A Versatile Workflow for Building 3D Hydrogeological Models Combining Subsurface and Groundwater Flow Modelling: A Case Study from Southern Sardinia (Italy)

Abstract

This research project aims to develop a basin-scaled 3D hydrogeological model by using Petrel E&P (Petrel 2021©) as the basis for a numerical groundwater flow model developed with “ModelMuse”. A relevant aspect of the project is the use of Petrel 2021© geologic modelling tools in the field of applied hydrogeology to improve the details of both hydrogeological and numerical groundwater flow models, and their predictive capabilities. The study area is located in South Sardinia (Campidano Plain), where previous hydrogeological and modelling studies were available. The hydrogeological model was developed by digitising and interpreting the facies in the available borehole logs; a grid was subsequently created, including the main hydrogeological surfaces and performing geostatistical modelling of the facies based on grain size percentages. Afterwards, an empiric formula, achieved from flow tests and laboratory analyses, was applied to the grain size distribution to obtain preliminary hydraulic conductivity values, calibrated during simulations. These simulations, under various groundwater head scenarios, established the boundary conditions and conductivity values needed to determine the hydrogeological balance of the study area. The probabilistic approach has produced a highly detailed model able to adequately represent the natural hydrogeological phenomena and the anthropic stresses in places underground.

1. Introduction

Shallow clastic granular sediments overlying the bedrock host key groundwater resources. Urban concentration and industrial clusters lead to increasing pressure on these aquifers in terms of both abstraction and environmental alteration [1,2,3,4,5]. Groundwater resource management needs to be assessed from a quantitative perspective using numerical flow models. The use of groundwater modelling has become prevalent in the field of environmental sciences where all stakeholders (e.g., academic and research organisations, public administration, industry and farming) aim to streamline the use of aquifer resources [6,7,8,9,10]. However, these clastic aquifers often show an intricate three-dimensional combination of interlayered gravel, sand, silt and clay, resulting in heterogeneous and anisotropic hydraulic properties, e.g., hydraulic conductivity (K), which are difficult to predict [11,12]. Therefore, stratigraphic characterisation is necessary to implement realistic numerical groundwater flow modelling in natural settings and to allow sustainable exploitation of water resources [13,14,15,16,17]. However, the construction of 3D hydrogeological models for clastic aquifers remains a major challenge for stakeholders because of the difficulty of collecting large amounts of hydrostratigraphic information [18] despite their significant development advances in recent years. Two primary approaches have been traditionally used for developing conceptual models: (i) the consensus model approach [19,20] and (ii) the multi-model approach [20,21]. The construction of conceptual models depends on available geological and hydrogeological data such as field observations [22,23], geophysics [24,25], borehole analysis and the definition of a depositional model providing a conceptual architecture of the sedimentary stratigraphic system [10,26,27]. In case of scarce data availability, the multi-model approach represents the best solution, since it can interpret the hydrogeological functioning of the aquifer system in different ways [20,21,28,29,30]. However, in recent years, the use of probabilistic approaches has significantly increased in the field of hydrogeological modelling, particularly when data are sparsely distributed in the study area [31,32,33,34,35,36,37].

In this paper, the case study (Capoterra Plain, Sardinia, Italy) is focused on a coastal aquifer, made up of marine and alluvial sediments. This aquifer underlies historical saltworks, which have been included in a protected natural area in recent years. Groundwater management requires numerical flow models, the usefulness of which strongly depends on the accuracy of hydrogeological characterisation [38,39]. The first step of the workflow consisted of the analysis of all available data (borehole logs) in relation to the regional geological context in order to define the stratigraphic framework. This represented the base for a 3D hydrogeological model, resulting from the geostatistical modelling of granulometric facies distribution and the integration of heterogeneous hydraulic properties (e.g., hydraulic conductivity). The hydrogeological model was implemented using software (Petrel 2021©) commonly used for oil and gas exploration [40,41], while ModelMuse was used for the numerical models; finally, boundary conditions controlling the hydrogeological balance of the study area were defined.

With respect to other studies that have been focusing on the use of Petrel 2021© as a tool for the development of hydrogeological units [42], the innovation of this project lies in the application of Petrel 2021© for the definition of a more detailed 3D hydrogeological model with a probabilistic hydraulic conductivity distribution nested into the hydrogeological model, which is then reproduced into the groundwater flow model, which is able to improve its predictive capabilities.

2. Geological and Hydrogeological Setting

The studied area is located in the southwestern portion of the Campidano Plain [43], which represents the largest flat surface in the Sardinia region (Italy) (Figure 1A). The area is delimited by a large NW-SE trending graben structure and is bounded to the east by a vast lagoon, to the west by hills, and to the south by the Tyrrhenian Sea. The river network is represented by torrents with a strong seasonal behaviour (i.e., Flumendosa and Cixerri rivers). The climate is Mediterranean, which is characterised by mild and humid winters and hot and dry summers.

2.1. Geological Setting

Sardinian rocks preserve the record of geological evolution during the entire Phanerozoic era [44,45,46,47,48,49]. Born as a passive margin of the Gondwana continent, Sardinia records the opening of the Rheic Ocean followed by the Variscan orogeny and the re-organisation of Pangea until the Permian time [50,51,52,53,54,55,56,57,58,59]. In the Mesozoic, the island mainly acted as a passive margin of the Tethys Ocean and it was marginally involved in the Alpine orogenic phase [60]. The post-Alpine evolution is marked by the opening of the Liguro-Provençal and Thyrrenian basins (Oligocene–Miocene), driving the drift of the Corsica-Sardinia block from the European margin to the present-day location [45,46,61,62,63,64,65,66,67].

The study area is located in the southwestern portion of the Campidano Plain, which is shaped into a graben formed during Oligo-Miocene times [43]. The graben is bounded by NW-SE trending faults reactivated during the Messinian [68] and the Plio-Pleistocene after the opening of the south Tyrrhenian basin [69,70,71,72]. The NW-SE trending faults display a Palaeozoic basement, which evolves into the mountain belts, while the infill is characterised by a sedimentary sequence of Oligocene–Holocene age (Figure 1B), where Quaternary sediments are expected to be at least 150 m thick, as shown by several borehole logs available in the Capoterra area [73] (Figure 2).

At the foot of mountain belts, Pleistocene–Holocene erosional piedmont deposits unconformably covered the Pleistocene (?)–Holocene alluvium (both included in the quaternary unit ‘Subsintema di Portoscuso’ belonging to the ‘Sintema di Portovesme’).

Pleistocene alluvium deposits are constituted by coarse gravel dominant on a minor sand–clay fraction. Where the bedrock crops out, these deposits have shown an erosional contact with the Paleozoic basement confirming erosion activity by the streams along the reliefs, which allows the definition of an alluvial fan depositional environment. Near the slopes, to the north, both the size of the clasts and the percentage of angular elements increase due to the short distance from the mountainous reliefs.

Holocene deposits include older alluvium and piedmont deposits covered by recent to present-day alluvium and marine deposits. The age of continental sediments can be easily assumed because of their succession with marine deposits, which are the only ones able to provide reliable dating based on fossil content. Ancient alluvium deposits, consisting of fan and alluvium sediments, are represented by conglomerates, gravels, and sands more or less packed, often in a silty/clayey matrix, while piedmont deposits are made up of coarse clastic material. Recent alluvium, which dominates the plain, includes alluvial, colluvial, aeolian deposits and littoral gravels; marine deposits are present along the coastline, while silty/clayey deposits crop out in the lagoon/saltworks area [45] (Figure 1B).

2.2. Hydrogeological Setting

The Capoterra Plain is characterised by two-aquifer systems [75,76,77]: (i) a shallow, phreatic aquifer about 30 m thick [73] and (ii) a multilayer aquifer, locally confined, about 100 m thick [73]. The first aquifer is mainly represented by recent alluvium deposits (Holocene) and terraced alluvium, while the second aquifer system is hosted in alluvium (Quaternary) characterised by a highly variable permeability, resulting in variation in local hydraulic conductivity due to internal facies heterogeneity [73,78]. In the easternmost part of the plain, a 10–25 m thick sandy/clayey lenticular layer separates these two aquifers [78]. The bottom of the deepest aquifer is instead characterised by a clayey layer to the east, corresponding to the transition with Miocene deposits, and by the crystalline basement to the west [78]. The fractured granite complexes in the western part of the plain, adjacent to the hills, represent the main source of water recharge [77].

Groundwater heads of the Capoterra Plain were the subject of previous studies. Figure 3 shows the comparison between groundwater contour maps for the shallow aquifer in January 1993 [79] (Figure 3A) and November 2008 [80] (Figure 3B). In both studies, groundwater heads decrease more or less regularly from the western sector towards the middle of the plain, with a W-E direction. Both groundwater contour maps indicate groundwater head depressions due to aquifer exploitation at least in two different areas, where groundwater heads decrease below the sea level. The first one is located on the northern side of the plain, while the second is located close to the saltworks and lagoon. Both interpolations show similar groundwater flow patterns.

The variation in the sedimentation inside the plain has produced discontinuous clayey levels, which reach the coastline but disappear towards the western part of the plain. Both aquifers are affected by saline intrusion, mainly due to large pumping rates linked to industrial activity combined with scarce meteoric input [81]. Figure 4 illustrates the average rainfall recorded by four meteorological stations in the study area. It is evident that precipitation has declined in recent years, especially during the rainiest months of the year, impacting the recharge of the aquifer. Furthermore, this variation in sedimentation gave rise to shallow clay lenses mainly distributed near the eastern part of the study area. Locally, these lenses can give place to perched aquifers.

3. Data and Methods

3.1. Data Source

The hydrogeological model was implemented by integrating surface mapping with information from lithological borehole logs. Surface geological data are derived from the 1:50,000 maps of the “Geological Map of Italy” (Carta Geologica d’Italia), specifically Capoterra [82], Assemini [74], Cagliari [83] and Pula [84] geological maps.

A total of 900 borehole logs were collected, of which 225 were from “Italian Institute for Environmental Protection and Research” (ISPRA) [85] and Sardinia Regional Environmental Agencies (ARPASs) while the remaining 675 were from private companies (Figure 5). The depth of the borehole logs is mainly limited to 15 m (42%) or between 15 and 30 m (43%) below ground level; only 15% of the boreholes reach greater depths, up to 187 m.

The database includes information on stratigraphy, granulometry and groundwater head information from wells and boreholes. Rough data were digitised and interpreted to identify the main granulometric classes based on the sediment lithological description. In detail, four main classes were defined: gravel, sand, silt and clay, each characterised by distinct hydraulic conductivity properties.

Groundwater flow model calibration was performed using groundwater head measurements collected between 2018 and the end of 2023 from 6 different industrial sites (Figure 6) where regular measurements are carried out and rainfall/climate data from four weather stations located in the study area, managed by ARPASs [86].

Figure 6 shows groundwater head seasonal fluctuations at site 2 (yellow line) and site 4 (blue line), with the latter showing higher values (i.e., larger seasonal oscillation amplitude) during rainy periods. This can be explained by the different positions of the two sites, with the former being closer to the coastline and the base level represented by the sea, and the latter being located at a higher elevation, closer to the upgradient hydrogeological boundary of the aquifer, represented by the less permeable Metamorphic Variscan Basement outcrop (see site location in Figure 5. This allows the quantification of the width of seasonal groundwater head oscillations and therefore identifies the possible scenarios to be used as reference for numerical flow simulations. For model calibration, an average groundwater head scenario was defined and identified in April 2021 (green box, Figure 6).

Figure 7 shows the phreatic aquifer groundwater contour map designed using data collected in April 2021. The main groundwater flow direction (W-E trend) is coherent with previous studies (Figure 3B). In the western sector of the plain, the groundwater contour map shows two high groundwater head zones [80], which are not visible in the interpolated groundwater contour map. This difference is related to the spatial distribution of the data used during the interpolation process. This project used only groundwater head values collected within the industrial sites, whereas the Consorzio Industriale Provinciale di Cagliari (CACIP) data were built using monitoring well data distributed throughout the plain. The information from groundwater contour line of CACIP [80] study, situated along the western part, was used to tune the numerical groundwater flow model due to a lack of evidence in the database.

3.2. Sedimentological Model

Starting from boreholes and surface data, geological cross-sections were drawn. Previous studies on the stratigraphy of the plain of Capoterra did not include a detailed description of most recent Quaternary sediments but described the general depositional context [75,76,77], which is associated with the interaction between alluvial and marine environments (Figure 8).

The areas near the saltworks and Santa Gilla lagoon are characterised by the presence of lagoon deposits (Holocene) above terraced alluvial deposits (Holocene) (Figure 8, cross-section A-A’). The former sediments are mostly composed of silt and clay, occasionally sandy and gravelly, while the latter sediments are composed of mainly gravel and sand. Moving towards the centre of the plain, the depositional environment changes from an alluvial fan depositional environment to terraced alluvial deposits, showing fine material layers in the deep portions (Figure 8).

Below Holocene deposits, the ‘Subsintema of Portoscuso’ and ‘Subsintema of Calamosca’, part of the ‘Sintema of Portovesme’ occur (Figure 8). The ‘Subsintema of Portoscuso’, which characterises the centre of the plain, represents a continental deposit made of medium to coarse terraced alluvial gravels with subordinate sand and gravel, having a planar cross-bedding stratification [82]. On the contrary, the ‘Subsintema of Calamosca’ represents a sandy deposit with a bidirectional tidal structure, made of sparse mollusks (i.e., Astrea Rugosa, Conus sp., Glycymeris glycymeris, Arca noae). Cross-section A-A’ (Figure 8) exhibits fine sediments of tentative Pleistocene age, in accordance with the presence of the ‘Subsintema of Portoscuso’ [73]. These fine sediments were supposed to be of a Pleistocene age, different from available cartography data.

3.3. Conceptual Model

The conceptual geological model summarises all available data and information showing an impact on the hydrogeology of the study area and provides a framework for creating the groundwater flow model [28]. The conceptual model phase is crucial and required in most environmental studies to comply with government regulations. The conceptual model defines the basic details of hydrogeological systems (geometry, hydraulic heads, hydraulic conductivity, etc.), contamination history, chemical processes acting on the subsurface and all the other features that influence the hydraulic behaviour of the system. In order to understand the aquifer behaviour and simulate the groundwater flow, it was necessary to outline some boundary conditions (specified head and the specified fluxes) and a detailed hydrogeological characterisation of the aquifer system. While the initial conditions include the hydraulic head distribution—assumed on historical groundwater head values from monitoring wells—the hydrological conditions, set along the boundaries of the conceptual model, determine the mathematical boundary conditions of the numerical model [28]. Such boundaries influence the groundwater flow direction calculated as a steady-state numerical model [28]. For the numerical model described in this article, the following constant heads were defined: the sea condition to the east and south, with a value set to 0, and a condition in the mountainous zone located to the west of the plain, with values ranging between 4 and 35 m. A recharge boundary was also established, with its value determined by the average precipitation recorded in four meteorological stations during the analysed piezometric period. Finally, the pumping values of the wells in the area were defined as specified flux boundaries. The model was divided into layers based on borehole data and groundwater head values, with each layer assigned to distinct hydraulic properties. The result is a model characterised by a shallow aquitard (approximately 10 m below ground level), which locally supports a perched aquifer, and a second aquitard located about 20 m below ground level, dividing the phreatic aquifer into two separate portions: a shallow portion and a deep portion locally and partially confined. Hydraulic conductivity was assigned based on the grain size distribution of each layer, considering the heterogeneity of the area. The recharge zone is located in the mountainous part of the study area, where the fractured basement is exposed, while the main discharge zones are the sea and areas of pumping well activity.

3.4. Three-Dimensional Hydrogeological Model

The hydrogeological model is based on the lithological correlation and the preliminary definition of hydrogeological units based on similar hydraulic properties and behaviour. An aquifer system consists mainly of three key components: aquifers, aquitards and aquiclude. Using geological data sets and litho-logical correlation, driven by hydraulic properties, these components have been successfully reconstructed.

Petrel 2021© software [41] was chosen because it is a widely recognised software mostly used in the field of oil and gas and offers powerful capabilities in subsurface modelling. Using Petrel 2021©, a 3D hydrogeological model was developed by integrating the lithological units with their hydraulic properties. In particular, it provided a high computational power in the geostatistical simulation and allows the management of discontinuous layers (e.g., layers which pinch out) and grid creation. The grid created for this project consisted of 50 m × 50 m cells distributed over 20 layers, each with an extension of about 132 km².

The hydrogeological model was developed from a three-dimensional grid populated by importing facies data.

Elevation values of the surfaces, obtained by stratigraphic correlation, as described in Section 4.2, were assigned to the grid, creating a 3D model consisting of the following hydrogeological units: perched aquifer, Aquitard 0 (about 10 m from b.g.l.), shallow phreatic aquifer, Aquitard 1 (about 20 m from b.g.l.) and deep phreatic aquifer.

Using borehole log data, the predominant facies were identified within every single layer and for each borehole; afterwards, facies and corresponding hydraulic conductivity values were assigned and distributed throughout the rest of the model, selecting the most appropriate method for the modelling phase. After many tests, the “Sequential Indicator Simulation” method was selected for the modelling process, being a pixel-based (or cell-based) distribution methodology constrained by directional variograms. This method will calculate the best stochastic realisation of property based on the upscaled well observation, variograms and other input parameters. The size of the variable range of the variogram and the main direction will directly affect the results of the stochastic simulation. Based on the sedimentary background and source direction of the study area, a main range of 400 m × 400 m and a vertical range of 1 m were selected. The variogram correlates all the data included into the range. Finally, facies were distributed (using the facies data as starting point).

To maintain aquifer heterogeneity, grain size distribution was uploaded. The stratigraphic descriptions were converted into granulometric classes in compliance with the Italian Geotechnical Society (Associazione Geotecnica Italiana—AGI, 1977) guidelines. The simulation of the grain size classes, in % value, was nested within the previous simulation using the “Sequential Gaussian Simulation” algorithm (SGS) for each single facies code. The SGS method is a conditional simulation following a sequential principle under the multi-Gaussian random function model [87,88].

To define the distribution of hydraulic conductivity (K), a database was created gathering all laboratory and pumping tests, with a total of 104 records. Lithology associated with lab test was synthesised as per log description, while, for pumping tests, an equivalent lithology was considered (weighted average on thickness). The sum of clay and silt in % showed, as mentioned, the best correlation with hydraulic conductivity (K). The 3D distribution of K was obtained with SGS and a bivariate algorithm, nested within the previous granulometric distribution.

3.5. Numerical Groundwater Flow Model

The numerical groundwater flow model was developed using MODFLOW 6, which is supported by ModelMuse version 5.1.1, an open-source graphical user interface provided by the U.S. Geological Survey (USGS; [89]). MODFLOW 6 efficiently simulates groundwater flow. The governing equation for groundwater flow is formulated based on a control volume finite difference approach. This equation can be expressed in three dimensions, considering hydraulic conductivity in the x, y and z directions, specific storage and external inflow/outflow [90]. The general form of the governing equation is

$${\displaystyle \frac{\partial }{\partial t}}\left(S_{s}h\right)=\mathrm{\nabla }\cdot (K\mathrm{\nabla }h)+W$$

(1)

where

• h is the hydraulic head (piezometric level).
• S_s is the specific storage of the porous media.
• K represents the hydraulic conductivity tensor.
• W includes all external water sources or sinks (e.g., recharge, pumping) [90].

This equation describes the behaviour of water flowing through porous media and is based on Darcy’s Law for flow and mass conservation.

The specific parameters of MODFLOW 6 are described in

Table 1. Specific parameters of MODFLOW 6.

Parameters	Symbol	Unit	Description
Hydraulic head	h	[m]	Elevation of the water surface in a well
Hydraulic conductivity	K	[m/s]	Measure of the material’s ability to transmit water
Specific storage	Ss	[s−1]	Volume of water released from storage per unit declines in hydraulic head
Time step	Δt	[m]	Time increment for numerical solution
Spatial step (x, y, z)	Δx, Δy, Δz	[m]	Grid size in the x, y and z directions
Source/sink term	W	[s−1]	Rate of water entering or leaving the system.
Storage coefficient	S	[-]	Product of specific storage and aquifer thickness in confined conditions.

.

The choice of ModelMuse, along with Petrel 2021© for hydrogeological numerical modelling, was driven by their compatibility in grid type and indexing. Data on the grid, surface elevation, and hydraulic conductivity distribution of Petrel 2021© were directly transferred to ModelMuse. Unlike Petrel 2021©, which can handle pinch-outs (cell thickness equal to zero), ModelMuse requires minimum cell thickness (0.1 cm in this project grid). Consequently, the hydrogeological model grid was modified in order to assign a minimum thickness to these discontinuous layers, minimising the impact on interpolation steps.

The model has been set up as a steady state. The Specified-Head (CHD) package was used to simulate specified head boundaries, the Recharge package (RCH) was implemented to input recharge over polygonal area, and the well package (WEL) allowed to input of a pumping rate. In addition, the Observation Utility Package (OBS) was used to input observed head values (about 300).

After having identified the groundwater head scenario (Figure 4) and the choice of the different packages, the flow model calibration process was finally started by collecting groundwater head data.

4. Results

4.1. Hydrostratigraphic Model

Once the hydrogeological units were defined and correlated, hydraulic conductivity values were assigned (

Table 2. Sedimentological and hydrogeological units relationship based on the hydraulic conductivity value obtained by pumping tests and literature. (* https://www.sardegnageoportale.it/ (accessed on 25 May 2024) carta delle permeabilità dei substrati della Sardegna) [91].

Sedimentological Units	Prevalent Lithological Description	Hydraulic Conductivity (m/s) *	Hydrogeological Units
Lagoon deposits	Silt and silty clay	10−9	Aquitard 0 and Aquitard 1
Alluvial deposits	Sand	10−4	Perched aquifer, shallow phreatic aquifer, deep phreatic aquifer
Terraced deposits	Gravel with sandy layer	10−3	Perched aquifer, shallow phreatic aquifer, deep phreatic aquifer
Subsintema di Portoscuso	Gravel and sand	10−3	Perched aquifer, shallow phreatic aquifer, deep phreatic aquifer
Subsintema di Calamosca	Sand	10−4	Perched aquifer, shallow phreatic aquifer, deep phreatic aquifer

) on the basis of grain size distribution.

The lithological units result in a complex hydrogeological setting, featuring a multilayer aquifer in the western region transitioning to a phreatic aquifer in the lagoon and/or marine area and occasionally presenting a perched aquifer. Figure 9 shows the simplified hydrogeological model developed through two cross-sectional representations extending from a mountain area (west side) to the Santa Gilla lagoon (east side) and showing the transition from an undifferentiated aquifer to a multilayer phreatic aquifer. The western sector is characterised by a depositional environment associated with an alluvial fan and terrace deposits; in this area, no continuous clay layers in the first 30 m below ground level (b.g.l.) were identified. Going eastward, the marine deposition dynamic becomes relevant. In particular, clay lenses are predominantly observed near Santa Gilla lagoon, resulting in a more complex architecture of the phreatic aquifer, which is locally split into a shallow and a deep (locally confined) portion. Nevertheless, it is possible to find a perched aquifer locally. The interdigitation of sandy and clay layers could be explained by eustatic variations.

4.2. Hydrogeological Model

The hydrogeological model was developed using Petrel 2021©. Borehole log analysis and facies interpretation of the lithological data were carried out and imported into the software. Subsequently, the hydrogeological correlation process was performed (Figure 10). Following the data logs, two aquitards were correlated, also considering groundwater head values (Figure 10): a shallow aquitard (10 m b.g.l.) locally supporting a perched aquifer and a second aquitard located about 20 m b.g.l., dividing the phreatic aquifer into two separated portions (a shallow and a deep one, the latter locally and partially confined) (Figure 9).

The result of the facies distribution, using the “Sequential indicator simulation” algorithm and a variogram (400 m × 400 m), is the distribution of the five main facies classes, which were obtained from the description of the lithological logs (Figure 11).

Figure 12 illustrates the cells’ percentage distribution assigned to each lithology within the model, after the application of various processes. The figure highlights how these percentages evolve through different stages: from the initial state, when well logs were first imported, to the scaling-up process, and finally to the lithological distribution carried out by the algorithm. These changes in percentages are influenced by both the number of layers used in the model and their respective thicknesses. Generally, the greater the number of layers, the thinner each layer becomes, resulting in smaller variations in cell distribution percentages during the processing stages.

The comparison between Figure 11 and Figure 13 (the high percentage of fine material is represented with grey colouring) shows how the distribution of granulometric percentages is associated with the distribution of facies. It can be observed that a significant percentage (up to 40%) is modelled inside the coarse facies (sand and gravel) according to the log description confirming the high heterogeneity observed. The advantage of uploading the grain size distribution using the “Sequential Gaussian Simulation” algorithm (SGS) is its simplicity and effectiveness in generating numerical models with correct spatial statistics. For this part, the sum of clay and silt percentage was considered as a generic “fine material” since hydraulic conductivity showed a negative correlation with this parameter (see purple line, Figure 14).

The granulometric distribution that was previously achieved, which was added with the combination of SGS with a bivariate algorithm, was able to reconstruct a distribution of a given cross-plot. The results are represented in Figure 14, where the distributed geostatistical samples of the facies were visualised as the Z-axis. Figure 14 shows how the gravel and sandy facies are much more concentrated in proximity to higher hydraulic conductivity values and have a lower percentage of fine granulometry. The hydraulic conductivity distribution was achieved by applying the bivariate algorithm with the granulometric percentages of the silt and clay distributions.

By comparing Figure 13 and Figure 15, it can be observed that the areas with high silt and clay content (grey colour in Figure 13) correspond to those having a lower conductivity (blue colour in Figure 15). On the contrary, areas with a lower content of fine material (yellow colour in Figure 13) correspond to zones with a greater hydraulic conductivity value, which, in Figure 15, are represented by colours tending towards red.

4.3. Numerical Groundwater Flow Model and Calibration

The hydrogeological model represented the frame for developing the numerical groundwater flow model, which was implemented in ModelMuse, reproducing the three-dimensional grid of the hydrogeological model. Nevertheless, to avoid the possibility of having two or more monitoring or pumping wells in the same cell, a quadtree refinement was performed. Hydraulic conductivity data were imported into the numerical model.

To simulate the numerical flow model for an average groundwater heads scenario, a steady-state model with a starting time equal to “−1 s” and an ending time equal to “0 s” was set up. As far as boundary conditions, two Specified-Heads (CHDs, usually associated with the constant head boundary) were assigned, with the first with values ranging between 4 and 35 m on the western part of the study area and the second set at 0 near the sea coastline, to represent the sea level. Recharge (RCH) values were calculated using rainfall data during the selected period. The same process was applied to the WEL package data, assigning a specific pumping rate to each active well (approximately 150). Groundwater heads measured at the monitoring wells network (about 300) were imported using the Observation package.

By running the model, the hydrogeological balance and the simulated groundwater contour map were produced.

The calibration process of this scenario was obtained by minimising the difference between measured and simulated groundwater heads by a trial-and-error procedure: boundary conditions or conductivity distributions were iteratively modified to enhance the final calibration results. Figure 16 shows a cross-plot where measured groundwater heads are plotted on the X-axis, and simulated groundwater heads are plotted on the Y-axis. The purpose of this graph is to show how plotted values of individual monitoring wells deviate from a bisector of the second and fourth quadrants. The calibration results of the average head scenario are shown.

Figure 16 shows the calibration result of an average head scenario. A significant correlation between observed and simulated groundwater heads is noted. While sites 4, 5 and 6 are well represented with very low residuals, some groundwater head measurements at site 2 show greater residuals between the observed and simulated groundwater heads (Appendix A).

These monitoring wells measure the groundwater head of the phreatic aquifer, which is the focus of the study. Figure 17 shows the simulated groundwater contour map. The comparison with the interpolated groundwater contour map (Figure 7) indicates a good correspondence. Both contour maps show a W-E main flow direction, despite the NNW-SSE secondary trend in the southern sector. The hydraulic gradient is the same in both interpretations.

The comparison with the groundwater contour map carried out by CACIP [80] (Figure 3B) reveals some differences, mainly related to the different data sets used. As mentioned above, in this project, only groundwater head data collected within industrial sites were considered, whilst CACIP used data throughout the plain. This allowed us to explain the differences in the water contour line in the western area of the plain, where these data were not available for the selected period. Conversely, the site areas have better groundwater contour line details. Other differences are related to the increase in exploitation activities in the industrial areas in recent years.

The hydrogeologic balance of the plain flow model showed a difference of 0.15% between the calculated in- and out-flow rates. It must be stated that data regarding groundwater withdrawal related to agricultural activities, drinking use and other industrial activities were not available; hence, they were not included (Figure 18).

5. Discussion

The development of a 3D hydrogeological model, based on borehole data compared with the traditional groundwater modelling approach, allows the creation of a more detailed spatial distribution of the geometry and thickness of the underground system because it incorporates the direct observations of subsurface conditions. In addition, by applying the probabilistic approach, it is possible to produce a realistic lithological representation, even for areas where data are lacking.

Scaling up from a site model to a regional model requires a homogeneous database distribution across the entire study area. This is necessary to develop an accurate geological model. However, since most of the database, about 75%, comes from industrial sites, only 25% of the borehole logs cover the rest of the plain. The result gives a detailed simulation close to industrial sites but is less extensive in other parts of the study area. The use of Petrel 2021© was propaedeutic to mitigate the gaps related to the heterogeneous distribution of borehole logs. Using Petrel 2021© calculation’s ability, it was possible to produce a probable facies distribution, starting from borehole data, covering areas with missing information through geostatistical interpolation processes.

This hydrogeological model took advantage of a previous study performed in similar areas, such as the coastal plain of Arborea in western Sardinia [10], near the Gulf of Oristano in the western Campidano Plain. Both areas show a transition from a multilayer aquifer in the mountains to a phreatic aquifer in the coastal/lagoon area.

Developing hydrogeological models with accurate aquifer geometry requires both borehole and geophysical data. The hydrogeological model made in the Arborea area was executed using both data sets. The hydrogeological model of this study area, due to a lack of geophysical information, was constructed using a large amount of borehole data and implemented a lithostratigraphic correlation process.

The model has two main aquitards. Their local extent was determined via the depth to groundwater surveys at all industrial sites over five years (2018–2023). The groundwater flow in the Capoterra Plain is very complex due to the interaction between various depositional processes in the study area.

While well-known recharge and discharge areas have been previously described in hydrogeological models [64,78], this study developed a more accurate model, especially with respect to industrial sites. These sites allowed us to define the presence of layers and lenses of fine material, which greatly affect groundwater flow. Nevertheless, some groundwater head variations in historical trends could be explained by these small elements interrupting the vertical continuity of the main aquifer.

While the aquifers of the western plain area are probably hydraulically connected, the coastal area has instead a mostly continuous phreatic aquifer and perched aquifers. In particular, site 5 has a continuous low hydraulic conductivity layer at its base (about 20 m), separating the deep part of the phreatic aquifer from the shallow one. Another fine layer, about 10 m b.g.l., creates a perched aquifer in the central-south portion of the model.

In the literature, there are few cases where Petrel 2021© was successfully used with typical software for hydrogeological simulation (e.g., Visual MODFLOW flex 10.0 and FEFLOW 8.1.3). This is because Petrel 2021© is not directly compatible with other software, needing the creation of several workflows to share outputs among software, such as a customised MATLAB R2022b script [92].

In this article, Petrel 2021© and ModelMuse were selected because they benefit from a large computational capacity and share some similarities, such as the use of the same grid type and grid indexing. This allows the reproduction of a 3D model grid and the assignment of cell attributes (e.g., surface elevation and permeability) as outputs from Petrel 2021© to ModelMuse. Nevertheless, both software can easily handle typical outputs coming from GIS (i.e., shapefiles, .grd files).

However, there are some restrictions on communication, with the first being cell thickness management: Petrel 2021© has a high computing power and can manage unstructured grids with discontinuous layers, while ModelMuse cannot operate unstructured grids but can handle structured ones with a minimum cell thickness, even centimetres, to work properly.

Another difference is related to the grid refining approach, which can be used to match each pumping or monitoring well to a stand-alone cell, thus avoiding multiple points within the same cell. Petrel 2021© applies the refinement tools to entire rows and columns, while ModelMuse uses the Discretisation by Vertices approach, which can directly refine individual cells. Although the Discretisation by Vertices approach is powerful, the algorithm changes the new cell indications. For this reason, grid refinement was applied directly in ModelMuse and exported as centroids. Afterwards, a workflow was defined to share outputs and, at the same time, maintain the quality of the calculation performed by Petrel 2021© with the geostatistical algorithm.

By using software such as Matlab or Python, it is possible to develop a useful code to speed up the distribution of hydraulic conductivity based on ModelMuse’s grid refinement.

Model calibration is a necessary process for validating the geological model. Unfortunately, calibration requires multiple changes to the boundary conditions and vertical recharge (infiltration). In the beginning, input rainfall rates were the average among the values measured on the day before and after groundwater head measurement. Subsequently, the recharge value was obtained from the average precipitation that occurred in the range between the five days before and after groundwater head measurement.

Another boundary condition that was modified several times was the upgradient constant head. In this case, adjustments were made by changing the position and value of the constant head in the upgradient part of the study area. These changes were applied using the information contained within the reconstructed groundwater head contour maps that were developed interpolating groundwater heads measured during the Sardinia Region study (2009) [80].

The groundwater contour map comparison from 1993 to 2021 showed an increase in hydraulic gradient, mainly in the eastern area of the plain close to the lagoon and sea. A possible cause might be the increase in the active exploitation of groundwater within the plain. The main groundwater flow direction is W-E, even if a secondary one, NNW-SSE, was considered.

The simulated hydrogeological balance allowed us to check the aquifer state, including over-exploitation due to industrial and civil activities. However, to reach the best hydrogeological balance, it is necessary to have data related to all existing exploitation activities within the plain, which are missing at this stage of the project.

6. Conclusions

In this work, a robust approach was applied to derive a coupled hydrogeological and flow model using only borehole log and groundwater head data in clastic aquifers. The methodology was applied to the Capoterra Plain in Southern Sardinia (Italy), being a coastal aquifer marked by a highly heterogeneous distribution of mixed, alluvial and marine sediments.

The analysis of sedimentary rocks and the related depositional environments from the borehole logs allowed us to build stratigraphic sections for the studied area. The relevant aspect of this project is the use of Petrel 2021©, a software developed for oil and gas geological modelling, to create the hydrogeological model. In detail, Petrel 2021© was used to define the surfaces delimiting aquifer system units and distribute borehole log data within the hydrogeological model. To maintain the heterogeneity of the aquifer, granulometry percentages, obtained from the description of the lithological logs, were distributed according to the facies distribution. Afterwards, applying the bivariate algorithm, the hydraulic conductivity distribution was set up.

Consequently, ModelMuse was used to run the numerical flow model by importing the hydrogeological model previously created with Petrel 2021©. The numerical flow model of the study area was run after defining the boundary conditions. Model calibration by a trial-and-error procedure produced a good fit between the measured and simulated groundwater heads, highlighting the validity of the coupled hydrogeological and flow model. On the other hand, the model calibration also highlighted the interdependence of the groundwater head within the plain on the presence of multiple layers of fine sediments, influencing groundwater flow.

Overall, the combination of borehole log and groundwater head data allowed us to derive a robust coupled hydrogeological and groundwater flow model, as shown by the good fit of the calibration test. The final purpose of quantifying the hydrogeological balance at the basin scale and managing water abstractions has thus been significantly improved by adopting such software for the development of the hydrogeological model.