Numerical Simulation Analysis of Elbow Erosion in Underground Gas Storage Process System

Abstract

Aiming at the erosion failure risk of key elbow components in the process system of underground gas storage (UGS), numerical simulation was adopted to investigate the erosion behavior and mechanism of elbows under the following three typical working conditions: gas injection, gas production, and wastewater treatment. The results show that the elbow in the gas injection system is under gas–solid two-phase flow, and the most severely eroded area is located at 45–50° on the outer arc side of the elbow. Small particles have stronger flow-following ability than large particles and collide with the wall more sufficiently, resulting in a higher erosion rate. For the tandem elbows in the gas production system, affected by centrifugal force and secondary flow, the outer arc side shows high pressure while the inner arc side shows low pressure. As the particle size increases, the erosion rates of both elbows decrease, with a larger reduction for the second elbow. The most severely eroded positions of the first and second elbows are at 50–55° and 40–45° on the outer arc side, respectively. The elbow in the wastewater treatment system has relatively slight erosion with a symmetrical distribution, but a small amount of natural gas accumulated on the inner side easily induces cavitation corrosion.

1. Introduction

The natural gas industry has entered a rapid development stage in China, and the role of UGS as seasonal peak adjustment and strategic natural gas reserve is getting more and more attention from the state [1,2]. As of the end of 2025, 40 UGSs have been put into operation in China, forming a peak-shaving capacity of 31.1 billion cubic meters of natural gas, with more than 20 others under planning and construction. Compared with conventional gas fields, UGS is characterized by large injection-production throughput, high-rate injection and production, and long-term operation, which puts forward the safety of production facilities [3,4]. During gas injection, the gas source is generally dry gas, which may contain trace dust. Due to the relatively deep burial of China’s UGS, the gas injection pressure is relatively high (20~40 MPa). Under the conditions of large flow rate, high pressure and intensive injection, pipelines are prone to erosion. During gas production, the produced medium mostly has three phases, oil–gas–water, which also leads to prominent corrosion problems [5]. In addition, under the conditions of long cycle, high displacement and alternating intensive injection and production, sand production from weakly cemented sandstone in strata is a common and serious problem in UGS [6,7]. Therefore, the erosion risk of the injection-production process system cannot be ignored, especially at positions with discontinuous structures such as elbows and reducing joints, where the erosion risk is even higher.

However, most of the current studies focus on preventive sand-proof completion methods and downhole tubing column erosion laws [8,9,10], neglecting the analysis and study of the erosion behavior and mechanism of processing pipes and fittings. In fact, the erosion of the elbow of the injection and production systems is generally more complex, which is manifested in the fluid presenting gas–solid two-phase, liquid–solid two-phase or even gas–solid–liquid–solid–liquid three-phase flow. Eman et al. [11] analyzed the differences in erosion behavior of three particle shapes (polyhedron, cylinder, and sphere) on 90° elbows. Oluwaseun et al. [12] investigated the influence of wall roughness and particle rotation on erosion patterns in 90° elbows. Rehan et al. [13] compared the erosion behavior of elbows under horizontal–vertical (H-V) and horizontal–horizontal (H-H) configurations. Eric et al. [14] conducted simulation analyses of erosion behavior in elbows with different geometric shapes or, respectively, aiming to explore elbow designs that mitigate erosion. Therefore, most existing studies only consider mechanical erosion under single-factor conditions and insufficiently reveal the comprehensive interaction mechanism under alternating injection-production pressure and gas–liquid–solid three-phase flow in UGS. It is difficult to reflect on the real damage process. In addition, conventional atmospheric/low-pressure pipeline erosion models and boundary conditions have poor applicability to the high-pressure and large-flow production conditions of UGS, resulting in relatively idealized simulation or experimental results.

Based on the above, this study conducts finite element numerical simulations on three types of elbows under actual production conditions of UGS, covering all process units including injection, production, and wastewater treatment. By establishing multiphase flow models, the erosion rate and distribution law of the elbows under different processes, particle sizes and other conditions are analyzed, which provides a scientific basis for the erosion monitoring and safety protection of elbows in UGS.

2. Materials and Methods

2.1. Basic Parameters

In this numerical simulation, three typical elbows are long radius.

Table 1. Basic parameters.

Elbow Types	Material	Specifications (External Diameter/Wall Thickness, mm)	Temperature (°C)	Pressure (MPa)	Gas Phase Flow Rate (×104 Nm3/d)	Liquid Phase Flow Rate (Nm3/d)
Gas injection	L245N	ϕ168/18.3 90° elbow	25	22	120	0
Gas production	16Mn	ϕ273/30 90° elbow	40	12	80	7.2
Wastewater treatment	20#	ϕ60/5 90° elbow	20	1	0	10

shows the basic parameters of them including material, specifications and service conditions.

2.2. Underlying Assumptions

(1)

It is assumed that the gas phase under study is a compressible fluid, that all fluids are constant flows, and that fluid properties are constants (parameters such as thermal conductivity, thermal fusion, and density). At the same time, the fluid in the pipe satisfies conservation of mass and conservation of momentum.

(2)

Considering the actual fluid velocity and pipe structure, the RNG k-ε two-equation turbulence model used in non-isothermal conditions is selected for the flow field calculation, where k is the turbulent pulsation kinetic energy per unit mass of fluid and ε is its dissipation rate. The detailed equations can be seen elsewhere [15].

(3)

The particles are assumed to be spherical. The particle inlet cross-section uses a surface jet source, i.e., the particle distribution in the inlet cross-section is determined by the sparseness of the inlet cross-section grid. The particle distribution in the inlet cross-section is more uniform.

(4)

In order to reduce the computational volume and processing difficulty, it is assumed that the particles are not broken, deformed or cracked after collision.

(5)

In order to simplify the problem and reduce the difficulty of calculation, it is assumed that there is no deformation of the wall of the elbow after collision and abrasion, and the wall material meets the uniformity assumption.

2.3. Erosion Rate Equation

Based on the type of elbow material and the actual situation of erosion particles in this study, the Tulsa model was selected to calculate and analyze the erosion rate under the corresponding working conditions sequentially, and its expression is [16]

$$E_c=C{\left(HB\right)}^{-0.59}{F}_s{f\left(\theta \right)V}_P^n$$

(1)

$$f\left(\theta \right)={\sum }_{i=1}^5{A}_i{\theta }^i$$

(2)

where $E_c$ stands for the erosion rate (kg/s·m²); $C$ stands for the wall material constant, generally take 2.17 × 10⁻⁹; $HB$ stands for its Brinell hardness; $F_s$ stands for the shape of the erosion particles coefficient, for the more sharp particles, semicircular particles and round particles, the value of 1, 0.53, 0.2, respectively; n stands for the velocity exponent, generally take 2.41; V_P stands for the particles of the impact velocity, m/s; $f\left(\theta \right)$ stands for the impact of the angle $\theta$ (unit selected radians) function, where $A_i$ (i from 1 to 5) is a known empirical coefficient.

In addition, since the collision of solid particles with the wall causes kinetic energy loss, the normal ${\epsilon }_n$ and tangential ${\epsilon }_t$ recovery coefficient equations are introduced in this study to reflect this process [17] as follows:

$${\epsilon }_n=0.993-1.76\theta +1.56{\theta }^2-0.49{\theta }^3$$

(3)

$${\epsilon }_t=0.998-1.66\theta +2.11{\theta }^2-0.67{\theta }^3$$

(4)

2.4. 3D Modeling

The above elbows were solidly modeled at 1:1 scale using the modeling tool, in which the vertical distance between the elbows in series was 2 m. In addition, in order to obtain the fully developed turbulence pattern, the pipe length was lengthened by 15 D in front of the inlet end, and 10 D after the outlet end, respectively. The final 3D geometrical modeling was obtained, as shown in Figure 1.

2.5. Grid Division

In order to improve the reliability of the calculation, a hexahedral mesh is selected to dissect all the above elbow models. A boundary layer is set to increase the calculation accuracy. Meanwhile, in order to ensure the mesh-independence of the results, the mesh dissection scale of all the above elbows is above 2 million, as shown in Figure 2.

2.6. Parameter Setting and Boundary Condition Loading

The gas and liquid physical parameters (flow rate, temperature, internal pressure, etc.) collected in Table 1 were loaded onto the model, while the inlet was in the form of velocity and the outlet was in the form of pressure. Another setting was seen elsewhere [15].

3. Results

3.1. Gas Injection System

The transport medium of elbow No. 1 is purified natural gas containing fine particles, which is in a gas–solid two-phase flow state. Figure 3 shows the results of the erosion velocity contour plots for different particle sizes (5 µm and 10 µm). It can be seen that when the particle amount is constant, the most serious location of erosion is located near the outer arc side of the elbow. Furthermore, the region with relatively high erosion presents a “rocket launching” shape, with a slender high-velocity zone in the middle and a tail extending along the flow direction until the end of the straight pipe section. This indicates that the elbow is more severely affected by erosion, which diffuses and attenuates along the flow direction, and the erosion rate drops sharply and then stabilizes once reaching the straight pipe section.

In addition, when the particle diameter is 5 μm, a distinct high erosion rate region (red area) appears on the outer curved surface of the elbow. When the particle diameter increases to 10 μm, there are almost no obvious red high erosion rate regions, and the overall color is dominated by yellow-green. This indicates that the erosion rate decreases significantly, the range of severe erosion is greatly reduced, and the erosion degree of the elbow is further lowered. This is because small-sized particles are more easily entrained by the fluid. At the elbow, small particles are more significantly affected by secondary flow, resulting in more sufficient collisions with the wall, leading to a higher erosion rate. In contrast, large-sized particles have greater inertia, so the fluid’s ability to carry them is relatively weaker. The collision mode and frequency of large particles at the elbow change, resulting in a lower erosion rate.

Figure 4 further presents the specific distribution of erosion velocity on the outer arc side. The most severe erosion in elbows occurs within the 45–50° range on the outer arc side. The maximum erosion velocity appears to be significantly reduced when the particles are increased from 5 um to 10 um, which decreases its value from 1.37 × 10⁻⁷ kg/s·m² to 6.8 × 10⁻⁸ kg/s·m². Moreover, consistent with the pattern shown in the contour plot of Figure 3, the erosion rate increases gradually from the elbow inlet (0°) along the flow direction. It begins to rise rapidly at approximately 35°, reaches the maximum value at 45–50°, then decreases slowly until around 75°, followed by a slight rebound. These results are consistent with previous works [18].

3.2. Gas Production System

Considering that the medium in the elbow of the gas production system is natural gas with water and a small amount of sand, a simulation analysis of the gas–liquid–solid three-phase flow is conducted. Meanwhile, the gas production and treatment process is relatively complex, and the pipeline network has a variable layout. Therefore, two consecutively connected elbows in series are selected as the simulation object in this study.

Figure 5 presents the results of the pressure field of the No. 2–3 tandem elbow, from which it can be seen that there are high-pressure zones on the outside of both elbows and low-pressure zones on the inside. This is because when the fluid changes direction in the elbow, the fluid is subjected to centrifugal force. The direction of centrifugal force points to the outer side of the elbow, causing the fluid to accumulate toward the outer wall, thereby increasing the pressure on the outer side. Meanwhile, the fluid at the inner wall is “pulled away” by centrifugal force, resulting in a decrease in pressure. The high-pressure region on the outer side of the elbow corresponds to a higher fluid impact force. When the fluid carries solid particles, they will impact the outer wall with greater momentum.

Figure 6 and Figure 7 show the contour plots of the erosion velocity of the tandem elbow of the No. 2–3 under different particle sizes, respectively. For the first elbow at the inlet, a distinct high erosion rate region (represented by red and yellow areas) is formed on the outer curved surface. As the particle diameter increases from 10 μm to 70 μm, the area of this high erosion region continuously shrinks, indicating a reduction in both the range of severe erosion and the overall erosion degree of the elbow. The erosion distribution pattern is highly similar to that observed in gas–solid two-phase flow (Figure 3), presenting a characteristic “rocket launching” shape—with a slender, high-velocity zone in the center and a tail extending along the flow direction into the straight pipe section, where the erosion rate attenuates sharply. For the second elbow in series, narrow strip-shaped red high erosion rate regions appear on the outer arc surface when the particle diameter is 10 μm and 30 μm. However, when the particle diameter is 50 μm and 70 μm, no obvious high erosion rate regions are observed. It can be seen that the flow fields of the series-connected elbows interact with each other. The secondary flow from the first elbow interferes with the flow field of the second elbow, making the fluid flow in the second elbow more complex and changing the collision mode of the particles. Especially for larger particles, due to their greater kinetic energy, these particles are intercepted by the first elbow under the action of centrifugal force, resulting in a higher erosion rate on the first elbow than on the second one.

Figure 8 shows the specific distribution of the erosion rate on the outer arc side of No. 2–3 elbow. The maximum erosion velocity gradually decreases with the increasing particle size. The maximum erosion velocity of the No. 2 elbow occurs on the outer arc side within the 50–55° range. The maximum erosion velocity of the No. 3 elbow occurs on the outer arc side within the 40–45° range, closer to the elbow entrance end. These results are consistent with previous works [19].

3.3. Wastewater Treatment System

No. 4 elbow working medium is mainly water, mixed with a small amount of natural gas and solid particles. Figure 9 shows the contour plots of the erosion velocity of the elbow of the No. 4 under the typical particle sizes of 10 μm and 30 μm. The working medium is mainly wastewater, resulting in impurity particles on the elbow of the erosion effect of the symmetrical distribution of the two sides, and its erosion hazards relative to the gas production system and the gas injection system are smaller.

In addition, a small amount of natural gas was entrained, and thus the distribution state of the natural gas content in the elbow was calculated using the multiphase flow homogeneous mixing model, as shown in Figure 10. According to the distribution of the gas phase fraction, the entrained natural gas mainly aggregates in the inner side of the elbow due to its lower density. In view of the velocity field, it is found that these aggregated natural gases have lower velocities, which can easily trigger the vacuolar corrosion in the inner side of the elbow. These results are consistent with previous works [20].

4. Conclusions

(1)

The elbow in the gas injection system is in a gas–solid two-phase flow state. The most severely eroded area is on the outer arc side of the elbow, presenting a “rocket launching” shape. The erosion rate of 5 μm particles is much higher than that of 10 μm particles, and the most severely eroded position is in the 45–50° range on the outer arc side. Smaller particles are more easily entrained by the fluid, are more affected by secondary flow, and collide more fully with the wall, resulting in more severe erosion.

(2)

The tandem elbows in the gas production system have a high-pressure zone on the outer side and a low-pressure zone on the inner side, which is caused by centrifugal force and secondary flow. As the particle size increases, the erosion rate of both elbows decreases, and the decrease amplitude of the second elbow is larger. The flow fields of the tandem elbows interact with each other and, the most severely eroded position of the first elbow is in the 50–55° range on the outer arc side, while that of the second one is in the 40–45° range.

(3)

The erosion hazard of the elbow in wastewater treatment system is relatively small, and the erosion distribution is symmetrical. A small amount of natural gas will accumulate on the inner side of the elbow, which easily causes cavitation corrosion.

(4)

It is recommended to thicken the outer arc side of the elbows in the gas injection and production systems, and the inner arc side of the elbows in the wastewater treatment system. Meanwhile, the fluid flow rate should be appropriately optimized and the purification effect of solid particles in the fluid enhanced to reduce the impact force on the elbows. In addition, regular wall thickness detection or real-time monitoring should be conducted on the outer arc side of the elbows in the gas injection and production systems, as well as on the inner arc side of the elbows in the wastewater treatment system.