Parameterisation of physically based solute transport models in sandy soils.
Although primarily a process reported in structured soils, the non-equilibrium behaviour of tracers had also been observed in sands and granular material (De Smedt and Wierenga 1984; Bond and Wierenga 1990; Ghodrati and Jury 1990). In these cases, the solute movement was successfully modelled using the mobile-immobile model (MIM) (Eqns 1 and 2) (De Smedt and Wierenga 1984; Bond and Wierenga 1990):
(1) [[theta].sub.m] [[differential][C.sub.m]/[differential]t] + [[theta].sub.im][[differential] [C.sub.im]/[differential]t] = [[theta].sub.m][D.sub.m] [[[differential].sup.2][C.sub.m]/[differential][z.sup.2]] - V [[differential][C.sub.m]/[differential]z]
(2) [[theta].sub.im] [[differential][C.sub.im]/[differential]t] = [alpha] ([C.sub.m] - [C.sub.im])
where [[theta].sub.m] and [[theta].sub.im] are the mobile and immobile water contents ([m.sup.3]/[m.sup.3]) and [theta] = [[theta].sub.m] + [[theta].sub.im], [C.sub.m] and[ C.sub.im] are the solute concentration in the mobile and immobile regions (g/[m.sup.3]), [D.sub.m] is the dispersion coefficient ([mm.sup.2]/h) only active in the mobile region, and V is pore water velocity as q = [V.sub.m][[theta].sub.m] where [V.sub.m] is velocity in the mobile region (mm/h), q is Darcy's water flux (mm/h), and [alpha] is a solute exchange coefficient between the mobile and immobile regions ([h.sup.-1]).
In granular materials such as sands and glass beads, researchers had found between 0% and 40% immobile water in laboratory and field experiments (Table 1). Conflicting results as to the presence of immobile water in non-aggregated porous media (sands) occur (Bond and Wierenga 1990). Steady unsaturated and saturated flow regimes indicated immobile water in sands, but not when the flow was unsteady (Bond and Wierenga 1990). Table 1 also revealed that the reported range of the MIM solute exchange coefficient (ct) varied greatly. In general, a solute pulse exhibited asymmetry when the exchange coefficient was small relative to flow rate.
The solute transport parameters could be determined using different methods, which included: (i) pulse breakthrough curves (pulse-BTC), (ii) frontal breakthrough curves (frontal-BTC), (iii) single tracer method (Clothier et al. 1992), or (iv) sequential tracer experiments (STE) (Jaynes et al. 1995). The amount of non-equilibrium present could also be estimated using BTCs (Jardine et al. 1993). Each method has various limitations for use, sensitivity to non-equilibrium and difficulty in measuring MIM parameters.
The ability to estimate MIM parameters for soil and flow properties would be extremely useful in solute transport studies. Predicted MIM parameters may give good initial estimates, which may assist in determination of the measurement technique to be used.
The leaching of fertiliser-derived nitrate below the root-zone is of international concern. In Western Australia, deep percolation below the root-zone of sandplain soils under lupin-cereal rotation was between 100-200 mm/year of water over the growing season (Anderson et al. 1998), whereas deep percolation in clays was only 10-40 mm/year (Peck et al. 1973). With approximately 2 million hectares of deep sands currently cropped mainly with 2-year lupin-cereal rotations, deep percolation and associated nitrate leaching is of particular importance because it constitutes a direct economic loss to growers and may also lead to long-term soil acidification (Ritchie 1996). The factors that control nitrate leaching could be investigated by solute transport modelling and it was important to ascertain if the CDE or MIM should be used as the basic physical model for solute transport in these sandy soils.
The aims of this paper were therefore to:
(1) examine if immobile water was present in these sands by the use of a variety of estimation techniques and if so how much influence does it have on the solute transport;
(2) determine whether for granular soils, the MIM or CDE parameters could be estimated from more basic soil properties;
(3) compare MIM and CDE descriptions of solute transport in this particular soil in order to guide model selection for leaching studies.
Measurement of MIM parameters
Solute transport parameters that involved immobile water were historically measured by column and field breakthrough curves fitted to Eqns 1 and 2 by programs such as CXTFIT 2.0 which used a non-linear least squares routine (Parker and van Genuchten 1984). Although curve fitting would produce good agreement between observed and fitted data, the parameters could not be predicted without an experimental breakthrough curve.
The existence of non-equilibrium was determined in column experiments by the early arrival of the solute in the effluent and 'tailing' of the pulse BTC curve (Jardine et al. 1998). However, at distances away from the source, the BTC may have a more regular shape and the mobile-immobile character of the system would only be revealed in the apparent hydrodynamic dispersion (Eqns 3-5) (De Smedt and Wierenga 1984):
(3) [[lambda].sub.cde] = D/V
(4) [[lambda].sub.mim] = [D.sub.m]/[V.sub.m]
(5) [[lambda].sub.eff mim] = [[lambda].sub.mim] + [[(1 - [beta]).sup.2] V[theta]/[alpha]]
where [[lambda].sub.cde] is the dispersivity for the CDE, [[lambda].sub.mim] is the dispersivity for the MIM model, and [[lambda].sub.eff mim] is the effective mobile-immobile dispersivity.
The second term in Eqn 5 accounted for the diffusion in and out of aggregates or stagnant water pools, where the local equilibrium assumption applied if it was small compared with the first term (Vanderborght et al. 1997). If [[lambda].sub.eff mim] [much greater than] [[lambda].sub.cde] the soil displayed some physical non-equilibrium (Valochii 1985).
The single tracer method (Clothier et al. 1992) measured the immobile water content in situ, using a tension infiltrometer and bromide tracer. If there were immobile regions in the liquid phase and the solute does not have sufficient time to invade the immobile regions, then the total concentration of the soil solution was less than the input concentration. The immobile concentration was then:
(6) [[theta].sub.im] = [theta](1 - C/[C.sub.o])
where C is the concentration in the soil solution and [C.sub.o] is the input concentration.
This method assumed that the diffusion into the immobile regions was very slow and thus provided a measure of the immobile water content fraction. However, it does not give any information about the solute exchange coefficient. By assuming that exchange was slow, the immobile water content of the soil may be underestimated.
Jaynes et al. (1995) extended this method to provide estimates of both immobile water and the mass exchange coefficient, [alpha] (Eqn 7), using a sequence of fluorobenzoate organic tracers (STE method). The 4 fluorobenzoic acids were inert, easily measured by the same instrument and have similar transport properties to bromide (Benson and Bowman 1994). The order of application of the tracers does not affect transport behaviour or the determination of immobile water (Jaynes et al. 1995; Casey et al. 1997).
The Jaynes et al. (1995) method started with 1 tracer and progressively increased the number of tracers in the invading solution to 4, which gave a sequence of different solute residence times for tracer exchange between the mobile and immobile regions. Using Eqn 7, the graph of ln(1 - C/[C.sub.o]) v. time resulted in the intercept equal to the natural log of the ratio of immobile to total soil water content and the gradient was equal to -[alpha]/[[theta].sub.im]:
(7) ln[1-(C/[C.sub.o])] = -at */[[theta].sub.im] + ln ([[theta].sub.im]/[theta])
where t is the sampling time and [t.sup.*] is t adjusted to take into account the time for the tracer front to reach the sampling depth, z (Jaynes and Horton 1998):
(8) [t.sup.*] = t - ([sup.z[theta]]im/[theta])
The solute front of the last applied tracer should be well past the sampling depth otherwise erroneous results occur.
The assumptions in the STE were: (i) the concentration of the tracer in the soil was initially zero; (ii) tracer concentration in the mobile domain was equal to the input concentration [C.sub.o]; (iii) the resident soil concentration was C; and (iv) Dispersion in the mobile domain was negligible at the time of sampling (Jaynes et al. 1995).
The STE was tested along a field transect in a loamy sand by Casey et al. (1997), who observed a wide variation in the total water content, the immobile water content, and the exchange coefficient, but found no spatial correlation. The STE-estimated MIM parameters were found to be comparable to MIM parameters from frontal BTCs (Lee et al. 2000); however, there were few other comparisons.
Limitations to the STE and Clothier techniques have recently been reported by Clothier et al. (1998), Jaynes and Horton (1998), Jaynes and Shao (1999), and Snow (1999). Velocity, dispersivity, [alpha], and infiltration conditions were required to be within a specific range for the Clothier et al. (1992) and Jaynes et al. (1995) methods to be valid.
The STE (Jaynes et al. 1995) method may overestimate the [[theta].sub.im] region because of the assumption that [C.sub.o] = [C.sub.m] does not account for a changing tracer concentration in the mobile region with time due to dispersion (Casey et al. 1997). The opportunity to sample was limited and accuracy of determining [[theta].sub.im] and [alpha] with the STE method was reduced for low immobile water content (Snow 1999). Using simulated conditions where [[theta].sub.m]/[theta] = 0.6 and V = 10 mm/h, the STE Eqn 7 was not valid when the dispersivity was >5 mm and when fast exchange occurred (Jaynes and Shao 1999; Snow 1999). For high dispersivity, [lambda] >20 mm, sampling should only occur if q >20 mm/h and the last applied tracer has infiltrated >80 mm (Snow 1999).
The Clothier technique was also limited in its use by the dispersivity and [[theta].sub.im] (Clothier et al. 1998; Snow 1999). At high dispersivity, [lambda], the [[theta].sub.im] was overestimated and the range of ct for which reasonable estimates of [[theta].sub.im] occurred was reduced. Snow (1999) recommended that if [[theta].sub.m]/[theta] equals 0.625, then acceptable results occurred when q >10 mm/h, I >[lambda], and I <1.25 h x q. When the [alpha] was fixed at [10.sup.-7] [S.sup.-1], the dispersivity needed to be <10 mm for the Clothier method to work (Snow 1999).
It appeared that most of the current methods available to quantify non-equilibrium require a high degree of non-equilibrium for the various assumptions to be valid. Initial estimates of [[theta].sub.im], [alpha], [lambda], and D may be useful in determining the most appropriate method for particular porous materials.
Prediction of MIM parameters
An examination of the existing published data for granular media helped to define some limits to the MIM parameters. In particular, we were interested in velocity effects on the mobile dispersion coefficient, [D.sub.m], the mobile water content fraction, [beta], and the solute exchange coefficient, [alpha]. The issue of interpreting model parameters has recently addressed in detail by Griffioen et al. (1998). However, their analysis includes data from a number of studies with sorbing systems which introduced considerable uncertainty in the estimation of [beta].
The literature used here included only non-sorbing solutes in glass bead experiments under saturated and unsaturated conditions (Krupp and Elrick 1968; De Smedt and Wierenga 1984), repacked sand columns under unsaturated conditions (Gaudet et al. 1977; Bond and Wierenga 1990; Maraqa et al. 1997), and intact columns (Jacobsen et al. 1992; Zurmuhl 1998). The experimental conditions and summary of results are reported in Table 1.
Immobile water fraction
For granular media, [beta] displayed no trend in relation to the log of mobile pore water velocity (Fig. 1). [beta] generally ranged from 0.65 to 1.0, but values as low as 0.25 had been reported. However, the datasets of Gaudet et al. (1977) and Maraqa et al. (1997) indicated that the mobile water content increased linearly with increased flow velocity. From Fig. 1, an initial estimate of 10% immobile water content independent of pore water velocity was not unreasonable. The immobile water content for unstructured coarse sands had also been related to the effective residual water content from the water retention function (Jaynes and Horton 1988). As the Jaynes et al. (1985) approach also predicted that [beta] = 0.9 for coarse sands, there may be some physical basis for a priori specification of the immobile water content in granular media.
[FIGURE 1 OMITTED]
Diffusion and mobile water content was related to [alpha] based on Ficks law (Eqn 9) (van Genuchten and Wierenga 1986):
(9) [alpha] = a[D.sub.0][[theta].sub.m]/[tau][l.sup.2]
However, Griffioen et al. (1998) considered that [alpha] was governed more by mobile phase velocity than by molecular diffusion. De Smedt and Wierenga (1984) credited the increase in [alpha] with increased pore-water velocity to a higher mixing in the mobile phase at high pore-water velocities, whereas van Genuchten and Wierenga (1977) related it to shorter diffusion path lengths as a result of a decrease in the amount of immobile water.
For the combined literature data on granular media, log [alpha] appeared to increase with increasing log pore-water velocity (Fig. 2). A good correlation ([r.sup.2] = 0.77) was found between log [alpha] and log [V.sub.m] suggesting that an initial approximation was Eqn 10:
(10) [alpha] = 8.8 x [10.sup.-5] [V.sub.m.sup.1.48] ([r.sup.2] = 0.77)
[FIGURE 2 OMITTED]
Maraqa (2001) calculated a relationship of [alpha] = 0.0034 [V.sub.m.sup.0.85] with [r.sup.2] = 0.57 using only the data on fine non-aggregated media from Krupp and Elrick (1968), De Smedt and Wierenga (1984), and De Smedt et al. (1986). Maraqa (2001) was able to improve the estimate of [alpha] ([r.sup.2] = 0.91) by correlation with residence time (LR/[V.sub.m]), which used column length, retardation, R (in the case of sorbing solutes) and pore water velocity. However, for the non-sorbing experiments (R = 1) from the set of literature data reported here, the correlation of [alpha] to log residence time was less ([r.sup.2] = 0.68) than for log [V.sub.m] ([r.sup.2] = 0.77).
The CDE, MIM, and STE all required an estimate of the dispersion coefficient or dispersivity in order to predict the spread of the solute front. The dispersion coefficient was obtained by fitting to breakthrough curves in the laboratory and the field. To date, it had not been possible to predict the dispersion coefficient from more basic soil properties, but analysis of the literature does reveal some trends with velocity.
For steady state flow systems at constant water content, simple relationships were used to describe the hydrodynamic dispersion in terms of velocity only. For the granular media data set (Fig. 3), there was only a low correlation between [D.sub.m] ([mm.sup.2]/h) and [V.sub.m] (mm/h) ([r.sup.2] = 0.40) giving Eqn 11:
(11) [D.sub.m] = 4.8 [V.sub.m.sup.0.78] [r.sup.2] = 0.40
[FIGURE 3 OMITTED]
The saturation of the column could markedly affect the relationship between the dispersion coefficient and velocity. In saturated soil the dispersion was thought to increase linearly with velocity. However, in unsaturated soil the dispersion increased more rapidly than the saturated dispersion coefficient up to a limiting water content where the [D.sub.sat] equalled the [D.sub.unsat] (Matsubayashi et al. 1997). Even though solute dispersion in unsaturated conditions could be up to 20 times higher than under saturated conditions, when unsaturated experiments were fitted to the MIM, the D values were consistent with those obtained from saturated experiments (De Smedt and Wierenga 1984).
In granular media the dispersion was also reported to be dependent on fundamental material parameters such as the average grain size. The more homogeneous the pore size distribution the less dispersion. For example, solute transport through uniform diameter glass bead systems typically exhibited low dispersion compared with less homogeneous systems (Starr and Parlange 1975).
The grain Peclet number accounted for the velocity, diffusion effects of different tracers, and different average particle diameters. Dispersion was related to the grain size Peclet number by (Rose 1977):
(12) D/[D.sub.0] = [tau] + a[Pe.sup.b.sub.g]
where [tau] is the tortuosity factor which equals D/[D.sub.o] when V = 0. In saturated porous media, [tau] is often assumed to be 0.67, [Pe.sub.g] is the grain size Peclet number = Vd/[D.sub.o], d is the characteristic dimension of the medium i.e. the mean particle diameter, V is the velocity and a and b are fitting parameters.
Plots of the log dispersion v. log grain Peclet number for the granular media were well correlated ([r.sup.2] = 0.68) giving Eqn 13 (Fig. 4):
(13) [D.sub.m] = 132 [Pe.sub.g.sup.0.84]
[FIGURE 4 OMITTED]
For this analysis of the literature data, the grain Peclet number was either provided in the original paper or calculated as the geometric mean cumulative mass fraction. Therefore, the grain Peclet number may be used to give an initial estimate of dispersion for granular media.
In the experiments reported here, the solute transport parameters were determined after analysis of column effluent breakthrough curves, sequential tracer experiments (Jaynes et al. 1995), and single tracer experiments (Clothier et al. 1992) on the same core. The measured velocity in column experiments was also used to predict [D.sub.m] from Eqn 13 and [alpha] from Eqn 10, assuming [beta] was 0.9 and the grain size was 0.157 mm. The ability to predict the solute BTC was tested using the literature relationships to predicted MIM parameters and the estimated parameters from the STE, with known [D.sub.m].
Materials and methods
Soil material and tracers
Soils from a sandplain profile from Moora, Western Australia, were used for the solute transport experiments. Topsoil (0-0.2 m) and the subsoil (0.2-1.5 m) were classified by Anderson et al. (1998) as Tenolsols (Isbell 1996); yellow siliceous sand (McArthur 1991); Typic Xeric Psamment (Soil Survey Staff 1987); Uc5.22 (Northcote 1979). In these sands the clay content increased with depth from 4% near the soil surface to nearly 10% at 1.5 m.
Tracers were added to the soil in solutions of 0.005 M Ca[Cl.sub.2] containing bromide (50 mg/L), 2,6-difluorobenzoic acid (DFBA) (50 mg/L), 2,3,6-trifluorobenzoic acid (TFBA) (50 mg/L), and pentafluorobenzoic acid (PFBA) (50 mg/L).
Fluorobenzoic acids were extracted from the soil solution by shaking 10 g of wet soil with 10 g of de-ionised water for 5 min then allowing the suspension to settle prior to filtration and analysis. Concentration of fluorobenzoic acids measured in the soil extract was corrected for the extraction dilution using the known wet soil water content, to give C. The concentration of the FBA in the final applied tracer mixtures gave [C.sub.o]. Samples of the outflow solution, and the infiltration rate was monitored during the experiment.
The FBA's and bromide were analysed using HPLC ion chromatography, using a spherisorb SAX (strong anion exchange) column (250 mm length and 4.5 mm diameter with 5 pm particle size) with a UV detector at 205 nm, and solute of 40% Acetonitrile and 60% 5 g/L K[H.sub.2]P[O.sub.4], pH adjusted to 2.7, at a flow of 1 mL/min. Deuterium was measured using mass spectrometry by the CSIRO (Land and Water) laboratories, Wembley, WA.
Laboratory core set-up
Repacked cores, 0.1 m diameter by 0.1 m length, at a bulk density of 1.6 Mg/[m.sup.3] for the topsoil and 1.8 Mg/[m.sup.3] for the subsoil, which had at least one wet-dry cycle, were used for this study. Repacked cores were used because the field site was deeply ripped annually. Consolidation occurred in the field after several wetting and drying cycles and the laboratory core preparation procedure was designed to mimic this process in order to produce reproducible uniform cores for experimentation. Comparisons were made with undisturbed field cores obtained later in the season after consolidation had occurred.
A laboratory solute transport set-up similar to Magesan et al. (1995) was used. This comprised a tension infiltrometer placed on a core to apply a tension at the surface and a mariotte tension control via a porous plate at the base to apply the same tension at the bottom of the core. This set-up established a uniform water content profile and unit hydraulic gradient across the core. The soil was equilibrated until a constant velocity was established using a solution of 0.005 U Ca[Cl.sub.2]. Tracer studies were performed at 2 flow rates by setting the surface supply and basal tension at -20 and -60 mm [H.sub.2]O following the method of Jaynes et al. (1995).
Breakthrough curves were obtained by applying a pulse of approximately 1 pore volume of tracer and collecting the outflow solution. The pore volume was determined by weighing the wet core at the cessation of the BTC experiment and deducting the dry weight of the soil core. The concentration of bromide, fluorobenzoic acid, or deuterium was measured and compared with the input concentration, [C.sub.o]. The volume flux density was measured and assumed equal to the hydraulic conductivity at unit gradient. The pore water velocity, V, was determined as the volume flux density divided by the volumetric water content of the core. The frontal BTCs (step input) measured during the STE, were also fitted to the MIM.
The replicates and experimental conditions for the pulse BTC and frontal BTC are provided in Table 2.
Sequential tracer experiment and single tracer methods
Each column from the BTC experiments was flushed with 0.005 M Ca[Cl.sub.2] for about 20-50 pore volumes until no residual fluorobenzoic acids were detected in the effluent. The sequential tracer experiments applied tracers for varying lengths of time to determine exchange into the immobile region. The soil was initially equilibrated with 0.005 M Ca[Cl.sub.2] and then the tension infiltrometer was replaced with a tension infiltrometer filled with the first tracer solution of bromide, and after approximately 2 pore volumes had infiltrated it was replaced with a tension infiltrometer containing bromide and DFBA. After a further 2 pore volumes it was then replaced with a tension infiltrometer containing bromide, DFBA, and PFBA, then finally replaced with a tension infiltrometer containing bromide, DFBA, PFBA, and TFBA. At the cessation of the experiment, the first 5 mm of the core was discarded as it contained contact material, then the next 20 mm of the core was subsampled, in quadruplicate, to extract the tracers and to measure the soil water contents.
For the STE, the immobile water and exchange coefficients were determined by Eqn 7 for the topsoil and subsoil at -20 mm and -60 mm water tension. The STE parameters were calculated from the ln(1 - C/[C.sub.o]) v. corrected time plots, where the intercept of the least squares regression was ln([[theta].sub.im]/[theta]) and gradient was -[alpha]/[[theta].sub.im]. The 95% confidence interval of the intercept and gradient in the regression of ln(l - C/[C.sub.o]) v. time data was transformed to determine the relative error and, therefore, 95% confidence interval in the [[theta].sub.im]/[theta]) and [alpha] STE parameters.
The immobile water content was calculated for the single tracer (Clothier et al. 1992) technique, using the concentration of the last applied tracer (TFBA) and using Eqn 6. The experimental conditions and replicates for the STE and single tracer experiment are provided in Table 2.
Results and discussion
The immobile water determined by the STE, ranged from 11 to 13% in the topsoil and 4.5 to 21% in the subsoil. The solute exchange coefficient ranged from 0.014 to 0.024 [h.sup.-1] in the topsoil and 0.002 to 0.3 [h.sup.-1] in the subsoil (Table 3). There was a strong linear relationship between ln(1 - C/[C.sub.o]) and time ([r.sup.2] > 0.9) in both the topsoil and subsoil sequential tracer experiment. This implied that Eqn 4 was a reasonable representation of physical non-equilibrium solute transport processes in the soil (Jaynes and Horton 1998). The 95% confidence interval for [[theta].sub.im]/[theta] in the topsoil was narrow for all the cores except for core 4 but was generally wide in the subsoil. The 95% confidence interval for a was wide in both the topsoil and subsoil.
The Clothier single tracer method had immobile water, which ranged from 6 to 10% in the topsoil and 3 to 13% in the subsoil (Table 3). Assuming that there was no exchange between the mobile and immobile region, such as the Clothier et al. (1992) method, produced lower immobile water content estimates than the STE.
The frontal BTCs in the topsoil and subsoil showed varied degrees of non-equilibrium, which ranged from no immobile water (core 1, core 2, and core 13), a small amount of immobile water of 4% (core 11), to large immobile water contents of 20% (core 3) (Table 3). Values of the solute exchange coefficient, [alpha], were undefined when immobile water content was zero (core 1, core 2, and core 13), 0 or 0.37 [h.sup.-1] with a wide 95% confidence interval (core 11 and core 3, respectively). An example of the frontal BTC is shown in Fig. 5. Unfortunately, wide 95% confidence intervals for both [[theta].sub.im]/[theta] and [alpha] caused difficulty in determining the presence of immobile water using frontal BTCs. The frontal BTC lacked the sensitivity to immobile water exchange that could be obtained from the tail of a pulse BTC, which may explain why the uncertainty in the MIM parameters increased 5-fold compared with the pulse BTC (Vanderborght et al. 1997).
[FIGURE 5 OMITTED]
Immobile water contents estimated from the pulse BTC ranged from 1 to 31% in the topsoil and 0 to 6% in the subsoil. There were generally wide 95% confidence intervals for the fitted [beta] parameters, which raised uncertainty about their physical validity. The [alpha] coefficient was even more variable as it ranged from 1 x [10.sup.-8] to 4.51 [h.sup.-1] in the topsoil and subsoil, with wide 95% confidence intervals. Wide 95% confidence intervals had also been reported by De Smedt and Wierenga (1984) and Schulin et al. (1987). Consequently, the exchange coefficient measured with the STE could not be confirmed by the BTC fitted data due to the very wide parameter confidence intervals obtained from CXTFIT.
The MIM only marginally increased the fit of the BTC compared with the CDE (Fig. 6), shown by the reduced sum of squares (SSQ) (Table 4).
[FIGURE 6 OMITTED]
The MIM parameters obtained from the STE were used to produce STE-BTCs using the forward problem of CXTFIT2.0 (Fig. 7). [D.sub.m] was the only unknown parameter and was taken from the pulse BTC fitted to the MIM (Table 4). The STE parameters produced reasonable BTCs for the laboratory data. Resident concentration profiles were used for calculating STE parameters, and this may explain some of the discrepancy when describing laboratory flux concentration BTCs (Lee et al. 2000).
[FIGURE 7 OMITTED]
The predicted BTC from literature relationships, Eqn 10 and Eqn 13, with [beta] equal to 0.9 compared well with the measured BTC (Fig. 7). However, as [D.sub.m] was generally higher in the measured BTCs than predicted from the literature (crosses in Fig. 4), the measured BTCs had lower peaks and more spread than predicted. Despite the wide confidence interval of the fitted [alpha] parameter, the literature derived parameter relations appear to be able to predict ct reasonably well, except for core 2, which had a nearly zero (1.5 x [10.sup.-8]) exchange coefficient.
The physical non-equilibrium in column experiments was tested by comparing the dispersivity of the CDE, [[lambda].sub.cde], and MIM, [[lambda].sub.mim] models with the effective dispersivity [[lambda].sub.eff] (Eqns 3-5) (Table 4). As [[lambda].sub.eff] was much larger than [[lambda].sub.cde], there were signs of non-equilibrium in this soil (Table 4). A possible reason for the insensitivity of the BTC to the degree of non-equilibrium was the large solute application time. However, the application time was similar to the application time in the STE.
The high pore water velocities that occurred in this soil may also reduce the ability to differentiate between equilibrium and non-equilibrium. Pulse BTCs with [V.sub.m] equal to 10 and 500 mm/h with [beta] = 0.9 and [D.sub.m] and [alpha] calculated from the literature relationships showed that the difference between the CDE- and MIM-predicted BTC decreased as [V.sub.m] increased (Fig. 8a, b).
[FIGURE 8 OMITTED]
The column length also influenced the ability to discriminate between equilibrium and non-equilibrium transport in column BTC experiments. The predicted position of the solute peak with a 1.5-m column was significantly different between the CDE and MIM when plotted against time, not pore volumes (Fig. 9). However, for shorter column lengths of 0.1 m and 0.5 m, there was less difference between the CDE and MIM (Fig. 9). Even though the MIM parameters appeared to be minor and inconsistent in these sands, the column length or solute leaching depth of interest was an important factor in solute transport model choice.
[FIGURE 9 OMITTED]
The low immobile water content possibly indicated that a low degree of physical non-equilibrium in the Moora sands was difficult to detect with the single tracer, STE and BTC methods under these laboratory conditions. Parameter optimisation methods, such as BTC fitted to the MIM, may not be able to effectively discriminate between equilibrium and non-equilibrium transport when the degree of non-equilibrium was low (Vanderborght et al. 1997; Nkedi-Kizza et al. 1983; Kool et al. 1987).
Average immobile water content of 10% was measured in the sandy soils from Moora using a frontal BTC, pulse BTC, single tracer method, and sequential tracer method. The rate of exchange between the mobile and immobile regions was estimated with the sequential tracer experiment, but could not be confirmed by analysis of the BTCs due to parameter insensitivity of the exchange coefficient in the fitting procedure.
The predicted BTC using the STE and literature approximated MIM parameters were very similar when the dispersion coefficient was held constant. As the immobile water content and dispersion coefficient were similar for the two methods, we may conclude that the MIM model was insensitive to alpha in these sands.
Prediction of solute transport parameters from basic soil properties was difficult, but some useful approximations have been found. In granular media, such as the Moora sands, an estimate of mobile water fraction, [beta] equal to 0.9, was reasonable for all the datasets. Good initial approximates of the mass exchange coefficient ([alpha]) and the mobile dispersion coefficient ([D.sub.m]) were found through a relationship with the mobile velocity ([V.sub.m]).
Results show that with increasing depth, the difference between the CDE and MIM became more pronounced. Therefore, the type of problem to be modelled may determine the choice between the CDE and MIM as the solute transport model in this sand.
Table 1. Experimental conditions and results of literature mobile-immobile solute transport experiments in sands and glass beads d was the average particle size radius Investigator Porous medium % Clay d Intact or (mm) repack Bond and Wierenga 1990 4.7 0.14 Repack De Smedt et al. 1986 - 0.3 Repack De Smedt and Wierenga 1984 Glass beads 0.1 Repack Gaudet et al. 1977 - 0.3 Repack Jacobsen et al. 1992 - - Intact Krupp and Elrick 1968 Glass beads 0.1 Repack Maraqa et al. 1997 1.5 - 2.0 0.24 Repack Zurmuhl 1998 4 - Intact Oliver and Smettem, current study 4-6 Repacked Lee et al. 2000 (A) 0 - Repacked Okom et al. 2000 (A) 5.5 - Field Investigator Experimental conditions State Column length (m) Bond and Wierenga 1990 Steady/ 0.25 unsteady De Smedt et al. 1986 Unsteady/ unsaturated 1 De Smedt and Wierenga 1984 Saturated/ 0.30 unsaturated Gaudet et al. 1977 Unsaturated 0.94 Jacobsen et al. 1992 Unsaturated 1.0 Krupp and Elrick 1968 Unsaturated 0.1 Maraqa et al. 1997 Unsaturated 0.302 Zurmuhl 1998 Unsaturated 0.145 Oliver and Smettem, current study Unsaturated 0.10 Lee et al. 2000 (A) Saturated 0.12 Okom et al. 2000 (A) Unsaturated - Investigator Experimental conditions Water Tracer content ([m.sup.3]/ [m.sup.3]) Bond and Wierenga 1990 0.340 [sup.3][H.sup.2]O De Smedt et al. 1986 0.055-0.127 [sup.3][H.sup.2]O De Smedt and Wierenga 1984 0.008-0.279 [sup.36]Cl Gaudet et al. 1977 0.200-0.256 Ca[Cl.sub.2] Jacobsen et al. 1992 0.148-0.156 Cl Krupp and Elrick 1968 0.098-0.370 Cl Maraqa et al. 1997 0.150-0.410 [sup.3][H.sub.2]O Zurmuhl 1998 0.207-0.234 [sup.3][H.sub.2]O Oliver and Smettem, current study 0.26-0.35 FBA Lee et al. 2000 (A) 0.390-0.400 FBA Okom et al. 2000 (A) - Br Investigator MIM fitted parameters [[theta].sub.im]/ [alpha] (1/h) [theta] Bond and Wierenga 1990 0.01-0.04 0.00-0.01 De Smedt et al. 1986 0.27-0.42 0.01-0.03 De Smedt and Wierenga 1984 0.12-0.20 0.03-2 Gaudet et al. 1977 0.04-0.40 0.03-0.1 Jacobsen et al. 1992 0.06-0.27 0.0002-0.0006 Krupp and Elrick 1968 0.00-0.16 0.016-0.280 Maraqa et al. 1997 0.02-0.10 0-0.0005 Zurmiihl 1998 0.12-0.17 0.067 Oliver and Smettem, current study 0.0-0.3 0-1.3 Lee et al. 2000 (A) 0.04-0.13 0.002-0.04 Okom et al. 2000 (A) 0.05-0.20 N/A (A) Not used in literature comparisons Table 2. Laboratory experimental conditions for the pulse BTC, frontal BTC, Clothier, and STE experiments Pulse BTC Applied tension K V [theta] (mm) (mm/h) (mm/h) Topsoil Core 1 -20 148 495 0.30 Core 2 47.4 153 0.31 Core 3 -60 30.0 103 0.29 Core 4 14.0 56 0.26 Subsoil Core 11 -20 96.9 373 0.26 Core 12 63.8 283 0.23 Core 13 -60 57.5 250 0.23 Core 14 52.5 219 0.24 STE, Clothier, and frontal BTC Frontal K V [theta] (Y/N) (mm/h) (mm/h) Topsoil Core 1 115 371 0.31 Y Core 2 56.9 186 0.31 Y Core 3 45.2 167 0.27 Y Core 4 22.1 85 0.26 N Subsoil Core 11 92 368 0.26 Y Core 12 54 234 0.23 N Core 13 14.5 75 0.19 Y Core 14 19.9 105 0.19 N Table 3. Immobile water content fraction and exchange coefficient ([h.sup.-1]) in the topsoil and subsoil cores determined by the frontal BTC, pulse BTC, STE, and Clothier methods [[theta].sub.im]/[theta] Frontal Pulse BTC BTC Core 1 [approximately equal to] 0 0.21 [+ or -] 0.62 Core 2 [approximately equal to] 0 0.01 [+ or -] 0.08 Core 3 0.20 [+ or -] 0.28 0.08 [+ or -] 0.13 Core 4 n.a. 0.31 [+ or -] 0.4 Core 11 0.041 [+ or -] 0.16 0.055 [+ or -] 0.19 Core 12 n.a. [approximately equal to] 0 Core 13 [approximately equal to] 0 [approximately equal to] 0 Core 14 n.a. 0.06 [+ or -] 0.15 [[theta].sub.im]/ [alpha] [theta] STE Clothier Frontal BTC Core 1 0.13 [+ or -] 0.02 0.10 u.d. Core 2 0.12 [+ or -] 0.02 0.06 u.d. Core 3 0.11 [+ or -] 0.02 0.06 0.37 [+ or -] 0.1 Core 4 0.13 [+ or -] 0.5 0.08 n.a. Core 11 0.045 [+ or -] 0.06 0.03 0.000 [+ or -] 0.14 Core 12 0.21 [+ or -] 0.16 0.12 u.d. Core 13 0.15 [+ or -] 0.12 0.11 u.d. Core 14 0.08 [+ or -] 0.08 0.13 n.a. [alpha] Pulse STE BTC Core 1 4.51 [+ or -] 0.66 0.014 [+ or -] 0.005 Core 2 1.5E-08 [+ or -] 0.04 0.024 [+ or -] 0.009 Core 3 0.015 [+ or -] 0.045 0.018 [+ or -] 0.004 Core 4 0.063 [+ or -] 0.17 0.015 [+ or -] 0.08 Core 11 0.13 [+ or -] 0.20 0.005 [+ or -] 0.02 Core 12 u.d. 0.3 [+ or -] 0.3 Core 13 u.d. 0.003 [+ or -] 0.01 Core 14 0.49 [+ or -] 0.07 0.002 [+ or -] 0.007 u.d., Exchange coefficient undefined; n.a., frontal experiment not performed for this core. Table 4. Topsoil and subsoil column fitted CDE and MIM parameters for the frontal BTC and pulse BTC Method CDE V D 1 (mm/h) ([mm.sup.2]/h) (mm) Core 1 Pulse 495 3820 [+ or -] 10 7.7 Core 1 Frontal 371 13240 [+ or -] 100 36 Core 2 Pulse 153 730 [+ or -] 10 4.7 Core 2 Frontal 186 760 [+ or -] 860 4.9 Core 3 Pulse 103 1280 [+ or -] 20 12.4 Core 3 Frontal 167 760 [+ or -] 10 4.6 Core 4 Pulse 56 580 [+ or -] 10 10.3 Core 11 Pulse 373 1420 [+ or -] 10 3.8 Core 11 Frontal 368 8220 [+ or -] 10 22.4 Core 12 Pulse 283 570 [+ or -] 10 2.0 Core 13 Pulse 250 1230 [+ or -] 20 4.9 Core 13 Frontal 75 550 [+ or -] 10 5.4 Core 14 Pulse 219 470 [+ or -] 10 2.2 Method SSQ [V.sub.m] ([10.sup.-3]) (mm/h) Core 1 Pulse 22 634 Core 1 Frontal 5 Core 2 Pulse 18 154 Core 2 Frontal 60 Core 3 Pulse 144 111 Core 3 Frontal 20 209 Core 4 Pulse 25 81 Core 11 Pulse 51 394 Core 11 Frontal 17 370 Core 12 Pulse 32 Core 13 Pulse 180 Core 13 Frontal 9 Core 14 Pulse 38 236 Method MIM [D.sub.m] [[lambda].sub.mim] ([mm.sup.2]/h) (mm) Core 1 Pulse 1750 [+ or -] 20 2.8 Core 1 Frontal Core 2 Pulse 720 [+ or -] 10 4.7 Core 2 Frontal Core 3 Pulse 1090 [+ or -] 20 9.8 Core 3 Frontal 210 [+ or -] 10 1.0 Core 4 Pulse 180 [+ or -] 30 2.2 Core 11 Pulse 1140 [+ or -] 20 2.9 Core 11 Frontal 770 [+ or -] 10 2.l Core 12 Pulse Core 13 Pulse Core 13 Frontal Core 14 Pulse 240 [+ or -] 10 1.0 Method [[lambda].sub.eff] SSQ (mm) ([10.sup.-3]) Core 1 Pulse 8.1 13 Core 1 Frontal Core 2 Pulse 4.7 17 Core 2 Frontal Core 3 Pulse 47.1 4 Core 3 Frontal 5.9 8 Core 4 Pulse 91.3 7 Core 11 Pulse 11.4 24 Core 11 Frontal 22500 12 Core 12 Pulse Core 13 Pulse Core 13 Frontal Core 14 Pulse 3.4 4
Thanks to Professor Graham Aylmore for his constructive criticism of this paper. The authors also thank the Grains Research and Development Council for financial support.
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Manuscript received 29 April 2002, accepted 18 November 2002
Y.M. Oliver (A) and K.R.J. Smettem (B,C)
(A) School of Earth and Geographical Sciences (Soil Science Discipline), Faculty of Natural and Agricultural Science, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia.
(B) Centre for Water Research, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia.
(C) Corresponding author; email: firstname.lastname@example.org
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|Publication:||Australian Journal of Soil Research|
|Article Type:||Author Abstract|
|Date:||Jul 1, 2003|
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