# An Integrated Approach Based on Numerical Modelling and Geophysical Survey to Map Groundwater Salinity in Fractured Coastal Aquifers

^{*}

## Abstract

**:**

## 1. Introduction

_{f}parallel fractures, which have the same mean aperture value 2b

_{m}and an impermeable rock matrix. To support the stochastic method in this work, the data derived from pumping tests on wells were necessary to implement the real heterogeneities of the filtration medium into each single fracture of the model.

## 2. Materials and Methods

^{2}/t], and conductivity, K [L/t], of the “Calcare di Bari” formation, have been determined by inverting the steady radial flow solution to a well (i.e., the Thiem’s equation) [27]. Results given by thirty-six (Table 1) pumping-well tests provide the experimental variogram of fracture apertures of the coastal aquifer. The model estimated the local fracture apertures by inverting mean aquifer conductivity formula, i.e., K = γ

_{w}/μ × nb

^{2}/3, where n [-] is the effective porosity of the saturated freshwater thickness. In fact the hydraulic conductivity in a single (smoothed) fracture with aperture 2b, was obtained by comparing the velocity defined by Hagen-Poiseuille equation, which is usually adopted [28] to determine the plane flow velocity in a fracture, with the velocity provided by Darcy equation.

#### 2.1. Fractures Description and Flow Solutions: Experimental Tests

^{2}

_{xy}(sill + nugget), ξ

_{x}and ξ

_{y}and (i.e., correlation lengths) can be calculated using SURFER (Golden Software Inc., Golden, CO, USA) on the basis of the spatial distribution of mean apertures determined from the results of pumping tests. For the Bari coastal aquifer, the best-fit of the experimental semi-variogram was made using the exponential model (Figure 2) with σ

^{2}

_{xy}= 0.268, ξ

_{x}= 1000 m and ξ

_{y}= 2000 m, using data derived from thirty-six tests (Table 1). However, at the field scale, it should also be considered the uncertainty (~15%) due to the prediction of the spatial covariance of fracture apertures, which is dependent upon the available number of field measurements (i.e., well pumping-tests). This uncertainty was due to non-ergodicity of the scholastic variable [29].

_{ij}[L

^{3}/t] = U × 2b × ΔxΔy, is the local discharge between grid nodes i and j into the single fracture, where Δx and Δy are the discretization grid steps. The finite difference method can be used to solve the continuity equation (i.e., ΣQ = 0) applied to each grid node of the discretized domain. The resulting set of equations was solved by the iterative successive-over-relaxation (SOR) method by using as boundary conditions the piezometric heads into the depressed areas (i.e., pumping wells) and along the border of the studied area.

#### Ghyben-Herzberg Freshwater/Saltwater Sharp Interface

_{d}[L] is the distance of the contour head φ

_{0}(for instance of 1 m) from the coastline given by the flow simulation results; H

_{s}[L] is the freshwater head at the outflow section (usually set to 0); Q

^{i}

_{0}[L

^{3}/t/L] is the groundwater (i.e., freshwater) discharge along the coast predicted by the model at grid node i; B [L] is the aquifer saturated thickness where is φ = φ

_{0}; and ${\delta}_{\gamma}={\gamma}_{w}/\left({\gamma}_{s}-{\gamma}_{w}\right)$ is the ratio of the water specific weights.

_{s}

_{0}= 1.54 g∙L

^{−1}, A

_{s}= 12.02 g∙L

^{−1}and D

_{s}= 592.65 m were estimated by fitting the groundwater salt concentrations measured in twenty-five boreholes of the coastal aquifer, at the depth of 1.0 m below the water table.

#### 2.2. ERT Survey

_{salt}) was proposed. For this investigation, additional six ERT profiles were performed close to the boreholes where the salinity of groundwater at 1 m of depth was directly measured using an electrical conductivity probe (MS5 OTT, Inc., Kempten, Germany). This means that from the twenty-five boreholes we selected six at different water salinities to carry out six additional ERT. We selected only six ERT/wells for a technical reason (i.e., low groundwater depth <3 m). In fact, to obtain a reliable empirical resistivity-salinity relationship, the ERT images must have a high resolution [32] and for this the depth of investigation must not exceed 5 m below the ground. This leads to a short inter-electrode spacing and to the high resolution ERT images.

^{2}= 0.93) constants and ρ (Ωm) is the monitored electrical resistivity of the groundwater. Despite of the few (six) boreholes considered, the spread of measured values of water salinity, which ranged from 1 to 5 g/L, allowed a high (Figure 4) correlation coefficient. The graph shows a lack of information for salt concentrations higher than 5 g/L, due to the absence of boreholes.

## 3. Results and Discussion

^{2}.

_{d}distance for each Δx along the coast. Then, the coast distance y

_{d}from the border domain at the assigned head (see Figure 5) was also considered to estimate all L

_{d}distances with respect to the coastline. Finally, the application of Equation (6) to all grid nodes of the domain led to a salinity map of the Bari aquifer (Figure 6), at a depth of 1 m below the water table.

_{salt}was implemented to convert the collected electrical resistivity into salt concentrations in groundwater. In order to compare the groundwater salinity derived from ERT profiles with modeling results, the two trends of salinities estimated by ERT into the Bari coastal aquifer have been plotted in Figure 8, together with results derived from model flow simulations (by including Ghyben-Herzberg estimations) at the depth of 1 m below the water table. This result successful validated the modeling output and at same time shows the efficacy of ERT to prove, experimentally, the seawater encroachment along the coast. Moreover direct measurements in boreholes by probes can be affected by the mixing due to water inflow coming from fractures at different depths of the water column, whereas the salinity estimations derived from ERT measurements can better represent real salt concentration into the fractures at a specific depth. This can be a valid support for modeling validations.

## 4. Conclusions

_{salt}, a higher number (>40) of appropriate measurements in wells is required.

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Bari site geological sketch and computational domain (red square) for groundwater flow and Ghyben-Herzberg simulations, and the positions of the electrical resistivity tomography (ERT) profiles of subsoil.

**Figure 2.**Experimental aperture variogram and model variogram parameters at Bari (Southern Italy) coastal fractured aquifer; Model: Exponential (Scale = 0.16; Length = 3000 m; Anisotropy: ratio = 2, angle = 64.5 degrees; Nugget Effect: error = 0.03518, micro = 0); Experimental: max lag distance = 4300 m, number of lag = 25, lag width = 172 m, vertical scale = 0.384.

**Figure 3.**ERT profile locations. Blue points are boreholes (six) used for salinity measurements to calibrate Equation (7) by using resistivity data provided by ERT profiles.

**Figure 4.**The relationship between electrical resistivity (ρ) and groundwater salt concentration (C

_{salt}) at the Bari coastal aquifer.

**Figure 5.**Model output: Freshwater heads (contour lines) in meters above sea level and water velocities (vectors) ranging from 10 (in blue) to 80 m/d (in red) in the studied area. White arrows and the gray border indicate the boundary conditions imposed during flow simulations; solid circles are wells.

**Figure 6.**Groundwater salinity map (at a depth of 1.0 m below the water table) given by Ghyben-Herzberg and flow simulation results at the Bari coastal aquifer. Open circles are measured salinities in boreholes.

**Figure 7.**Inverted ERT profiles at Line A (

**a**) (from E1 to E5) and at Line B (

**b**) (from E6 to E10): ERT model error: <5%. E4 shows freshwater thickness reduction due to seawater intrusion.

**Figure 8.**Comparison between salinity trends estimated by using ERT (red lines) and by using the Ghyben Herzberg model (blue lines). Solid lines represent the Line A groundwater section; dotted lines represent the Line B groundwater section.

**Table 1.**Estimations of the mean fracture apertures at the Bari coastal aquifer, by inverting the solution of the steady radial water flow to a well during pumping.

X (m) | Y (m) | K (m/s) | Well ID | 2b (mm) |
---|---|---|---|---|

Pumping Test | ||||

654,627.88 | 4,548,060.78 | 4.05 × 10^{−6} | PT1 | 248.79 |

654,668.04 | 4,548,542.57 | 2.40 × 10^{−5} | PT2 | 336.14 |

655,009.30 | 4,548,492.39 | 2.21 × 10^{−5} | PT3 | 331.71 |

654,979.19 | 4,548,151.12 | 4.90 × 10^{−5} | PT4 | 378.25 |

656,378.54 | 4,549,873.53 | 6.64 × 10^{−4} | PT7 | 629.59 |

648,038.69 | 4,552,384.46 | 1.86 × 10^{−5} | PT8 | 322.25 |

648,794.68 | 4,551,906.47 | 1.14 × 10^{−5} | PT9 | 297.27 |

648,351.69 | 4,551,897.47 | 2.32 × 10^{−5} | PT10 | 334.38 |

647,309.71 | 4,551,475.47 | 2.76 × 10^{−5} | PT11 | 344.01 |

647,914.70 | 4,551,580.47 | 1.92 × 10^{−5} | PT12 | 324.11 |

648,341.69 | 4,551,249.48 | 5.77 × 10^{−5} | PT13 | 388.76 |

648,686.68 | 4,551,472.47 | 2.66 × 10^{−5} | PT14 | 342.00 |

653,466.00 | 4,552,424.00 | 2.71 × 10^{−3} | IS1 | 958.84 |

655,868.00 | 4,554,156.00 | 4.25 × 10^{−4} | IS2 | 566.99 |

655,515.00 | 4,552,586.00 | 9.74 × 10^{−5} | IS4 | 425.37 |

655,272.00 | 4,552,018.00 | 6.40 × 10^{−6} | IS5 | 269.43 |

654,726.00 | 4,551,838.00 | 1.19 × 10^{−5} | IS7 | 299.38 |

654,599.00 | 4,551,852.00 | 7.25 × 10^{−5} | IS8 | 404.13 |

651,985.00 | 4,553,569.00 | 3.80 × 10^{−3} | IS9 | 1089.42 |

651,172.00 | 4,552,620.00 | 9.25 × 10^{−6} | IS10 | 286.87 |

651,558.00 | 4,550,230.00 | 2.37 × 10^{−4} | IS11 | 501.40 |

650,678.00 | 4,554,592.00 | 3.45 × 10^{−5} | IS13 | 356.91 |

651,256.00 | 4,554,586.00 | 1.47 × 10^{−5} | IS14 | 310.07 |

647,153.00 | 4,553,736.00 | 6.26 × 10^{−6} | IS19 | 268.41 |

645,754.00 | 4,553,926.00 | 7.03 × 10^{−6} | IS21 | 273.81 |

653,419.00 | 4,549,497.00 | 3.72 × 10^{−5} | IS22 | 361.33 |

654,415.00 | 4,550,306.00 | 1.27 × 10^{−5} | IS23 | 302.37 |

654,812.00 | 4,550,479.00 | 1.26 × 10^{−5} | IS24 | 302.08 |

654,559.00 | 4,551,970.00 | 1.19 × 10^{−5} | IS25 | 299.38 |

656,315.00 | 4,552,223.00 | 5.48 × 10^{−5} | IS26 | 385.45 |

656,919.00 | 4,550,832.00 | 1.47 × 10^{−5} | IS28 | 310.07 |

652,850.93 | 4,553,352.70 | 4.17 × 10^{−3} | L4 | 1130.53 |

653,252.50 | 4,555,151.70 | 2.17 × 10^{−3} | PSUD | 887.25 |

652,430.90 | 4,554,429.80 | 6.43 × 10^{−3} | L3-S | 1360.49 |

647,930.70 | 4,551,813.20 | 1.33 × 10^{−4} | L5-S | 449.84 |

654,679.50 | 4,555,109.10 | 2.29 × 10^{−3} | L12-S | 903.60 |

Mean value | 6.58 × 10^{−4} | 471.69 |

Injection Pulse Duration | 250 ms |

Minimum and maximum number of cycles for each measurement | 3–6 |

Standard deviation of the measurements in a cycle | 5% |

Parameter | Lower Bound | Upper Bound |
---|---|---|

Injection current (mA) | 5 | 1000 |

Potential measurement (mV) | 5 | 5000 |

Deviation standard of the measurements in a cycle (%) | 0 | 5 |

Percentage difference between direct and reciprocal data (%) | 0 | 5 |

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**MDPI and ACS Style**

Masciopinto, C.; Liso, I.S.; Caputo, M.C.; De Carlo, L.
An Integrated Approach Based on Numerical Modelling and Geophysical Survey to Map Groundwater Salinity in Fractured Coastal Aquifers. *Water* **2017**, *9*, 875.
https://doi.org/10.3390/w9110875

**AMA Style**

Masciopinto C, Liso IS, Caputo MC, De Carlo L.
An Integrated Approach Based on Numerical Modelling and Geophysical Survey to Map Groundwater Salinity in Fractured Coastal Aquifers. *Water*. 2017; 9(11):875.
https://doi.org/10.3390/w9110875

**Chicago/Turabian Style**

Masciopinto, Costantino, Isabella Serena Liso, Maria Clementina Caputo, and Lorenzo De Carlo.
2017. "An Integrated Approach Based on Numerical Modelling and Geophysical Survey to Map Groundwater Salinity in Fractured Coastal Aquifers" *Water* 9, no. 11: 875.
https://doi.org/10.3390/w9110875