A high-resolution non-invasive approach to quantify oxygen transport across the capillary fringe and within the underlying groundwater
Research Highlights
► An innovative method to measure O2 at the unsaturated/saturated interface is presented. ► The mass transfer of oxygen at the interface is limited on the water-side. ► Very similar Dt-values in the capillary fringe and in the saturated zone are measured. ► Steep oxygen gradient starts to develop when water saturation is very high.
Introduction
During the past decades, considerable effort has been undertaken to deepen the understanding of the capillary fringe and how it may influence mass transfer between the vadose and the saturated zones. A consistent definition of the capillary fringe is difficult to find in the literature (Berkowitz et al., 2004). Generally, it is considered the transition zone between the unsaturated and the saturated zones, the lower boundary being the groundwater table, at which the water and the atmospheric pressures are identical. The upper boundary is less clearly defined: a rigorous definition limits the capillary fringe to the water-saturated zone directly above the water table, where the water pressure is smaller than the atmospheric pressure due to capillary forces, whereas an extended definition of the capillary fringe includes the tension-saturated zone and the contiguous variably saturated parts above. Referring to the latter description, the capillary fringe reveals gradually decreasing water contents toward higher elevations, eventually reaching field capacity (Caron et al., 1998).
The relationship between water content and matric potential at the interface between the vadose and the saturated zone can be described by several empirical models. Two parameterizations, with numerous modifications, are most commonly used: the Brooks and Corey, 1964, Brooks and Corey, 1966 and the van Genuchten (1980) models. Both models are based on the assumption that the volumetric water content θaq [−] ranges between a minimum, so-called residual water content θr [−] and a maximum value θs [−], denoted saturated water content, which is identical to the storage-effective porosity. The residual water content is considered to be confined to small pores, which do not necessarily form a continuous network. The effective water saturation Se [−], ranging between zero and one, normalizes the actual water content θaq to the scale between θr and θs:
The van Genuchten model assumes a gradual change of water content from the water table up to the unsaturated zone until residual saturation is reached, i.e.,where α [L−1] is the capillary pressure parameter, which can be estimated as the reciprocal value of the capillary fringe height. h [L] is the matric head (difference between air and water pressure heads; a negative quantity above the water table), and n [−] and m ≈ 1-n−1 [−] are shape parameters, usually obtained by fitting.
In contrast to the van Genuchten model, the Brooks–Corey model assumes that the soil pores remain fully water-saturated up to some distance above the water table as long as the matric potential is higher than a critical potential, i.e., the air-entry pressure of the largest pore. Such a fully saturated zone exists in very fine and homogeneous soils (Ronen et al., 1997). The water-retention curve is then described byin which hb [L] represents the air-entry pressure head or bubbling pressure head. This is approximately the minimum suction in the drainage cycle at which a continuous non-wetting phase (air) exists in a porous medium (Bear and Cheng, 2010). λ [-] is called the pore-size distribution index.
Pedotransfer functions (PTFs) can be used to predict soil hydraulic parameters, e.g., α and n in the van Genuchten model, from easy-to-determine soil variables, such as texture and bulk density (e.g., Carsel and Parrish, 1988, Schaap and Leij, 1998). Bloemen (1977) probably was the first to derive the relationships between the parameters of the Brooks–Corey model and particle-size distribution.
The capillary fringe thickness depends on the pore-size distribution and, thus, on soil type, vertical infiltration rates, fluctuations of the groundwater table (Berkowitz et al., 2004), and the presence of surface-active solutes (Henry and Smith, 2002). Significant lateral flow in the capillary fringe is restricted to the zone of high water content, i.e., below a critical height above the groundwater table (Berkowitz et al., 2004, Ronen et al., 1997).
Vertical mass transfer across the capillary fringe can cause groundwater contamination by volatile compounds (Baehr, 1987, McCarthy and Johnson, 1993), but it may also represent an important mechanism of oxygen supply. The latter process plays a pivotal role for subsurface microbial activity, providing the electron acceptor necessary for aerobic metabolism and influencing the redox potential within the aquifer. Mass transfer in porous media differs from diffusion through free fluids as the presence of solids reduces the cross-sectional area and increases the mean path length for compounds transported in soils. In the unsaturated zone, the effective diffusion coefficient additionally takes the volumetric water and gas content into account. With increasing water saturation from the unsaturated zone toward the groundwater, the effective gaseous diffusion coefficient decreases (Affek et al., 1998, Maier et al., 2007). Simultaneously, the horizontal flow velocity increases and hydrodynamic dispersion in the aqueous phase becomes important.
Many experimental and computational studies have been conducted to evaluate longitudinal hydrodynamic dispersion as a function of water saturation and its effect on transport of dissolved compounds (e.g., De Smedt et al., 1986, Elrick and French, 1966, Lake, 1989, Maraqa et al., 1997, Matsubayashi et al., 1997, Mayer et al., 2008, Nützmann et al., 2002, Padilla et al., 1999, Sahimi, 1993, Sahimi and Imdakm, 1988, Salter and Mohanty, 1982, Seyfried and Rao, 1987, Toride et al., 2003). In case of decreasing water content, higher dispersion coefficients were found, which were attributed to significant increases in the diversity of solute travel times or in the tortuosity of flow at the pore scale. In contrast to that finding, Orlob and Radhakrishna (1958) concluded, from their experimental work using chloride as tracer, that a 10% increase in gas saturation reduced longitudinal hydrodynamic dispersion by about 50%. Vanderborght and Vereecken (2007) also pointed out that several studies found lower dispersion coefficients in unsaturated than in saturated systems. Roth and Hammel (1996) demonstrated that the variability of the flow field in heterogeneous soils strongly depends on water content, resulting in minimal longitudinal hydrodynamic dispersion coefficients at intermediate saturations, and elevated dispersion coefficients under very dry conditions.
With regard to the mass transfer of volatile compounds across the capillary fringe, earlier works (e.g., Klenk and Grathwohl, 2002, Liu, 2008) showed that transverse vertical dispersion is essential in experiments conducted at the bench-scale. Klenk and Grathwohl (2002) suggested that flow in the capillary fringe also enhances transverse dispersion due to the presence of entrapped gas bubbles, which lead to more tortuous flow paths. In addition, the gas bubbles act as ‘mixing chambers’ because of fast diffusion within the gas phase.
The contrasting findings about the role of hydrodynamic dispersion in variably saturated soils and the lack of studies dealing with the mass transfer of volatile compounds across the capillary fringe indicate the need of further investigations directly comparing transverse dispersion at the interface and in the fully water-saturated zone. This is the main objective of the present study. Additionally, we present a non-invasive approach to determine profiles of oxygen concentration across the capillary fringe and in the fully water-saturated zone at the pore-scale resolution. The method is based on an optode technology, in which luminescence within a polymer foil is quenched in the presence of oxygen. We demonstrate the applicability of the proposed method under various conservative and reactive conditions. Analytical solutions of the governing transport equation under different boundary conditions are used to quantitatively interpret the experimental results. Numerical simulations of flow and transport further confirm the results for an illustrative case of oxygen mass transfer across the capillary fringe.
Section snippets
Experimental setup
We performed quasi two-dimensional flow-through experiments to study oxygen transport. Recently, such experimental settings have been used to investigate solute transport by high-resolution imaging techniques (e.g., Catania et al., 2008, Jaeger et al., 2009, Oates and Harvey, 2006, Olsson and Grathwohl, 2007, Werth et al., 2010, Zinn et al., 2004), to perform multi-tracer experiments with different dissolved compounds (Chiogna et al., 2010), and to study coupled mixing and reactive processes,
Modeling conservative and reactive transport
The advection–dispersion equation for conservative, non-volatile solutes in variably saturated porous media reads asin which D [L2 T−1] represents the dispersion tensor, C [M L−3] is the volumetric concentration of the compound of interest in water, q [L T−1] is the specific-discharge vector, and t [T] is the time. Various analytical solutions of Eq. (6) have been derived for simplified cases.
For a compound partitioning between the aqueous and gaseous phases, storage and
Evaluation of the experimental results
We measured high-resolution oxygen concentration profiles, both in the saturated zone and in the capillary fringe, under identical hydraulic conditions. Fig. 2 shows the distribution of oxygen concentration in a conservative experimental run at a distance of x = 45 cm from the inlet of the flow-through chamber. Two typical oxygen profiles, characteristic of both types of oxygen sources, are displayed in the plot. The lower profile is determined by the oxygen plume in the saturated zone and
Summary and conclusions
This study focused on the mass transport of oxygen across the interface between the unsaturated and the saturated zones and within groundwater. The experiments were carried out in homogeneous porous media with relatively uniform grain sizes. We applied a non-invasive technique to measure profiles of equivalent aqueous oxygen concentration at high spatial (vertical) resolution at distinct cross-sections. The oxygen concentrations were measured directly inside the porous medium without disturbing
Acknowledgement
This study was funded by the DFG (German Research Foundation) through the Research Group FOR 831 ‘Dynamic Capillary Fringes: A Multidisciplinary Approach’ (Grant GR971/22-1).
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