# Water Seepage in Rocks at Micro-Scale

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−5}and 6 × 10

^{−5}kg/s. Bai [34] utilized Fluent software to carry out 3D digital core pore model seepage. The simulated unidirectional seepage velocity ranged from 2 m/s to 20 m/s under 3 MPa of pressure. The range is 16.58–42.27 m/s. Wei [35] investigated single-phase and two-phase seepage simulations of a sandstone digital core model under a pressure gradient of 1 MPa through the docking technology of Avizo and COMSOL. Lu [36] employed the CFD software Fluent to simulate the seepage simulation of the rock pore model under pressure gradients of 2.5 MPa, 5 MPa, and 7.5 MPa, and discovered that the seepage velocity ranged from 2 m/s to 23 m/s. Gong [37] used Fluent software to set the inlet pressure to 1.01 × 10

^{2}~1.01 × 10

^{7}Pa and to set the outlet pressure to 0 Pa in order to simulate the seepage flow and obtained the seepage pressure field and velocity field law of water. Hou [38] selected Fluent software to investigate the microscopic seepage characteristics of uranium-bearing sandstone digital cores and simulated the seepage velocity range of 0–500 cm/d in the range of 0–0.045 MPa under a pressure gradient of 0.01 MPa.

## 2. Pore Types and Rock 3D Structure Creation

#### 2.1. Pore Types

_{1}, a

_{2}). The average pore diameter is in the range of 10 μm~150 μm.

_{1}, b

_{2}), followed by interstitials ((c

_{1}, c

_{2}) and (d

_{1}, d

_{2})), and rock debris (e

_{1}, e

_{2}) and the edge dissolution of quartz particles (f

_{1}, f

_{2}).

_{1}, g

_{2}). Mold pores are formed after the soluble minerals are completely dissolved (h

_{1}, h

_{2}), retaining the original shape and contour of the particles.

_{1}, i

_{2}).

#### 2.2. Rock 3D Structure Creation

## 3. Numerical Simulation of Micro Seepage in Rock under Different Conditions

#### 3.1. Setting of Boundary Conditions and Assumptions

- (1)
- Water only flows in the pores of the rock mass and will not penetrate the rock matrix.
- (2)
- Water is a continuously flowing incompressible fluid, and its temperature is constant during the process of pore flow.
- (3)
- Water is only affected by gravity and pressure.

#### 3.2. Unidirectional Seepage Simulation of Pore Model under Different Pressures

#### 3.3. Simulation Study of Positive Single Channel Seepage Flow

## 4. Discussion

#### 4.1. Negative Channel Seepape

#### 4.2. Restrictions and Uncertainties

## 5. Conclusions

- (1)
- The change trend of the overall pressure for the same model under different pressure gradients is a gradual decrease from the ENS to the EXS. The pressure drops sharply at a corner, and a threshold pressure must be exceeded to initiate the water seepage process. Seepage mainly occurs through pores with large radii. The seepage velocity increases with the ENP, but the seepage path is basically unchanged. In a pore channel, the largest seepage velocity occurs in the center of the pore, and the seepage velocity decreases with decreasing distance to the WS.
- (2)
- For the same model, the change trend and range of the seepage pressure in different seepage directions are similar, and the seepage pressure in all directions gradually decreases along the seepage direction. The average seepage velocity along the seepage direction increases and then gradually decreases with increasing distance from the ENS.
- (3)
- The fluid seepage law in the rock obtained in this study can effectively guide the arrangement of drainage pipes and other equipment and can serve as a reference for improving the efficiency of groundwater diversion. Although the techniques in this study can reflect the engineering situation to a certain extent, they are not completely consistent with the actual situation. Therefore, in the future, additional parameters can be considered, and more complex numerical models can be established to calculate results that are closer to reality. The disadvantage of this study is that the coupling effect of multiple parameters, such as multidirectional rock pressure, porosity change, and porosity were not fully considered.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Schematic diagram of the principle of two-dimensional CT image superposition. (

**a**) Slice scene graph. (

**b**) 3D model diagram.

**Figure 8.**Streamline diagram of seepage velocity distribution at the X direction entrance under different pressures.

**Figure 9.**Vector diagram of the seepage velocity distribution at the X direction entrance under different pressures.

**Figure 10.**X, Y, and Z positive single channel seepage pressure distribution. (

**a**) X positive direction, (

**b**) Y positive direction, and (

**c**) Z positive direction.

**Figure 11.**Streamline diagram of X, Y, and Z positive single channel seepage velocity distribution. (

**a**) X positive direction, (

**b**) Y positive direction, and (

**c**) Z positive direction.

**Figure 12.**X, Y, and Z positive single channel seepage velocity distribution vector diagram. (

**a**) X positive direction, (

**b**) Y positive direction, and (

**c**) Z positive direction.

**Figure 13.**X, Y, and Z positive single channel seepage pressure cloud diagram of different cross-sections.

**Figure 14.**X, Y, and Z positive single channel seepage velocity cloud diagram at different cross-sections.

**Figure 19.**X, Y, and Z negative single channel seepage water pressure distribution diagram. (

**a**) X negative direction, (

**b**) Y negative direction, and (

**c**) Z negative direction.

**Figure 20.**X, Y, and Z negative single channel seepage velocity distribution streamline diagram. (

**a**) X negative direction, (

**b**) Y negative direction, and (

**c**) Z negative direction.

**Figure 21.**X, Y, and Z negative single channel seepage velocity distribution vector diagram. (

**a**) X negative direction, (

**b**) Y negative direction, and (

**c**) Z negative direction.

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.; Li, Y.-Z.; Qiao, W.-G.; Fan, Z.-W.; Zhang, S.; Chen, K.; Zhang, L.
Water Seepage in Rocks at Micro-Scale. *Water* **2022**, *14*, 2827.
https://doi.org/10.3390/w14182827

**AMA Style**

Wu Y, Li Y-Z, Qiao W-G, Fan Z-W, Zhang S, Chen K, Zhang L.
Water Seepage in Rocks at Micro-Scale. *Water*. 2022; 14(18):2827.
https://doi.org/10.3390/w14182827

**Chicago/Turabian Style**

Wu, Yue, Yan-Zhi Li, Wei-Guo Qiao, Zhen-Wang Fan, Shuai Zhang, Kui Chen, and Lei Zhang.
2022. "Water Seepage in Rocks at Micro-Scale" *Water* 14, no. 18: 2827.
https://doi.org/10.3390/w14182827