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High-Resolution Sensor System to Investigate Solute Transport in Saturated Sediments
Eatedal Alqusaireen1,*, Claudio Meier2, Farhad Jazaei3
Published in Journal of the ASABE 67(4): 909-915 (doi: 10.13031/ja.15876). Copyright 2024 American Society of Agricultural and Biological Engineers.
1 Department of Engineering, The University of Tennessee, Martin, Tennessee, USA.
2 Department of Civil Engineering, The University of Memphis, Memphis, Tennessee, USA.
3 The University of Memphis, Memphis, Tennessee, USA.
* Correspondence: ealqusai@utm.edu
Submitted for review on 30 October 2023 as manuscript number NRES 15876; approved for publication as a Research Article and as part of the “Digital Water: Computing Tools, Technologies, and Trends” Collection by Associate Editor Dr. Debabrata Sahoo and Community Editor Dr. Kati Migliaccio of the Natural Resources & Environmental Systems Community of ASABE on 30 April 2024.
Citation: Alqusaireen, E., Meier, C., & Jazaei, F. (2024). High resolution sensor system to investigate solute transport in saturated sediment. J. ASABE, 67(4), 909-915. https://doi.org/10.13031/ja.15876
Highlights
Abstract. Hyporheic exchange flow, the movement of river water into streambed sediments and its subsequent return to the surface water after suffering biogeochemical transformations, impacts a stream’s water quality and ecology. These processes, which are the basis for the self-purification capacity of river systems, depend on the quantity and travel time of the flow within the sediments. Different tracer-based approaches have been deployed for studying flow in saturated sediments, but few of these experimental methodologies are able to attain the high temporal resolutions that are needed to adequately capture the passage of a solute plume in a porous medium. To allow for a better description of such flows, we designed and fabricated an innovative, low-cost sensor system able to detect solute transport at multiple locations simultaneously at very high time resolutions. The sensors measure electrical conductivity as voltage drops at a frequency of up to 10 Hz, allowing for detailed solute breakthrough curves (BTCs). The fabricated sensors were tested in a laboratory experimental setup designed to examine solute transport under conditions that reproduce 1D flow in saturated sediments. The sensor system was able to successfully detect electrical conductivity (expressed as voltage drop) in real-time, at high temporal resolution, and at multiple locations. Solute BTCs collected with the system were consistent and highly repeatable under the same conditions. One-dimensional solute transport equations were modeled numerically using the finite differences technique, and the results showed good agreement between the measured and modeled BTCs for all materials. The proposed system is inexpensive compared to conventional EC probes, easy to operate, and sensitive to low solute concentrations.
The movement of river water into subsurface, near-streambed sediments and its return to surface waters after relatively short travel pathways is known as hyporheic exchange flow (HEF). It brings both solutes and particles into high specific-surface-area environments, where they suffer biogeochemical transformations that impact a stream’s water quality and ecology. These processes, which are the basis for the self-purification capacity of river systems, depend on the quantity and travel time of flow within the sediments.
Several methods can be used to estimate flow velocities and travel times in such saturated sediments, including computing the specific discharge from piezometer data (to obtain hydraulic gradients) and hydraulic conductivity (Baxter et al., 2003; Cardenas et al., 2004; Derx et al., 2010), heat-tracer methods (based on vertical temperature profiles within the streambed; Constantz, 2008; Swanson and Cardenas, 2010), and mass-balance approaches (solute-tracer methods; Zarnetske et al., 2011; Trauth et al., 2015).
Because advection is the dominant process controlling biogeochemical transformations in streambeds (Comer-Warner et al., 2021), different solutes have been used as tracers to estimate the actual advective travel time of flow in saturated sediments (Zarnetske et al., 2011; Schmidt et al., 2012). Solute tracers can be detected by repeatedly measuring the solute concentration (or the electrical conductivity (EC), when salt is used). Besides the requirement of intensive sampling and lab work, measuring solute concentrations can be expensive. If a salt (e.g., NaCl) is used as a tracer, though, the electrical conductivity (EC) of the water becomes a good proxy measure or detector of the tracer instead of its concentration (Zarnetske et al., 2011). Electrical-conductivity breakthrough curves (BTCs) at different depths can be used to measure the travel time of the solute in the sediments (Zarnetske et al., 2011). The BTCs are plots that show the relative concentration of a given substance (ratio of the actual concentration to the source concentration) versus time. The travel time of HEF is obtained from the BTC as a median travel time, which is the time to peak in the case of a pulse tracer injection and the time to reach half the maximum concentration (or plateau concentration) for a continuous tracer injection (Runkel, 2002; Dent et al., 2007; Zarnetske et al., 2011). Electrical conductivity can be measured using probes or meters (e.g., YSI meters) at different frequencies, but these are relatively costly and typically cannot record the time series of the measured EC or, if they do, only offer rather low temporal resolutions. Moreover, commercial probes do not fit inside the narrow PVC or stainless steel mini-piezometers typically used in hyporheic research.
The tracer should be monitored at a high spatio-temporal (x, y, z, t) resolution; otherwise, its plume might be missed or lost. In this work, we focus on a sensor system that: (1) achieves a high temporal resolution; and (2) has a low per-unit cost, so that multiple locations can be potentially sampled in a simultaneous fashion economically, helping achieve the spatial resolution needed in any specific study. In previous research, the shortest interval for measuring solute transport, either through its concentration (e.g., Dent et al., 2007) or as EC measurements (e.g., Zarnetske et al., 2011), was 1 minute. Schmidt et al. (2012) emphasized the need to detect flow exchanges between the water column and the subsurface at higher temporal resolutions, although they only measured EC at intervals of 10 minutes. When sampling tracers at high spatial resolutions (down to a few centimeters), high temporal resolutions (of a few seconds) are necessary to detect the passage of the tracer. One of the limitations in this regard could be the affordability of sensors that can measure electrical conductivity at short intervals and at many locations simultaneously. Tracers such as NaCl are used to assess solute exchange between in-stream water and pore water because of their low cost and their resistance to decay, but most electrical conductivity meters or probes fail to detect and measure the low concentrations that might be needed in river bar sediments (Tonina, 2005). Therefore, there is a need for developing novel methods to explore the spatial variability of actual flows within bar sediments using solute tracers sampled at high temporal and spatial resolutions.
The objective of this study was to build an inexpensive EC-sensing system able to generate BTCs for electrical conductivity expressed in voltage drop at high temporal resolution, in real time, at multiple different locations within a saturated porous medium. The voltage drop can be detected at very fine spatial resolutions (down to ~ 25 centimeters or even less if needed) and at high temporal resolutions (up to 10 Hz). The voltage-drop breakthrough curves were calibrated to solute concentration and modeled.
Solute Transport Theory
Solute transport in the saturated subsurface is a combination of two processes: advection (convection) and dispersion. Advective transport refers to the solute that is transported by the flowing water in the subsurface, while dispersive transport is the solute transported by hydrodynamic dispersion through the fluid phase only (Salehin et al., 2004).
The 1D solute transport equation is a partial differential equation known as the Advection-Dispersion Equation (ADE), shown in equation 1 (Huang et al., 1995; Leij and van Genuchten, 2002; Shi et al., 2016):
(1)
where
C = volume-averaged solution concentration
t = time
vf = fluid velocity (vf = q / ne, where q is water flux and ne is the effective porosity)
D = solute dispersion coefficient, also known as the hydrodynamic dispersion coefficient.
The equation of solute transport shows the two processes of advection and dispersion. Advective solute transport is presented in the term –vf (?C / ?x), while dispersive solute transport is represented in the term D(?C2 / ?x2), which includes the effect of both molecular diffusion and mechanical dispersion, as D sums up both coefficients, as described in equation 2. Hydrodynamic dispersion is due to local velocity variations within the pore spaces (Konikow et al., 1996).
(2)
where
D0 = molecular diffusion coefficient of the solute in water
t = tortuosity factor of the porous medium (greater than 1)
a = dispersivity factor
vf = fluid velocity.
Molecular diffusion can be neglected when the local velocities are high in the pore spaces, so that mechanical dispersion is much larger. In most studies, the dispersion coefficient (D) is represented by the mechanical dispersion coefficient, which is a function of the dispersivity factor and fluid velocity. The dispersivity is considered a uniform characteristic of the entire medium (Bear, 1972) and is in the order of 0.1 to 5 cm for homogeneous sandy columns (Huang et al., 1995). However, studies that investigate the hydrodynamic dispersion coefficient in porous media are relatively scarce (Shi et al., 2016).
Materials and Methods
Laboratory experimental design setups were developed to test the ability of the proposed sensor system to detect solute transport in saturated porous media in 1D at very fine spatial scales and high temporal resolution. The solute tracer is detected as a BTC by measuring voltage drops using innovative voltage sensors at high temporal and spatial resolutions. A complete sensor system has been designed and fabricated that is capable of detecting real-time voltage drops and logging the observed time series. The designed hydraulic apparatus contains well-sorted saturated sediments, replicating flow conditions in saturated sediments such as those found in a river’s streambed but without the natural spatial variability. This section describes the design and fabrication of the voltage sensors, the voltage data-collection system, the experimental apparatus and set-up with the procedure, and the materials that were used as porous media.
Voltage Sensors, Circuit-Board Design, and Fabrication
The sensors were designed to detect the voltage drop in water when injecting a saline solution as a tracer, because it is easier to measure and record the voltage drop than electrical conductivity. A voltage drop can be detected using a conductivity sensor, where an electric current is circulated between two metal plates in the water sample and the conductance (how readily the current flows) between the plates is measured. The higher the concentration of salt in the water, the stronger the current flow and the lesser the resistance. The voltage sensors were made out of two metal plates (obtained from a “one-sided silver-clad circuit board”) separated by a plastic spacer, as shown in figure 1. A silver-clad circuit board was used to fabricate the plates to avoid corrosion and buildup problems that occurred when other metals (e.g., copper) were initially tested. The plates are 1.2 cm x 1.2 cm with a thickness of 1.66 mm. The plastic spacer is 1.2 cm x 1.2 cm with a thickness of 1.14 mm. The space between the plates (L) is 9.72 mm. Based on the dimensions of both plates and spacer, the cell constant (K = L / a, where L is the distance between the plates and a is the area of the plate) for the sensors is 0.78 cm-1, which is within the typical range for measuring low electrical conductivities. The dimensions of the plates and the spacer are selected based on the cell constant and considering the diameters of common mini-piezometers used for hyporheic research in the field. The cost of the plates for one sensor and spacer is almost $1.
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| Figure 1. Example of the voltage sensors used in the experiments. |
In order to measure the voltage drop between sensor plates, reflecting changes in salt concentration, a circuit was designed based on the basic salt circuit with some modifications. Basically, a resistor (R1) was added to the salt circuit to be able to measure the voltage drop across that resistor, which is proportional to that between plates. (fig. 2). Additional components were added to the circuit, which are described below.
The circuit board for each sensor has the following components, as shown in figure 3: AC Source (18V AC Power Transformer 2 Amp) set up to 9 volts (center-tabbed); 1 kOhm “trimpot” or trimmer potentiometer 3296 W, which can be adjusted based on the injected salt concentration and the used AC voltage; 1 Amp 100 Volt DF01M full-wave bridge rectifier, used to convert the AC source to DC output; a 220 uF 35V 105c radial electrolytic capacitor, used to smoothen the DC; and an X RadioShack 1k-Ohm 1/2-Watt 5% carbon film resistor, used to discharge the stored voltage from the capacitor. As was the case for the sensor plates, the circuit board was drawn using Dip Trace software and cut by the milling machine. The materials to fabricate four sensors and the circuit add up to almost $40.
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| Figure 2. Initial sensor circuit. |
In the calibration process of the voltage sensors, standardized solutions of NaCl were used, which were prepared in the Chemistry Lab at UT Martin. Different solution concentrations ranging from 0 to 6 g/L were prepared. The sensors were placed in each solution separately and the corresponding voltage was measured. The non-linear relationships between concentrations and voltages were fitted using SRS1 Cubic Spline Functions in Excel. Figure 4 shows an example of the relationships between concentration and voltage for five sensors. The calibration results were used to back-calculate solute concentrations from the voltage data.
Voltage Data Collection System
A Lab Pro Vernier interface system was used to measure and collect voltage data from the sensors connected to it. It included a Vernier Lab Pro interface, a voltage probe that connects the interface with the circuit, and a connector to link the interface with the computer. Initial measurements with regular voltage probes gave incorrect measurements, whereby all sensors replicated the first sensor readings. After noticing that this was due to all interface channels sharing a common ground, we used special differential voltage probes that can measure up to 6 volts. A digital display variable AC voltage regulator (110V single-phase Variac transformer 2000W 20Amp automobile regulator) was used to adjust the input AC to 6 volts. The Lab Pro devices communicate through Logger Pro 3.15 software, which enables the recording of all the measurements in time based on the chosen sampling rate. Each Lab Pro interface has four input channels, each connected to a voltage sensor. Several interfaces can be connected simultaneously to measure voltage at multiple locations simultaneously. The price for this interface, which can measure voltage drops from four sensors simultaneously, is almost $150, while each differential voltage probe costs $30. Based on these prices, the unit cost per sensor amounted to almost $80. Modern, high-resolution (1 Hz) EC sensors can cost around $900, but they will not fit in a mini-piezometer and cannot be buried in the sediment, so using them in hyporheic research would require driving larger-diameter wells, with all the accompanying time and cost restrictions. This would also limit the possibility of using high-spatial-resolution grids and would disturb streambed sediments much more than driving mini-piezometers, thus affecting measurements.
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| (a) | (b) | |||
| Figure 3. (a) Schematic of one sensor circuit; (b) Photo of the circuit board with five sensors. | ||||
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| Figure 4. Concentration-voltage relationships for the five different sensors (S1, S2, S3, S4, S5). |
Experimental Apparatus to Test the System
The behavior of the proposed voltage sensors in describing solute tracer flow was examined in a hydraulic apparatus specifically designed to mimic flow in saturated sediments in a one-dimensional force-convective/advective transport column to validate the tracer-detection capabilities of the sensor system with fewer variables under known conditions minimizing the effects of lateral dispersion (fig. 5). The apparatus was built of a 4-ft long, vertical, clear (with a blue tint) PVC pipe with 3.998" ID, 4.500" OD, and 0.251" wall thickness. The pipe was connected from the bottom with a 1 1/2”–2” three-port valve. The valve was connected from two sides with 1–1/2" ID low-pressure clear flexible PVC heavy-duty tubing. Each tube was connected to a reservoir at a known hydraulic head; one side was for tap water as a source of water, while the other side was for injecting saline water.
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| Figure 5. Photo of the 1D column apparatus and setup. |
Experimental Procedures
The first step when running the experiment was to prepare the voltage sensors. They were wrapped with a nylon mesh to prevent sand from getting between the plates and were then attached to a glass rod centered along the axis of the column at five locations: 0.00 m (S1), 0.25 m (S2), 0.50 m (S3), 0.75 m (S4), and 1.00 m (S5) from the bottom of the rod/column. Note that in a field application where the sensors are meant to be lowered in a mini-piezometer, such wrapping would not be necessary. The column was then filled with the porous medium; three different materials were tested in the fine-sand to gravel size range. Reservoirs were set at a specified head (42 cm or 60 cm) before tap water started to flow through the column. Water was allowed to flow until the whole system reached steady-state conditions. The voltage sensors were hooked to the Vernier system, with the Lab Pro programmed to continuously measure the voltage at a frequency of 10 Hz. At a specified time, a saline water solution with a concentration of 6 g/L was continuously injected while the tap water valve was simultaneously closed. In the meantime, Lab Pro continuously logged the sensor-collected data in real-time. Once the voltage drop reached the plateau value for all sensors, the injection stopped, and the tap water valve was opened. While running the experiment, the discharge was measured regularly to ensure steady-state conditions.
Materials Properties
Three materials were used: fine sand, coarse sand, and glass beads, selected to provide a range of flow velocities for the experimental hydraulic head conditions. The fine sand was sieved out from washed concrete sand bought from a local sand quarry using standard ASTM sieves, collecting the sediment retained between sieves numbers 30 and 16 (0.0234" and 0.0469" or 0.4 mm and 0.63 mm). The coarse sand was purchased from APAC-Central; the sizes were those retained between sieves numbers 12 and 8. Glass beads were manufactured as spheres with a 3.50 mm diameter, purchased from Ceroglass. For all materials, densities, specific gravities, and porosity were estimated in accordance with ASTM standards and are shown in table 1. Specific discharge (q, also known as Darcy velocity) and fluid velocity (vf) data for the experiments are summarized in table 2.
| Table 1. Materials properties. | ||||||
| Material | Bulk Dry Density (kg/m3) | Solid Density (kg/m3) | Porosity | Particle Size (D50) (mm) | Specific Heat Capacity (kJ/kg C) | Thermal Conductivity (W/m C) |
| Fine Sand | 1606 | 2590 | 0.380 | 0.89 | 0.80 | 0.84–1.42 |
| Coarse Sand | 1588 | 2570 | 0.382 | 1.90 | 0.80 | 1.21–2.47 |
| Glass Beads | 1533 | 2578 | 0.405 | 3.50 | 0.84 | 0.220 |
| Table 2. Specific discharge and fluid velocity for all materials at two heads. | ||||
| Material | q at head 42 (cm/s) | vfat head 42 (cm/s) | q at head 60 (cm/s) | vfat head 60 (cm/s) |
| Fine Sand | 0.15 | 0.40 | 0.21 | 0.56 |
| Coarse Sand | 0.37 | 0.98 | 0.48 | 1.27 |
| Glass Beads | 1.72 | 4.23 | 2.19 | 5.39 |
Results and Discussion
The designed voltage-sensing system was tested in a controlled laboratory environment using the 1D column apparatus for the three materials listed above. The average flow rates (in cm3/s) measured for each material were: fine sand (12.3, 17.2), coarse sand (30.3, 39.2), and glass beads (138.9, 177.3) for the 42 and 60 cm head, respectively.
The voltage sensor system allowed us to measure and record the voltages at different locations in the column at a high, 10 Hz frequency, which is at least tenfold higher than conventional EC probes used in previous studies, and instantly generate the solute BTCs with the Logger Pro software. The injection period varied between 4 and 15 minutes, depending on the porous material used, where fine sand required the longest injection time, followed by coarse sand, and then the glass beads. To check for replicability, all experiments were repeated twice for each material and head. An example of two replicate measurements of solute BTCs (for all five sensors in the 1D column, with fine sand, for a head of 42 cm) is shown in figure 6; the method yields consistent and highly repeatable results, as both replicates are virtually identical for each one of the five sensors, in all cases.
All BTCs were truncated to show the voltage variation from the beginning of detection at the first sensor until all sensors had reached their maximum values at their respective plateaus. The truncation of BTCs was needed to better represent the time offsets of the voltage detection and curve plateau for each sensor. BTCs were smoothed at their plateau value using moving averages, and curves were then normalized as a proportion of the plateau value.
Solute BTCs for the case of fine sand at a 42 cm head (first replicate) are shown in figure 7. The time required to generate all five BTCs was longest for this case (500 s at a flow rate of 12.3 cm3/s), but it went sharply down to 40 s when using glass beads at a head of 60 cm, with a discharge of 177.3 cm3/s.
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| Figure 6. Comparison of two replicates for solute BTCs for five sensors in 1D column with fine sand, for a head of 42 cm at five locations (0.00 m (S1), 0.25 m (S2), 0.50 m (S3), 0.75 m (S4), and 1.00 m (S5) from the bottom of the column). |
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| Figure 7. Solute BTCs for all five sensors (at 0.00 m (S1), 0.25 m (S2), 0.50 m (S3), 0.75 m (S4), and 1.00 m (S5) from the bottom of the column) in fine sand for a 42 cm head (first replicate). |
The shape of the solute BTCs depends on which term is dominant in the advection-dispersion equation of solute transport (eq. 3). Advective solute transport is represented by the term vf (?C / ?x), while dispersive solute transport is represented by the term D(?C2 / ?x2). For example, if the dominant process in solute transport is dispersion (relatively low flow velocities and relatively high materials dispersivities), then the equation becomes parabolic. Higher dispersivity of the material results in a less sharp solute front (Trauth et al., 2015). On the other hand, if the dominant process is advective transport, then the equation becomes hyperbolic like those that describe the propagation of a wave or a shock front (Konikow et al. 1996). Visual observations show that all of our BTCs have relatively sharp fronts with steep concentration gradients, which means that the dominant process is advective transport, as expected. Figure 8 shows the steepness of the gradients for all materials used. It can be noted here that the BTCs for glass beads display steeper gradients than those for the other materials because of the higher flow velocity in that case.
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| Figure 8. Solute BTCs at Sensor 4 (0.75 m from the bottom of the column) for all materials at a head of 42 cm. |
Solute transport was modeled using a numerical solution for 1D forced advective flow in a porous column test. The solute transport equation in 1D can be written as the Advection Dispersion Equation (ADE) with a retardation factor equal to one (i.e., no interaction between solute and solid, Konikow et al., 1996; Leij and van Genuchten, 2002; Van der Zee and Leijnse, 2013), as shown in equation 3:
(3)
where
Deff = avf
C = solute concentration
t = time
vf = fluid velocity
R = retardation factor
Deff = effective solute dispersion coefficient
a = solute dispersivity
x = distance.
The solute transport equation was modeled numerically in MATLAB using the finite differences approach. The model shows sensitivity to dispersivity (a) and fluid velocity (vf) and was calibrated using those parameter values that resulted in the best fit of the BTCs at all locations. The calibrated (effective) velocity (veff) had a slight discrepancy from the originally estimated values from the experiment (as q / n, where q is water flux and n is the effective porosity). The calibrated dispersivities (a) for all materials were within the theoretical values obtained from the literature, ranging from 0.1 to 5 cm (Huang et al., 1995), except for glass beads at a head of 60 cm. The results of the solute transport model showed a satisfactory agreement between the measured (experimental) and fitted (modeled) BTCs for all materials, including the glass beads; Figure 9 shows an example for all solute BTCs, for the case of fine sand at 42 cm head.
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| Figure 9. Solute transport model best fits for fine sand at heads 42 cm. |
Conclusion
We propose an inexpensive sensor system that measures EC expressed as voltage drop, allowing us to investigate solute transport in porous media at multiple locations simultaneously with very high temporal resolutions. The voltage drop was detected in a laboratory apparatus at very fine spatial resolutions (down to ~ 25 centimeters) and at high temporal resolutions (up to 10 Hz). We designed and fabricated this system and then performed a series of 1D laboratory experiments to detect the passage of solute tracers in saturated sediments at multiple locations and high frequencies. The experiments aimed to reproduce the main features of flow in saturated sediments in a 1D configuration, investigating and confirming the ability of the voltage sensors to generate solute BTCs in real time.
Solute BTCs obtained using the proposed sensor system were consistent, highly repeatable, and easy to detect with the real-time feature. The repeatability of our results indicates that the system accurately detects the passage of solute plumes. The shape of the solute BTCs varied as a function of the material and the flow velocity, but they all showed sharp fronts, meaning that advection was the dominant transport process in our experiments. Because our voltage sensor system is sensitive to low solute concentrations, economic and allows for simultaneous measurements at multiple locations with high temporal resolution, we propose it is a good tool for use in field studies of hyporheic exchange flow.
Solute transport in the 1D column was numerically modeled. The modeled solute BTCs were in good agreement with the measured ones for all the materials at both heads. This agreement validates the applicability of our sensor system to detect solute transport in 1D saturated sediments in a lab environment, which display conditions that are similar to HEF in the field, except that the latter would occur in 3D with the natural variability in sediment hydraulic properties and local hydraulic gradients. The calibrated model is a useful tool to predict solute BTCs at any location in the one-dimensional configuration. A potential limitation of our system is that the sensors are not rugged, so they must be handled delicately.
Acknowledgments
We would like to acknowledge both Lee Bennett and Dan Comer from the University of Tennessee at Martin for their help in fabricating the sensors and the experimental setup. Also, we would like to thank Francesco Dell'Aira and Benjamin Ledesma from the University of Memphis for their help in developing the solute transport model.
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