# Experimental and Numerical Study to Investigate the Impact of Changing the Boundary Water Levels on Saltwater Intrusion in Coastal Aquifers

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## Abstract

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^{3}of freshwater storage per each kilometer width of the Biscayne aquifer. This study provides a better understanding and a quantitative assessment for the impacts of changing water levels’ boundaries on intrusion of seawater in coastal aquifers.

## 1. Introduction

^{3}/year to 513 billion m

^{3}/year. Morgan et al. [14] carried out numerical modeling to study the occurrence of seawater intrusion overshoot and demonstrated that it can occur on the field scale in unconfined aquifers. Abd-Elaty et al. [15] developed an analytical solution and numerical model to identify SWI in the Middle Nile Delta aquifer, Egypt, due to a change in boundary conditions. The analytical model gave good results compared to the numerical one and was recommended for similar studies. Yang et al. [16] investigated the effect of rising sea level and storm surge in a 2D aquifer at the North German coast. They investigated the effect of heterogeneity on the movement of salt plumes in the aquifer. The results showed that a 1 m sea level rise has moved the fresh water/saline water interface up to 1250 m landward, and the salinized zone has expanded up to 2050 m landward. Abd-Elaty et al. [17,18,19] simulated SWI in a coastal aquifer considering overpumping due to population growth and sea level rise; the results indicated that the aquifer salinity is sensitive to the future impacts.

## 2. Materials and Methods

#### 2.1. Experimental Model

#### 2.2. Numerical Model

_{o}: is the fluid density (ML

^{−3}) at the reference concentration and reference temperature; ρ: is density of saline ground water (ML

^{−3}); μ

_{o}: is dynamic viscosity of the fresh ground water (ML

^{−1}T

^{−1}); μ: is dynamic viscosity of saline ground water (ML

^{−1}T

^{−1}); K

_{0}: is the hydraulic conductivity tensor of material saturated with the reference fluid (LT

^{−1}); h

_{0}: is the hydraulic head (L) measured in terms of the reference fluid of a specified concentration and temperature (as the reference fluid is commonly freshwater); S

_{s,0}: is the specific storage (L

^{−1}), defined as the volume of water released from storage per unit volume per unit decline of h

_{0}; t: is time (T); θ: is porosity; C: is salt concentration (ML

^{−3}); and q

^{’s}:is a source or sink (T

^{−1}) of fluid with density ρ

_{s}.

_{b}: is the bulk density (mass of the solids divided by the total volume) (ML

^{−3}); K

_{dk}: is the distribution coefficient of species k (L

^{3}M

^{−1}); C

_{k}: is the concentration of species k (ML

^{−3}); D: is the hydrodynamic dispersion coefficient tensor (L

^{2}T

^{−1}); q: is specific discharge (LT

^{−1}); and C

_{sk}: is the source or sink concentration (ML

^{−3}) of species k.

#### 2.3. Real Case Study (Biscayne Aquifer, Florida, USA)

_{L}and α

_{T}, were taken as 10 and 1 m, respectively, and the dispersion coefficient in the x-direction, D

_{x}, and the y-direction, D

_{y}, were considered to be velocity dependent. Based on the reported data, the flux from the land side was 15 m

^{3}day

^{−1}(per meter length of shoreline) and the annual recharge from rainfall was 380 mm. The densities of fresh water ρ

_{f}and seawater ρ

_{s}were set as 1000 and 1025 kg/m

^{3}, respectively (Langevin) [34].

## 3. Results and Discussion

#### 3.1. Future Scenarios for the Hypothetical Experimental Model

#### 3.2. Future Scenarios for the Hypothetical Numerical Model

#### 3.3. Analysis of Experimental and Numerical Results

#### 3.4. Future Scenarios for Biscayne Aquifer Model

^{3}/day per meter length of the shoreline. All other parameters remained unchanged. As compared to the current conditions, an additional intrusion of 144 m, measured at the bottom of the aquifer for equi-concentration line 17,500 ppm, was observed (Figure 10a). The intrusion length was 605 m, measured at the bottom. In Scenario Two, the seawater level was raised by 25 cm. The freshwater flux at the landside (15 m

^{3}/day per meter length) and all other parameters were kept at their original values.

^{3}of freshwater will be lost per each km width of the aquifer. It is therefore concluded that the Biscayne aquifer is highly vulnerable to additional seawater intrusion due to climate change and rising sea levels.

## 4. Conclusions

^{3}per each kilometer width of the Biscayne aquifer; a 28% reduction in freshwater flux from the landside caused a loss of 0.35 million m

^{3}of fresh groundwater; and a combination of the two cases increased the loss in fresh groundwater by 0.83 million m

^{3}. Using both an experimental and numerical model, this study provides a better understanding of the future possible impacts of changing boundary water levels on saline water intrusion in coastal aquifers, including rising sea levels due to climate change.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Location and cross section of Biscayne aquifer with boundary conditions for head and concentration [34].

**Figure 6.**Concentration distribution in Biscayne aquifer [30].

Parameter | Values | Units |
---|---|---|

Porosity (n) | 0.30 | Dimensionless |

Inland Freshwater head | 0.312 | (m) |

Saltwater head (h_{s}) | 0.30 | (m) |

Freshwater density (ρ_{f}) | 1000 | (kg/m^{3}) |

Saltwater density (ρ_{s}) | 1025 | (kg/m^{3}) |

Freshwater concentration (C_{f}) | 200 | (mg/L) |

Saltwater concentration (C_{s}) | 35,000 | (mg/L) |

Hydraulic conductivity (k) | 28.50 | (m/day) |

Specific Storage | 1 × 10^{−5} | (1/m) |

Longitudinal dispersivity (α_{L}) | 0.50 | (cm) |

Transverse dispersivity (α_{T}) | 0.05 | (cm) |

Molecular diffusion coefficient (D*) | 0 | (m^{2}/day) |

Case | Scenario | Freshwater Level (cm) | Seawater Level (cm) | Intrusion Length | Difference (cm) | |
---|---|---|---|---|---|---|

Experimental | Numerical | |||||

Base | 1 | 31.20 | 30 | 14.25 | 15.50 | 1.25 |

One | 2 | 31.20 | 30.30 | 21.75 | 22.50 | 0.75 |

3 | 31.20 | 30.60 | 30.75 | 32.50 | 1.75 | |

4 | 31.20 | 30.90 | 40.50 | 41.25 | 0.75 | |

Two | 5 | 30.90 | 30 | 21.25 | 21.75 | 0.50 |

6 | 30.60 | 30 | 30 | 31.50 | 1.50 | |

7 | 30.30 | 30 | 39.50 | 40.75 | 1.25 | |

Three | 8 | 30.90 | 30.30 | 30.50 | 31.75 | 1.25 |

9 | 30.60 | 30.60 | 54.50 | 56.50 | 2.00 | |

10 | 30.30 | 30.90 | 60 | 58.50 | −1.50 |

Scenario | Saline Water Volume (m^{3}/km^{\}) | Freshwater Water Volume (m^{3}/km^{\}) | Losses of Freshwater Volume (m^{3}/km^{\}) |
---|---|---|---|

Current conditions | 5,617,502 | 8,766,758 | - |

One | 6,109,158 | 8,275,102 | 491,656 |

Two | 5,966,312 | 8,417,948 | 348,810 |

Three | 6,451,324 | 7,932,936 | 833,822 |

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**MDPI and ACS Style**

Abd-Elhamid, H.F.; Abdel-Aal, G.M.; Fahmy, M.; Sherif, M.; Zeleňáková, M.; Abd-Elaty, I.
Experimental and Numerical Study to Investigate the Impact of Changing the Boundary Water Levels on Saltwater Intrusion in Coastal Aquifers. *Water* **2022**, *14*, 631.
https://doi.org/10.3390/w14040631

**AMA Style**

Abd-Elhamid HF, Abdel-Aal GM, Fahmy M, Sherif M, Zeleňáková M, Abd-Elaty I.
Experimental and Numerical Study to Investigate the Impact of Changing the Boundary Water Levels on Saltwater Intrusion in Coastal Aquifers. *Water*. 2022; 14(4):631.
https://doi.org/10.3390/w14040631

**Chicago/Turabian Style**

Abd-Elhamid, Hany F., Gamal M. Abdel-Aal, Maha Fahmy, Mohsen Sherif, Martina Zeleňáková, and Ismail Abd-Elaty.
2022. "Experimental and Numerical Study to Investigate the Impact of Changing the Boundary Water Levels on Saltwater Intrusion in Coastal Aquifers" *Water* 14, no. 4: 631.
https://doi.org/10.3390/w14040631