Geophysical Research Letters

Natural free convection in porous media: First field documentation in groundwater

Authors


Abstract

[1] Natural free convection is a process of great importance in disciplines from hydrology to meteorology, oceanography, planetary sciences, and economic geology, and for applications in carbon sequestration and nuclear waste disposal. It has been studied for over a century – but almost exclusively in theoretical and laboratory settings. Despite its importance, conclusive primary evidence of free convection in porous media does not currently exist in a natural field setting. Here, we present recent electrical resistivity measurements from a sabkha aquifer near Abu Dhabi, United Arab Emirates, where large density inversions exist. The geophysical images from this site provide, for the first time, compelling field evidence of fingering associated with natural free convection in groundwater.

1. Introduction

[2] Natural free convection has been studied for over a century – but almost exclusively in theoretical and laboratory settings [Nield and Bejan, 2006]. This process is an effective mechanism for heat and solute transport that occurs over larger spatial scales and shorter time scales than diffusion. Concerns about energy resources and environmental pollution have led to an increased interest in density driven flow and free convection processes in groundwater systems and other natural porous media. Recent studies have shown the critical importance of these processes for dense contaminant transport [Koch and Zhang, 1992; Liu and Dane, 1996; Mao et al., 2006; Schincariol and Schwartz, 1990; Zhang and Schwartz, 1995], hydrothermal ore deposition [Coumou et al., 2008; Garven et al., 1999], and diagenesis [Sanford et al., 1998], as well as practical considerations for carbon sequestration [Riaz et al., 2006], nuclear waste disposal [Yang and Edwards, 2000], and brine reflux beneath salt lakes [Holzbecher, 2005; Rogers and Dreiss, 1995; Wooding et al., 1997]. Despite its importance, and the increasing number of theoretical, modeling, and laboratory based publications on free convection, it has not yet been conclusively detected in natural groundwater field settings [Simmons, 2005].

[3] The theory of unstable convective motion in porous media is well understood. Large contrasts in fluid density, due to differences in solute concentrations and temperatures, can cause fingering instabilities associated with unstable free convection. In these simple settings, when the critical condition for the onset of free convection is exceeded, theory predicts that nearly square circulations will develop with a steady state fingering wavelength equal to twice the thickness of the layer in which convection occurs [Diersch and Kolditz, 2002].

[4] The massive body of theoretical work and knowledge completely eclipses the very limited understanding of free convection processes in natural environments and, in fact, presupposes the existence of these phenomena in the field. Theoretical knowledge of free convective phenomena continues to grow in the absence of even a single reported study that directly demonstrates the existence of these processes in the field. Given the inherent complexity of these convective processes, direct measurement is virtually impossible using traditional measurements of the subsurface. It is therefore hardly surprising that field based evidence does not exist in support of the theoretical literature. A few studies have used secondary evidence to infer the existence of free convection including: 1) numerical simulations, 2) fluid flux observations, 3) calculation of a system's Rayleigh number, and 4) observed salt deficits in saline lakes. These secondary approaches, however, are often speculative and do not provide direct or conclusive evidence of free convection [Simmons, 2005].

[5] For the above stated reasons, the detection of free convection in field based settings would constitute a major advance in this field of geoscience research. It would provide increased impetus for further theoretical and field based study, demonstrate that free convection may be more common in nature than is currently believed, and generate critical new insights to link theoretical knowledge to natural phenomena. High-resolution field measurements of the subsurface are clearly needed to accurately resolve fingering patterns caused by the unstable free convection process.

[6] Electrical resistivity imaging (ERI) is a promising and emerging approach for measuring fluid conductivity variations in natural groundwater field settings with fine enough spatial resolution to detect free convection. This method works on the premise that fluid conductivity variations induced by salinity differences can be measured as changes in bulk electrical resistivity. Recent modeling and field studies have clearly demonstrated the capability of ERI to measure resistivity changes in highly saline environments [Amidu and Dunbar, 2008]. ERI has successfully characterized the distribution of saline and fresh waters in coastal settings [Kruse et al., 1998; Nowroozi et al., 1999; Tronicke et al., 1999] and an apparent density anomaly beneath an island in the Okavango Delta, Botswana [Bauer et al., 2006]. However, the complex spatial fingering patterns associated with free convection that are pervasive in theoretical and laboratory models (Figure 1) have not previously been detected.

Figure 1.

Representative examples of fingering associated with unstable free convection in groundwater from (a) laboratory experiments and (b) numerical modeling. Details of these studies are given by Simmons et al. [2002] and Simmons et al. [2001], respectively.

[7] Recently, rapid vertical mixing of groundwater through free convection has been proposed to occur for a sabkha (salt flat) system near Abu Dhabi, United Arab Emirates (UAE), based on an unusual tritium distribution [Wood et al., 2002]. In this paper, we evaluate the existence of free convection in this natural setting using ERI, and compare our field measurements with theory.

2. Methods

[8] The field site is located ∼5 km from the coast, 60 km west of Abu Dhabi (Figure 2). The sabkha in this area has a wedge-shaped profile that thins from ∼15 m near the coast to 11.5 m at the geophysical research site, and zero thickness at the proximal edge, ∼20 km from the coast. Paleo-channels, erosional remnants of underlying Miocene-age carbonates, and Pleistocene dunes cause local variations in thickness. The sabkha sediments below the water table consist of uniform, fine sand (0.16–0.22 mm) from reworked dunes. They are composed of detrital carbonates (60%) and quartz (35%), minor percentages of feldspar, anhydrite, and heavy minerals, with no detectable authigenic minerals. The material has a nearly homogeneous porosity of 0.38 and hydraulic conductivity of 1.0 ± 0.2 m/day [Wood et al., 2002].

Figure 2.

Location of the sabkha study area. (a) Regional setting, (b) geophysical research site, water sample sites (Table 1), and weather station, and (c) layout of geophysical survey lines.

[9] Chemistry data from the coastal area of the UAE show that the sabkha groundwater has a greater density than the water in the underlying Miocene carbonates (Table 1). Data from seven piezometers in this underlying unit were used to estimate an upward flux of 4 mm/yr into the sabkha [Wood et al., 2005]. Brine-saturated water collected on the sabkha surface after a rainfall event had very high density and TDS values (Table 1). Potential drivers for free convective instabilities in this system include: 1) sabkha waters overlying less dense Miocene formation water, and 2) episodic downward infiltration of higher density water after significant rainfall events that redissolve the sabkha halite crust. For both conditions, the Rayleigh number is orders of magnitude greater than the common stability criterion [Nield et al., 2008] of Rac = 4π2 = 39.48. Free convection is therefore expected to occur in this system (auxiliary material Text S1).

Table 1. Chemistry Data for Well and Surface Water Samples Within a 10 km Radius of the Research Sitea
 Number of SamplesTDS (mg/L)Density (g/cm3)
Surface water3394,0081.2799
Sabkha water33275,8101.1809
Miocene formation water2101,4531.0753

[10] Monthly climate data from World Meteorological Organization station 41217 (Figure 2) show that the 10-year (1998–2007) mean annual precipitation on the sabkha is 30.9 mm (97% occurs from October to April) with strong inter-annual fluctuations (σ = 25.9 mm). Two unusually large precipitation events in 2007 and 2008 set the stage for our field investigations from March 3–6, 2008. A 50.0 mm event on October 23, 2007, was followed by 55.9 mm of precipitation on January 15 and 16, seven weeks prior to our field campaign (an additional 8.1 mm fell from January 12–14). The last time an event larger than 30 mm occurred was in November 1998.

[11] The average evaporative flux from the sabkha is approximately 60 mm per year [Wood et al., 2002]. Since the average annual precipitation over the last decade has only been 52% of this flux, it is reasonable to assume that a significant mass of salt accumulated in a near surface crust. The water in the sabkha within a 10-km radius of the research site has an average TDS of 275,810 mg/L (Table 1). The dominant ions in solution are sodium (84,627 mg/L) and chloride (164,133 mg/L), confirming that halite (NaCl) is the most common salt that precipitates near the surface.

[12] Based on the 60 mm of average annual evaporation, the annual deposition of sodium, which is the limiting ion for halite deposition, per square meter can be estimated using 60 L × 84,627 mg/L = 5.08 kg Na. Using the weight for the equivalent amount of chloride (7.83 kg) and the density of halite (2.16 g/cm3), we can calculate the maximum volume of halite deposited per square meter as 5976 cm3 or ∼5.98 mm per year. The amount of halite available for redissolution at the surface would be reduced by eolian transport and any overland flow that may occur during large precipitation events. This simple halite mass balance and the low average annual precipitation over the last decade clearly illustrate that there is sufficient salt stored in the crust and unsaturated zone to create hypersaline brines during the October 2007 and January 2008 precipitation events.

[13] The sabkha system was characterized using ERI by introducing current into the ground with a pair of electrodes, while measuring the potential field with separate pairs of electrodes. The measured bulk resistivity is primarily a function of porosity, moisture content, temperature, and fluid conductivity. We used multi-electrode arrays to measure the apparent subsurface resistivity distribution in two dimensions. These apparent resistivity data are inverted to estimate the resistivity distribution at a site. The sabkha system was also characterized using electromagnetic (EM) methods, as well as measurements of water table depth, salinity, electrical conductivity, and soil temperature.

3. Results

[14] Two-dimensional ERI images were collected using three arrays of 84 ten-cm long graphite electrodes that were carefully installed into the sabkha sediments (Text S2). Array a-a′ with 1 meter electrode separations was oriented roughly parallel to the coast; two perpendicular arrays were installed 2 meters apart with electrode separations of 1 m (b-b′) and 0.5 m (c-c′), respectively (Figure 2). EM data were collected along both a-a′ and b-b′ lines using a 1-m measurement interval. The ERI data were collected using dipole-dipole, pole-dipole, and pole-pole arrays. Here we focus on the results for the dipole-dipole array, which is most sensitive to lateral variations [Dahlin and Zhou, 2004].

[15] All three multi-electrode dipole-dipole datasets from the site show several characteristic features (Figure 3). The highest electrical resistivity values were measured in the top ∼0.75 m (vadose zone). The resistivity then quickly drops to a minimum at 2.7 m depth for the arrays with 1 m electrode spacing, and 1.7 m depth for the array with 0.5 m electrode spacing due to increased resolution. Several vertical structures originate in this 2 to 3 meter thick low-resistivity zone, protrude into a more resistive background, and extend to the bottom of the sabkha aquifer. The pole-pole data show that the zone below the sabkha aquifer is even more resistive (Text S3).

Figure 3.

Inverted resistivity images from dipole-dipole resistivity surveys. (a) Section a-a′ and (b) section b-b′ with a 1 m electrode spacing; (c) section c-c′ with a 0.5 m electrode spacing (different scale). The logarithmic color scale shows both resistivity (ρ) and its inverse, electrical conductivity (σ). A maximum resistivity of approximately 0.7 Ωm was measured in the shallow unsaturated zone with the 0.5 m electrode separation in c-c′. The minimum resistivity estimate is 0.16 Ωm near 2.7 m depth in both a-a′ and b-b′; the more resistive background has a maximum of 0.39 Ωm at approximately 5 m depth in a-a′.

[16] The resistivity images (Figure 3) have similar character as laboratory and numerical results for free convection (Figure 1). The lateral wavelength of the resistivity anomalies below 5.2 m depth is 11.25 m based on spectral analysis [Kendall and Hyndman, 2007], which is nearly half the value predicted by a steady state circulation in a 10.75 m thick zone of circulation. At shallower depths, the imaged anomalies have multiple shorter wavelengths. The differences in solutions at survey line intersections (Figure 3) illustrate smoothing in the inversion and out-of-plane effects, which are likely due to the 3D nature of the subsurface anomalies.

[17] Several conceptual models may explain these field observations. The simplest model involves formation of fingers due to the two precipitation-induced redissolution events, which then migrated to different depths. An alternative conceptual model is that the precipitation-induced shallower fingers are superimposed on a pre-existing convection pattern. Such a pattern is hypothesized to exist due to continuous evapoconcentration of fluids in the sabkha aquifer overlying upwelling lower-density Miocene formation water, resulting in episodic or quasi-steady convection processes [Nield et al., 2008].

[18] It is important to note that the observed resistivity data are unlikely to be explained with other conceptual models, such as those that rely on textural heterogeneity and geological features at the site. Sampling and analysis from more than 400 wells in the sabkha aquifer show that the reworked sands are essentially homogeneous [Wood et al., 2002]. Therefore, the resistivity anomalies are most likely attributed to salinity variations of the pore fluid.

4. Conclusions

[19] Geophysical imaging shows a fingering pattern with lobe structures that descend to variable depths into the aquifer. Spectral analysis of the geophysical data suggests finger wavelengths similar to laboratory observations and numerical simulations. This pattern is consistent with fingering caused by redissolution of brine in the unsaturated zone after the precipitation events. However, we contend that in addition to the precipitation-induced shallower fingering, a pre-existing convection pattern is likely required to explain the observed deeper anomalies. We conclude that we have imaged anomalies that are caused by free convection at some point in their transient life cycle, and that multiple modes of free convection appear to be operating in this system.

[20] This paper, for the first time, presents compelling field evidence of free convection fingering in a groundwater system. Unlike previous studies, our results show a complex spatial pattern of fingering that bears striking similarity to gravitational instabilities that have been observed for over a century in classical theoretical and experimental work as well as numerous contemporary modeling studies of flow in porous media. This geophysical dataset provides unprecedented documentation of the complex fingering pattern associated with free convection in a natural aquifer system. Exploring the three-dimensional characteristics and the transient nature (onset, growth, persistence, and decay) of free convection processes in groundwater field settings is an important area for future research.

Acknowledgments

[21] We thank Kamal Al Aidrous (NDC, UAE) and David Clark (USGS) for facilitating the fieldwork, Mohamud Giama (NDC), Abdel Hamid Osman (NDC), and Duncan Sibley (MSU) for field assistance, Yaoguo Li (CSM) for lending equipment, Abby Norton (MSU) for help with drafting, and three reviewers for their constructive comments. Support was provided by NSF (EAR0903508).

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