach increases the number of wells and enhances storage capacity. Well No. 1 in the second-phase storage area at China National Salt Jintan Ganghua Gas Storage is situated at a depth of 835.7 to 985.6 m, with a salt rock stratum thickness of 138.5 m. Within the salt layer, the maximum single-layer thickness is 31.25 m, the minimum is 1.75 m, and the average thickness is 6.1 m, with a cumulative salt layer thickness of 115.8 m. High-quality salt rock accounts for 83.61% of the stratum. Interlayer thickness ranges from a maximum of 3.4 m to a minimum of 0.2 m, with an average thickness of 1.19 m and a cumulative interlayer thickness of 22.7 m. The interlayer ratio is 16.39%, and the interlayer within the salt rock stratum is primarily composed of mudstone and secondary salt formations. Geological information for the salt mine is depicted in Figure 4.

3. Numerical Simulation

To better achieve the research objectives, this paper utilized numerical simulation methods, involving three-dimensional modeling of the gas storage reservoir and the determination of computational parameters.

3.1. 3D Geomechanical Model

Considering factors such as cavern construction and stability, the shape of the dissolution cavern was ultimately designed as a combination of a semi-ellipse at the upper part and a semi-circle at the lower part. The chosen shape and size of the cavern are illustrated in Figure 5. The top and bottom plates of the cavern were buried at depths of 700.1 m and 780.1 m, respectively. The upper part of the cavern took on an ellipsoidal form, while the lower part was hemispherical. The sphere had a radius of 30 m, the long semi-axis of the ellipsoid had a radius of 50 m, the cavern’s height was 80 m, and its volume amounted to approximately 104,000 cubic meters.

The model’s coordinate system was established with its origin situated on the surface ground plane, aligned with the center of the dissolved cavern. The XY-plane represented the horizontal plane within the coordinate system, while the vertical direction corresponded to the Z-axis. The numerical calculation model extended to a boundary range six times the cavern’s diameter. Outside this range, and independent of the excavation, the modeling encompassed the rock layers spanning from an elevation of −651.95 m to −1213.30 m, covering a height of −561.35 m. The weight of the overlying rock layer at stratum −651.95 m was simplified as an upper surface load for the cubic model, with a density set at the average value of 2.35 g/cm³ for the stratum [10].

A three-way isobaric self-weight stress field was employed, and the lower surface of the model was constrained with simple support to limit vertical displacement. The four longitudinal surfaces were also constrained in their respective normal directions. In essence, geological bodies other than the front, back, left, right, and lower end surfaces of the model were considered rigid bodies, disallowed from generating normal movement.

The storage capacity of an individual salt cavern gas storage facility is inherently limited, and its peaking capacity may not be sufficient. Consequently, gas storage peaking stations established within salt mines typically consist of multiple underground cavities, forming what is known as a storage cluster. These reservoir groups can be arranged in a triangular pattern, where the external pressure on one cavern is influenced by the pressure from the surrounding four cavities. Taking into account the specific conditions of the Maoxing well area in Jintan, as well as the second phase of the salt resource mining program and mining safety considerations, the design of the brine extraction well group program was devised with a focus on the worst-case scenario (Figure 6). A considerable area was allocated to evenly distribute the brine extraction well group. Due to the symmetrical layout of the well group and cavern shape, the influence of stratigraphic dip angles between adjacent cavities was disregarded. The shaded region, as illustrated in Figure 7, was selected as the designated modeling range and subjected to analysis. In this instance, the entire 3D analysis calculation model was utilized (Figure 8), and the calculation area was configured as a triangular column.

To determine the minimum safe mine pillar width, a numerical simulation calculation scheme was designed, as shown in

Table 1. Calculation scheme of pillar width.

Schemes	Scheme 1	Scheme 2	Scheme 3	Scheme 4	Scheme 5
Pillar width	1.0 D (60 m)	1.5 D (90 m)	2.0 D (120 m)	2.5 D (150 m)	3.0 D (180 m)

.

In Table 1, D indicates the maximum diameter of the cavern for the calculation model, and a cavern design scheme with a diameter of 60 m was used in this calculation, given that the maximum operating pressure of the storage reservoir is 17 MPa and the minimum operating pressure is 6.5 MPa.

3.2. Determination of Parameters

The parameters for numerical simulation calculations were finalized through experimental analysis and parameter determination in this study.

3.2.1. Experimental Analysis

To obtain the necessary parameters for the cores, mechanical and permeability tests were conducted. According to the geological structure of the Jintan salt mine, all cores for this test study were taken from Formations 14 and 31 of Maoxing Well No. 17 in the Maoxing Well Area, where the Jintan salt mine area in Jiangsu Province is located. These results provided the necessary parameters for analyzing the long-term operational safety of the salt cavern gas storage reservoir built in the Jintan salt mine.

In this study, uniaxial and triaxial compressive strength tests (Figure 9 and Figure 10) were conducted, from which the elastic modulus, Poisson’s ratio, cohesion (C), and internal friction angle (φ) of the salt rock in the target mining area were obtained, as presented in

Table 2. Uniaxial and triaxial compression test results of Jintan rock samples.

Lithology	Specimen ID	Type of Test	Uniaxial Compression Strength (MPa)	Elastic Modulus (GPa)	Average (GPa)	Poisson’s Ratio	Average
Rock salt	DZ-1	Uniaxial compression test	23.616	2.12	2.85	0.293	0.280
	DZ-2		19.853	1.62		0.247
	DZ-3		18.088	0.933		0.258
	DZ-4		26.27	2.41		0.299
	DZ-5		14.753	5.25		0.304
Lithology	Specimen ID	Type of test	Axial stress-strain (%)	Triaxial compression strength (MPa)	Cohesion (MPa)	Friction angle (°)	\
Rock salt	SZ-1	Tiaxial compression test	5.57	25.01	5.450	30.510	\
	SZ-2		20.31	84.12
	SZ-6		6.08	64.82
	SZ-11		13.06	51.39
	SZ-9		19.62	96.53
	SZ-13		6.51	36.71
	SZ-12		21.23	115.90

[11].

Permeability tests were also conducted in this study, and the obtained permeability parameters are presented in

Table 3. Results for samples used in permeability tests.

Lithology	Specimen ID	Permeability (m2)	Average (m2)	Method
Rock salt	ST-1	1.00 × 10−20	5.65 × 10−21	Unsteady-state
	ST-2	9.44 × 10−21
	ST-3	3.01 × 10−21
	ST-4	1.86 × 10−21
	ST-5	1.20 × 10−21
	SZ-3	9.58 × 10−16
	SZ-8	6.78 × 10−21
	SZ-7	8.77 × 10−21
	SZ-5	6.15 × 10−21
	DZ-14	4.05 × 10−21

[12]. The core used for the test is shown in Figure 11 [13].

3.2.2. Settled Parameters

The creep parameters of the salt rock, along with the physical mechanical parameters of the interlayers, were obtained from previous studies. All the parameters used in the numerical simulations in this study are listed in

Table 4. Basic rock mechanics parameters of salt and mudstone.

Lithology	Elastic Modulus (GPa)	Poisson’s Ratio	Cohesion (MPa)	Friction Angle (°)	Tensile Strength (MPa)
Salt rock	3.830	0.280	5.450	30.510	1.080
Interlayer	4.720	0.185	8.190	39.570	1.670

,

Table 5. Strain softening model parameters.

Deformation Parameters	6.00 × 10−4	8.00 × 10−4	9.00 × 10−4	1.00 × 10−3	3.00 × 10−3	5.00 × 10−3	1.00 × 10−2
c	4.613°	6.536°	4.275°	7.719°	11.364°	18.399°	24.789°
ψ	12.388	12.569	12.448	11.259	10.575	6.745	2.663

and

Table 6. Creep parameter value.

Lithology	Creep Parameters A (MPa)−n⋅h−1	Creep Parameters n
Salt rock	2.996 × 10−9	4.480

[10].

4. Results and Analysis

Based on numerical simulation calculations, stability analysis and tightness analysis were conducted on the simulation results.

4.1. Stability Analysis

Stability analysis evaluation criteria include five evaluation indices, including displacement, plastic zone, volume shrinkage, equivalent strain, expansion safety factor, and equivalent effect variation [14].

4.1.1. Plastic Zone

Salt cavern gas storage reservoirs are designed for a standard cycle of more than 50 years. The salt cavern envelope deforms over the time of operation, which can reduce the stability of the column. The Mohr–Coulomb yield criterion is one of the most commonly used criteria in soil and rock engineering under the assumption of ideal elastic-plastic rock salt and entrapment. It has been used by many scholars to predict the plastic zone of the rock surrounding the salt cavern UGS and has been shown to be able to accurately assess whether plastic failure has occurred in the rock surrounding the cavern. The general expression of the Mohr–Coulomb criterion is:

$$f^s={\sigma }_1-\frac{1+\sin \phi }{1-\sin \phi }{\sigma }_3-\frac{2c·\cos \phi }{1-\sin \phi }$$

(1)

$$f^t={\sigma }_t-{\sigma }_3$$

(2)

where c is the cohesion (Pa); $\phi$ is the friction angle (degrees); ${\sigma }_t$ is the tensile strength (Pa); ${\sigma }_1$, ${\sigma }_2$, ${\sigma }_3$ are the first, second, and third principal stresses, respectively; and ${\sigma }_1$ ≥ ${\sigma }_2$ ≥ ${\sigma }_3$ (Pa). The compressive stresses are negative [15].

In Figure 12, it can be seen that the wider the column is, the smaller the breakage zone of the surrounding rock is, and no unit damage (expressed as shear-n or tension-n in FLAC^3D software Version 6.0, Itasca Consulting Group Inc., Minneapolis, NY, USA) occurred after the static calculation of the five calculation schemes. The breakage zones in the middle, top, and bottom of the cavern were mainly tensile damage (expressed as tension-p), and the upper and lower parts of the cavern had shear damage as the main damage area during the calculation (denoted as shear-p in FLAC^3D software) [16].

4.1.2. Displacement

Displacement is a readily detectable parameter in numerical simulations, and it offers a straightforward and clear physical interpretation. Therefore, it is one of the most commonly utilized indicators for evaluating the deformation of the salt cavern envelope. It has been proposed that, following 30 years of operation, the maximum displacement of the surrounding rock within the salt cavern, except for the bottom, should not surpass 10% of the cavern’s diameter, as suggested by Wang. Some researchers also argue that, to prevent issues such as roof collapse, spalling, and subsidence, and particularly in the context of underground gas storage in the Jintan salt cavern, the maximum displacement should not exceed 5% of the cavern’s maximum diameter. In this study, a minimum critical threshold of 5% is adopted as the evaluation criterion [17].

The cavern deformation after 30 years of operation for each scenario is shown in

Table 7. The deformation of the cavern after 30 years of operation for various pillar widths.

Conditions	Scheme 1 (1.0 D)	Scheme 2 (1.5 D)	Scheme 3 (2.0 D)	Scheme 4 (2.5 D)	Scheme 5 (3.0 D)
Maximum displacement around cavern (m)	6.4488	5.3460	4.2652	3.6940	3.2413
Volume shrinkage rate (%)	35.270	30.540	25.6360	23.270	20.766

. In Figure 13, the volume shrinkage rate and the maximum displacement of the cavern perimeter after 30 years of cavern creep showed obvious increasing trends as the width of the ore column increased.

4.1.3. Volume Shrinkage

The volume shrinkage rate is the ratio of the volume shrinkage during the operation of the salt cavern gas storage to the total volume of the original salt cavern. If the volume reduction is too large, then it affects the economics of the salt cavern gas storage reservoir. According to the characteristics of the stratified rock salt formation in China and its physical parameters, combined with field monitoring data, the volume shrinkage rate is proposed to be no more than 30% for the design life (30 years) to ensure safety and economy (

Table 8. Comparison table of volume shrinkage after 30 years of operation under different pillar widths.

	1 Year	5 Years	10 Years	20 Years	30 Years
Scheme 1 (1.0 D)	2.050	8.160	14.860	23.950	35.270
Scheme 2 (1.5 D)	1.997	7.270	12.860	22.480	30.540
Scheme 3 (2.0 D)	1.950	6.470	10.999	18.850	25.636
Scheme 4 (2.5 D)	2.010	6.270	10.350	17.220	23.270
Scheme 5 (3.0 D)	1.978	5.910	9.550	15.570	20.766

). However, there is no similar threshold value for salt cavern gas storage, and some scholars assess standard salt cavern gas storage operation for 1 year with a volume shrinkage rate not more than 1%, while some scholars use the threshold value of 30% as an indicator to evaluate the volume shrinkage of salt cavern gas storage after 30 years of operation. Considering the long-term stability of gas storage, this paper suggests 30% as the threshold value for volume shrinkage after 30 years [18].

Figure 14 shows that a threshold of 30% was used as an indicator to evaluate the volume shrinkage of the salt cavern gas storage reservoir. Under this criterion, neither Scheme 1 or 2 qualified.

According to the relationship between the maximum displacement around the cavity and the width of the mine pillar in Figure 15, linear fitting is carried out, and the following linear equation is obtained:

$$De=-0.1209P+41.6076$$

(3)

where De is 100 times the maximum displacement around the cavity, and P is the pillar width.

According to Equation (3), when the volume shrinkage rate is 30%, the width of the mine pillar is 95.9861 m, which is 1.58 times the maximum diameter of the gas storage.

4.1.4. Dilatancy Safety Factor

As per previous research, the mechanical characteristics of salt rock undergo a significant transformation when it enters an expanded state. Scholars in the past have employed the concept of an expansion boundary to delineate the pivotal point where the transition from rock compression to expansion occurs. This demarcation effectively partitions the stress space into two distinct regions: the compaction domain and the expansion domain, situated near the excavation area and separated by the expansion boundary. Consequently, in order to ensure the safety of salt caverns, a criterion for assessing salt rock damage has been proposed. This criterion can be expressed in terms of volumetric strain and principal stress. Since the latter part of the 20th century, the damage potential (DP) criterion has been utilized to assess the safety of salt cavern gas storage reservoirs, and it is represented as follows [19]:

$$\sqrt{J_2}=b·I_1+c$$

(4)

where $I_1$ is the first invariant of the stress tensor, $I_1={\sigma }_1+{\sigma }_2+{\sigma }_3$; $J_2$ is the second invariant of the deviatoric stress tensor, $J_2=[{({\sigma }_1-{\sigma }_2)}^2+{({\sigma }_2-{\sigma }_3)}^2+{({\sigma }_1-{\sigma }_3)}^2]$; ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$are the first, second, and third principal stresses, respectively; and b and c are parameters related to the stress state of rock salt.

We specify the following swelling criteria to assess the potential damage of salt cavern enclosures [20]:

$$SF=\frac{b·I_1+c}{\sqrt{J_2}}$$

(5)

When the safety factor is less than 0.6, the rock will collapse. When the safety factor is greater than 0.6 and less than 1.0, the rock will be damaged. When the safety factor is greater than 1.0 and less than 1.5, the rock will be damaged. When the safety factor is greater than 2.0, the rock will be intact. Usually, b and c are material constants. According to previous scholars who usually take the value of b as 0.27, Wang Tongtao et al. first introduced this criterion into China and applied it to the safety assessment of the Jintan gas storage reservoir, taking the value of b as 0.27. Later, some scholars successively applied this criterion to the Jintan oil storage reservoir, Huai’an salt cavern [15], Ningjin salt cavern [17], and so forth. In this paper, according to the triaxial test data fitting in Section 3.2, b and c were 0.289 and 8.66, respectively.

Figure 16 shows the contour of the safety factor (SF) after 30 years of salt cavern reservoir operation for different ore column widths. Under the influence of different ore column widths, there was a small safety factor appearing in the salt cavern interlayer due to the low strength of the interlayer after it was soaked with brine during leaching when it collapsed. When the width of the ore column was narrow (1.0 D, 1.5 D), a small safety factor area was obtained around the cavern wall. When the width of the ore column increased (more than 1.5 D), the general safety factor was greater than 1.5, and the area with a safety factor less than 3 gradually decreased. The above results indicated that the width of the ore pillar should be no less than 1.5 D to prevent the expansive damage of the rock around the cavern.

4.1.5. Equivalent Strain

Due to the ability of salt rock to undergo densification, its deformation characteristics when stressed are similar to those of ductile metals [17]. Thus, equivalent effect variation is introduced as an assessment index to evaluate the stability of salt cavern gas storage reservoirs, and its mathematical expression is [21]:

$$ES=\sqrt{\frac{2}{3}{\epsilon }_{dev}{\epsilon }_{dev}}$$

(6)

where ES is the effective strain, and ${\epsilon }_{dev}$ is the deviatoric strain tensor. This paper stipulates that the equivalent effect variation (ES) of the rock around the cavern should not exceed 3% after 30 years [22].

In Figure 17, the contour lines display the distribution of the equivalent effect variation (ES) around the salt cavern after 30 years for different column widths, as determined by Equation (5). Given the significant disparity in mechanical parameters between the rock salt and the interbedded layer, the region exhibiting high equivalent effect variation (depicted in green) was primarily situated within the interbedded layer of the salt cavern reservoir. In this interbedded region, the ES values exhibited substantial variations due to stress concentration. The simulation results revealed a reduction in the ES of the rock surrounding the salt cavern reservoir as the width of the ore column increased. From the perspective of ES, it is recommended that a minimum ore column width of 1.5 times the diameter (1.5 D) be utilized for the salt cavern reservoir.

4.2. Tightness Analysis

In assessing the tightness of salt caverns, especially given the extremely low permeability of salt rock, which serves as an effective gas barrier, previous studies have revealed a scarcity of reliable criteria. Wu et al. emphasized the prohibition of tensile stresses resulting from internal gas pressure fluctuations within the column [23]. This “no tensile stress” criterion has become widely adopted to evaluate the tightness and stability of salt cavern gas storage structures. Wang et al. introduced a criterion that requires the pore pressure in the middle of the pillars between adjacent caverns to remain lower than the minimum internal gas pressure, thereby evaluating the gas tightness in laminated rock salt formations [24].

Furthermore, it is insufficient to solely consider tensile fractures of the pillars while ignoring shear damage [25]. Additionally, there is a need to limit the amount of gas leakage to ensure the economic feasibility and suitability of the cavern, the maintenance of internal gas pressure, and to account for scenarios where multiple permeable interlayers intersect the cavern chamber in laminated salt caverns. Some of these interlayers possess high permeability, while others exhibit low permeability [26]. In such cases, while the stability requirements may be met, there remains a risk of gas leakage. To address this, Liu Wei and colleagues have introduced the concept of gas leakage as a supplementary component to the confinement evaluation [27].

Based on research findings and engineering practices related to stratified salt storage reservoirs in China, the evaluation of confinement in salt cavern gas storage reservoirs typically hinges on the fulfillment of three specific criteria [28]. All three criteria must be met simultaneously [29]: ① the stored gas cannot break through the cap layer during the operation of salt cavern gas storage; ② the pore pressure at the center of the column should be less than the minimum operating pressure of the cavern during the operation of salt cavern gas storage; and ③ the total gas leakage should not be more than 1% of the total gas storage volume during the operation of salt cavern gas storage [30].

4.2.1. Seepage around the Salt Cavern USG

Gas seepage in the formation surrounding the salt cavern is mainly driven by the pressure gradient. A sufficient condition for gas flow to stop is that the pressure gradient is equal to the starting pressure gradient at depth λ. The distance of flow at this point is the seepage extent. Once seepage penetrates, it leads to a risk of leakage from the gas storage reservoir. Monitoring the seepage range is necessary to ensure the economics and safety of gas storage [28].

In Figure 18, the permeation range of natural gas within the salt rock proved to be exceedingly minimal, significantly smaller than the permeation range within the interlayer. This can be attributed to the extremely low pore permeability properties of the salt rock. Consequently, it was evident that the interlayer served as the primary conduit for natural gas seepage. Furthermore, the permeation ranges for natural gas within the interlayer expanded as the reservoir operation time increased.

The permeation range of natural gas within the interlayer of the reservoir exhibited significant variation over time. In Scheme 1, the gas permeation range between adjacent reservoirs had penetrated the interlayer after 5 years of reservoir operation. This led to a gradual increase in pore pressure within the center of the ore column, which posed challenges to the long-term stability of the reservoir. Further safety analysis is required to assess various working conditions related to ore column width.

It is worth noting that none of the gas penetration ranges breached the reservoir cap layer in any of the working conditions. Thus, all of the working conditions met the first criterion of the gas storage tightness evaluation standard.

4.2.2. Pore Pressure Variation along the Interlayer

The operational mode of a salt cavern gas reservoir, characterized by high-frequency gas injection and production, results in a cyclic pattern of pore pressure seepage within the rock mass [31]. This cyclic behavior can have detrimental effects on the overall stability of the cavern, particularly concerning the stability of the ore column. Salt rock’s extremely low pore permeability characteristics mean that the permeation range for natural gas in the salt rock is exceedingly small, significantly smaller than that in the interburden rock layers [32]. Consequently, the interburden rock acts as the primary pathway for natural gas seepage. The seepage through interlayers plays a crucial role in the confinement and safety of the pillar [33]. Therefore, it is essential to conduct a comprehensive investigation into the evolution of pore pressure related to interlayer seepage during reservoir operation.

Interlayer seepage significantly impacts the confinement and safety of the pillar, making it essential to investigate the evolution of pore pressure in the interlayers during reservoir operation. In this section, pore pressure data from two interlayers of the salt cavern reservoir were extracted and analyzed concerning the pillar’s center over a 30-year operational period (Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23).

Table 9. Pore pressure (PP) at the center point of different interlayer columns after 30 years of operation of each scheme.

Conditions	PP in Interlayer 1 (MPa)	PP in Interlayer 2 (MPa)
Scheme 1 (1.0 D)	9.9	7.47
Scheme 2 (1.5 D)	6.26	4.33
Scheme 3 (2.0 D)	3.53	2.41
Scheme 4 (2.5 D)	2.01	1.12
Scheme 5 (3.0 D)	1.08	0.672

presents the pore pressure values at the center point of various interlayer columns after 30 years of operation. According to the second criterion of the gas storage reservoir tightness evaluation standards, the pore pressure at the center of the pillar should be lower than the minimum operational pressure of the cavity (6.5 MPa). Therefore, based on the results of the gas reservoir seepage calculations, when the pillar width is 1.0 D, the pore pressure at the center of the pillar exceeds the allowable range specified by the tightness evaluation standards. In other words, it does not meet the tightness requirements of the cavity. However, when the pillar width is greater than 1.44 D, the conditions meet the tightness requirements.

4.2.3. Loss Rate of the Leakage

Based on previous research by scholars, the permeability measured in in situ tests ranged from approximately 10⁻¹⁹ to 10⁻²⁰ m², or even lower. In the case of natural gas storage, the hydraulic conductivity of rock salt is approximately 1.6 × (10⁻¹⁰–10⁻¹¹) m/s. When a permeable interlayer intersects with a rock cavern, it significantly enhances gas leakage. Considering both safety and economic factors, the amount of gas loss should be carefully evaluated [34].

Given the extremely low level of gas seepage in the salt rock, for the sake of simplifying calculations related to the total gas seepage in the surrounding rock of the reservoir, the analysis focused solely on the amount of gas seepage in the primary seepage channel, which is the interlayer.

The steady seepage in the salt cavern reservoir interlayer can also be calculated using the two-dimensional planar radial seepage theory. According to Boyle’s law [22],

$$P_0{V}_{cavern}=P_{air}{V}_{total}$$

(7)

where $P_0$ is the current intracavern pressure for calculation of seepage (MPa); $P_{air}$ is the standard atmospheric pressure, usually calculated as 0.101 MPa; and $V_{total}$ is the total volume of high-pressure gas in the reservoir at standard atmospheric pressure (m³).

Similarly, for the calculation of the total volume of seepage gas $V_{leakage}^{gas}$ in the pores of the rock,

$$V_{leakage}^{gas}=\frac{{{\displaystyle \sum }}^{}{P}_{pore}{V}_{pore}}{P_{air}}$$

(8)

That is,

$$V_{leakage}^{gas}=\frac{{{\displaystyle \sum }}_{i=1}^4{{\displaystyle \int }}_{r_{in}^i}^{r_e^i}2\pi r{h}_i{\phi }_i{P}_{r}dr}{P_{air}}$$

(9)

where $P_{pore}$ is the pore pressure corresponding to any point in the interlayer (MPa); and $V_{pore}$ is the gas volume at standard air pressure contained at any point in the interlayer (m³) [35].

Table 10. Maximum seepage distance of natural gas in interlayer 1 and interlayer 2 after 30 years.

Conditions	Pillar Width (m)	Maximum Seepage Distance (m)
		Interlayer 1	Interlayer 2
Scheme 1 (1.0 D)	(1.0 D) 60	28.128	42.94
Scheme 2 (1.5 D)	(1.5 D) 90	48.69	57.94
Scheme 3 (2.0 D)	(2 D) 120	63.69	72.94
Scheme 4 (2.5 D)	(2.5 D) 150	78.69	87.94
Scheme 5 (3.0 D)	(3 D) 180	93.69	102.94

displays the maximum percolation distance of natural gas from the first interlayer (interlayer 1) to the second interlayer (interlayer 2) after 30 years of operation in the salt cavern reservoir under different operational conditions.

Based on the calculations of seepage in each interlayer after 30 years of storage operation and Equation (8), the gas seepage from interlayer 1 to interlayer 2 (at standard atmospheric pressure) was determined, as presented in

Table 11. Gas seepage in interlayer 1 and interlayer 2 after 30 years (at standard atmospheric pressure).

Conditions	Pillar Width (m)	Gas Seepage Volume (m3)		$\mathbf{Total}\mathbf{Seepage}\mathbf{Volume}{\mathit{V}}_{\mathit{l}\mathit{e}\mathit{a}\mathit{k}\mathit{a}\mathit{g}\mathit{e}}^{\mathit{g}\mathit{a}\mathit{s}}$
		Interlayer 1	Interlayer 2
Scheme 1 (1.0 D)	(1.0 D) 60	387.75	921.024	1308.774
Scheme 2 (1.5 D)	(1.5 D) 90	1161.861	1676.888	2838.749
Scheme 3 (2.0 D)	(2 D) 120	1988.001	2657.547	4645.548
Scheme 4 (2.5 D)	(2.5 D) 150	3034.682	3862.966	6897.638
Scheme 5 (3.0 D)	(3 D) 180	3291.902	3993.161	7285.063

.

The total leakage rate of natural gas in the reservoir, ${\delta }_{leakage}^{gas}$, was calculated as follows [34]:

$${\delta }_{leakage}^{gas}=\frac{ V_{leakage}^{gas}}{V_{total}}\times 100\%$$

(10)

where $V_{total}$ is 744,380.198 m³, and the total leakage rate ${\delta }_{leakage}^{gas}$ of natural gas in the reservoir was 0.979% when the pillar width is 3 D.

Following the third criterion of the gas storage tightness evaluation standard, the total natural gas leakage rate ${\delta }_{leakage}^{gas}$ < 1% during the operation of salt cavern gas storage under each working condition was found to be less than 1%, thus meeting the standard requirements.

4.3. Overall Analysis

When a triangular well layout is used, stability analysis suggests a recommended minimum pillar width of 1.58 times the maximum cavern diameter, while tightness analysis recommends a minimum pillar width of 1.44 times the maximum cavern diameter. With a safety factor of 1.05, the comprehensive conclusion is that when using a triangular well layout, the recommended pillar width is 1.67 times the maximum cavern diameter. In practical cavern construction, the cavity’s shape cannot be entirely controlled, resulting in potential differences between the final cavity shape and the designed one. As a result, the final maximum cavity diameter and pillar width, as well as well spacing, are subject to uncertainty, as shown in

Table 12. Examples of possible final calculations.

Maximum Cavity Diameter D (m)	Pillar Width P (m)	Distance between Wellheads (m)
60	100.2	160.2
70	116.9	186.9
80	133.6	213.6

.

5. Conclusions

This study optimized the evaluation criteria for long-term operational safety analysis of salt cavern reservoirs, obtained salt rock mechanical parameters of salt rock and permeability coefficients through single triaxial and permeability experiments on salt rock, established a model for finite element calculations of salt cavern reservoirs using FLAC^3D, conducted long-term operational safety analysis of salt cavern gas reservoirs under triangular layouts of wells, optimized the width of the safety pillar, and obtained the following conclusions:

• A set of evaluation criteria for the long-term operational safety analysis of salt cavern gas reservoirs has been proposed. The stability and integrity of these caverns are assessed through indicators such as cavity wall displacement, plastic zone characteristics, volume shrinkage, safety factors, seepage range, changes in pore pressure, and seepage rates.
• Numerical simulations were performed, utilizing the Jintan salt cavern in China as a case study. The results of these simulations were analyzed based on the criteria for assessing long-term operational safety, leading to the optimization of pillar safety. For a triangular well layout, the suggested pillar width is 1.67 times the maximum diameter of the salt cavern.
• The evaluation criteria for long-term operational safety analysis of salt cavern gas storage reservoirs and the optimization results for pillar safety obtained through numerical simulations presented in this study can offer valuable recommendations for the construction of salt cavern storage reservoirs that include interbedded layers.