We analyze the combined effects of aquifer heterogeneity and pumping operations on seawater intrusion (SWI), a phenomenon which is threatening coastal aquifers worldwide. Our investigation is set within a probabilistic framework and relies on a numerical Monte Carlo approach targeting transient variable-density flow and solute transport in a three-dimensional randomly heterogeneous porous domain. The geological setting is patterned after the Argentona river basin, in the Maresme region of Catalonia (Spain). Our numerical study is concerned with exploring the effects of (a) random heterogeneity of the domain on SWI in combination with (b) a variety of groundwater withdrawal schemes. The latter have been designed by varying the screen location along the vertical direction and the distance of the wellbore from the coastline and from the location of the freshwater–saltwater mixing zone which is in place prior to pumping. For each random realization of the aquifer permeability field and for each pumping scheme, a quantitative depiction of SWI phenomena is inferred from an original set of metrics characterizing (a) the inland penetration of the saltwater wedge and (b) the width of the mixing zone across the whole three-dimensional system. Our results indicate that the stochastic nature of the system heterogeneity significantly affects the statistical description of the main features of the seawater wedge either in the presence or in the absence of pumping, yielding a general reduction of toe penetration and an increase of the width of the mixing zone. Simultaneous extraction of fresh and saltwater from two screens along the same wellbore located, prior to pumping, within the freshwater–saltwater mixing zone is effective in limiting SWI in the context of groundwater resources exploitation.

Groundwater resources in coastal aquifers are seriously threatened by seawater intrusion (SWI), which can deteriorate the quality of freshwater aquifers, thus limiting their potential use. This situation is particularly exacerbated within areas with intense anthropogenic activities, which are associated with competitive uses of groundwater in connection, e.g., with agricultural processes, industrial processes and/or high urban water supply demand. Critical SWI scenarios are attained when seawater reaches extraction wells designed for urban freshwater supply, with severe environmental, social and economic implications (e.g., Custodio, 2010; Mas-Pla et al., 2014; Mazi et al., 2014).

The development of effective strategies for sustainable use of groundwater
resources in coastal regions should be based on a comprehensive
understanding of SWI phenomena. This challenging problem has been originally
studied by assuming a static equilibrium between freshwater (FW) and seawater
(SW) and a sharp FW–SW interface, where FW and SW are considered as
immiscible fluids. Under these hypotheses, the vertical position of the FW–SW
interface below the sea level,

A more realistic approach relies on the formulation and solution of a variable-density problem, in which SW and FW are considered as miscible fluids and groundwater density depends on salt concentration. The complexity of the problem typically prevents finding a solution via analytical or semi-analytical methods, with a few notable exceptions (Henry, 1964; Dentz et al., 2006; Bolster et al., 2007; Zidane et al., 2012; Fahs et al., 2014). Henry (1964) developed a semi-analytical solution for a variable-density diffusion problem in a (vertical) two-dimensional homogeneous and isotropic domain. Dentz et al. (2006) and Bolster et al. (2007) applied perturbation techniques to solve analytically the Henry problem for a range of (small and intermediate) values of the Péclet number, which characterizes the relative strength of convective and dispersive transport mechanisms. Zidane et al. (2012) solved the Henry problem for realistic (small) values of the diffusion coefficient. Finally, Fahs et al. (2014) presented a semi-analytical solution for a square porous cavity system subject to diverse salt concentrations at its vertical walls. Practical applicability of these solutions is quite limited, due to their markedly simplified characteristics. Various numerical codes have been proposed to solve variable-density flow and transport equations (e.g., Voss and Provost, 2002; Ackerer et al., 2004; Soto Meca et al., 2007; Ackerer and Younes, 2008; Albets-Chico and Kassinos, 2013). Numerical simulations can provide valuable insights into the effects of dispersion on SWI, a feature that is typically neglected in analytical and semi-analytical solutions. Abarca et al. (2007) introduced a modified Henry problem to account for dispersive solute transport and anisotropy in hydraulic conductivity. Kerrou and Renard (2010) analyzed the dispersive Henry problem within two- and three-dimensional randomly heterogeneous aquifer systems. These authors relied on computational analyses performed on a single three-dimensional realization, invoking ergodicity assumptions. Lu et al. (2013) performed a set of laboratory experiments and numerical simulations to investigate the effect of geological stratification on SW–FW mixing. Riva et al. (2015) considered the same setting as in Abarca et al. (2007) and studied the way quantification of uncertainty associated with SWI features is influenced by lack of knowledge of four key dimensionless parameters controlling the process, i.e., gravity number, permeability anisotropy ratio and transverse and longitudinal Péclet numbers. Enhancement of mixing in the presence of tidal fluctuations and/or FW table oscillations has been analyzed by Ataie-Ashtiani et al. (1999), Lu et al. (2009, 2015) and Pool et al. (2014) in homogeneous aquifers and by Pool et al. (2015) in randomly heterogeneous three-dimensional systems (under ergodic conditions). Recent reviews on the topic are offered by Werner et al. (2013) and Ketabchi et al. (2016).

Several numerical modeling studies have been performed with the aim of identifying the most effective strategy for the exploitation of groundwater resources in domains mimicking the behavior of specific sites. Dausman and Langevin (2005) examined the influence of hydrologic stresses and water management practices on SWI in a superficial aquifer (Broward County, USA) by developing a variable-density model formed by two homogeneous hydrogeological units. Werner and Gallagher (2006) studied SWI in the coastal aquifer of the Pioneer Valley (Australia), illustrating the advantages of combining hydrogeological and hydrochemical analyses to understand salinization processes. Misut and Voss (2007) analyzed the impact of aquifer storage and recovery practices on the transition zone associated with the salt water wedge in the New York City aquifer, which was modeled as a perfectly stratified system. Cobaner et al. (2012) studied the effect of transient pumping rates from multiple wells on SWI in the Gosku deltaic plain (Turkey) by means of a three-dimensional heterogeneous model, calibrated using head and salinity data.

All the aforementioned field-scale contributions are framed within a deterministic approach, where the system attributes (e.g., permeability) are known (or determined via an inverse modeling procedure), so that the impact of uncertainty of hydrogeological properties on target environmental (or engineering) performance metrics is not considered. Exclusive reliance on a deterministic approach is in stark contrast with the widely documented and recognized observation that a complete knowledge of aquifer properties is unfeasible. This is due to a number of reasons, including observation uncertainties and data availability, i.e., available data are most often too scarce or too sparse to yield an accurate depiction of the subsurface system in all of its relevant details. Stochastic approaches enable us not only to provide predictions (in terms of best estimates) of quantities of interest, but also to quantify the uncertainty associated with such predictions. The latter can then be transferred, for example, into probabilistic risk assessment, management and protection protocols for environmental systems and water resources.

Only a few contributions studying SWI within a stochastic framework have been published to date. The vast majority of these works considers idealized synthetic showcases and/or simplified systems. To the best of our knowledge, only two studies (Lecca and Cau, 2009; Kerrou et al., 2013) have analyzed the transient behavior of a realistic costal aquifer within a probabilistic framework. Lecca and Cau (2009) evaluated SWI in the Oristano (Italy) aquifer by considering a stratified system where the aquitard is characterized by random heterogeneity. Kerrou et al. (2013) analyzed the effects of uncertainty in permeability and distribution of pumping rates on SWI in the Korba aquifer (Tunisia). Both works characterize the uncertainty of SWI phenomena in terms of the planar extent of the system characterized by a target probability of exceedance of a given threshold concentration.

Our stochastic numerical study has been designed to mimic the general behavior of the Argentona aquifer, in the Maresme region of Catalonia (Spain). This area, as well as other Mediterranean deltaic sites, is particularly vulnerable to SWI (Custodio, 2010). We note that the objective of this study is not the quantification of the SWI dynamics of a particular field site. Our emphasis is on the analysis of the impact of random aquifer heterogeneity and withdrawals on SWI patterns in a realistic scenario. Key elements of novelty in our work include the introduction and the study of a new set of metrics, aimed at investigating quantitatively the effects of random heterogeneity on the three-dimensional extent of the SW wedge penetration and of the FW–SW mixing zone. The impact of random heterogeneity is assessed in combination with three diverse withdrawal scenarios, designed by varying (i) the distance of the wellbore from the coastline and from the FW–SW mixing zone and (ii) the screen location along the vertical direction. We frame our analysis within a numerical Monte Carlo (MC) approach.

Section 2 provides a general description of the field site, the mathematical model adopted to simulate flow and transport phenomena in three-dimensional heterogeneous systems and the numerical settings. Section 3 illustrates the key results of our work and Sect. 4 contains our concluding remarks.

To consider a realistic scenario that is relevant to SWI problems in highly exploited aquifers, we cast our analysis in a setting inspired from the Argentona river basin, located in the region of Maresme, in Catalonia, Spain (see Fig. 1a). This aquifer is a typical deltaic site, characterized by shallow sedimentary units and a flat topography. As such, it has a strategic value for anthropogenic (including agricultural, industrial and touristic) activities. The geological formation hosting the groundwater resource is mainly composed of a granitic Permian unit. A secondary unit of quaternary sediments is concentrated along the Argentona river.

Rodriguez Fernandez (2015) developed a conceptual and numerical model to
simulate transient two-dimensional (horizontal) constant-density flow in the
Argentona river basin across the area of about 35 km

Our numerical analysis focuses on the coastal portion of the Argentona basin (Fig. 1c). This region extends for about 2.5 km along the coast (i.e., along the full width of the basin) and up to 750 m inland from the coast. The offshore extension of the aquifer is not considered. The size of the study area has been selected on the basis of the results of preliminary simulations on larger domains, which highlighted that salt concentration values were appreciable only within a narrow (less than 400 m wide) region close to the coast. The vertical thickness of the domain ranges from 50 m along the coast up to 60 m at the inland boundary, the underlying clay sequence being considered to represent the impermeable bottom of the aquifer. SWI is simulated by means of a three-dimensional variable-density flow and solute transport model based on the well-established finite element USGS SUTRA code (Voss and Provost, 2002) over the 8-year time window 2006–2013. Details of the mathematical and numerical model are discussed in the following sections.

Fluid flow is governed by mass conservation and Darcy's law:

The domain depicted in Fig. 1c is discretized through an unstructured
three-dimensional grid formed by 101 632 hexahedral elements. The resolution
of the mesh increases towards the sea, where our analysis requires the
highest spatial detail. The element size along both horizontal directions

Parameters adopted in the numerical model.

A sequential Gaussian simulation algorithm (Deutsch and Journel, 1998) is
employed to generate unconditional log permeability fields,

Equations (1)–(5) are solved jointly, adopting the following boundary
conditions. The lateral boundaries perpendicular to the coastline and the
base of the aquifer are impervious; along the inland boundary we set a
time-dependent prescribed hydraulic head,

A pumping well is activated at time

Graphical representation of the SWI metrics defined in Sect. 2.4.

To provide a comprehensive characterization of SWI phenomena across the whole three-dimensional domain, we quantify the extent of the SW wedge and of the associated mixing zone on the basis of seven metrics, as illustrated in Fig. 3.

For each MC realization and along each vertical cross-section perpendicular
to the coast, we evaluate (i) toe penetration, ^{™} i7-6900K CPU@ 3.20 GHz
processor). Results illustrated in the following sections are based on a
suite of 400 MC simulations (i.e., 100 MC simulation for each scenario,
S0–S3). Details concerning the analysis of convergence of the first and
second statistical moments of the metrics here introduced are provided in
Appendix A.

Permeability distribution (color contour plots), streamlines (black
dashed curves) and iso-concentration curves

The effects of heterogeneity on SWI are inferred by comparing the results of
our MC simulations against those obtained for an equivalent homogeneous
aquifer, characterized by an effective permeability,

Figure 5 depicts isolines

MC-based (dotted blue curves) iso-concentration lines

Metrics

In the following, we analyze values of

Here, we investigate SWI phenomena in heterogeneous systems when a pumping
scheme is activated as described in Sect. 2.3. Figure 7 collects contour maps
of relative concentration

Concentration distribution (color contour plots) and
iso-concentration lines

Temporal evolution of

The combined effects of groundwater withdrawal and stochastic heterogeneity on SWI are investigated quantitatively through the analysis of the temporal evolution of the seven metrics introduced in Sect. 2.4.

Figure 8 illustrates mean values of

Isolines

The fully three-dimensional nature of the analyzed problem is exemplified in
Fig. 9, where we depict isolines

Temporal evolution of

Temporal evolution of

We quantify the global effect of pumping on the three-dimensional SW wedge by
evaluating, for each pumping scenario and each MC realization, the temporal
evolution of

Our analyses document that for a stochastically heterogeneous aquifer an
operational scheme of the kind engineered in S3 (i) is particularly efficient
for the reduction of SWI maximum penetration (localized at the bottom of the
aquifer) and (ii) is advantageous in controlling the extent of the volume of
the SW wedge, as compared to the double-negative barrier implemented in S2.
However, this withdrawal system may lead to the salinization of the FW
extracted from the upper screen due to upconing effects. This aspect is
further analyzed in Fig. 12 where the temporal evolution of

Temporal evolution of

We investigate quantitatively the role of stochastic heterogeneity and
groundwater withdrawal on seawater intrusion (SWI) in a randomly
heterogeneous coastal aquifer through a suite of numerical Monte Carlo (MC)
simulations of transient variable-density flow and transport in a three-dimensional
domain. Our work attempts to include the effects of random heterogeneity of
permeability and groundwater withdrawal within a realistic and relevant
scenario. For this purpose, the numerical model has been tailored to the
general hydrogeological setting of a coastal aquifer, i.e., the Argentona
river basin (Spain), a region which is plagued by SWI. To account for the
inherent uncertainty associated with aquifer hydrogeological properties, we
conceptualize our target system as a heterogeneous medium whose permeability
is a random function of space. The SWI phenomenon is studied through the
analysis of (a) the general pattern of iso-concentration curves and (b) a set
of seven dimensionless metrics describing the toe penetration and the extent
of the mixing or transition zone. We compare results obtained across a
collection of

Heterogeneity of the system affects the SW wedge along all directions both in the presence and absence of pumping. On average, our heterogeneous system is characterized by toe penetration and extent of the mixing zone that are, respectively, smaller and larger than their counterparts computed in the equivalent homogeneous system.

Ensemble (i.e., across the MC realizations) mean values of linear,

Ensemble mean values of linear,

All of the tested pumping schemes lead to an increased SW wedge volume compared to the scenario where pumping is absent. The key aspect controlling the effects of groundwater withdrawal on SWI is the position of the wellbore with respect to the location of the saltwater wedge in place prior to pumping. The toe penetration decreases or increases depending on whether the well is initially (i.e., before pumping) located within or outside the seawater intruded region, respectively. The water withdrawal scheme that is most efficient for the reduction of the maximum inland penetration of the seawater toe is the one according to which freshwater and saltwater are, respectively, extracted from the top and the bottom of the same borehole, initially located within the SW wedge. This result suggests the potential effectiveness of the so-called “negative barriers” in limiting intrusion, even when considering the uncertainty effects stemming from our incomplete knowledge of permeability spatial distributions.

Salt concentration,

Future development of our work includes the analysis of the influence of the degree of heterogeneity and of the functional format of the covariance structure of the permeability field on SWI, also in the presence of multiple pumping wells.

All data used in the paper will be retained by the authors for at least 5 years after publication and will be available to the readers upon request.

The authors declare that they have no conflict of interest.

The authors would like to thank the EU and MIUR for funding, in the frame of the collaborative international consortium (WE-NEED) financed under the ERA-NET WaterWorks2014 Cofunded Call. This ERA-NET is an integral part of the 2015 Joint Activities developed by the Water Challenges for a Changing World Joint Programme Initiative (Water JPI). We are grateful to Albert Folch, Xavier Sanchez-Vila and Laura del Val Alonso of the Universitat Politècnica de Catalunya and Jesus Carrera of the Spanish Council for Scientific Research for sharing data on the hydrogeological characterization of the Argentona site with us. Edited by: Bill X. Hu Reviewed by: Damiano Pasetto and two anonymous referees