# Numerical Simulation of Critical Production Pressure Drop of Injection and Production Wells in Gas Storage Based on Gas-Solid Coupling

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## Abstract

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## 1. Introduction

## 2. Discrete Element Numerical Simulation Model and Experimental Conditions

^{−3}. Creating crack network in particle system model to simulate the original crack of core sample. In the discrete element model of particle flow, discs with a certain size are used to simulate cracks [15,16,17]. According to the size of the numerical model, the size range of crack diameter is 0.7–1.2 cm, and the number of cracks is 180. The complex crack network model created is shown in Figure 1b. The complex crack network model is embedded into the particle system model. Figure 1c is the established core sample complex crack network particle model.

## 3. Results

#### 3.1. Influence of Gas-Solid Coupling on Microstructure Change

#### 3.1.1. Influence of Injection-Production Cycle and Differential Pressure on Sand Cementation

#### 3.1.2. Influence of Injection-Production Cycle and Differential Pressure on Crack Evolution

#### 3.2. Influence of Gas-Solid Coupling on Macro Mechanical Properties

#### 3.2.1. Influence of Injection-Production Cycle and Differential Pressure on Elastic Modulus

#### 3.2.2. Influence of Injection-Production Cycle and Differential Pressure on Poisson’s Ratio

#### 3.2.3. Influence of Injection-Production Cycle and Differential Pressure on Cohesion Ratio

#### 3.2.4. Influence of Injection-Production Cycle and Differential Pressure on Internal Friction Angle

## 4. Discussion

#### 4.1. Dynamic Prediction Model of Critical Production Pressure Drop under Gas-Solid Coupling in Gas Storage

#### 4.2. Comparison and Analysis of Prediction Results of Dynamic Prediction Models for Critical Production Pressure Drop of Gas Storage

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zheng, D.; Xu, H.; Wang, J.; Sun, J.; Zhao, K.; Li, C.; Shi, L.; Tang, L. Key technologies for construction and evaluation of gas reservoir type gas storage. Pet. Explor. Dev.
**2017**, 44, 794–801. [Google Scholar] [CrossRef] - Ding, G.; Wei, H. Review and prospect of underground gas storage construction in China in 20 years. Oil Gas Storage Transp.
**2020**, 39, 25–31. [Google Scholar] - Xu, H.; Dong, H.; Lv, J.; Wu, G.; Wang, J.; Zhao, K.; Li, C. Reasonable injection allocation method at the initial stage of operation of water invasion depleted gas reservoir gas storage. Nat. Gas Ind.
**2017**, 37, 93–95. [Google Scholar] - Yin, H.; Chen, J.; Lan, Y.; Lan, Y.; Liu, Z. Technical development status and Enlightenment of typical gas storage in North America. Oil Gas Storage Transp.
**2013**, 32, 815–818. [Google Scholar] - Ma, X.; Zheng, D.; Shen, R.; Wang, C.; Luo, J.; Sun, J. Key technology and practice of building gas reservoir with complex geological conditions in China. Pet. Explor. Dev.
**2018**, 45, 489–499. [Google Scholar] [CrossRef] - Li, X.; Zhang, Q.; Li, H. Grain-based discrete element method (GB-DEM) modeling of multi-scale fracturing in rocks under dynamic loading. Rock Mech. Rock Eng.
**2018**, 51, 3785–3817. [Google Scholar] [CrossRef] - Erarslan, N. Microstructural investigation of subcritical crack propagation and crack process zone (FPZ) by the reduction of rock crack toughness under cyclic loading. Eng. Geol.
**2016**, 208, 181–190. [Google Scholar] [CrossRef] - Oluyemi, G.F.; Oyeneyin, M.B. Analytical critical drawdown (CDD) failure model for real time sanding potential prediction based on Hoek and Brown failure criterion. J. Pet. Gas Eng.
**2010**, 1, 16–25. [Google Scholar] - Adeyanju, O.; Oyekunle, L. A new model for the prediction of real time critical drawdown sand failure in petroleum reservoirs. Pet. Sci. Technol.
**2014**, 32, 140–149. [Google Scholar] [CrossRef] - Ge, X.; Ren, J.; Pu, Y.; Ma, W.; Zhu, Y. Preliminary study on CT mesoscopic analysis of fatigue damage propagation law of rock. Acta Geotech. Eng.
**2001**, 23, 191–195. [Google Scholar] - Nguyen, N.H.T.; Bui, H.H.; Kodikara, J.; Arooran, S.; Darve, F. A discrete element modeling approach for fatigue damage growth in cemented materials. Int. J. Plast.
**2019**, 112, 68–88. [Google Scholar] [CrossRef] - Liu, X.; Liang, L.; Yang, L.; Zeng, X.; Cao, J.; Long, Y.; Liu, H. Influence of branch well configuration on critical production pressure difference in unconsolidated sandstone reservoir. J. Pet. Sci.
**2011**, 32, 717–721. [Google Scholar] - Arora, K.; Chakraborty, T.; Rao, K.S. Experimental study on stiffness degradation of rock under uniaxial cyclic sinusoidal compression loading. Rock Mech. Rock Eng.
**2019**, 52, 4785–4797. [Google Scholar] [CrossRef] - Li, S.; Chen, Y. Optimization of drawdown pressure about the ultra-deep cracked carbonate reservoir. In SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition; SPE192394; OnePetro: Richardson, TX, USA, 2018. [Google Scholar]
- Jiang, M.; Zhang, N.; Shen, Z.; Chen, H. Discrete element analysis of crack propagation mechanism of cracked rock mass under uniaxial compression. Rock Soil Mech.
**2015**, 36, 3294–3298. [Google Scholar] - Sun, X.; Liu, C.; Xve, S. Application of mixed finite element and discrete element method in crack propagation. J. China Univ. Pet.
**2013**, 37, 126–136. [Google Scholar] - Zhang, C.; Tu, S.; Bai, Q. Evaluation of pore size and distribution impacts on uniaxial compressive strength of lithologic rock. Arab. J. Sci. Eng.
**2018**, 43, 1236–1244. [Google Scholar] [CrossRef] - Hu, W. Study on Mechanical Characteristics of Jointed Rock Mass Based on Smooth Joint Model; Wuhan University: Wuhan, China, 2017; pp. 41–52. [Google Scholar]
- Wang, T.; Zhao, H.; Li, K.; Gan, L.; Huo, Q. A seismic petrophysical model of shale considering complex pore structure. J. China Univ. Pet.
**2019**, 43, 45–55. [Google Scholar]

**Figure 1.**Particle model of complex crack network for core sample. (

**a**) Granular system. (

**b**) Crack network. (

**c**) Numerical core.

**Figure 4.**Bond contact crack characteristics at different stages of alternating load loading. (

**a**) Load 1 cycle. (

**b**) Load 30 cycles. (

**c**) Load 60 cycles.

**Figure 6.**Crack development characteristics at different stages of alternating load loading. (

**a**) Load 1 cycle. (

**b**) Load 30 cycles. (

**c**) Load 60 cycles.

**Figure 8.**Elastic modulus ratio changes under different injection-production differential pressure and cycle.

**Figure 10.**Relative Poisson’s ratio changes of minimum principal stress direction under different injection-production differential pressure and cycle.

**Figure 12.**Relative Poisson’s ratio changes of maximum principal stress direction under different injection-production differential pressure and cycle.

**Figure 14.**Cohesion ratio changes under different injection-production differential pressure and cycle.

**Figure 16.**Internal friction angle ratio changes under different injection-production differential pressure and cycle.

**Figure 17.**Fitting parameters ($\mathsf{\lambda}$ and $\mathsf{\beta}$) change with stress increase range.

Contact Parameter | Linear Parallel Bond | Smooth Joint | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$\mathsf{\mu}$ | $\mathbf{E}$ | ${\mathbf{k}}_{\mathbf{n}}/{\mathbf{k}}_{\mathbf{s}}$ | $\mathsf{\phi}$ (°) | $\stackrel{\_}{\mathbf{E}}$ (Gpa) | ${\stackrel{\_}{\mathbf{k}}}_{\mathrm{n}}/{\stackrel{\_}{\mathbf{k}}}_{\mathbf{s}}$ | ${\stackrel{\_}{\mathsf{\sigma}}}_{\mathbf{c}}$ (Mpa) | ${\stackrel{\_}{\mathsf{\tau}}}_{\mathbf{c}}$ (Mpa) | ${\mathsf{\mu}}_{\mathbf{s}}$ | ${\mathbf{k}}_{\mathbf{n}}$ (N·m^{−1})
| ${\mathbf{k}}_{\mathbf{s}}$ (N·m^{−1})
| ${\mathsf{\sigma}}_{\mathbf{c}}$ (MPa) | ${\mathsf{\tau}}_{\mathbf{c}}$ (MPa) | |

Values | 0.5 | 5.0 | 7.0 | 40 | 9.2 | 7.0 | 12.0 | 10.0 | 0.35 | 2 × 10^{9} | 2 × 10^{9} | 0.5 | 1.0 |

Formation Parameter | ${\mathbf{E}}_{\mathbf{i}}$/MPa | ${\mathbf{v}}_{\mathbf{i}}$/(N·m^{−1})
| ${\mathbf{c}}_{\mathbf{i}}$/MPa | ${\mathsf{\phi}}_{\mathbf{i}}$/(°) |
---|---|---|---|---|

Values | 9.2 | 7.0 | 0.4 | 12.0 |

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**MDPI and ACS Style**

Sui, Y.; Luo, M.; Lin, T.; Liu, G.; Zhao, Y.; Wu, Y.; Ren, L.
Numerical Simulation of Critical Production Pressure Drop of Injection and Production Wells in Gas Storage Based on Gas-Solid Coupling. *Separations* **2022**, *9*, 305.
https://doi.org/10.3390/separations9100305

**AMA Style**

Sui Y, Luo M, Lin T, Liu G, Zhao Y, Wu Y, Ren L.
Numerical Simulation of Critical Production Pressure Drop of Injection and Production Wells in Gas Storage Based on Gas-Solid Coupling. *Separations*. 2022; 9(10):305.
https://doi.org/10.3390/separations9100305

**Chicago/Turabian Style**

Sui, Yiyong, Mengying Luo, Tangmao Lin, Guihua Liu, Yuan Zhao, Yazhou Wu, and Lanqing Ren.
2022. "Numerical Simulation of Critical Production Pressure Drop of Injection and Production Wells in Gas Storage Based on Gas-Solid Coupling" *Separations* 9, no. 10: 305.
https://doi.org/10.3390/separations9100305