# Analysis of the Saltwater Wedge in a Coastal Karst Aquifer with a Double Conduit Network, Numerical Simulations and Sensitivity Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Study Site

#### 2.2. Hydrological Parameter

^{3}), respectively.

## 3. Results and Discussions

#### 3.1. Spatial and Temporal Discretization

^{2}and 45 m depth is set to a rectangular parallelepiped (see Figure 3) of 10 km long (with 400 column), 1 km width (with 33 rows) and a thickness of 26 layers in the cross-section, for a total number of 343,200 cells. In general, a fine resolution vertical grid is required for accurately modeling the density-dependent flow and solute transport.

#### 3.2. Initial and Boundary Conditions

#### 3.3. Sensitivity Analysis

#### 3.3.1. Local Sensitivity Analysis of Numerical Simulations in the Conduits

#### 3.3.2. Local Sensitivity Analysis of Numerical Simulations in the Fractured Medium

#### 3.4. Numerical Simulations Results of Seawater Intrusion Scenarios

^{3}(Figure 12a) to 10 kg/m

^{3}(Figure 12e). A value of 10 kg/m

^{3}is not present in nature and we used it to understand how the shape changes from the maximum value of salinity to almost freshwater. It is also interesting to notice how the two-steps like pattern disappear when the salt concentration decreases. In this Figure, we also depicted the position of the two karst conduits, which are represented as two parallel blue lines of 1 m thick each.

^{3}(a), three different step-like shapes may be identified in the salinity profile. One at the left sea boundary of the figure (x = 0) and the other two in concomitance with both conduits, similar to those appearing in Figure 2. Apparently, the presence of the two karst conduits prevent the formation of the typical salt wedge intrusion (as in Figure 13 where the salinity profile is computed away from both conduits, in row 25) and, instead, shows a step-like shape in which the freshwater coming from the aquifer conduit push away the seawater that in any case may enter into the karst conduits more or less, depending on the calibration of the different parameters such as, the hydraulic conductivity or the initial value of the heads.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Electrical Conductivity (EC) variation with depth in “well 18” [21].

**Figure 3.**Three-dimensional grid used for the numerical simulations. The two red parallel lines correspond to the karst conduits. This figure was generated using FloPy [32].

**Figure 4.**(

**a**) Calculated composite scaled sensitivity (Css) values of all parameters (HCf, HCc, SC and VA) with respect to salinity numerical simulations in the conduit (layer n. 10, 16) and j = 16, in the local sensitivity analysis; (

**b**) Calculated Css values of all parameters with respect to head numerical simulations in the conduit (same as (

**a**)). HCf, HCc, SC and VA represent the hydraulic conductivity (fractured medium), the hydraulic conductivity (conduits), salt concentration and vertical anisotropy, respectively.

**Figure 5.**Calculated Css values of all parameters with respect to: (

**a**) Salinity simulations in the fractured medium (layer n. 6, 13, 21) and row 16; (

**b**) Head simulations in the fractured medium (layer n. 6, 13, 21) and row 16.

**Figure 6.**Calculated Css values of all parameters with respect to: (

**a**) Salinity simulations in the fractured medium, away (j = 25) from de two conduits (layer n. 6, 13, 21); (

**b**) Head simulations in the fractured medium, away (j = 25) from the two conduits (layer n. 6, 13, 21).

**Figure 7.**Calculated Css values of selected parameters at different locations along the: (

**a**) First conduit; (

**b**) Second conduit.

**Figure 8.**Calculated Css values of selected parameters at different locations in the fractured medium: (

**a**) above the first conduit; (

**b**) between the two conduits; (

**c**) below conduits, and row 25.

**Figure 9.**Correlation coefficient matrix for all four parameters in different locations of the aquifer: conduits, fractured medium near and away conduits.

**Figure 10.**The nonlinear relationship between: (

**a**) salinity and (

**b**) head simulations with respect to the parameters SC (Salt Concentration) for both conduits.

**Figure 11.**Nonlinear relationship between: (

**a**) Salinity and salt concentration; (

**b**) Salinity and HDf both in the fractured medium away from the conduits using the locations where the Css are maximum.

**Figure 12.**Salinity profile at row j = 16 as a function of the depth at different distances from the sea (0.0m). The blue line, the red bold line and the orange line correspond to a distance of 50 m, 150 m and 325 m, respectively, from the sea boundary. And a salt concentration at the boundary of: (

**a**) 37 $\mathrm{kg}/{\mathrm{m}}^{3}$; (

**b**) 35 $\mathrm{kg}/{\mathrm{m}}^{3}$; (

**c**) 30 $\mathrm{kg}/{\mathrm{m}}^{3}$; (

**d**) 20 $\mathrm{kg}/{\mathrm{m}}^{3}$; (

**e**) 10 $\mathrm{kg}/{\mathrm{m}}^{3}.$

**Figure 13.**Salinity profile away from the conduits (j = 25), to be compared with the previous Figure 10a. In this case the scenario is similar to a salt intrusion without the two-steps pattern, that is, the presence of both conduits does not affect the salinity profile when it is measured away from them.

**Figure 14.**Differences between the salinity profile and wedge intrusion as a function of the depth with a constant-head equal to 10.0 m (red line) and 8.0 m (blue line) for an aquifer of: (

**a**) −45 m a.s.l.; (

**b**) −220 m a.s.l. Notice the presence of the two steps-shape in both scenarios.

**Figure 16.**(

**a**) Comparison of the EC profile with a numerical simulation where the whole three-dimensional grid is filled up with a salt concentration of 37 $\mathrm{kg}/{\mathrm{m}}^{3}$. The cross-section is at row 16 and the column 305; (

**b**) a zoom in the region of interest. Notice that due to the hydraulic conductivity the salt is pushed away in the direction toward the sea. It is observed the two-steps shape.

**Table 1.**Definitions of the parameters used in this paper, the specific evaluated values in the local sensitivity analysis and evaluation ranges (the lower and upper ones) of each parameter in the global sensitivity analysis.

Parameter | Definition | Lower | Upper | Evaluated Value | Units |
---|---|---|---|---|---|

HCf | Hydraulic conductivity (fractured medium) | 10.0 | 3000.0 | 1045.0 | $\mathrm{m}/\mathrm{d}$ay |

HCc | Hydraulic conductivity (conduits) | $1.0\times {10}^{6}$ | $3.0\times {10}^{6}$ | $2.4\times {10}^{6}$ | $\mathrm{m}/\mathrm{day}$ |

VA | Vertical anisotropy | 1.0 | 10.0 | 1.0 | dimensionless |

POf | Porosity (fractured medium) | 0.1 | dimensionless | ||

POc | Porosity (conduits) | 1.0 | dimensionless | ||

LDf | Longitudinal dispersivity (fractured medium) | 10.0 | $\mathrm{m}$ | ||

LDc | Longitudinal dispersivity (conduits) | 0.3 | $\mathrm{m}$ | ||

SC | Salinity concentration | 10.0 | 37.0 | 37.0 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

SH | Specified head boundary conditions | 8.0 | 10.0 | 10.0 | $\mathrm{m}$ |

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**MDPI and ACS Style**

Feo, A.; Zanini, A.; Petrella, E.; Hernàndez-Diaz, R.; Celico, F.
Analysis of the Saltwater Wedge in a Coastal Karst Aquifer with a Double Conduit Network, Numerical Simulations and Sensitivity Analysis. *Water* **2019**, *11*, 2311.
https://doi.org/10.3390/w11112311

**AMA Style**

Feo A, Zanini A, Petrella E, Hernàndez-Diaz R, Celico F.
Analysis of the Saltwater Wedge in a Coastal Karst Aquifer with a Double Conduit Network, Numerical Simulations and Sensitivity Analysis. *Water*. 2019; 11(11):2311.
https://doi.org/10.3390/w11112311

**Chicago/Turabian Style**

Feo, Alessandra, Andrea Zanini, Emma Petrella, Rebeca Hernàndez-Diaz, and Fulvio Celico.
2019. "Analysis of the Saltwater Wedge in a Coastal Karst Aquifer with a Double Conduit Network, Numerical Simulations and Sensitivity Analysis" *Water* 11, no. 11: 2311.
https://doi.org/10.3390/w11112311