Multiphase flow in porous media has been the subject of intensive study for many decades, motivated, amongst other factors, by important economic considerations linked to the petroleum industry. Another field where interaction of pore fluids having different physical properties, which is of particular importance, is saline–freshwater systems. In this case, important density and viscosity differences between saline and fresh waters control the relative motion and mixing of the two phases. Characterizing and modeling these coupled flow and transport phenomena is a very challenging task, particularly in the presence of the hydraulic heterogeneities always present in natural porous media (e.g., Werner et al., 2013; Ketabchi et al., 2016).

The most common situation where saline–freshwater systems have practical environmental and socio-economic implications is related to seawater intrusion in coastal aquifers, often exacerbated by overexploitation of groundwater, particularly in arid and semi-arid regions such as those surrounding the Mediterranean basin (e.g., Kallioras et al., 2010; Rey et al., 2013; Dentoni et al., 2015). Another context where the study of saline–freshwater interactions is highly important is the injection and storage of freshwater in brackish or salty aquifers for later use in agriculture or for domestic purposes, also known as aquifer storage and recovery (ASR; e.g., Pyne, 1995; Dillon, 2005).

Many studies of density-dependent flow and transport phenomena in porous media have been conducted over the past decades (e.g., Gambolati et al., 1999; Simmons et al., 2001; Diersch and Kolditz, 2002). Instabilities and fingering can take place when denser water overlies lighter water (e.g., Simmons et al., 2001). Ward et al. (2007) gave an introductive literature review on density-dependent modeling, with a particular focus on ASR. The first studies on the injection of freshwater into a saline aquifer were performed by Bear and Jacobs (1965) and Esmail and Kimbler (1967). The latter investigated the tilting of the saltwater–freshwater interface, a phenomenon known as “buoyancy stratification”. More recent studies have analyzed the efficiency of ASR for both field and synthetic cases (e.g., Kumar and Kimbler, 1970; Moulder, 1970; Kimbler et al., 1975; Ward et al., 2007, 2008; Lu et al., 2011; Zuurbier et al., 2014). Ward et al. (2008) conducted a numerical study to evaluate the efficiency of ASR under density-dependent conditions with anisotropy and heterogeneity of high and low permeable layers. Van Ginkel et al. (2014) studied the possibility of extracting saltwater below the freshwater injection to prevent the spreading of freshwater at the top of the aquifer. Alaghmand et al. (2015) investigated fresh river water injection into a saline floodplain aquifer and developed a numerical model for the optimization of injection scenarios.

The behavior of saline–freshwater systems becomes increasingly complex with larger density and viscosity contrasts. To date, very little research has been done on the effects of freshwater injection in highly saline aquifers that can reach total dissolved solids concentrations of 100 g L-1. Understanding these complex systems is limited not only by the need to develop non-trivial coupled flow and transport models but also by the scarce availability of effective monitoring techniques. The latter are, under field conditions, typically limited to borehole measurements that can only provide point information in spatially heterogeneous hydraulic systems with time-changing salt concentrations.

As in many other subsurface characterization problems, a major contribution can be made by non-invasive, spatially extensive, geophysical techniques. In particular, electrical and electromagnetic methods are very suitable in the context of saline–freshwater interactions, since electrical conductivity varies over orders of magnitude depending on solute concentrations. While the use of these methods is common in seawater intrusion studies (e.g., Goldman and Kafri, 2006; Nguyen et al., 2009), only few studies have used geophysics to monitor ASR experiments. Davis et al. (2008) used time-lapse microgravity surveys to monitor the utilization of an abandoned coal mine as an artificial ASR site. Maliva et al. (2009) investigated the use of geophysical borehole logging tools applied to managed aquifer recharge systems, including ASR, to improve the characterization of aquifer properties. Minsley et al. (2011) developed an integrated hydro-geophysical methodology for the siting, operation and monitoring of ASR systems using electrical resistivity, time-domain electromagnetics and seismic methods. Parsekian et al. (2014) applied geoelectrical imaging of the subsurface below an aquifer recharge and recovery site alongside with hydrochemical measurements to identify preferential flow paths.

A major step forward in saline–freshwater systems monitoring can be made by improving the efficiency of advanced geophysical techniques, and electrical tomographic methods in particular. Electrical resistivity tomography (ERT) is widely used today in hydro-geological and environmental investigations. Often applied in tracer studies (e.g., Kemna et al., 2002; Vanderborght et al., 2005; Cassiani et al., 2006; Doetsch et al., 2012), ERT is a natural choice for saline–freshwater interaction monitoring, given the correlation between the salinity of a pore fluid and its electrical conductivity. Time-lapse ERT, where only the changes in electrical conductivity over time are imaged (e.g., Kemna et al., 2002; Singha and Gorelick, 2005; Perri et al., 2012), can be especially effective in tracking dynamic processes. Whereas tracer studies are typically designed with injection of a saline tracer into fresh surrounding groundwater, only very few studies have dealt with the inverse case of freshwater injection into a saline formation. For instance, Müller et al. (2010) conducted tracer tests also using a less dense tracer with lower electrical conductivity than the ambient groundwater, monitored with ERT.

The goal of this study is to present a general approach for the characterization, monitoring and modeling of complex saline–freshwater systems, based on the combination of non-invasive techniques and accurate numerical modeling. To our knowledge, no such a comprehensive hydro-geophysical approach concerning freshwater injection in saline aquifers has been presented so far in the scientific literature; thus, we believe this case study can be very useful as a starting point for other, more comprehensive methodological testing. In this study we limit ourselves to integrating field data and modeling in a loose manner, with no aim at this stage to develop a full data assimilation framework, as implemented elsewhere for simpler systems (e.g., Manoli et al., 2015; Rossi et al., 2015). The key message that can be derived from the joint use of advanced field techniques and advanced numerical modeling is nonetheless apparent in the presented case study, and more complete assimilation approaches are possible provided that the advantages and limitations of the individual components (data and models) are fully understood as shown in the present paper.

The approach is presented in the context of a case study where we injected freshwater into a hyper-saline aquifer in the Molentargius Saline Regional Park in southern Sardinia, Italy. The experiment was monitored using cross-hole time-lapse ERT. To investigate the mixing processes, the resulting ERT images are compared with the results of a synthetic numerical study of the same experiment. We consider here both homogeneous and heterogeneous (layered) systems. For a quantitative comparison between the field and synthetic studies, spatial moments of the freshwater bulb are calculated.

In order to investigate the behavior of the injected freshwater bulb, and assess in particular the influence of the subsurface hydraulic properties on the bulb evolution, we performed a synthetic study based on the field experiment. This was undertaken using a density-dependent flow and transport simulator. Given the computational burden of the simulations and our goal of examining in detail some of the governing parameters, we did not use a data assimilation approach at this stage, opting instead for analyses of specific scenarios. We considered four scenarios of hydraulic conductivity distribution, and compared the simulated results to each other and with the field evidence in order to gain some first insights on the dynamic response of the hyper-saline–freshwater system.

As a first step, let us consider the results of the synthetic study. Figure 10 shows the salt concentration of the flow and transport simulations for scenario 4, which represents the most complex parameterization of the aquifer and is assumed to be most realistic for the test site (see the site stratigraphy reported in Fig. 2). A general upward motion of the injected bulb is visible, with the highest velocities occurring within the injection hole. After some time, the freshwater starts to enter the aquifer along the entire borehole length. Although its density is much less than the density of the surrounding saltwater, the freshwater also moves downwards within the borehole, pushed by the pressure gradients. The 1.2 m thick fine-material layer also plays a clear role in the bulb dynamics. This is expected. In correspondence to this layer, the flow only takes place along the borehole and the backfill material. Above the fine layer the plume expands laterally into the aquifer. Also the transition between the saltwater and the upper freshwater layer above 7.4 m depth moves entirely upwards since the overall movement in the model domain is upwards. One can also observe in the simulation results the tilting of the freshwater–saltwater interface in the lower part of the borehole as well as below the groundwater level, as described by Ward et al. (2007, 2008). The higher the ratio of hydraulic conductivity between the two layers, the stronger is the tilting, as predicted by Ward et al. (2008) (results not shown here).

Figure 11 shows the inverted images for four different subsurface scenarios at time 4.2 h after start of injection for the flow and transport simulations and the synthetic ERT monitoring (see Table 2 for definition of the scenarios). The figure clearly shows the dramatic influence of the hydraulic conductivity distribution on the shape of the freshwater bulb, both in the “real” images and in the corresponding inverted ERT images. Scenario 4, which includes the fine layer, is closest to the field results as already discussed above. However, scenario 3, with just two layers, shows a similar behavior in terms of plume development. In general, given the strong influence that hydraulic conductivity has on the results, it is conceptually possible to try and infer the site's hydraulic properties on the basis of the freshwater injection experiment. However, it is also apparent that calibrating in detail the true hydraulic conductivity distribution in the field experiment starting from the ERT images alone may be a very challenging task. In fact, while some main features are clearly identifiable, other smaller details may prove difficult to capture.

Indeed, the governing hydraulic effect comes from the different conductivities of the upper and lower parts of the aquifer (scenarios 1 + 2 vs. 3 + 4), and the fine layer does not play such an important role as expected a priori. From the simulation results it is difficult to say whether scenario 3 or scenario 4 is closest to reality. However, for scenarios 1 and 2 ERT clearly overestimates the extent of the freshwater plume, whereas for scenarios 3 and 4 the plume extension is reconstructed quite well, in particular in the deeper region (Fig. 10).

It is instructive to examine in detail (Fig. 12) the similarities and differences between the ERT field data and the reconstructed ERT images from the simulation scenario that visually appears better than the others (scenario 4). The simulated ERT images show the same general behavior in response to the injection process and associated plume development as the ERT field results. In the field ERT images the freshwater body disappears much faster. After 24 h, although in the field ERT images the freshwater bulb is hardly visible, the simulation still shows its presence. It should be noted that in the simulations the boundary condition at the well is imposed as a Dirichlet (head) condition, so flux is computed depending on the applied head. We applied the head as actually measured in the injection tank. Consequently, the flow is never zero, not even at the end of the experiment. On the other hand, the tilting of the freshwater–saltwater interface as seen in the flow and transport model results is much less visible in the ERT images.

The imaged resistivity changes in the field experiment show less contrast than in the synthetic study. The salinity difference between the freshwater and the saltwater is very large and thus so is the NaCl concentration. Within this range, the electrical conductivity of the water might no longer follow a linear relation with concentration (e.g., Wagner et al., 2013), while here it is assumed to be linear. This can lead to a shifting in the contrast when the concentration is converted into electrical conductivity.

Note also that the gradual change of electrical conductivity in the transition zone (i.e., between 5 and 7.4 m depth) is not visible in the ERT images (Fig. 11). In the transport simulations it can be seen that this zone also moves upwards in the aquifer and becomes thinner (Fig. 10).

Another difference between the field and the synthetic ERT results is the sharpness of the freshwater body; the boundaries appear smoother in the field study. Although dispersion effects were not further investigated in this study, a higher value of αL and αV in the simulations would obviously lead to a smoother gradient across the plume boundaries. On the other hand, in the field results this may also be partly explained by the fact that one ERT measurement frame took about 40 min, and since the overall plume migration was relatively fast, the process is to some degree smeared in the inverted images.

Figure 13 shows the spatial moments (0th moment: total mass; 1st moment: center of mass) of the freshwater bulb for the field and synthetic ERT inversion results, as well as the “true” moments from the flow and transport model (see Sect. 3.3). The total mass is well recovered by the synthetic ERT results (using backwards the same Archie's law parameterization used in the forward modeling). However, the field ERT underestimates the total mass. While this is a known characteristic of moment analysis applied to ERT data for tracer tests (e.g., Singha and Gorelick, 2005), in this specific case it looks likely that the chosen Archie's law parameters are not fully adequate to represent the electrical conductivity–salinity relationship. Considering that even linearity of Ohm's law is questionable at the high salt concentrations observed at the site, one could also question the overall validity of Archie's law. Note that all other factors normally contributing to bad ERT mass recovery under field conditions are the same in the synthetic and the true case, and thus cannot be called into play.

In contrast to the total mass, the vertical center of mass is, despite some early oscillations, well recovered also for the field data. This, however, is known to be a very robust indicator (e.g., Binley et al., 2002; Deiana et al., 2007, 2008).

Overall, and in spite of the differences described above, the comparison between observed and modeled ERT images is satisfactory, particularly in the face of uncertainties concerning the heterogeneities of the real system that could not be investigated in extreme detail. In addition, we cannot exclude the possibility that the linearity of the current flow equation may be violated in such a highly conductive environment, thus leading to inconsistencies between field reality and theoretical assumptions.

Despite the above limitations, the comparison shows that ERT imaging is a viable tool for monitoring freshwater injection in a hyper-saline aquifer. This, by itself, was not an obvious result. The ERT dataset was collected under extreme, challenging conditions. Even so, the ERT data are of fairly good quality considering that we retained only data that passed a fairly strict reciprocity check, knowing that larger reciprocity errors are likely to be related to nonlinear current effects occurring in such high electrical conductivity environments. The study also indicates how an accurate coupled model can mimic in an effective manner the behavior of the observed freshwater bulb that was injected into the domain, and this too was not self-evident.

In this paper we present a hydro-geophysical approach that can be used to study freshwater injections in saline aquifers. In particular the approach is used to monitor and describe a freshwater injection experiment conducted in a hyper-saline aquifer in the Molentargius Saline Regional Park in the south of Sardinia (Italy). The experiment was monitored using time-lapse ERT in five boreholes. A numerical study of the experiment (density-dependent flow and transport modeling in conjunction with ERT simulations) was carried out to investigate the plume migration dynamics and the influence of different hydraulic conductivity parameterizations. The numerical algorithm of the coupled flow and transport model proved to be stable and accurate despite the challenging conditions.

The results demonstrate the feasibility and benefit of using a combination of (a) time-lapse cross-borehole ERT and (b) numerical modeling of coupled flow and transport to predict the same ERT results. The comparison between measured and simulated ERT images was used as the key diagnostics aimed at estimating the system's governing parameters and consequently describing the saltwater–freshwater dynamics. More sophisticated data assimilation techniques can be used to further refine the presented approach in future work. We can conclude from the present study the following: a.

The complex dynamics of hyper-saline–freshwater systems can be tracked using high-resolution spatially extensive time-lapse non-invasive monitoring. On the contrary, traditional monitoring techniques alone (e.g., conductivity logs, as in Fig. 3) give only a very partial image, largely inconclusive to understand the system dynamics.

Measured raw cross-borehole time-lapse ERT field data, additional field data, inverted ERT field data as well as the modeling data in terms of the concentration distribution of the density-dependent flow and transport model and the inverted synthetic ERT monitoring results can be accessed at 10.5281/zenodo.322630 (Haaken et al., 2017).