# Dynamic Variation Characteristics of Seawater Intrusion in Underground Water-Sealed Oil Storage Cavern under Island Tidal Environment

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Area

#### 2.1. Project Overview

^{2}(as shown in Figure 2). The storage capacity of the proposed underground water-sealed oil storage cavern is approximately 750 × 10

^{4}m

^{3}, consisting of 16 caverns. According to the island topography, the length of the main caverns can be divided into four types: 1000 m, 930 m, 620 m and 465 m. The main cavern spacing is divided into four cases of 30 m, 50 m, 70 m and 95 m. The underground oil storage cavern cross-section has a horseshoe shape, 20 m wide, 30 m high. The elevation of the top of the cavern is −45 m, and the axis direction of the caverns is NE 80°.

#### 2.2. Engineering Geology

#### 2.3. Hydrogeology

^{3}. The most abundant ions in the seawater are chloride ions and sodium ions. The concentration of chloride ion in the seawater is 0.31 mol/kg, the concentration of sodium ion in the seawater is 0.22 mol/kg.

## 3. Simulation Method

#### 3.1. Numerical Model

#### 3.2. Governing Equation

- (1)
- The underground seepage field is subject to the seepage continuity equation (Equation (6)) and Darcy’s law (Equation (7)) and [41]:$$\left[\frac{\partial}{\partial t}\left({n\rho}_{w}\right)+\nabla \xb7\left({\rho}_{w}\mathit{v}\right)\right]{=Q}_{m}$$$$\mathit{v}=-\frac{k}{{\rho}_{w}g}(\nabla {p+\rho}_{w}g\nabla z)$$$$\frac{\partial {\rho}_{w}}{\partial {C}_{w}}=\frac{{\rho}_{sw}-{\rho}_{fw}}{{C}_{sw}}$$
**v**is the Darcy’s flux (m/s), p is the pore water pressure (Pa), z is the vertical coordinate (m), g is the gravitational acceleration (m/s^{2}), ${\rho}_{w}$ is the density of water (kg/m^{3}), ${\rho}_{fw}$ is the density of freshwater (kg/m^{3}), ${\rho}_{sw}$ is the density of seawater (kg/m^{3}), ${C}_{w}$ is the concentration of chlorine ions in water (kg/m^{3}) and ${C}_{sw}$ is the concentration of chlorine ions in seawater (kg/m^{3}). - (2)
- In the three-dimensional numerical model, the solute transport equation can be described as follows [42]:$$\frac{\partial}{\partial t}(n{C}_{w})-\nabla (n\mathit{D}\nabla {C}_{w})+\nabla {(C}_{w}{\mathit{v})=Q}_{m}{C}_{q}$$$$\mathit{D}=\left[\begin{array}{ccc}{D}_{xx}& {D}_{xy}& {D}_{xz}\\ {D}_{yx}& {D}_{yy}& {D}_{yz}\\ {D}_{zx}& {D}_{zy}& {D}_{zz}\end{array}\right]$$$${D}_{ii}{=D}^{*}{+\text{}\alpha}_{T}{u+(\alpha}_{L}{-\alpha}_{T})\frac{{u}_{i}{}^{2}}{u},\text{}i=x,\text{}y,\text{}z$$$${D}_{ij}{=D}^{*}+({\alpha}_{L}-{\alpha}_{T})\frac{{u}_{i}{u}_{j}}{u},\text{}i,\text{}j=x,\text{}y,\text{}z\text{}\mathrm{and}\text{}i\text{}\ne \text{}j$$$$u=\sqrt{{u}_{x}^{2}+{u}_{y}^{2}+{u}_{z}^{2}}$$
**D**is the hydrodynamic dispersion coefficient tensor (m^{2}/s), D_{ii}and D_{ij}are the components of the hydrodynamic dispersion coefficient tensor (m^{2}/s), D* is the diffusion coefficient (m^{2}/s), ${\alpha}_{L}$ is the longitudinal dispersity (m), ${\alpha}_{T}$ is the transversal dispersity (m), ${u}_{x}$, ${u}_{y}$ and ${u}_{z}$ are the three components of the seepage velocity (m/s).

#### 3.3. Model Parameters

#### 3.4. Boundary and Initial Conditions

- 1
- There are several types of boundary and initial conditions for the transient seepage of groundwater:
- (1)
- Initial conditions:$${H}^{*}\left(x,\text{}y,\text{}z,\text{}0\right){=H}_{0}^{*}(x,\text{}y,\text{}z)$$
- (2)
- The first boundary condition is:$${H}^{*}\left(x,\text{}y,\text{}z,\text{}t\right){\text{}=\text{}H}_{1}^{*},\text{}(x,\text{}y,\text{}z)\text{}\in {\text{}\Gamma}_{1}$$
- (3)
- The second boundary condition is:$${q}_{\Gamma}{\text{}=\text{}q}^{*}(x,\text{}y,\text{}z,\text{}t),\text{}(x,\text{}y,\text{}z)\text{}\in {\text{}\Gamma}_{2}$$

_{0}is the ground elevation over the position. The bottom of the model is set as the second boundary condition, as a no-flow boundary. The underground cavern is set as the zero-pressure boundary.

- 2
- The boundary conditions of the solute transport field mainly include the following:
- (1)
- Initial conditions:$${C}_{\Gamma}(x,\text{}y,\text{}z,\text{}0)={C}_{0}\left(x,y,z\right)$$
- (2)
- The first boundary condition, also known as the Dirichlet boundary condition, where the solute concentration is known:$${C}_{\Gamma}(x,\text{}y,\text{}z,\text{}t)={C}_{1}(x,\text{}y,\text{}z,\text{}t)$$
- (3)
- The second boundary condition, also called Neumann boundary condition, which describes the change rate of the solute concentration in normal direction at the boundary:$$-n\mathit{D}\nabla {C}_{w}={q}_{1}(x,\text{}y,\text{}z,\text{}t)$$
- (4)
- Input boundary condition. Under the effect of groundwater flow and hydrodynamic dispersion, the solute flux across the boundary is known:$$-n\mathit{D}\nabla {C}_{w}{+C}_{w}u={q}_{2}(x,\text{}y,\text{}z,\text{}t)$$
^{−2}$\xb7$s^{−1}).

## 4. Results

#### 4.1. Validation of the Numerical Model

#### 4.2. Characteristics of Groundwater Seepage

#### 4.2.1. Groundwater Seepage Direction

#### 4.2.2. Groundwater Seepage Velocity

^{−8}m/s. Above the underground caverns, the groundwater seepage velocity of the horizontal water curtain model is the highest. At the elevation of −40 m (as shown in Figure 9b), the groundwater seepage velocities of the four conditions are less than 8.5 × 10

^{−8}m/s. Compared with the elevation of −20 m, the groundwater seepage velocity under the vertical water curtain system condition increases the most. At the elevation of −60 m (as shown in Figure 9c), the measuring line passes through the underground caverns. The groundwater seepage velocities of the four conditions are less than 13.2 × 10

^{−8}m/s. The seepage velocity of the groundwater in the location of the underground cavern fluctuates sharply, and the local maximum value of the groundwater seepage velocity is obtained at the location of the underground cavern. Compared with the other 3 conditions, the groundwater seepage velocity of the vertical water curtain system increased significantly. At the elevation of −80 m (as shown in Figure 9d), the measuring line is located below the underground caverns. The groundwater seepage velocity of the un-excavated condition, the excavated condition and the horizontal water curtain system condition decrease slightly compared with −60 m. On the contrary, under the influence of the vertical water curtain, the groundwater seepage velocity increases with a maximum value of 19.3 × 10

^{−8}m/s. Figure 9e,f show the groundwater seepage velocity on the measuring line at the elevation of −100 m and −120 m respectively. The maximum groundwater seepage velocities decrease to 2.27 × 10

^{−8}m/s and 1.1 × 10

^{−8}m/s respectively. And at the elevation of −120 m, the groundwater seepage velocity of the un-excavated condition is higher than the other three conditions between the 4# cavern and the 14# cavern.

#### 4.2.3. Groundwater Level

#### 4.3. Characteristics of Seawater Intrusion

#### 4.3.1. Temporal-Spatial Variations of Seawater Intrusion

#### 4.3.2. Influence of Water Curtain System on Seawater Intrusion

#### 4.3.3. Tidal Influence on Seawater Intrusion

^{3}. The maximum fluctuation amplitude of the chlorine ion concentration of the un-excavated condition and the vertical water curtain system condition is approximately 0.0015 mol/m

^{3}. Therefore, the excavation of the underground cavern will increase the influence of tidal fluctuation on seawater intrusion, and a vertical water curtain system can better decrease the influence of the tidal fluctuation on seawater intrusion than horizontal water curtain system.

## 5. Discussion

- (1)
- Under the island tidal environment, the groundwater level within the island is affected by tidal fluctuations, which show fluctuation characteristics. When the underground water-sealed oil storage cavern is built in the island, the fluctuation amplitude damping rate of the groundwater level can be successively sorted from low to high: excavated, un-excavated, with a horizontal water curtain system and with a vertical water curtain system (as shown in Figure 13). The tidal wave is transmitted from the shoreline to the island, and the wave energy decreases continually in the process of transmission, so the amplitude damping is generated. After the underground cavern is excavated, the groundwater seeps into the underground cavern, which accelerates the velocity of groundwater flow. Therefore, the amplitude damping velocity of the groundwater level is smaller than that of the un-excavated condition. After the water curtain system is set, the water curtain system recharges the groundwater, and the groundwater seepage around the island is restrained, so the amplitude of the groundwater level damps faster than that without the water curtain system. The amplitude damping velocity under the influence of a vertical water curtain system is greater than that of a horizontal water curtain system, which indicates that the vertical water curtain system has a greater barrier effect on the seepage flow of groundwater into the island. This phenomenon reveals the advantages of vertical water curtain systems in the construction of underground water-sealed oil storage caverns in island tidal environments.
- (2)
- Before the excavation of the underground cavern (as shown in Figure 17a), the chloride ion concentration at the monitoring point shows a decreasing trend. According to the governing equation, seawater intrusion is affected by the groundwater flow and the hydrodynamic dispersion of solute ions. In the case of an un-excavated island, groundwater seeps from the island to the shoreline (as shown in Figure 8). In contrast, solute diffusion is affected by its concentration, from high concentration to low concentration, that is, it diffuses from the shoreline to the island interior. It can be seen from the results that at the location of the monitoring point, the influence of the groundwater flow on seawater intrusion is greater than that of hydrodynamic dispersion.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Geological map of the study area: (

**a**) plane map, ZK1-ZK9 are the number of groundwater table monitoring boreholes; (

**b**) profile map.

**Figure 5.**Tidal monitoring data and the fitting curve: (

**a**) tidal monitoring data; (

**b**) tidal amplitude and its fitting curve; (

**c**) sinusoidal setover and its fitting curve; (

**d**) fitting curve. Data source: The Navigation Guarantee Department of Chinese Navy Headquarters.

**Figure 7.**The amplitude attenuation and phase lag of the groundwater table in the un-excavated condition: (

**a**) the fluctuation amplitude; (

**b**) the fluctuation phase, Δφ phase difference.

**Figure 8.**Groundwater seepage direction: (

**a**) un-excavated; (

**b**) excavated; (

**c**) horizontal water curtain system; (

**d**) vertical water curtain system.

**Figure 9.**Groundwater seepage velocity: (

**a**) elevation of −20 m; (

**b**) elevation of −40 m; (

**c**) elevation of −60 m; (

**d**) elevation of −80 m; (

**e**) elevation of −100 m; (

**f**) elevation of −120 m.

**Figure 10.**Seepage velocity fluctuation amplitude: (

**a**) different distance from shoreline under excavated condition; (

**b**) fluctuation amplitude damping.

**Figure 11.**Groundwater level: (

**a**) un-excavated; (

**b**) excavated; (

**c**) horizontal water curtain system; (

**d**) vertical water curtain system.

**Figure 12.**Groundwater level fluctuation with different distance from shoreline: (

**a**) un-excavated; (

**b**) excavated; (

**c**) horizontal water curtain; (

**d**) vertical water curtain; $\Delta \mathsf{\phi}$ phase difference.

**Figure 14.**Temporal-spatial variations of seawater intrusion: (

**a**) 0 year; (

**b**) 10 years; (

**c**) 20 years; (

**d**) 30 years; (

**e**) 40 years; (

**f**) 50 years.

**Figure 16.**Contrast of seawater intrusion in fifty years: (

**a**) un-excavated; (

**b**) excavated; (

**c**) horizontal water curtain system; (

**d**) vertical water curtain system.

**Figure 17.**Chloride concentration curve: (

**a**) chloride concentration varies over time; (

**b**) chloride concentration fluctuation.

Items | Four Conditions | |||
---|---|---|---|---|

Un-Excavated | Excavated | Horizontal Water Curtain | Vertical Water Curtain | |

Number of elements | 440,710 | 970,463 | 1,083,967 | 3,054,415 |

Minimum element size (m) | 9.45 | 4.26 | 1.54 | 1.29 |

Maximum element size (m) | 94.75 | 91.65 | 80.72 | 92.452 |

Average element size (m) | 51.22 | 46.98 | 44.39 | 44.59 |

Granite Density ${\mathbf{\rho}}_{\mathit{g}}\text{}(\mathbf{kg}/{\mathbf{m}}^{3})$ | Freshwater Density ${\mathbf{\rho}}_{\mathit{fw}}\text{}(\mathbf{kg}/{\mathbf{m}}^{3})$ | Seawater Density ${\mathbf{\rho}}_{\mathit{sw}}\text{}(\mathbf{kg}/{\mathbf{m}}^{3})$ | Porosity n | Diffusion Coefficients D* (m ^{2}/s) | Longitudinal Dispersity ${\mathbf{\alpha}}_{\mathit{L}}\text{}\left(\mathbf{m}\right)$ | Transversal Dispersity ${\mathbf{\alpha}}_{\mathit{T}}\text{}\left(\mathbf{m}\right)$ |
---|---|---|---|---|---|---|

2600 | 1000 | 1025 | 0.015 | $1.7\times {10}^{-11}$ | 21.3 | 4.2 |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Zhang, B.; Shi, L.; Ye, Y.
Dynamic Variation Characteristics of Seawater Intrusion in Underground Water-Sealed Oil Storage Cavern under Island Tidal Environment. *Water* **2019**, *11*, 130.
https://doi.org/10.3390/w11010130

**AMA Style**

Li Y, Zhang B, Shi L, Ye Y.
Dynamic Variation Characteristics of Seawater Intrusion in Underground Water-Sealed Oil Storage Cavern under Island Tidal Environment. *Water*. 2019; 11(1):130.
https://doi.org/10.3390/w11010130

**Chicago/Turabian Style**

Li, Yutao, Bin Zhang, Lei Shi, and Yiwei Ye.
2019. "Dynamic Variation Characteristics of Seawater Intrusion in Underground Water-Sealed Oil Storage Cavern under Island Tidal Environment" *Water* 11, no. 1: 130.
https://doi.org/10.3390/w11010130