Salt dissolution potential estimated from two-dimensional vertical thermohaline flow and transport modeling along a Transylvanian salt diapir, Romania

The town of Ocna Mures, which is built around the salt diapir, is situated near to the western border of the Transylvanian Basin (Fig. 1). The basin consists of mainly Late Cretaceous to Late Miocene sediments (e.g. Krézsek et al. 2010; Tiliţă et al. 2013; Fig. 2). The salt diapir at Ocna Mures penetrated its cover of mainly shallow marine sediments and distinct tuff layers and reached a near surface position. The Quaternary cover is dominated by alluvial sediments of the post glacial river systems including the River Mures. The diapir itself evolved from a salt layer of early Badenian age (e.g. Ciulavu et al. 2000). Boreholes documented a base of the salt diapir in a depth between 1,000 and 1,700 m. The sedimentary rocks adjacent to the salt diapir are of middle to late Miocene age. They consist mainly of marls, sandstones, claystones and tuff units. While at Ocna Mures marls are dominating they are successively influenced towards the east by an increasing sand content forming intercalations of sandstone in the Middle Miocene (Fig. 2). The lithostratigraphic column of the Transylvanian Basin describes four sandstone units in between the distinct tuff layers “Hadareni” on top, and “Borsa–Apahida, Iclod, Turda” at the base (Tiliţă et al. 2013). Freshwater springs have been described within sandstone layers east of Ocna Mures, indicating the possible presence of smaller sandstone aquifers within the Miocene marls (Posepny 1867).

The Ocna Mureş salt diapir is, unlike many other salt domes (e.g. Murray 1966), also characterized by an almost complete lack of a caprock cover. This could possibly be explained by the very high content of NaCl within the salt dome (over 98%; Stoica and Gherasie 1981), because caprocks are often an accumulation of less soluble minerals contained in the salt. The lack of less soluble minerals such as calcite, anhydrite/gypsum and clay would also result in a higher vulnerability of the diapir flanks to salt dissolution from subsaturated fluids.

Huismans et al. (1997) acknowledged a compressional tectonic origin of salt diapirs structures in the Transylvanian Basin. However, no structures have been found in the field to document the stress field responsible for the diapirs. Distinct faults are not known in the area of Ocna Mures, but interpretation of seismic sections (Krezsek and Bally 2006; Onac 2010) crossing the Ocna Mures–Turda anticline indicate an eastward dipping thrust at which the diapir was possibly initiated, and which could border the Ocna Mures diapir along its eastern flank. A possible thrust of Miocene age, combined with a diapir rise may have led to a geomechanical weakening of sediments adjacent to the salt diapir. A possible increase of effective vertical permeability due to vertical faulting near rising salt domes together with groundwater being channelled along such faults has been discussed also by Evans and Nunn (1989). Therefore, the conceptual hydrogeological model used for the thermohaline simulations assumes for most scenarios a fault zone, which is hydraulically more permeable along the eastern border of the diapir.

The developed geological 3D model of the salt dome area includes all relevant available geological information in the area such as existing maps and cross-sections (Posepny 1867), borehole data, and geological publications of the Transylvanian Basin and forms the base for developing density-dependent groundwater flow and transport models. The model includes the structure of the salt diapir, the bedrock surface of the Quaternary unconsolidated rocks, the bottom structure of the saline lakes on top of the dome, and the structure of the Lake “Plus” southwest (SW) of the salt dome. Three tuff “lead” horizons within the Miocene bedrock units were modeled to estimate the internal structure of the Miocene sediments adjacent to the diapir. Of main interest for hydrogeological modeling was the layering of sandstone layers within the Lower Sarmatian sediments (Fig. 2) due to their possibly increased hydraulic conductivity compared to the marls.

Based on topographical maps and on 24 2D cross sections, the six mine structures Stefania, located in the southeastern of the Ocna Mures diapir, Ferdinand, Francis and Josif (southwestern part of the diapir), 6th Martie (northwestern part of the diapir), and the Mine 1st Mai (northern part of the diapir) were constructed (Figs. 3 and 4). The mining chambers are mostly located in a zone in between 50 and 150 m depth below the top of the diapir. A horizontal model cross-section at 100 m depth shows that mine chambers Stefania in the southeastern part of the diapir were excavated the closest to the side walls of the diapir (Fig. 3b). Some of the southeastern edges of the chambers were even excavated into the marls outside of the diapir, and almost below the 2010 collapsed structure of Lake Plus. A NNW–ESE striking vertical cross-section through the diapir and the 2010 formed Lake Plus was extracted from the 3D model and used as a conceptual model for the development of the 2D thermohaline groundwater model scenarios (Fig. 4).

Aims of the 2D vertical density dependent flow and transport model were to investigate the possibility of density-driven thermohaline flow along subvertical fault zones of higher permeability next to the salt diapir, and the potential for subsaturated groundwater to dissolve the upper sides of the diapir. Due to the fact that former mining chambers in the SE (southeast) of the diapir were excavated very close to the boundary of the diapir, the potential for collapse of the side walls is higher in the SE of the diapir up to depths of more than 100 m. Different scenarios of 2D vertical flow and transport models were developed, which differ in (1) hydrogeological properties of permeable sandstone units in the Miocene sediments, of (2) the fault zone next to the diapir, and (3) the hydrostatic pressure imposed on permeable sandstone units and the fault zone. The scenarios were set up based on a WNW–ESE-striking 2D cross section through the diapir, the Lake Plus, and approximately 3,000 m into the Banta Hills, with a maximum depth of 1,300 m below sea level, and a maximum height of 425 m asl (“above sea level”; see also Figs. 3b and 4). The spatial location of the 2D cross section was based on the following criteria: (1) to explore potential salt dissolution at the likely most vulnerable section of the salt dome flanks, which, according to the 2010 collapse leading to the formation of Lake Plus, is located in southeastern part of the dome and includes Lake Plus; (2) to include the modeled structures of the sandstone layers east of the dome due to their potential capacity to bring more “corrosive” freshwater close to the southeastern flanks of the salt dome; and (3) to extend the 2D section towards the ESE for up to 3 km in order to include the groundwater recharge area of the Banta Hills located SE of the dome. Groundwater recharge from comparably higher topographic elevations might explain overpressure, which creates increased flux of freshwater towards the flanks of the diapir.

The limitation of 2D for the presented groundwater flow and transport scenarios is firstly due to the necessity to limit the number of unknown parameters in an area, where data on hydrogeological processes in the subsurface are very sparse. Secondly, simulation of density-driven thermohaline flow and transport on a larger regional scale with high density contrasts presents a challenging task even at the 2D scale. Finally, the chosen direct path from the flanks of the salt dome to the Banta Hills increases the possibility that the main direction of regional groundwater drainage towards the salt dome is parallel to the cross section.

The governing equations of variable-density fluid flow, mass, and heat transport were solved with the finite element software FEFLOW v6.2 (Diersch 2014). The 2D vertical models had between 20,000 and 25,000 triangular finite elements, depending on the scenario and the required mesh density for numerical stability: resulting sizes of triangle sides varied between less than 1 m to close to 50 m. Smaller elements with sides typically below 5 m were in and close to zones of higher hydraulic conductivities and, therefore, also were the highest density contrasts occurred (fault zone, sandstone layers, alluvials; Fig. 5a). The authors found that full upwinding was the only appropriate numerical scheme to face numerical oscillations and to ensure convergence of the solution. The typical drawback of the scheme, which is numerical dispersion (Diersch 2014), has been regarded as being of less importance, due to the fact that numerical dispersion is expected to be more important regarding the larger-sized elements, which are not located in areas where salt dissolution is simulated (boundary condition along upper parts of salt dome), and where the salt flux is higher (zones of higher hydraulic conductivities, see the preceding text). The density variation of the groundwater was coupled to the fluid concentration of rock salt NaCl, which resulted in a density range from 1,000 kg/m³ (0 g/l NaCl) to 1,200 kg/m³ (300 g/l NaCl). Viscosity variation of the fluid is calculated depending on simulated pressure, temperature and NaCl concentration with a relationship suggested by Diersch (2014), which is based on previous work from Lever and Jackson (1985), Hassanizadeh (1988), and Mercer and Pinder (1974).

The presented simulated scenarios were selected based on the idea to study the effect of unknown parameters such as hydraulic boundary conditions and hydraulic conductivities on salt dissolution at the vulnerable parts of the salt dome. Scenario 1 represents the model with the initial estimates of distribution of physical parameters and boundary conditions. Scenarios 2 and 3 differ from the initial scenario 1 with the variation of 1st type boundary condition for hydraulic head in order to explore the effect of under-, or overpressure within the fault zone and the sandstone layers. The next scenarios 4, 5 and 6 all focus on the effect of different (unknown) physical properties by lowering the hydraulic conductivities of the sandstone layers and the fault zone by up to two magnitudes. In addition, a scenario 1.1 with the same boundary conditions and model parameters as the initial scenario 1 was simulated with constant viscosity in order to estimate its effect on the simulated salt fluxes along the relevant upper 180 m of the diapir (see also section ‘Results on near-surface scale’). Similarly, a scenario 1.2 with different geothermal parameters compared to the standard scenario 1 was simulated to study the estimated effect of (unknown) geothermal parameters on the resulting salt fluxes.

Model boundary conditions for fluid flow are prescribed head along the top of the model and follow the topographic elevation of the Banta Hills from 3 m below (topographic elevation) in valleys to 6 m below on hilltops, respectively (Figs. 4 and 5a). This approach was considered most appropriate considering the fact that no field data for groundwater recharge were available, and it follows basic approaches for regional groundwater flow (e.g. Hubbert 1940). Possible simulated flux errors due to the unknown effective piezometric head were considered of less relevance due the low permeability of the underlying marls (i.e. K = 1.0 × 10⁻⁹ m/s), which results in small simulated fluxes. The four permeable sandstone units and the fault zone along the diapir were assumed to be 10 m wide. Both the four more permeable sandstone units and the fault zone have prescribed hydraulic heads at its east-southeastern end which are either (scenario 2) equal to the topographic elevation at that location, or are overpressured with prescribed heads of 350 m asl (scenario 1) and 500 masl (scenario 3). The 500-m asl overpressure from scenario 3 assumes a lateral hydraulic connection of the more permeable sandstone and fault zone units with the highest elevations of the Banta Hills, which in fact are located a few kilometers south of the studied cross section. The 350-m asl overpressure from scenario 1 corresponds to an average elevation of the Banta Hills. The highest elevation of the Banta Hills within the studies cross section reaches 425 m asl (Fig. 4).

Boundary conditions for mass transport are a prescribed concentration of 300 g/l for the top of the halite of the diapir all along the bottom of the model, which corresponds to a maximum density of 1,200 kg/m³. Similarly, boundary conditions for heat transport are a prescribed temperature varying from 15 to 60 °C along the diapir, which corresponds to an average geothermal gradient of 30 °C/km depth increase.

Physical rock parameters were based on estimates for similar-type rocks, but could not be verified with field measurements at the site, except for conducted pump tests to estimate hydraulic conductivities of Quaternary sediments. For scenario 1, model parameters of hydraulic conductivities are K = 1.0 × 10⁻⁵ m/s for the Quaternary alluvial foothill sediments (in the upper left model corner), K = 1.0 × 10⁻⁷ m/s for the Miocene sandstone units, and the fault zone along the diapir, and K = 1.0 × 10⁻⁹ m/s for the Miocene marls, respectively (Table 1). Uniform values have been assigned to the porosity (0.1), longitudinal dispersivity (10 m), transverse dispersivity (1 m), rock volumetric heat capacity (3.0 × 10⁶ Jm⁻³ K⁻¹), and rock thermal conductivity (2.0 Wm⁻¹ K⁻¹). Both rock volumetric heat capacity and thermal conductivity were lowered by 33% in scenario 1.2 in order to estimate these parameter sensitivities on simulated salt fluxes. Initial conditions for hydraulic heads, salt concentrations, and temperatures within the model domain were all set to 0. Simulation time was 10,000 years for all scenarios in order to reach close to steady-state conditions for thermohaline transport. To use the same geological 2D cross-section for longer simulations times has not been considered, also because geological boundary conditions around a potentially still-rising salt dome are nonstationary over longer time spans.

Results on the model scale are presented for scenarios 1, 2, and 5, because these scenarios show exemplary differences in hydraulic heads and salt concentration (Fig. 5). Distributions of temperature do not vary significantly between scenarios and follow the imposed temperature gradient from 15 °C at the top towards 60 °C at the bottom of the model section, e.g. for scenario 1 (Fig. 5e). Simulated hydraulic heads after 10,000 years reflect the imposed boundary conditions along the topography, which reaches up to more than 400 m asl in the Banta Hills (Fig. 5b–d). The increasing hydraulic head towards the model bottom in scenario 1, however, is due to the increasing fluid density, because the displayed equivalent freshwater heads as used by FEFLOW increase with the density ratio towards the bottom (Fig. 5b; see also Diersch 2014). The reason for the increasing density ratio is visible by comparing it with the significantly increasing simulated salt concentration at the same location towards the bottom (Fig. 5f). Imposing lower hydraulic heads equivalent to the topographic elevation like in scenario 2 creates an underpressure in the sandstone layers, and, moreover, in the lower part of the faultzone near the imposed boundary condition. Simulated concentrations after 10,000 years differ in between scenarios. As expected, highest concentrations up to saturation are simulated along the boundary condition along the flank of the diapir (Fig. 5f–h). Salinization within the model domain is dependent on the hydraulic boundary conditions imposed on the sandstone units of higher permeability: the lower imposed hydraulic head of scenario 2 leads to a “contamination” with denser saline water which propagates along the dip of the sandstone units, seeps towards the bottom of the model, and results in higher salinities in the lower model domain. Higher imposed hydraulic heads in the east of the sandstone units pushes freshwater along these units towards the upper part of the diapir reducing the fluid salinity and, therefore, increasing dissolution in these vulnerable parts (scenario 1, Figs. 5 and 6, and, even more so, scenario 3, Fig. 6). A scenario without any permeable sandstone units, and fault zone, respectively, results in a near-zero salinity in most of the model domain, except a very small and sharp concentration front along the flanks of the diapir (Fig. 5h).

The upper 180 m along the eastern flanks of the diapir represents the area suspected to be prone to collapse hazards. To understand possible causes of collapse, flow patterns and distributions of salt concentration are presented with close-ups of this area (Fig. 6; see also the upper left model corner in Fig. 5a). The distribution of flow vectors at the end of the simulation offers a direct interpretation of flow patterns. For visibility reasons schematic flow vectors are used to summarize the nodal flow vectors simulated by FEFLOW after 10,000 years (white arrows in Fig. 6). The six scenarios are compared with the simulated salt flux from the prescribed concentration boundary condition along the upper (0–65 m), middle (65–130 m), and lower (130–180 m) part of the upper 180 m of the diapir, respectively. This corresponds also to the depths of former salt excavation chambers within the diapir (Figs. 3 and 4). Salt fluxes in g/day were integrated over each of the three parts at the end of the simulation time of 10,000 years for each of the scenarios. Integrated salt fluxes over the three parts Upper, Middle and Lower were sensitive to changes in the scenarios (Table 2). The salt fluxes were also converted to potential subrosion rates (mm/year) along each the Upper, Middle, and Lower parts of the diapir based on a density of 2,170 kg/m³ for halite (Table 2).

As expected, the simulated salt fluxes are strongly controlled by the exchange rate of groundwater along the boundary of the diapir, i.e. the access of freshwater towards the boundary of the diapir, and the transport of saturated saline water away from the boundary. Groundwater exchange is enhanced by the following factors: (1) increased hydraulic conductivity of the fault zone along the diapir, (2) a nearby connected larger freshwater reservoir like the more permeable Quaternary aquifer on top of the fault zone, and/or (3) larger pressure gradients due to boundary conditions representing increased regional groundwater recharge in connected sandstone layers. Salinity increase in the fault zone along the diapir typically leads to a downward flux due to the higher densities in almost all the simulated scenarios (Fig. 6). This results in a recharge of freshwater from the Quaternary aquifer on top, and, therefore, to increased salt fluxes, or subrosion in the Upper part along the diapir. Except if downward flux velocities are slowed down due to an upwelling of about equally pressured groundwater from the lateral sandstone units (scenario 1), or generally lower flux velocities due a decreased permeability in the fault zone (scenario 5). Larger overpressure in the sandstone units (scenario 3), or larger hydraulic conductivities in the upper part of the fault zone (scenario 6) lead to partly upward flow of freshwater in the fault zone, and, therefore to an increase of salt dissolution in that upper part, compared to the middle, or lower parts, respectively. Highest salt fluxes are simulated in the upper part when the sandstone units are underpressured, inducing a downward flow in both the fault zone and sandstones, and a compensation of more freshwater recharge from the Quaternary (scenario 2). Similarly, the model without more permeable sandstone units (scenario 4) creates an undisturbed downward flux in the fault zone inducing increased access of freshwater from the Quaternary.

Results of two additional scenarios were used to test model sensitivities to salt fluxes for simulations with constant viscosity (scenario 1.1) and varied geothermal parameters (scenario 1.2) compared to the standard scenario 1 (Table 2). Lowering geothermal parameters of volumetric heat capacity and thermal conductivity affects simulated salt fluxes not more than 12%. Using constant instead of variable viscosity in thermohaline transport simulation, however, affects salt fluxes in the upper, middle, and lower part by up to more than 50%, respectively.

Corresponding potential subrosion rates differ largely in between 0.1 mm/year (scenario 5; all parts) and 85 mm/year (scenario 2; upper part). All model scenarios, except scenario 1, indicate that the upper part is the most vulnerable to subrosion, and the lower part the less vulnerable (except scenario 5).

The Ocna Mures study site offers almost no relevant data of hydraulic heads, salt concentration, or temperature distribution within the 2D vertical model domain for model calibration, or even model verification. However, measurements have been collected within the Quaternary aquifer, which is included in the upper few meters in the WNW corner of the 2D model scenarios. Because predominant groundwater flow in the Quaternary alluvials is horizontal, most of these measurements are influenced by flow directions not parallel to the 2D vertical plane of the model scenarios. Measured piezometric heads in well 5200, which is located less than 50 m southeast of saline Lake Stefania, and about 100 m south of saline Lake Plus (Fig. 3b), show values which are significantly higher than stage levels in both nearby lakes (Fig. 7), and also surrounding piezometers. Therefore, the authors assume that recharge to well 5200 is strongly influenced from saline vertical upwelling along the diapir, and within a possible fault zone. The projected model location of well 5200 is also approximately 300 m away from the nearest imposed 1st type boundary condition (of 257.00 m asl). Simulated piezometric heads and salt concentrations from model scenarios 1–6 and a model depth of 4 m are compared with measurements taken in 2014–2015 at a well depth of 4–5 m (Fig. 7). Simulated values of salt concentrations vary between 50 and 240 g/l (average measurements well 5200: 148 g/l), and simulated piezometric heads between 252.30 and almost 260 m asl (average measurements well 5200: 257.10 m asl). Scenario 6 with its more permeable upper fault zone (K = 1.10⁻⁶ m/s) simulated almost the same values like the measurements. On the other hand, model scenarios with either strongly underpressured (scenario 2), or overpressured (scenario 3) sandstone layers under, or overestimate piezometric heads by up to 3 m, respectively. The model scenario with no permeable fault zone and sandstone units underestimates salt concentration by approx. 100 g/l, whereas model scenarios with overpressured sandstone layers (scenario 3), uniform fault zone hydraulic conductivity and average pressure on sandstone units (scenario 1) overestimate salt concentration by almost 100 g/l.