# A New Method to Infer Advancement of Saline Front in Coastal Groundwater Systems by 3D: The Case of Bari (Southern Italy) Fractured Aquifer

^{*}

## Abstract

**:**

^{−1}during the transition period of 112.8 days was easily highlighted on 3D salinity maps of Bari aquifer.

## 1. Introduction

## 2. Methodology

^{2}. Pumping and/or injection tests carried out into Bari wells, allowed the identification of the average aperture of all fractures of the set at each well position in order to determine the experimental variogram of spatial aperture covariance. Experiments on model calibrations and validations have been extensively reported by Masciopinto [14], Masciopinto et al. [13,15], and Masciopinto and Palmiotta [16]. The flow solution given by the flow model yields the freshwater discharge along the top border of domain. This freshwater discharge was used to determine the Ghyben-Herzberg sharp (50%) freshwater/saltwater interface [14]. These results defined also the saline front position along the coast.

**Figure 1.**(

**a**) Parallel set of horizontal (x-y) fractures with permeability equivalent to the real fractured medium; (

**b**) modeled fracture apertures in each single fracture of the set: the aperture variation in the x-y plane is obtained by means of the experimental variogram derived from results of well pumping (or injection) tests.

**Figure 2.**Flowchart of the applied methodology to produce transient 3D maps of the groundwater salinity.

## 3. The Case Study and Field Tests

^{2}due to streams that flow into the Adriatic Sea. In this coastal area groundwater is confined within the limestone (Cretaceous) formation, and water flows in horizontal fractures in SW-NE direction, i.e., towards the coast. Geologically, the Bari aquifer is located in the Murgia region. In the tested area (coastal area of the Murgia region), rock permeability is low and discontinuous both horizontally and vertically. The geological sequence of layers observed during borehole drilling, from top downward, is Pleistocene sandstone (3–5 m thick), Cretaceous limestone (26 m thick), and Jurassic dolomite (>20 m thick). Murgia shows neo-tectonic sub-vertical fractures of the Mesozoic rocks that are relatively frequent and barely open or are sealed by calcspar and terra rossa (bulk density 1.26 ± 0.1 g/cm

^{3}). The Bari aquifer is not highly karstified. This means that calcite dissolution had taken place inside fractures of the Bari/IRSA aquifer, and an increase in hydraulic conductivity to 0.42 cm/s was found with respect to the quasi non-karstified limestone with 0.01–0.04 cm/s of hydraulic conductivity close (<1 km) to the sea coast.

**Figure 3.**Spatial distribution of wells (red circles and tringles) and flow simulation results with distance d of each well from position of Ghyben-Herzberg saline front in groundwater. The yellow lines (and polygon) refer to actual groundwater flow simulation. The blue lines (and polygon) consider the flow modifications due to new pumping of 335 L·s

^{-1}. The blue dashed line is the contour head at 1 m.

#### 3.1. Field Set Up

^{2}·t

^{−1}] (l stand for length; t stands for time) and hydraulic conductivity K [l·t

^{−1}] were determined by inverting the semi-analytical solution of Thiem’s equation. The results of 58 pumping tests and 10 tracer tests (Figure 4) carried out by IRSA on the Bari aquifer boreholes, were considered in this work. In particular, pumping (or injection) and tracer tests under undisturbed (or natural) gradient were carried out in order to estimate local values of both aquifer hydraulic transmissivity and groundwater specific discharge (see Table 1). The analytical solution of tracer (chlorophyllin) dispersion into the water was applied [13] to the breakthrough curves in Figure 4 in order to determine the horizontal water velocity in each borehole.

**Figure 4.**Breakthrough curves of relative tracer (chlorophyllin) concentrations during injection tests in ten boreholes of Bari aquifer.

Well ID | Coordinates (UTM) | Tracer Test | Internal Diameter (m) | Piezometric Head (m above Sea Level) January–February 2012 | Aquifer Hydraulic Transmissivity (m^{2}/s) | Ground Water Specific Discharge (m/day) | ||
---|---|---|---|---|---|---|---|---|

E | N | |||||||

P10 | 652,892.8 | 4,553,271.3 | 0.300 | 4.480 | 0.09 | |||

L1-S | 652,994.3 | 4,552,693.5 | X | 0.180 | 4.268 | 5.278 | 0.6 × 10^{−3} ± 1.8 × 10^{−4} | 1.3 |

P11 | 654,726.9 | 4,552,308.3 | >1.0 | 1.251 | 1.611 | 0.02 | ||

P19 | 654,580.1 | 4,552,382.9 | >1.0 | 0.77 | 1.110 | 0.02 | ||

P14 | 654,093.3 | 4,554,883.8 | 0.012 | 0.311 | 0.321 | 0.045 | ||

L2-S | 653,252.5 | 4,555,151.7 | X | >1.0 | 0.582 | 0.722 | 0.047 ± 0.01 | 0.5 |

P4 | 653,053.8 | 4,554,841.5 | 0.012 | 0.266 | 0.386 | 0.06 | ||

L3-S | 652,431.0 | 4,554,429.8 | X | >1.0 | 1.903 | 2.163 | 0.043 ± 0.02 | 2.6 |

P3 | 651,569.2 | 4,553,208.7 | 0.300 | 4.321 | 5.441 | 0.07 | ||

P16 | 652,360.0 | 4,553,741.7 | 0.014 | 2.658 | 3.538 | 0.09 | ||

L4-S | 652,850.9 | 4,553,352.7 | X | 0.300 | 2.535 | 3.450 | 0.033 ± 0.03 | 2.2 |

P18 | 652,442.4 | 4,552,454.1 | 0.200 | 6.926 | 0.07 | |||

L5-S | 647,930.7 | 4,551,813.2 | X | 0.325 | 33.649 | 3.0 × 10^{−3} ± 1.8 × 10^{−3} | 0.2 | |

L8-S | 652,094.5 | 4,551,194.2 | X | 0.080 | 8.532 | 0.02 ± 0.01 | 0.4 | |

L7-S | 652,237.3 | 4,550,862.3 | X | 0.080 | 7.880 | 0.5 × 10^{−2} ± 0.4 × 10^{−2} | 0.6 | |

L6-S | 651,974.4 | 4,550,961.1 | X | 0.080 | 8.892 | 0.11 ± 0.01 | 1.4 | |

P13 | 651,750.4 | 4,554,936.6 | 0.300 | 0.807 | 0.02 | |||

L9 | 654,682.2 | 4,555,123.7 | 0.100 | 0.705 | 0.1 | |||

L10 | 654,572.7 | 4,555,144.1 | 0.100 | 0.167 | 0.01 | |||

L11 | 654,588.5 | 4,555,126.1 | 0.100 | 0.317 | 0.01 | |||

L12-S | 654,679.5 | 4,555,109.1 | X | 0.300 | 0.360 | 0.01 ± 0.7 × 10^{−3} | 0.3 | |

L13 | 654,777.0 | 4,555,188.8 | 0.100 | 0.418 | 1.2 × 10^{−5} | |||

L14-S | 649,860.6 | 4,552,197.6 | X | 0.080 | 34.370 | 1.1 × 10^{−4} ± 5.3 × 10^{−5} | 0.6 | |

L15 | 649,623.8 | 4,552,059.7 | 0.080 | 35.260 | 1.2 × 10^{−5} | |||

P2 | 651,595.4 | 4,551,934.3 | 0.300 | 6.760 | 0.025 |

#### 3.2. Experiment Methodology

^{−1}and from 3 to 6 L·s

^{−1}, on average. In addition water table depth was simultaneously monitored (and recorded) by means of the pressure probe (mini-log data logger, SIM Instrument SNC, Milan, Italy). The flow rate of each pumping (or injection) was kept constant for about 2 h; at the end of the test, pumping was stopped and the rise (or decline, after an injection) in water depth was recorded during the recovery period.

^{3}of water was marked with 500 g of chlorophyll powder commercially sold as E141 hydro soluble or sodium copper chlorophyllin, which is usually used for foodstuffs such as pickles, ice creams, candies and fruit juices, and therefore it is not dangerous for human health. After mixing water and chlorophyllin powder in a tank of 1 m

^{3}volume, the traced mixture was injected with a constant flow rate of around 2 L·s

^{−1}into a borehole, using a submersible pump and a pipeline (3 inch internal diameter). The traced water was injected at an assigned water depth (3 m) for about 8 min. The injection pipeline was then removed and groundwater was sampled at regular time intervals via a sampling pump (Grundfos BTI/MP1, Downers Grove, IL, USA) placed at the assigned water depth of 3 m into the well. Each water sample was stored in a plastic (Polyvinyl chloride or PVC) black bottle and transported in the laboratory where samples were monitored for water absorbance. Groundwater was sampled as long as the background tracer value of 10

^{−3}absorbance units (AU) [20] was again achieved in the well. During injection water depth was monitored and recorded using a pressure probe and the data logger (SIM Instrument, Milano, Italy). The measurement of tracer concentration in the borehole referred to a calibration curve previously determined in the laboratory using a spectrophotometer (HACH DR/2000, Hach Lange Srl, Lainate, Italy) at a frequency of 405 nm. Test results suggest an aquifer discretization of 80 smoothed (and parallel) fractures. In fact, as n [–] defines the effective aquifer porosity, it is the uniform ratio of the void-space per unit volume of aquifer and, in each cross-section, it will be:

_{i}[l] is the sum of all horizontal fracture apertures of the aquifer column with unitary horizontal area (1 × 1 m

^{2}) and thickness B [l], while N

_{f}[–] is the total number of the fractures of the parallel set (see Figure 1). Assuming that all fractures of the set have the same aperture of 1.3 mm, i.e., ∑2b

_{i}= N

_{f}× 2b = n × B and for n = 0.35% and B = 30 m (see test results Table 1), Equation (1) suggests N

_{f}= 80.

## 4. Groundwater Flow Simulation and Ghyben-Herzberg Interface Toe Position

^{2}) every fracture belonging to the 3D parallel set (Figure 1) was discretized using a grid step size of Δx = Δy = 150 m (i.e., 49 × 43 grid nodes). The steady and non-uniform groundwater flow was addressed in a series of parallel and horizontal fractures, with each single fracture having a spatially variable aperture and impermeable rock matrix. The model implemented the approximated analytical radial flow solution to a well in order to determine the mean conductivity of aquifer fractures at each well position by using K = nb

^{2}/3 γ

_{w}/µ, where γ

_{w}[M·l

^{−2}·t

^{−2}] (M stands for mass) is the water specific weight and µ [M·l

^{−1}·t

^{−1}] is the dynamic water viscosity. The experimental variogram regarding the fracture apertures derived from well pumping tests was employed to perform the stochastic generation of apertures in each horizontal fracture belonging to the set. The discharge/head relationship in each fracture is defined as [15]

_{ij}[l

^{3}·t

^{−1}] is the flow rate of each fracture between two generic grid nodes i and j; Δx [l] and Δy [l] are the grid steps; and φ = p/γ

_{w}[l] is the water head, whilst g [l·t

^{−2}] is the gravity acceleration. It should be noted that Equation (2) supports flow calculations at any Reynolds number. By imposing the continuity equation, i.e., ∑Q

_{ij}= 0, in every grid node, a system of equations was defined. The over-relaxation method was applied to solve the system of equations after that the boundary conditions were assigned. The flow simulation results enabled calculations of the seawater/freshwater 50% sharp interface positions with respect to the coastline, by applying the Ghyben-Herzberg equation. Indeed, to predict the interface toe position L [l] with respect to the coastline, the resulting groundwater outflow was managed in order to calculate the length of intrusion for every position along the coast defines as [14]

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

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

_{s}[l] is the sharp interface depth at the outflow (usually set = 0); ${Q}_{0}^{i}$ [l

^{2}·t

^{−1}] is the groundwater discharge along the coast predicted by model at grid node i; and ${\delta}_{\gamma}={\gamma}_{w}/\left({\gamma}_{s}-{\gamma}_{w}\right)$ [–] is the ratio of the specific weights.

^{−1}(assuming that reinjections of pumped water are not allowed). Figure 3 shows how the new pumping changes the saline front position with respect to the coast. Simulation results provided a total decreases of 12% of freshwater ${Q}_{0}$ discharged into the sea, i.e., from 10.8 to 9.5 m

^{3}·day

^{−1}·m

^{−1}in each fracture of the parallel set, due to new (or apparent) pumping wells. The maximum distance d of pumping wells from interface (see Figure 3) decreased of about 1000–1500 m, on average, due to new pumping.

#### Advancement of Saline Front in a Fracture Using N-S

^{−3}] is water density, and u

_{α}is the velocity [l·t

^{−1}] of the fluid particle; x

_{α}[l] and x

_{β}[l] are two spatial position coordinates of the fluid particle (Einstein notation); g

_{α}[l·t

^{−2}] is the component of the gravity vector. The tensor component of the Newtonian stress component σ

_{αβ}[M·t

^{−2}·l

^{−1}], which was applied to each particle subject to the pressure pδ

_{αβ}[M·t

^{−2}·l

^{−1}] can be defined:

^{−2}·l

^{−1}] of the viscosity can be defined using [21,22]:

_{αβ}[–] is the Kroneker delta; ${\overline{\tau}}_{\alpha \beta}$ is the average sub-grid stress due to the fluctuating variation of velocities around the averaged values during turbulent flows. Similarly, Reynolds stress can be determined by assuming the eddy viscosity theory (Boussinesq’s hypothesis), and by the Smagorinsky constant [23].

**u***given by N-S conservation momentum Equation (5) is included in the following (Poisson) [25] equation:

**u*** is the intermediate velocity whose value is based on the viscous stress. Equation (8) is then used in a finite difference model (FDM) [16] in order to estimate the pressure of water via a separate numerical calculation. In particular, the conjugate gradient numerical method was applied to solve Equation (8) in order to calculate the water pressure by forcing the flow divergence to zero. After that the water pressure was determined, the correct velocity is obtained by Equation (9). Thus, at the next time step, the N-S momentum conservation Equation (4) is solved again to calculate the new intermediate water velocity. Moreover, in order to account for flow density variations due to the saline front advancement in the FDM code, the velocity

**u***derived from Equation (5) was updated at each time step according to the new distribution of water densities into the cells of the fracture domain. This water density distribution due to mass salt flow advancement in the fracture was determined at every instant of the flow simulation by solving the salt advection and dispersion equation into the freshwater of the fracture, using a hydrodynamic dispersion coefficient of 10

^{−9}m

^{2}·s

^{−1}. In this way in every cell of the domain the divergence of the salt mass flux in the x and z directions was predicted at each simulation time.

^{−1}of total concentration. Moreover, the reduction of 1.3 m

^{3}·day

^{−1}·m

^{−1}of freshwater discharge Q

_{0}in each fracture was also applied at the inflow section as the initial conditions during N-S simulations. Flow through the fracture cross-section (2b × 1 m

^{2}) was driven by a momentum (per unit volume) equal to 12,375 kg·m

^{−2}·day

^{−1}. This was defined by the product of the reduction of freshwater flowrate along the coast (from 102.9 to 90.5 m·day

^{−1}) (due to new pumping of 335 L·s

^{−1}) and the freshwater density (12.4 m·day

^{−1}× 1000 kg·m

^{−3}). Furthermore, at t = t

_{0}= 0, the salt density distribution in all cells of fracture was also imposed as initial condition.

_{s}[l] in the studied fracture at specific simulation time. Using twelve simulation run results the following linear equation was (0.99 of correlation) close-fitting in TableCurve2D:

_{s}= 1.08 × 10

^{−1}m and B

_{s}= 9.36 × 10

^{−3}m·min

^{−1}(or 13.3 m·day

^{−1}). The results of the N-S code simulations confirmed the strong influence of fracture aperture size on water velocity estimation. For a fracture with 3 cm aperture, the mean water velocity (and Reynolds number) may be 100 times higher than the value determined for a fracture with 3 mm aperture. The quasi linear trend of the saline front advancement given by Equation (10) well matches the temporal trend of the progression of toe positions given by [26] during simulations. The rate of seawater advancement given by the N-S code (i.e., 13.3 m·day

^{−1}) is close to the expected value (12.4 m·day

^{−1}), which is driven by the prescribed momentum. Using these N-S solutions, maximum elapsed time from the start of pumping to reach the new position of freshwater/saltwater sharp interface in the Bari groundwater is equal to 112.8 day (i.e., 1500 m/(13.3 m·day

^{−1})). Material concerning the advancement of sea movement intrusion is very useful for groundwater management practices of coastal aquifers [26,27,28].

**Figure 5.**N-S solutions in a fracture (of aperture 2b = 3 mm, 2b stands for the fracture aperture in the manuscript.) of the Bari aquifer. The rate of saline front advancement was used to determine the effects of new pumping of 335 L·s

^{−1}on the freshwater/saltwater transition zone in coastal aquifers.

**Figure 6.**N-S solution at time t = 243.03 min from the beginning of the new pumping of 335 L·s

^{−1}: horizontal flow velocity magnitude map due to freshwater/saltwater mixing in the fracture, and Reynolds number distribution.

## 5. Conversion of Distances from Interface into Groundwater Salinity Data

#### 5.1. Field Monitored Data

^{−1}(at the surface) to 0.3 mg·L

^{−1}or less (at 37 m depth) in Bari’s wells, and the water temperature. Each probe was previously calibrated in the laboratory in order to directly provide proper values of water salinity, temperature, pressure and dissolved oxygen vs. water depth. The relative monitored water specific conductance in 14 boreholes is displayed in Figure 7, where C/C

_{min}is the ratio of each measurement to the minimum recorded value at each specific borehole location. Figure 7 presents anomalous salinity trends in the polluted sites that are characterized by high water temperatures.

**Figure 7.**Relative specific conductance vs. water depth in 14 boreholes of the Bari aquifer positioned at different distance from Ghyben-Herzberg freshwater/sweater (50%) sharp interface position (Winter 2012) and best-fit equation (dashed line).

#### 5.2. Ghyben-Herzberg Data

_{s}

_{0}= 1.54 g∙L

^{−1}, A

_{s}= 12.02 g∙L

^{−1}and D

_{s}= 592.65 m. At distances d > 1500 m the following best-fit equation:

_{s}= 2.54 log(g·L

^{−1}) and I

_{s}= 0.04177 log(g·L

^{−1}∙m

^{−0.5}) are the best fit constants.

_{s}and F

_{s}are two dimensionless interpolating functions with polynomial form:

_{0}is minimum salinity value at the specific borehole location. Equation (12) is valid up to a water depth of 140 m. Moreover, the following best-fit function (correlation coefficient of 0.93) could also replace Equation (12):

^{−1}) (see Table 2) at depth of 1 m below water table and it may be reduced by increasing the number of boreholes for salinity measurements.

**Table 2.**Comparison between modelled (Mod) values of groundwater salinity (i.e., Rockwork15 input data at t = 0) and measurements (Mea) at three water depths into boreholes of the Bari aquifer. SD stands for the standard deviation between measured and modelled values.

ID Borehole | Actual (Winter 2012) Groundwater Salinity (g·L^{−1}) at Different Water Depths | ||||||||
---|---|---|---|---|---|---|---|---|---|

1 m | 11 m | 31 m | |||||||

Mod | Mea | ±SD | Mod | Mea | ±SD | Mod | Mea | ±SD | |

L1-S | 0.9 | 1.54 | 0.46 | 1.06 | 1.65 | 0.41 | 1.31 | ||

P11 | 2.76 | 2.99 | 0.16 | 3.14 | 3.9 | ||||

P19 | 3.75 | 3.71 | 0.03 | 4.27 | 5.29 | ||||

L2-S | 3.12 | 2.63 | 0.34 | 3.55 | 4.39 | ||||

L3-S | 2.11 | 3.40 | 0.91 | 2.4 | 2.97 | ||||

L4 | 0.98 | 1.05 | 0.05 | 1.1 | 1.72 | 0.44 | 1.38 | 2.77 | 0.98 |

L8-S | 0.5 | 0.71 | 0.15 | 0.52 | 0.65 | ||||

L7-S | 0.5 | 0.58 | 0.06 | 0.6 | 0.74 | ||||

L6-S | 0.5 | 0.67 | 0.12 | 0.52 | 0.78 | 0.19 | 0.65 | ||

L9 | 2.02 | 1.54 | 0.34 | 2.3 | 2.85 | ||||

L14-S | 0.93 | 0.59 | 0.24 | 1.06 | 0.56 | 0.35 | 1.31 | 1.03 | 0.20 |

L15-S | 0.93 | 0.86 | 0.05 | 1.06 | 0.95 | 0.08 | 1.31 | 1.75 | 0.31 |

L5-S | 0.5 | 0.63 | 0.09 | 0.52 | 0.68 | 0.12 | 0.65 | 1.50 | 0.60 |

L12 | 2.02 | 0.56 | 1.03 | 2.3 | 2.26 | 0.03 | 2.85 | ||

Mean | 1.53 | ±0.32 | 1.23 | ±0.23 | 1.76 | ±0.52 |

#### 5.3. Data from Solutions of N-S Equations

^{−1}.

**Figure 8.**(

**a**) 3D map of groundwater salinity during winter 2012 (t = 0 day) and its comparison with groundwater salinity maps after (

**b**) 30; (

**c**) 75 and (

**d**) 112.8 days of a simulated continuous pumping of 335 L∙s

^{−1}.

## 6. Discussion and Conclusions

^{−1}. The 3D maps are useful tools for coastal groundwater management and show how over-abstractions may affect groundwater salinity changes. The same method can be applied to others aquifers with discrete fractures and it requires two data sets: (i) field salinity data in boreholes (i.e., logs); and (ii) results of groundwater flow model simulation to represent actual 3D maps of aquifer salinity. Moreover, solutions of the N-S equations in a fracture can provide the rate (on average) of saline front advancement in fractures during time. This result allows updates of actual salt concentrations, by defining 3D salinity maps at specific simulation times during a new pumping. Although mapping based on the sharp interface approach is not representative of real conditions of the salt mass transport in fractures, the salinity front positions at the initial and final stage of the simulated pumping stress condition in this method, take into account for the real flow conditions in the fractured aquifer. Moreover, by including approximations due to the interpolation stages (correlation coefficients >0.92–0.93) authors have estimated the 20% of uncertainty of results at the Bari aquifer. This uncertainty established an acceptable distance of results from reality.

^{−1}.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Masciopinto, C.; Palmiotta, D.
A New Method to Infer Advancement of Saline Front in Coastal Groundwater Systems by 3D: The Case of Bari (Southern Italy) Fractured Aquifer. *Computation* **2016**, *4*, 9.
https://doi.org/10.3390/computation4010009

**AMA Style**

Masciopinto C, Palmiotta D.
A New Method to Infer Advancement of Saline Front in Coastal Groundwater Systems by 3D: The Case of Bari (Southern Italy) Fractured Aquifer. *Computation*. 2016; 4(1):9.
https://doi.org/10.3390/computation4010009

**Chicago/Turabian Style**

Masciopinto, Costantino, and Domenico Palmiotta.
2016. "A New Method to Infer Advancement of Saline Front in Coastal Groundwater Systems by 3D: The Case of Bari (Southern Italy) Fractured Aquifer" *Computation* 4, no. 1: 9.
https://doi.org/10.3390/computation4010009