# Assessment of Tidal Current Energy Resources in the Pearl River Estuary Using a Numerical Method

^{1}

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## Abstract

**:**

^{2}. The theoretical potential of tidal current energy resources in the Pearl River Estuary is assessed to be approximately 11,000 kW.

## 1. Introduction

^{−4}mg/L in the 2021 Greenhouse Gas Bulletin published by the World Meteorological Organization (WMO), which corresponds to an increase of 149% compared to the pre-industrial level in 1750 [1]. Reducing global carbon emissions and addressing the climate and environmental issues caused by global warming has become major challenge faced by all of humanity. Due to its abundant reserves, ocean renewable energy has become an important means to address this challenge. Tidal current energy, which is generated by seawater’s periodic horizontal motion caused by the moon’s gravitational forces and the sun, is an important component of ocean renewable energy. Compared to other forms of marine energy, tidal energy has strong regularity and predictability (Lamy and Azevedo, 2018) [2]. Tidal energy conversion devices are typically installed on the seabed or float on the ocean surface, minimizing environmental impacts on ocean ecosystems and requiring minimal land resources. Tidal energy has a higher energy density compared to wind energy (approximately four times) and solar energy (approximately thirty times) [3]. The utilization of tidal current energy resources is a significant focus of energy research worldwide.

^{®}[4]. Coles et al. (2017) developed a new Telemac2D model with a resolution of 1 km to assess tidal current energy at various sites around the Channel Islands [5]. This model aimed to provide a comprehensive understanding of tidal dynamics in the region and assess the potential for tidal current energy resources. The open-source hydrodynamic model ADCIRC (ADvanced CIRCulation model) was employed by Bonar et al. (2018) to assess the tidal current energy resources of multiple candidate sites in Malaysia [6]. Park et al. (2019) numerically investigated the tidal current energy resources in the Southwestern Sea of Korea using a numerical model, Modelo Hidrodinâmico (MOHID) [7]. Based on a finite-volume community ocean model (FVCOM), Karsten et al. (2008) assessed the tidal current energy in the Minas Passage, Bay of Fundy. Similarly, Wang and Yang (2020) assessed the tidal current energy in the Cook Inlet of Alaska, and Yang et al. (2020) assessed the tidal current energy in the Western Passage [8,9,10]. Chen et al. (2013) employed a 3D semi-implicit Eulerian-Lagrangian finite-element model called SELFE to explore the tidal characteristics within the Taiwan Strait and identify possible sites for the utilization of tidal current energy [11]. Based on an improvement of the originally developed SELFE model, 3D hydrodynamic model SCHISM (Semi-implicit Cross-scale Hydroscience Integrated System Model), Burić et al. (2021) investigated the potential tidal current energy resource in the strait of Novsko Zdrilo [12].

## 2. Materials and Methods

#### 2.1. Model Setup

^{−4}rad/s; ϕ is the geographic latitude; g is the Earth’s gravitational acceleration; ρ is the water density; ρ

_{0}is the reference density of water; τ

_{sx}and τ

_{sy}are the surface wind stress components; τ

_{bx}and τ

_{by}are the bottom stress components; s

_{xx}, s

_{xy}, s

_{yx}, and s

_{yy}are the radiation stress components; p

_{a}is the local atmospheric pressure; S is the source term; u

_{s}and v

_{s}are the velocity components of the source term;${T}_{xx}=2A\frac{\mathsf{\partial}\overline{u}}{\mathsf{\partial}x}$, ${T}_{xy}={T}_{yx}=A\left(\frac{\mathsf{\partial}\overline{u}}{\mathsf{\partial}y}+\frac{\mathsf{\partial}\overline{v}}{\mathsf{\partial}x}\right)$ and ${T}_{yy}=2A\frac{\mathsf{\partial}\overline{v}}{\mathsf{\partial}y}$ are the transverse stress components; A is the horizontal eddy viscosity.

_{f}and M

_{m}. The hydrostatic level at the open boundary is determined based on the average sea level. The tidal level at the open boundaries is calculated by the following formula:

_{0}represents the tidal level at the boundary, and ζ

_{p}represents the hydrostatic level at the boundary; the index i ranges from 1 to 10, with its value corresponding to the aforementioned tidal components; ${w}_{i}$ denotes the angular frequency of the tide; A

_{i}and α

_{i}stand for the amplitudes and phase angles of the tide at three boundaries, respectively.

^{2}/s.

#### 2.2. Computation Domain and Bathymetry

#### 2.3. Model Validation

## 3. Tidal Characteristics

#### 3.1. The Current Speed Fields of the Rapid Flood and Ebb Tides

#### 3.2. The Annual Current Speed

## 4. Tidal Current Energy Estimation

#### 4.1. Average Tidal Current Energy Power Density

^{2}), ρ is the seawater density (kg/m

^{3}), and V is the tidal current speed (m/s).

^{2}, 0.05 kW/m

^{2}, 0.05 kW/m

^{2}, and 0.05 kW/m

^{2}, correspondingly. In Cross section II, the average monthly power densities for January, April, July, and October are 0.06 kW/m

^{2}, 0.05 kW/m

^{2}, 0.06 kW/m

^{2}, and 0.06 kW/m

^{2}, respectively. Within Cross section III, the monthly average power densities for January, April, July, and October amount to 0.04 kW/m

^{2}, 0.04 kW/m

^{2}, 0.04 kW/m

^{2}, and 0.04 kW/m

^{2}, respectively. The average power densities of tidal currents in summer and autumn are larger, followed by winter. The spring season has the lowest average power density.

^{2}.

#### 4.2. Potential Resources

_{total,}is calculated using the following formula:

_{total}represents the theoretical average power of tidal current energy in kilowatts (kW), P

_{m}represents the average power density of tidal current energy in kilowatts per square meter (kW/m

^{2}), and A represents the cross-sectional area of the waterway in square meters (m

^{2}).

^{2}, resulting in a theoretical potential of 11,000 kW. For Cross section II, the annual average power density of tidal current energy is 0.05 kW/m

^{2}, resulting in a theoretical potential of 9000 kW. For Cross section III, the annual average power density of tidal current energy is 0.04 kW/m

^{2}, resulting in a theoretical potential of 5000 kW. Section I has the highest theoretical potential resource, followed by Section II, and Section III has the lowest potential. The theoretical potential resources tend to increase with the increase in water depth.

## 5. Conclusions

- The distribution of annual average tidal current power density in the Pearl River Estuary is generally consistent with the distribution of the tidal current fields. The average power densities of tidal currents in summer and autumn are larger, followed by winter, and it is the smallest in spring.
- The annual average power density of tidal energy is generally smaller than 0.10 kW/m
^{2}. The theoretical resource potential increases with the increase in water depth. The theoretical potential of tidal energy resources in the Pearl River Estuary was finally assessed to be about 11,000 kW. - The tidal range in the Pearl River Estuary is small, resulting in a relatively weak tidal power and low average power density of tidal energy. Therefore, the tidal energy resources in the estuary are limited.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sketch of computation domain and grid; (

**b**) Sketch of computation domain and bathymetry.

**Figure 5.**The tidal current field at the fastest flood (

**a**) and at the fastest ebb (

**b**) during spring tides.

**Figure 8.**The distribution of monthly average tidal current energy power density, (

**a**) January, (

**b**) April, (

**c**) July, (

**d**) October.

Station Full Name | Longitude (°, E) | Latitude (°, N) |
---|---|---|

Neilingding | 113.8017 | 22.4265 |

Jinxinggang | 113.6151 | 22.3816 |

Chiwan | 113.8698 | 22.4710 |

Dachan’gang | 113.8484 | 22.5452 |

Zhengqiang Port | 113.7765 | 22.6570 |

Shanbanzhou | 113.6605 | 22.7125 |

Wanqingsha | 113.6287 | 22.5689 |

Hengmen | 113.5199 | 22.5762 |

Nansha | 113.5615 | 22.7435 |

Xianwujiao | 113.6157 | 22.7997 |

Station | Longitude (°, E) | Latitude (°, N) |
---|---|---|

S1 | 113.6934 | 22.7107 |

S2 | 113.7474 | 22.6201 |

S3 | 113.8019 | 22.5926 |

S4 | 113.7804 | 22.5168 |

S5 | 113.8586 | 22.5150 |

S6 | 113.8739 | 22.5333 |

S7 | 113.7227 | 22.4460 |

S8 | 113.8678 | 22.4491 |

S9 | 113.9282 | 22.4612 |

S10 | 113.7231 | 22.3392 |

S11 | 113.7952 | 22.3421 |

Station | Observation (m/s) | Model (m/s) | ARE (%) |
---|---|---|---|

S1 | 0.49 | 0.35 | −29 |

S2 | 0.33 | 0.41 | 24 |

S3 | 0.33 | 0.30 | −9 |

S4 | 0.45 | 0.45 | 0 |

S5 | 0.41 | 0.52 | 27 |

S6 | 0.16 | 0.13 | −18 |

S7 | 0.42 | 0.39 | −9 |

S8 | 0.38 | 0.45 | 18 |

S9 | 0.21 | 0.20 | −4 |

S10 | 0.45 | 0.39 | −12 |

S11 | 0.45 | 0.42 | −7 |

**Table 4.**Statistics for reserves in the theory of tidal current energy in the estuary of Pearl River.

Cross Section | Width (m) | Average Water Depth (m) | Cross-Sectional Area (m^{2}) | Annual Average Power Density (kW/m ^{2}) | Theoretical Potential Resource (10,000 kW) |
---|---|---|---|---|---|

I | 26,466 | 8.4 | 223,110.7 | 0.05 | 1.1 |

II | 28,455 | 6.4 | 183,252.5 | 0.05 | 0.9 |

III | 29,187 | 4.5 | 129,883.7 | 0.04 | 0.5 |

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**MDPI and ACS Style**

Wang, W.; Hu, Z.; Li, M.; Zhang, H.
Assessment of Tidal Current Energy Resources in the Pearl River Estuary Using a Numerical Method. *Water* **2023**, *15*, 3990.
https://doi.org/10.3390/w15223990

**AMA Style**

Wang W, Hu Z, Li M, Zhang H.
Assessment of Tidal Current Energy Resources in the Pearl River Estuary Using a Numerical Method. *Water*. 2023; 15(22):3990.
https://doi.org/10.3390/w15223990

**Chicago/Turabian Style**

Wang, Weiyuan, Zijun Hu, Mengyu Li, and Hongxing Zhang.
2023. "Assessment of Tidal Current Energy Resources in the Pearl River Estuary Using a Numerical Method" *Water* 15, no. 22: 3990.
https://doi.org/10.3390/w15223990