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DIVISION S-1-SOIL PHYSICS

Small-Scale Variability in Solute Transport Processes in a Homogeneous Clay Loam Soil

^a Division of Ecosystem Sciences, Dep. of Environmental Science, Policy and Management, Univ. of California, Berkeley, CA 94720-3110 USA

ghodrati{at}nature.berkeley.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions REFERENCES

 
Small-scale variations in transport parameters may have a profound influence on larger scale flow processes. Fiber-optic miniprobes (FOMPs) provide the opportunity to continuously measure solute resident concentration in small soil volumes. A 20-channel multiplexed-FOMP system was used in repeated miscible displacements in a repacked clay loam soil column (20 cm long and 10-cm diam.) to examine small-scale, point-to-point variability in convective–dispersive transport processes. Transport parameters, measured 10 cm below the surface, were compared at two drip irrigation point densities and two fluxes. Irrigation densities of one irrigation drip point per 4 cm² and 11 cm² of column surface area produced similar results. The breakthrough curves measured at 0.10 cm h^-1 had a larger immobile phase than at a flux of 1.07 cm h^-1. In the clay loam soil the mobile–immobile model fit the breakthrough curves better than the convective–dispersive equation (CDE), with r² values of 99.6 and 97.1, respectively. This analysis demonstrated that dispersion and mass recovery were much more variable than pore water velocity in this repacked clay loam soil. However, even in the most variable transport conditions encountered, only 17 sampling points were necessary to describe the column average transport parameters within 20% of the mean.

Abbreviations: BTC, breakthrough curve • CDE, convective–dispersive equation • CV, coefficient of variation • FOMP, fiber-optic miniprobe • MIM, mobile–immobile water model • TDR, time domain reflectometry

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions REFERENCES

 
MODELING INVESTIGATIONS have demonstrated that small-scale variations in pore water velocity have a strong influence on soil solute transport parameters (e.g., dispersion) (Amoozegard-Fard et al., 1982). While this result may be demonstrated using physically based models of homogeneous media, experimental investigations to support this result often do not have the sensitivity to make such conclusions. While a majority of the studies examining solute transport have been performed at the laboratory-column scale (Beven et al., 1993), few transport studies have been performed at small scales (Northrup et al., 1993). This has resulted in a fundamental lack of information for model development and validation of small-scale solute transport in soil.

Physical processes acting on solute transport at the pore scale may be quite important to larger-scale observations. For example, Wan and Wilson (1994) demonstrated that the air–water interface in unsaturated porous media plays a significant role in the reaction and transport of colloids. This finding supports the work of Brusseau (1993), which showed that in multiple-phase porous media, where film and intraparticle dispersion are present, even the size of the solute molecule becomes important to its transport characteristics.

Since pore-scale observations are more likely to be closer to the underlying physical processes controlling transport, in situ techniques are needed that may collect data at these small scales (Soll et al., 1993). Many authors have used micromodels and columns of glass beads to examine the physical processes of transport (e.g., dispersion) at the pore scale (Nielsen et al., 1991; Northrup et al., 1993; Soll et al., 1993; Wan and Wilson, 1994; Rashidi et al., 1996) and also to develop network and particle-tracking models to describe observations (Soll and Celia, 1993; Roth and Hammel, 1996). As the number of models describing solute transport at small-scale and pore-scale increases, it is important to develop monitoring methods for the purpose of model validation (Binley et al., 1996).

Some of the common techniques to examine in situ solute transport in soil include solution samplers and electrical-resistance probes (e.g., Bear, 1961). Time domain reflectometry (TDR) is another method used in column-, plot-, and field-scale studies (Mallants et al., 1996; Kachanoski et al., 1992; Radcliffe et al., 1998). Recently, Nissen et al. (1998) recognized the need for smaller-scale measurements of water content and developed a coiled TDR probe 1.5 cm long.

A newer option, fiber-optic probes, can measure solute transport at a point scale (Ghodrati, 1999), which is far less than the volume-averaged measurements of the existing TDR probes. The effective measurement zone of FOMPs is approximately a cylindrical zone of soil immediately in front of the probe with a volume ranging from 5 to 15 mm³ for a 2.5-mm-diam. probe (Garrido et al., 1999). This system measures the intensity of reflected light from a fluorescent tracer (Ghodrati, 1999). The light intensity, which is monitored in real time, is calibrated to the concentration of the fluorescent tracer so that breakthrough curves (BTCs) can be measured.

A 20-channel multiplexed fiber-optic system has been developed by Ghodrati et al. (1999) and recently tested to determine its accuracy and applicability to measure transport in a silica sand column. One important finding was that the system measures resident solute concentration, which is important to accurately fit transport parameters. Since the probes measure resident concentration, it would be expected that in a soil with a greater distribution of small pore sizes the immobile phase should be more significant and warrant the use of the mobile–immobile water model (MIM).

In this study, miscible displacements were repeated in a repacked clay loam soil column to examine small-scale solute transport. A multiplexed FOMP system was used to obtain BTCs at 20 points in a single cross-sectional plane within the column. For the purpose of comparison, the convective–dispersive equation (CDE) and MIM were fit to this data to estimate transport parameters. Using these BTCs, the spatial variability in transport parameters within the repacked soil column was examined. Finally, transport parameters under two fluxes and irrigation drip point densities were examined and the minimum sample size at that scale necessary to describe the average column response was estimated.

	Materials and methods

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions REFERENCES

 
Multichannel Fiber-Optic Miniprobe System
The multichannel-FOMP system used in this study has been developed based on Remote Fiber Optic Fluorometry techniques (Krohn, 1988) and is described in detail in Ghodrati (1999). The single-FOMP system consists of transmitting a constant beam of light through the input leg of a bifurcated fiber-optic bundle to a remote point of observation within the soil matrix (Fig. 1) . The common end of this bifurcated cable is encased in a stainless-steel cylindrical tube (3-mm o.d.) to constitute the fiber-optic miniprobe. At its end, the incoming light exits the probe, interacts with the directly adjacent soil volume, and is partially reflected back into the probe. The resulting light is carried through the output leg of the bifurcated fiber-optic bundle to a photodetector. A datalogger connected to the photodetector records the output light intensity as a function of time. Similar to a conventional spectrofluorometer, a narrow band filter selects the fluorescence excitation light wavelength from the light source. The emitted fluorescence light is filtered by a broad-band filter before it enters into the photodetector to increase the analytical sensitivity. This single-FOMP system has been multiplexed (Fig. 1) by (i) using a polyfurcated fiber-optic bundle with a common end connected to the light source and 20 legs each connected to a single bifurcated fiber-optic bundle and (ii) constructing 20 individual photodetectors to provide continuous data collection for 20 individual FOMPs (Ghodrati et al., 1999).

View larger version (45K): [in this window] [in a new window]   Fig. 1 Schematic of multiplexed fiber-optic miniprobe system

A multichannel drip-irrigation system connected to a peristaltic pump was used to uniformly deliver 6 mmol of CaCl₂ as a background solution to the soil surface at a steady flux.

Miscible Displacement Studies
To study the spatial variability in transport parameters, a series of miscible displacement studies were performed using pyranine (8–hydroxy–1,3,6–pyrenetrisulfonic acid trisodium) as a fluorescent tracer. Experiments were done using three different drip irrigation point configurations homogeneously positioned over the column at densities of 4, 11, and 78 cm² of soil surface area per irrigation drip point from 19, 7, and 1 irrigation drip points, respectively (Table 1) . Two replications of 1-cm pulses (pulse volume = column surface area x 1 cm) of 4000 mg/L pyranine were performed for each irrigation density established at a steady flux of 1.07 cm h^-1. In addition, using seven drip irrigation points, another miscible displacement was performed at a much lower flux of 0.10 cm h^-1. In all experiments, an air gap was left between the tracer and the background solution to prevent dispersion in the irrigation tubes. A total of seven miscible displacements were performed on the column under different conditions summarized in Table 1.

Output light intensity is related to the fluorescent tracer concentration passing in front of the probe, as well as to the bulk reflective properties of the soil matrix in contact with the sensor. A calibration procedure was necessary to convert output light intensity to tracer concentration in front of each FOMP. The fiber optic was first inserted into the column and the water flux was set to a steady-state. Then, consecutive solutions of known concentrations were applied to the column until a constant output light intensity was reached (2–5 pore volumes for each step). The process was repeated for five different concentration steps. Once the calibration was finished, the entire column was irrigated with 6 mmol of CaCl₂ until the dye had been completely flushed from the column and the initial output light intensity was again reached. With this procedure, a calibration curve for each individual FOMP was constructed. A separate calibration procedure was performed for each change in irrigation point density and the calibration curves were found to be similar for all conditions.

Data Analysis and Parameter Estimation
Twenty FOMPs were used to measure 20 BTCs at one-minute measurement intervals. The BTCs were fitted to the physical equilibrium model (i.e., CDE) and the two-region physical nonequilibrium MIM using CXTFIT (Toride et al., 1995). The differential equation for the CDE (Eq. [1]) is

(1)

where

R =retardation factor (dimensionless),C =concentration (mg cm^-3),t =time (h),D =dispersion (cm² h^-1),x =depth in soil (cm),v =pore water velocity (cm h^-1),

and the differential equations of the MIM (Eq. [2] and [3]) are

(2)

(3)

where

_m =volumetric water content of the mobile fraction (cm³ cm^-3),C_m =concentration in the mobile zone (mg cm^-3),_v =total volumetric water content (cm³ cm^-3),D_m =dispersion in the mobile zone (cm² h^-1),v_m =pore water velocity of the mobile fraction (cm h^-1), =first-order mass transfer coefficient (h^-1),_im =volumetric water content of the immobile fraction (cm³ cm^-3),C_im =concentration in the immobile zone (mg cm^-3).The MIM was solved with the boundary conditions of Eq. [4]:

(4)

where the term M(t) assumes a dirac delta function to describe the input pulse, and Eq. [5]:

(5)

The initial condition was (Eq. [6])

(6)

The CDE differential equation was solved with similar boundary and initial conditions to Eq. [4], [5], and [6] (except that no immobile phase existed that reduced all mobile and immobile-phase parameters to the parameters describing the entire soil).

Retardation of the fluorescent tracer was measured independently using a separately packed column of the same bulk density and water content. Nitrate was used as a conservative tracer, and miscible displacement experiments were performed for both the NO₃ and pyranine, where the pulses were applied at a flux rate of 1.07 cm h^-1, as described earlier. Both the NO₃ and pyranine concentrations were measured continuously at the effluent point, using a sampling system as described in Chendorain and Ghodrati (1999), and the concentrations were calibrated to light absorptance for both tracers. Retardation was determined by comparing the breakthrough times of the NO₃ and pyranine, using the relationship (Eq. [7])

(7)

where t_bR is the breakthrough time for the retarding solute (h) and t_b is the breakthrough time of the nonretarding solute (h). The retardation factor for pyranine was determined to be 1.43 for the Botella clay loam at a bulk density of 1.37 g cm^-3.

Average concentrations for the 20 FOMPs were compiled together to produce an average breakthrough curve. The average BTCs were fitted using both the CDE and MIM to compare the two models. The variability in estimated parameters and mass recoveries from each probe and corresponding BTC was examined.

	Results and discussion

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions REFERENCES

 
General Transport Variability
The BTCs for all 20 FOMPs for two separate miscible displacement experiments are shown in Fig. 2 and 3 . Note that the FOMPs are consecutively numbered in relation to their position (i.e., Probe 1 is between Probe 20 and Probe 2, etc.). These figures correspond to the first two miscible displacement experiments (Exp. 1 and 2), where 19 irrigation drip points were used. As observed by Ghodrati et al. (1999), differences in the measured BTCs are a result of differences in small-scale variability in transport processes in the column.

View larger version (40K): [in this window] [in a new window]   Fig. 2 Breakthrough curves of the 20 fiber-optic miniprobes (FOMPs) from the first miscible displacement experiment with 19 irrigation drip points and at a flux of 1.07 cm h-1. Pv refers to normalized time expressed as pore volumes. Concentration is in mg/L

View larger version (41K): [in this window] [in a new window]   Fig. 3 Breakthrough curves of the 20 fiber-optic miniprobes (FOMPs) from the second miscible displacement experiment with 19 irrigation drip points and at a flux of 1.07 cm h-1. Pv refers to normalized time expressed as pore volumes. Concentration is in mg/L

In contrast, a difference in breakthrough time was observed at Probe 13, so that not all transport characteristics were conserved at this measurement point. Such differences are even more pronounced at other measurement points in the column. Transport measured at Probe 15 completely changed between the replicate runs with a much greater mass recovered and faster breakthrough time in the first run. Other probes also demonstrated this lack of consistency (e.g., Probes 3, 4, and 14).

It appears, at this scale of measurement, that transport response does not vary at certain locations. However, at other locations, small changes between replicate column experiments may produce a completely different response. Although the boundary conditions were assumed to be the same and the column was at steady state, the BTC response measured by the FOMPs varied from point to point and also from run to run. This may indicate differences in the actual boundary conditions and changes in flow pathways at this measurement scale for the two identical displacement runs. As discussed, this is exemplified in the transport behavior observed by Probe 15 (Fig. 2 and 3).

Plotting the corresponding CV for all 20 measurement points (FOMPs) as a function of time may be an additional characterization technique for miscible displacement experiments. A similar analysis was performed by Lennartz and Kamra (1998) in 24 undisturbed soil samples. The column-average BTCs (for 20 FOMPs) for the first five miscible displacements may be seen in Fig. 4 . The second y-axis is the coefficient of variation (CV) of the average concentration from all 20 channels for each sampling time. Plotting CV as a function of time enabled us to view the heterogeneity associated with important properties of a BTC (such as arrival time, maximum concentration, tailing, etc.) at 20 points within a soil column.

View larger version (17K): [in this window] [in a new window]   Fig. 4 Average breakthrough curves (BTCs) and corresponding coefficient of variation as a function of time for (a) BTC 1, (b) BTC 2, (c) BTC 3, (d) BTC 4, and (e) BTC 5

This analytical tool enabled a more complete description of the spatial variability in BTCs from the 20 measurement points. The response of CV as a function of time would be minimized when the porous media is homogenous. Therefore the strength of the CV response would increase when the media is more variable. This approach can then be used to characterize the media's heterogeneity with respect to solute transport processes.

Transport Parameter Variability
Column-averaged BTCs (average of 20 individual FOMP BTCs) for each of the five displacement studies were used to test whether the CDE or MIM was a more appropriate representation of the data. It is clear in Fig. 5 that the MIM produced a much better fit to the solute BTCs measured by the FOMPs. The correlation coefficients (r²) for the CDE were 97.5, 97.9, 98.1, 98.4, and 93.6% for BTCs 1 through 5, respectively. The r² values for the MIM, presented in Table 2 , were all >99.2% and some exceeded 99.9%. Mass recoveries calculated using the MIM were nearly identical to that of the BTCs (Table 2).

View larger version (32K): [in this window] [in a new window]   Fig. 5 Average breakthrough curves (BTCs) and corresponding fits of the mobile–immobile water model (MIM) and convective–dispersive equation (CDE) for (a) BTC 1, (b) BTC 2, (c) BTC 3, (d) BTC 4, and (e) BTC 5

Mass recoveries of 60 to 70% indicate that 20 sampling points at this scale may not adequately describe flow processes for the entire cross-sectional area of the column within a 95% confidence (Tables 2 and 3) . Alternatively, it is possible that even in homogeneously packed columns that a majority of the solute transport occurs in a small percentage of the total pore space (Rashidi et al., 1996). If this is the case, depending on the size and distribution of the low- and high-flow domains relative to the FOMP measurement size, measurements from the FOMPs may give greater weight to the lower-flow domain. If this occurs, a flux-dependent bias in the mass recovery may result. The large range of mass recoveries for the individual measurement points in the miscible displacement experiments may also be the result of such an effect. For example, mass recoveries in BTC 1 ranged from 19 to 106%, with an average of 66% and CVs all >20% (Table 2). This issue of whether the FOMPs samples a representative proportion of the existing flow domains at this scale warrants further examination.

These results are in contrast to results from a similar study of a silica sand column, which required only one to six sampling points at the small scale to characterize mass recovery with a 90% confidence level (Ghodrati et al., 1999). This difference is likely explained by the more complex flow behavior and the greater pore size distribution in the clay loam soil. The estimated minimum number of samples also illustrates the changes in variability with the number of drip irrigation points and flux. The minimum sample size needed to characterize mass recovery increases as the flux decreases, ranging from 71 to 267 at 95% confidence and 5 to 17 at 80% confidence (Table 3).

The immobile-phase parameters _m and are more difficult to interpret, due to their lack of uniqueness (White et al., 1998). Although the sample sizes necessary to characterize these parameters are relatively low, this may be misleading, due to their inability to quantitatively describe the physical processes. Hence we report these values for their qualitative information. The presence of the immobile phase is apparent in the improved fits of the BTCs by the MIM. Subsequently, _m and can help explain the results of the experiments that studied different irrigation systems and flux rates.

Effect of Different Irrigation Systems
One could expect that a decrease in the number of irrigation drip points would increase the variability in transport response. This would occur when there are not enough irrigation drip points to have uniform (i.e., one-dimensional) flow at a specific measurement depth. Two additional BTCs (6 and 7) were performed, using only one drip irrigation point and resulting in an average mass recovery for all 20 channels of 0.36 and 0.24, with CVs of 16 and 30% respectively (data not shown). These CVs are not different from the other BTC values seen in Table 2; however, the low mass recovered (averaging 0.36, 0.24) suggests that flow was not yet one-dimensional using only one irrigation point for the entire 78 cm² soil surface area. This consistently low mass recovery for one irrigation drip point suggests that the majority of the mass bypassed the probes. Since the drip point was placed over the center of the column, the flow was focused through the center of the column. In this instance, solute transport would not be one-dimensional.

Examination of the mass recovered and corresponding CVs for the 7 and 19 irrigation points (comparing BTCs 1 and 2 to 3 and 4) demonstrates that both one channel per 4 and 11 cm² surfaces were acceptable to produce consistent results at a 10-cm depth. A greater density of irrigation points may be necessary for more heterogeneous undisturbed soils.

Effect of Flux Rate
Breakthrough curve 5 was performed at a flux nearly one order of magnitude below the others. Comparing data from BTCs 3 and 4 to BTC 5, we observed that the CVs for most parameters were similar except for mass recovery, where the CV for BTC 5 (39%) is slightly larger than the BTCs 3 and 4 (20 and 31%). At the lower flux, greater tailing is obvious, likely explained by the increasing role of the immobile phase (noted by the lower _m, and ). The lower flux allows more time for interaction between the soil and the solute. As a result, the combined effects of a decreased immobile partitioning and an increased immobile phase create greater variability in mass recovery.

	Summary and conclusions

TOP ABSTRACT INTRODUCTION Materials and methods Results and discussion Summary and conclusions REFERENCES

 
This study examined small-scale measurements of solute transport in a repacked clay loam soil column using a multiplexed-FOMP system. FOMPs were found to be an accurate tool for measuring solute transport at spatial scales comparable to soil aggregates. In the clay loam soil, the MIM fit the solute BTCs better than the CDE. This study was designed to compare point-to-point variability in transport processes using FOMPs as the measurement tool.

Plotted CVs of the average BTC of 20 probes may be a useful analytical technique to better understand spatial variability in transport processes. The maximum CV occurred as the solute moves into the measurement plane, while a second increase in CV became visible as the mobile phase exited. Then, the signal slowly returned to the background variability as the immobile phase left the sampling depth. This approach has the potential to be developed for further examinations in solute transport variability.

Analysis of the minimum number of sample points at this scale demonstrated that dispersion and mass recovery were much more variable than pore water velocity in this soil. However, even in BTC 5 with the lowest flux and most variable conditions, only 17 sampling points were necessary to describe the column-averaged transport parameters within 20% of the mean.

Through a comparison of two different irrigation densities and two different fluxes, we observed some tendencies in solute transport variability. There appears to be little difference between using one irrigation channel per each 4 and 11 cm² of column surface area. However, it was found that one channel per 78 cm² of the column surface was not adequate to produce one-dimensional flow at a depth of 10 cm and at a flux of 1.07 cm h^-1. The BTC run at the low flux (0.1 cm h^-1, i.e., one order of magnitude below the others) had a greater immobile phase. The reduced flux allowed greater time for interaction between the soil matrix and the solute, resulting in greater spatial variability in mass recovery. We also observed that flux rate appeared to have more influence on variability in solute transport parameters than density of irrigation points.Krohn Jorgensen 1988

	ACKNOWLEDGMENTS

 
The authors thank the Kearney Foundation of Soil Science for supporting this research. Dr. Garrido has been supported by a postdoctoral grant from the Ministerio de Educacion y Cultura (Spain).

Received for publication February 8, 1999.

	REFERENCES

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