Measuring and modelling salt and heat transport in low-land drainage canals

Abstract

This thesis explores a new measuring approach to quantify the seepage flux from boils. Boils are preferential groundwater seeps and are a consequence of the groundwater flow that works its way through the soil matrix by creating vents of higher conductive material. In the Netherlands, boils often occur in deep polders (reclaimed lakes situated 4–7 m below sea level), transporting water directly from the deep aquifer. Because this saline aquifer is connected to the sea, the pressure difference between the sea water level and the polder water level is the main driver of the upward seepage flux. At the surface, boils seep out through canal beds and sometimes on land. This thesis focusses on boils that directly discharge into polder drainage canals. Although boils are usually highly saline compared to the fresh surface water, this research also includes an example of a relatively fresh boil.
The seeping groundwater has a fairly constant temperature throughout the year.
Because the surface water temperature fluctuates over the year and over the day,
temperature is an ideal tracer to measure the groundwater - surface water interaction. Previous studies applied temperature and salinity samples taken at different depths in the soil to quantify the boil seepage flux. Because the boil vents are usually not strictly vertical and can be disturbed when probing the soil, this research aims to measure the boil seepage flux from a surface water perspective. The intended measurement approach samples the surface water at a very high resolution in three dimensions, compares the temperature profiles with those in a free-surface transport model, and infers the boil flux as the bottom boundary flux of the model.
Over the past decades, fibre-optic distributed temperature sensing (DTS) has
developed toward an effective means to obtain spatially distributed temperature
samples. When releasing a laser signal through an optical fibre, the returning signal carries temperature information in its wavelengths. Current DTS machines allow measuring temperature down to every 25 cm along a fibre-optic cable. To obtain even higher resolutions, researchers often wrap cables to a coil. However, cable bends and the construction supporting the coil affect the measurement accuracy. Chapter 3 investigates how cable bends influence the temperature measurements in coil-wrapped DTS set-ups in order to account for this in the design of a highresolution DTS set-up for this research. It is concluded that, with a decreasing bending radius, the cable bends increasingly affect the temperature measurements in multiple ways. The non-linearity in the bend-induced decay of the laser signal complicates compensation for these effects and requires a very careful temperature calibration approach.
To avoid continuously bent cables, the design of the three-dimensional (3-D)
high-resolution DTS set-up applied a weaving pattern instead of coils (Chapter 4). This way, cables are only bent at each turnaround, intermitted by straight stretches of 1 m. By selecting the desired vertical spacing of the woven ’layers’, one can customize the vertical resolution of the set-up. To infer the seepage flux from the stream bed, the design of the set-up required very high resolutions near the bottom boundary. The set-up proved to measure very detailed temperature profiles in a water body, and even uncovered unexpected seeps in a laboratory set-up to simulate boil seepage. In the field, the measured temperatures near the stream bed displayed an accumulation of sediment around the boil during the measurement periods. Most interestingly for the current application, the detailed temperature profiles were able to capture double-diffusive phenomena.
Double-diffusion occurs when two adjacent water layers have different temperatures and salinities, and the density gradients for the temperature and salinity are opposed. For example, when cold (denser) and fresh (lighter) water overtops a warm and saline water layer, a system of convective layers develops with a very sharp temperature and salinity interface between the convective layers (i.e., double-diffusive convection). A more curious phenomenon occurs when the warm and saline layer is on top. In this case, a finger-like pattern develops at the sharp interface between the layers (i.e., salt-fingering). These systems are different from normal diffusive interfaces, which tend to fade over time. Therefore, water bodies with salt and temperature gradients demand a careful modelling of the flow processes.
To accurately model the boil-covering water body with large density gradients,
a mass and momentum conservative free-surface model was selected. The model was extended with a transport module and modules accounting for temperature and salinity dependent densities, viscosities, and specific heats. Moreover, the model was extended with the option to include atmospheric heat exchange in the calculations. The performance of the model was tested on a solar pond (Chapter 5). Such ponds are double-diffusive convective water bodies with very strong density gradients, which store solar energy as heat in their bottom hypersaline layer. The model well captured the flow of warm water along the sloping edge of the solar pond and demonstrated the onset of small seiches in the pond due to the density gradients. The onset of convective layers was also captured, although their extents were not in complete agreement with measurement data. In general, the results confirmed the model capability to simulate double-diffusive convection.
Due to the boil’s circular shape and the availability of 3-D temperature profiles, a 3-D modelling grid would be preferable for the boil seepage simulations. The dense grid needed for the transport simulation, however, yields too large computation times. Therefore, Chapter 6 investigated the potential of a quasi 3-D axisymmetric set-up for these simulations. To this end, the 2-DV model code was extended with few additional terms which hardly increased the computation time and kept the solution procedure mass and momentum conservative. Qualitative case studies demonstrated the model capability to simulate salt-fingers and double-diffusive convection. An analytical benchmark was set up for the axisymmetric expansion of an unconditionally stable layer from a central cold and saline seepage inflow. For the case of laminar flow conditions, the model results were in agreement with the analytical solution. Turbulent convection dispersed heat and salt significantly quicker.
The unexpected seeps in the laboratory set-up for boil seepage simulations complicated the comparison of these measurements with model output, because the exact flow paths were unknown and could not be modelled. Chapter 7 shows a comparison of the measurements with model results for the intended seepage flow. Although double-diffusive convective and unconditionally stable layers develop in both the model and the measurement results, the growth rates, and specifically the locations where the layers grow at a faster rate, are different. Moreover, the unexpected seeps seem to have a higher flow velocity, leading to a larger mixing of heat at the interface between the layers. It is concluded that the model can not be validated based on the laboratory data and additional measurements are recommended.
Although the horizontal stream flow across the boil should be negligible when
applying an axisymmetric modelling approach, knowledge of the stream discharge is still relevant. For this reason, this thesis starts with exploring the possibilities to modernize and potentially automate the rising bubble technique for discharge measurement (Chapter 2). The study shows that the complicated dual camera set-up and position calculations for the air bubbles in previous publications can be avoided with modern image processing algorithms. Reflecting sun light sometimes impedes the visibility of the air bubbles on the water surface. We displayed an example of how a statistical tool still uncovers the signatures of air bubbles in digital images that would normally hardly be visible. Such tools could also be applied in pattern recognition algorithms that automatically find the air bubbles on the water surface. Although further research is necessary, the results seem to support the hypothesis that the rising bubble technique can be applied as an automatic discharge measurement technique.
We conclude that the boil seepage inversion from double-diffusive models is
currently still very challenging (Chapter 8). The locations and extents of double-diffusive convection cells and salt-fingers are dependent on sub-grid processes.
Moreover, these phenomena are very sensitive to local density gradients which will never be modelled ’perfectly’. The importance of model boundary conditions when the layer of seepage water is still thin could also affect the inversion of the seepage flux at the bottom boundary. For all these issues, the local temperature deviations can highly influence the inversion step, yielding a high noise in the outcome. Nevertheless, we see potential in a less complicated inversion of the growth of an unconditionally stable layer above a cold and saline boil after the water body is fully mixed. This approach still requires high-resolution temperature measurements. Further research to this method is recommended.