Solute transport in low-permeability media such as clay has not been studied carefully up to present, and we are often unclear what the proper governing law is for describing the transport process in such media. In this study, we composed and analyzed the breakthrough curve (BTC) data and the development of leaching in one-dimensional solute transport experiments in low-permeability homogeneous and saturated media at small scale, to identify key parameters controlling the transport process. Sodium chloride (NaCl) was chosen to be the tracer. A number of tracer tests were conducted to inspect the transport process under different conditions. The observed velocity-time behavior for different columns indicated the decline of soil permeability when switching from tracer introducing to tracer flushing. The modeling approaches considered were the Advection-Dispersion Equation (ADE), Two-Region Model (TRM), Continuous Time Random Walk (CTRW), and Fractional Advection-Dispersion Equation (FADE). It was found that all the models can fit the transport process very well; however, ADE and TRM were somewhat unable to characterize the transport behavior in leaching. The CTRW and FADE models were better in capturing the full evaluation of tracer-breakthrough curve and late-time tailing in leaching.
Low-permeability porous media (LPPM) exist extensively in natural sedimentary deposits such as shale and clay. They have played critical roles in protecting groundwater resources, affecting the accumulation of petroleum and ore deposits, and controlling geological processes such as structural evolution of the crust [
A large body of literature related to solute transport in LPPM often involved the so-called “numerical experiments” or numerical simulations where an imaginary rather than an actual experiment was conducted. For example, Guimerà and Carrera [
Despite the above-mentioned investigations, solute transport in LPPM is still poorly understood in a general sense. For example, it is still unclear what governing equation to use for properly describing the transport process in such media and whether one can use the Fick’s law to describe the transport process or not. Furthermore, if Fick’s law can be used, what is the proper range of dispersivity values for LPPM, and how different are they from those for permeable sandy aquifers? One can only answer these questions by conducting the laboratory and/or field transport experiments in such media. Performance and analysis of controlled experiments in the laboratory permit the investigation of various flow phenomena and their parameters on relatively small scales of distance and time [
Tracer tests have been commonly used for several decades as benchmark experiments for investigating solute transport in porous media. A main contribution of this study that is different from previous tracer tests is to characterize transport in subsurface low-permeability media and the validity of the transport theories at various scales in such media. Ballard et al. [
Cumbie and McKay [
The discharge from low-permeability area in the groundwater can be considered a durable source that often challenges remediation strategies [
On the other hand, Huang et al. [
The objective of this study is to report a series of carefully designed tracer test results of low-permeability clay soil columns. Three set of experiments were conducted: (i) same column diameter (14 cm) with different sample lengths (3 cm, 5 cm, and 8 cm); (ii) same sample length (5 cm) with different column diameters (7 cm, 9 cm, and 10 cm); (iii) columns with rough inner wall, having the same diameter (14 cm) with different sample lengths (3 cm, 5 cm, and 8 cm). Four different models including ADE, FADE, TRM, and CTRW were used to simulate the experimental results, and the transport behavior in LPPM was thorough analyzed.
We have conducted a series of laboratory experiments for one-dimensional solute transport in low-permeability homogeneous and saturated soil columns using vertical Plexiglas columns with various sample diameters of 7–14 cm and various sample lengths of 3–8 cm. The homogeneous columns were filled with clay soil samples, which were taken from the nearby mountains in Wuhan, Hubei Province, China. For the clay media (i.e., Heavy silty- clay) used in this study hydraulic conductivity was found to be around 10−5 cm s−1 [
Summary of soils sample diameters and particle size distribution (%).
>0.075 mm | 0.075 mm~0.05 mm | 0.05 mm~0.01 mm | 0.01 mm~0.005 mm | 0.005 mm~0.002 mm | <0.002 mm | Soil sample name |
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6.1% | 5.9% | 20.1% | 17.8% | 0.6% | 49.5% | Heavy silty clay |
Summary of soil packing density and total porosity (
Soil column length | 3 cm with smooth wall | 5 cm with smooth wall | 8 cm with smooth wall | 5 cm with smooth wall | 5 cm with smooth wall | 5 cm with smooth wall | 3 cm with rough wall | 5 cm with rough wall | 8 cm with rough wall |
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Column inner Diameter (cm) | 14 | 14 | 14 | 7 | 9 | 10 | 14 | 14 | 14 |
Density (g cm−3) | 1.28 | 1.25 | 1.31 | 1.36 | 1.38 | 1.37 | 1.27 | 1.24 | 1.26 |
Total porosity ( |
0.55 | 0.7 | 0.62 | 0.49 | 0.67 | 0.65 | 0.6 | 0.61 | 0.64 |
The test installation comprised primarily of a water-supply device (Mabottle), a Plexiglas column, and a water outflow installment (steady-flow water tank); schematic diagram for the experiments is shown in Figure
Schematic diagram for homogeneous and saturated columns experiments.
The column was then filled from bottom with tap water for 48–72 hours to make the soil fully saturated. During water saturation process, if the bubbles or cracks appeared within the soil columns, the soils were extracted from the columns then refilled and saturated again from the bottom to ensure that no bubbles or cracks can be found and the soils were as homogeneous as possible. After establishing steady-state saturated flow through the column, two conjugate tracer tests were carried out with each of three sets of soil columns.
During the experiments, the temperature in the laboratory was around 25°C, meaning that the viscosity of the water can be regarded as constant. The electrical conductivity of the water samples from the tap was measured using a portable conductivity meter DDBJ-350 which has a precision of ±1.0%. The first test was a tracer introducing test with a constant NaCl source concentration of 5 g L−1 (or 0.085 mol L−1) and the subsequent second test was a flushing (or leaching) test after the exit tracer concentration became stable. A tracer injection experiment in the homogeneous clay soil column was done by replacing inflowing tap water with a NaCl concentration (5 g/L) and in leaching experiment the initial concentration (5 g/L) was replaced with the tap water. The concentration used in the experiment may be higher than values used in some other experiments but this value should not affect the conclusion of this study as we were dealing with the relative concentration (i.e., the ratio of actual concentration over the constant source concentration). One benefit of using a higher concentration was for the easy measurement and likely reduction of relative measurement errors. NaCl is favorable to estimate ground water flow and transport properties, and is also environmentally benign. Similarly high values of NaCl [
The Darcian velocity is an essential element in solute transport and is calculated from the following [
In three sets of experiments, Darcian velocity was found to decrease with time, as shown in Figures
Darcian velocity versus time for three column experiments: (a) smooth wall soil columns with the same inner diameter (14 cm) but different lengths; (b) smooth wall soil columns with the same column length (5 cm) but different column inner diameters; (c) rough wall soil columns with the same inner diameter (14 cm) but different column lengths.
In the first set-up of our experiment (case (i)), the same diameter (14 cm) with different column lengths (3 cm, 5 cm, and 8 cm) was applied. The Darcian velocities (
Figure
At the tracer introducing period in Figure
The mathematical and numerical simulation methods for ADE, FADE, TRM, and CTRW were provided in Supplementary Material available online at
Figures
Estimated parameters of transport process for ADE, FADE, TRM, and CTRW (TPL) for three sets of low-permeability homogeneous soil columns.
Column length | Column inner diameter | ADE | FADE | TRM | CTRW (TPL) | ||||||||||
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3 cm with smooth wall | 14 cm | 0.410 | 0.032 | 0.078 | 0.11 | 0.034 | 1.99 | 0.099 | 0.558 | 0.086 | 0.488 | 0.094 | 1.35 |
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5 cm with smooth wall | 14 cm | 0.230 | 0.045 | 0.196 | 0.11 | 0.076 | 1.99 | 0.094 | 0.847 | 0.07 | 0.33 | 0.101 | 1.36 |
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8 cm with smooth wall | 14 cm | 0.032 | 0.0189 | 0.591 | 0.03 | 0.019 | 1.99 | 0.022 | 0.424 | 0.16 | 0.034 | 0.031 | 1.68 |
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5 cm with smooth wall | 7 cm | 0.120 | 0.016 | 0.133 | 0.11 | 0.19 | 1.88 | 0.026 | 0.577 | 0.024 | 0.147 | 0.045 | 1.30 |
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5 cm with smooth wall | 9 cm | 0.112 | 0.033 | 0.292 | 0.10 | 0.06 | 1.81 | 0.033 | 0.467 | 0.022 | 0.182 | 0.068 | 1.38 |
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5 cm with smooth wall | 10 cm | 0.170 | 0.082 | 0.482 | 0.1 | 0.09 | 1.89 | 0.048 | 0.563 | 0.07 | 0.288 | 0.143 | 1.39 |
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3 cm with rough wall | 14 cm | 0.340 | 0.029 | 0.085 | 0.10 | 0.03 | 1.91 | 0.092 | 0.614 | 1.71 | 0.432 | 0.139 | 1.18 |
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5 cm with rough wall | 14 cm | 0.113 | 0.041 | 0.363 | 0.07 | 0.05 | 1.90 | 0.058 | 0.799 | 0.256 | 0.184 | 0.114 | 1.34 |
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8 cm with rough wall | 14 cm | 0.033 | 0.031 | 0.939 | 0.05 | 0.06 | 1.91 | 0.032 | 0.867 | 0.328 | 0.085 | 0.09 | 1.39 |
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Three sets of measured breakthrough curves fitted with ADE, FADETRM, and CTRW (based on TPL), for the homogeneous, saturated, and smooth wall soil columns with the same inner diameter (14 cm) but different column lengths: (a) 3 cm; (b) 5 cm; (c) 8 cm.
Three sets of measured breakthrough curves fitted with ADE, FADE, TRM, and CTRW (based on TPL), for the homogeneous, saturated, and smooth wall soil column with the same column lengths (5 cm) but different column inner diameters: (a) 7 cm; (b) 9 cm; (c) 10 cm.
Three sets of measured breakthrough curves fitted with ADE, FADE, TRM, and CTRW (based on TPL), for the homogeneous, saturated, and rough wall soil columns with the same inner column diameter (14 cm) but different column lengths: (a) 3 cm; (b) 5 cm; (c) 8 cm.
The values of dispersivity (
It was found that the dispersion coefficient (
A slow rise of BTCs was observed in columns with diameters of 7 cm and 9 cm compared to the column with a diameter of 10 cm (Figure
As seen in Table
Figure
The leaching process (or solute flushing period) was well simulated with CTRW and FADE in Figures
Three sets of measured leaching curves fitted with ADE, FADE, TRM, and CTRW (based on TPL), for the homogeneous, saturated, and smooth wall soil columns with the same inner diameter (14 cm) but different column lengths: (a) 3 cm; (b) 5 cm; (c) 8 cm.
Three sets of measured leaching curves fitted with ADE, FADE, TRM, and CTRW (based on TPL), for the homogeneous, saturated, and smooth wall soil columns with the same column length (5 cm) but different column inner diameters: (a) 7 cm; (b) 9 cm; (c) 10 cm.
Three sets of measured leaching curves fitted with ADE, FADE, TRM, and CTRW (based on TPL) for the homogeneous, saturated, and rough wall soil columns with the same inner diameter (14 cm) but different lengths: (a) 3 cm; (b) 5 cm; (c) 8 cm.
Figure
Estimated parameters of leaching process for ADE, FADE, TRM, and CTRW (TPL) in three sets of homogeneous soil columns.
Column length | Column inner diameter | ADE | FADE | TRM | CTRW (TPL) | ||||||||||
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3 cm with smooth wall | 14 cm | 0.120 | 0.036 | 0.300 | 0.110 | 0.026 | 1.7 | 0.11 | 0.350 | 0.621 | 0.120 | 0.011 | 1.15 | 0.045 | 0.099 |
5 cm with smooth wall | 14 cm | 0.080 | 0.047 | 0.88 | 0.081 | 0.037 | 1.7 | 0.08 | 0.596 | 0.036 | 0.106 | 0.066 | 1.35 | 0.013 | 0.082 |
8 cm with smooth wall | 14 cm | 0.036 | 0.029 | 0.806 | 0.037 | 0.012 | 1.7 | 0.034 | 0.325 | 2.04 | 0.070 | 0.08 | 1.4 | 0.035 | 0.107 |
5 cm with smooth wall | 7 cm | 0.096 | 0.026 | 0.271 | 0.096 | 0.020 | 1.6 | 0.093 | 0.526 | 0.039 | 0.06 | 0.12 | 1.3 | 0.037 | 0.21 |
5 cm with smooth wall | 9 cm | 0.055 | 0.034 | 0.630 | 0.057 | 0.018 | 1.8 | 0.054 | 0.322 | 0.040 | 0.475 | 1.208 | 1.26 | 0.013 | 0.022 |
5 cm with smooth wall | 10 cm | 0.047 | 0.085 | 1.828 | 0.039 | 0.032 | 1.6 | 0.046 | 0.416 | 0.131 | 0.038 | 0.09 | 1.4 | 0.061 | 0.081 |
3 cm with rough wall | 14 cm | 0.126 | 0.039 | 0.310 | 0.124 | 0.03 | 1.7 | 0.124 | 0.158 | 0.125 | 0.105 | 0.05 | 1.3 | 0.046 | 0.076 |
5 cm with rough wall | 14 cm | 0.098 | 0.065 | 0.663 | 0.104 | 0.045 | 1.7 | 0.098 | 0.392 | 0.035 | 0.093 | 0.07 | 1.24 | 0.028 | 0.100 |
8 cm with rough wall | 14 cm | 0.041 | 0.038 | 0.927 | 0.048 | 0.023 | 1.6 | 0.041 | 0.604 | 1.11 | 0.044 | 0.12 | 1.4 | 0.031 | 0.074 |
A slight increase of measured concentration (bump) was found around 200 hr in Figure
The above experimental results indicate that the hydraulic conductivity value depends on the clay soil structure and it might also be changed by the contaminants in the leaching process. On the other hand, Darcian velocity tends to decrease with time because of the decline of soil permeability that may be caused by the clay dispersion and swelling in the saline water. The decline of Darcian velocity is also likely due to the column wall roughness.
An interesting finding for transport in clay media is that the leaching process is not a simple reversal of the breakthrough process, as often assumed for transport in sandy porous media before. Instead, the leaching process sometimes exhibits very different behavior from the breakthrough process, most likely due to the clay dispersion and swelling problem. This implies that when studying transport in LPPM such as clay, it is advisable to investigate both the breakthrough and leaching processes, rather than the breakthrough process alone. Another interesting feature is that the dispersivity (
It is found that CTRW and FADE models can better describe the late-time tailing in the leaching process than ADE and TRM. Therefore, ADE and TRM are not recommended to explain the leaching process, although they are acceptable in describing the breakthrough process (Figures
We have to point out that this study deals with relatively small scales of columns with lengths ranging from 3 cm to 8 cm and column diameters from 7 cm to 14 cm. Actually, this study can be regarded as a pilot study and the first attempt of conducting transport experiments in LPPM to see how different transport in LPPM is from transport in other permeability media such as sand. Such a pilot study and experiment gained from this study will be very useful steps for more complete, full scale investigation of transport in LPPM, including conducting repetitive experiments. Therefore, whether the findings of this study can be extended to field scales or not is unknown and needs further investigations. Nevertheless, this study offers some interesting results about transport in clay, and, most importantly, it emphasizes the importance of analyzing both the breakthrough and leaching processes in clay.
The following conclusions can be drawn from this study: Three stages of Darcian velocity were found when switching from breakthrough process (or tracer introducing stage) to leaching process (or tracer flushing stage), suggesting alternation of soil permeability during such a process switching, probably due to clay dispersion and swelling. For the breakthrough process, the Fickian transport was evident from the increased pattern of For the leaching process, the non-Fickian transport was noted by the smaller values of For better understanding the transport behavior in LPPM such as clay, it is important to analyze data from both the breakthrough process and leaching process.
The authors declare that they have no conflicts of interest.
This research was partially supported by the National Natural Science Foundation of China (Grant nos. 41372253, 41521001) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant no. CUG140503). The authors sincerely thank Dr. Brain Berkowitz and Dr. Yunwu Xiong for the critical discussion on the initial version of this manuscript and David Weldon for his editing of this paper.