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Lateral Water Diffusion in an Artificial Macroporous System

Modeling and Experimental Evidence

P. Castiglione^*,a, B. P. Mohanty^,a, P. J. Shouse^a, J. Simunek^a, M. Th. van Genuchten^a and A. Santini^b

^a George E. Brown, Jr. Salinity Laboratory, 450 W. Big Springs Road, USDA, ARS, Riverside, CA
^b Department of Agricultural Engineering, University of Naples "Federico II", Italy
^* Corresponding author (paoloc{at}uidaho.edu)

B.P. Mohanty, currently, Biological and Agricultural Engineering, Texas A&M University, College Station, TX.

Received 14 June 2002.

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
In two-domain schematizations of macroporous soils or fractured rock systems, lateral mass exchange between macropores and the soil matrix is generally modeled as an apparent first-order process. With respect to lateral diffusion, the system is thus characterized by a single parameter, the transfer rate coefficient, which is difficult to estimate a priori. We conducted water infiltration experiments in a laboratory column with an artificial macropore. The novel design of the experimental setup allowed us to discriminate between matrix flow and macropore flow, from which we could estimate the water exchange flux between the two domains. Most of the parameters in a dual-permeability model could be determined independently of the experimental data. In particular, a theoretical expression for the transfer rate coefficient was derived by assuming lateral water and solute diffusion to be similar processes. Numerical analysis of the water exchange process revealed that the transfer coefficient depended also on the macropore conductivity. When this dependency was taken into account, the model reproduced the experimental data reasonably well.

Abbreviations: BTC, breakthrough curve • DPM, dual-permeability model • FOA, first-order approximation • MIM, mobile–immobile model • PAM, polyacrylamide

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
MOST DETERMINISTIC APPROACHES for modeling preferential flow in macroporous soils or unsaturated fractured rock rely on two- or multidomain continuum assumptions (Smettem and Kirkby, 1990; Cushman, 1990; Othmer et al., 1991; Pruess, 1999; National Resource Council, 2001). Typically, heterogeneous media are modeled as two overlapping porous systems, a high permeability domain associated with the macropore or fracture network and a low permeability domain associated with the matrix blocks. Exchange of mass (water and/or solute) between the two systems will occur in response to nonequilibrium conditions, thus reproducing lateral exchange phenomena often recognized in structured media (Beven and Germann, 1982). Inter-domain transfer processes are diffusion based and as such depend on the diffusivity of the matrix blocks and the geometric configuration of the preferred flow paths. When these processes are modeled by means of a first-order approximation (FOA), the system can be characterized by one unique parameter, the mass transfer rate coefficient. Despite extensive efforts in the past two decades, how closely the actual mass exchange process is captured by the first-order approximation and how to determine the transfer rate coefficients remain poorly understood.

First-order mass transfer models have been widely used to interpret results from solute transport experiments. For certain conditions (e.g., negligible matrix domain flux, steady-state water flow and instantaneous adsorption), the transfer rate coefficients for solute (_s) can be determined from moment analysis of the concentration breakthrough curve (BTC) (e.g., Valocchi, 1990). This methodology was tested by Hu and Brusseau (1995) in a series of leaching experiments through artificial soil columns. The authors explored different aggregate geometries, for which theoretical expressions of the transfer coefficients are available, and with most of the parameters of the two-region Mobile–Immobile Model (MIM) (van Genuchten and Wierenga, 1976) determined independently of the data.

In more general cases, for example when water moves through both the matrix and the macropore regions, experimental measurements of the mass exchange are difficult to make since more complex models with a large number of parameters are generally required. Matrix and macropore flows cannot be easily discriminated during water flow experiments, thus making the hydraulic characterization of the two domains very uncertain. On the basis of an analogy between water and solute transfer processes, Gerke and van Genuchten (1993b) suggested that the transfer rate coefficient for water (_w) can be derived from the corresponding coefficient for solute (_s), as determined using the MIM hypotheses. To date, this assumption has not been validated by experimental evidence, mostly because of technical limitations in monitoring the lateral exchange process.

We present results from infiltration experiments conducted on a soil column with an artificial macropore. Detailed knowledge of the geometry of the system and soil matrix properties, as well as the controlled laboratory conditions, allowed us to address some of the uncertainties mentioned above. For instance, we were able to discriminate matrix flow from macropore flow, and to measure the depth-integrated water exchange flux between the two domains. The experimental results were described reasonably well with a dual-permeability model, with most of the parameters determined independently of the data. A numerical analysis of the water transfer process also allowed us to determine the transfer rate coefficient for water, which otherwise would be a fitting parameter.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The dual-permeability model (DPM) used in this study to simulate vertical water flow through a single-macropore column was described in detail by Gerke and van Genuchten (1993a). The governing equations for one-dimensional flow are

[1]

[2]

in which the subscript "f" refers to the macropore domain, and "m" to the matrix domain; h (L) is the matric potential, K (L T^-1) the hydraulic conductivity, z (L) is the spatial coordinate, t (T) is time, _w (T^-1) is the water transfer term, representing the flux of water being exchanged between macropores and the soil matrix per unit volume of bulk soil, and w_f is a dimensionless weighting factor. The volumetric water content _f in Eq. [1] is defined as the ratio of the volume of water of the fracture domain (V_w,f) to the total volume of fractures (V_t,f) _f = V_w,f/V_t,f. Analogously, _m = V_w,m/V_t,m. The volumetric weighting factor (w_f) is defined as the ratio of the fracture domain volume relative to the total soil volume (V_t):

[3]

While some macroscopic quantities, such as water content or flux, for a dual-permeability medium are defined as weighted averages of the corresponding properties of the individual domains, this cannot be done for the hydraulic conductivity, since in general no unique pressure head gradient exists (Beven and Germann, 1982). When the system is in hydraulic equilibrium (h_f = h_m), however, it is possible to define the hydraulic conductivity as (Peters and Klavetter, 1988):

[4]

Equation [4] holds in particular for saturated conditions and thus permits us to estimate the macropore saturated conductivity (K_f,sat) from K_sat, K_m,sat, and w_f.

The interdomain water exchange flux is modeled by means of the first-order approximation (FOA):

[5]

in which h_f and h_m are averaged over some representative elementary volume, and _w (L^-1 T^-1) is the mass transfer rate coefficient for water. Assuming analogy between water and solute lateral exchange processes, Gerke and van Genuchten, (1993b) derived _w from the equivalent transfer rate coefficient for solute. The FOA for solute exchange flux (_s) is expressed as:

[6]

where _s (T^-1) is the transfer rate coefficient for solute, and c_f and c_m (M L^-3) are the solute concentrations for the fracture and the matrix domain, respectively. Assuming applicability of MIM (van Genuchten and Wierenga, 1976), _s is fully determined by geometry and diffusivity of the soil aggregates, and is generally approximated by the expression (van Genuchten and Dalton, 1986):

[7]

where H is a dimensionless geometry-dependent coefficient and (L) is the characteristic length of the matrix structure (e.g., the radius for spherical or cylindrical aggregates, or one-half of the fracture spacing for parallel rectangular matrix blocks); D_a,m (L² T^-1) is the effective diffusion coefficient of solute in the soil matrix (notice that the subscript "m" represents here the soil "matrix," not the "mobile" domain as is commonly done in literature). For simple geometries of the aggregates, theoretical values for the geometrical parameters in Eq. [7] can be derived (Valocchi, 1990; van Genuchten and Dalton, 1986). In particular, several expressions are reported in literature for cylindrical macropores (van Genuchten and Dalton, 1986; Gerke and van Genuchten, 1996; Young and Ball, 1995), which we found to give very similar results. Below we adopt the expression proposed by Young and Ball (1995) to be used in Eq. [7]:

[8]

[9]

In Eq. [8] and [9], a is the radius of the macropore, and b is the radius of the soil mantle surrounding the macropore (see Fig. 1).

View larger version (13K): [in this window] [in a new window]   Fig. 1. Scheme of the soil column with a vertical cylindrical macropore.

[10]

which is derived from Eq. [7] with the term K_aw replacing _mD_a,m. In Eq. [10], _w is a dimensionless scaling factor and K_a (L T^-1) the effective hydraulic conductivity function of the macropore–matrix interface, evaluated in terms of both h_m and h_f as follows:

[11]

In the absence of organic matter or other deposits along the macropore wall (which may alter the permeability of the aggregates at the interface), K_a is best represented by the matrix conductivity function K_m (Gerke and van Genuchten, 1993a).

Gerke and van Genuchten (1993b) and Gerke and van Genuchten (1996) tested the applicability of Eq. [10] for several aggregate geometries (spherical, rectangular slab, and cylindrical macropores) by comparing simulation results of the one-dimensional DPM with those generated using equivalent two-dimensional geometry-based transport models. For simplicity, the effects of gravity were neglected in their calculations. These numerical studies revealed that, in general, Eq. [10] performs well as long as the dimensions of the matrix blocks are not too large. Their results also suggest that, provided Eq. [11] is used, an average value of 0.4 for the scaling factor _w should be reasonably applicable to all of the geometries investigated. This value, however, may not be appropriate for describing water exchange when the vertical water flow in the matrix is considered, or for initial and boundary conditions different from those used in the original studies of Gerke and van Genuchten (1993b). To take this scenario-related dependency into account, we performed a numerical analysis of the water exchange process in a single macropore system for the same initial and boundary conditions reproduced in our experiments. Our calculations allowed us to determine an optimal value for the scaling factor _w, which subsequently will be used in the analysis of our experimental data.

Numerical Analysis of the Water Transfer Process
We generated series of synthetic data for lateral water exchange by simulating water infiltration through a soil column with a single macropore, as depicted in Fig. 1. Since the process is axial-symmetric, a modified version of the two-dimensional HYDRUS-2D code (Simunek et al., 1999) could be used. The synthetic water transfer data were subsequently compared with results of the one-dimensional dual-permeability model to test the applicability of Eq. [8], and to determine a value of the scaling factor _w that best describes the exchange process for the initial and boundary conditions used in our experiments. For both the two- and the one-dimensional simulations, and for both the matrix and macropore domain, the initial pressure head profile varied linearly from -155 cm at the top to -135 cm at the bottom. The pressure head was equal to zero at the top of the column, while seepage conditions were imposed at the bottom boundary. In our simulation we explicitly considered vertical water flow in the soil matrix.

Two-Dimensional Simulations
The HYDRUS-2D code solves the axial-symmetric flow equations in the r–z plane using a mass lumped Galerkin finite element scheme. The flow domain consisted of two connecting porous media: a single macropore (r 0.5 mm) at the center and the surrounding matrix region. A very fine finite element grid, as well as small time steps (t_min was 10^-9 h), were used to increase the accuracy of the calculations. We initially experienced some numerical problems, even with a very fine discretization near the macropore–matrix interface. This was caused by the fact that in HYDRUS-2D the independent variables and hydraulic properties are assigned to nodes, and smoothed linearly between neighboring nodes, as is traditionally done in finite element schemes. This approach causes flow and transport properties to be smoothed across the interfaces between different materials. Most of the numerical problems were solved by modifying the code to allow assignment of material properties to elements, rather than to individual nodes.

The van Genuchten–Mualem model (van Genuchten, 1980) was used to describe the retention and conductivity functions of both the matrix and the macropore domain:

[12]

[13]

where Se = ( - _r)/(_s - _r) is the effective saturation, (L^-1), n and l are empirical parameters, _r is the residual water content, _s is the saturated water content, and K_s (L T^-1) is the saturated hydraulic conductivity. We used the m = 1 - 1/n constraint so that each domain is characterized by a total of six parameters (hereafter referred to as "VGM parameters"). For our calculations, the matrix domain was assigned the VGM parameters estimated (as will be shown later) through inverse analysis of data from an infiltration experiment without a macropore (_s = 0.38; K_s = 0.08 cm h^-1; l = 0.5; _r = 0.20, = 0.005, and n = 1.664). In contrast, three different hydraulic functions were considered for the macropore domain. The saturated conductivity (K_f,sat) was chosen equal to 2000, 20 000, and 100 000 cm h^-1, while the remaining parameters were in all cases fixed at _r = 0, _s = 0.5, = 0.1, n = 2, and l = 0.5. Two somewhat conflicting requirements were considered when choosing the VGM parameters for the macropore domain: (i) having a small air-entry tension (high value), below which the hydraulic conductivity drops sharply to negligible values (high n value), and (ii) facilitating a stable numerical solution of the flow equations. Each simulation was repeated for three different soil mantle radii: 1.7, 2.7, and 12 cm.

One-Dimensional Simulations
Infiltration processes were simulated for the same scenarios (geometry, hydraulic properties, initial and boundary conditions) considered in the previous section using the one-dimensional DPM (as incorporated into HYDRUS-1D; Simunek et al., 1998). We next performed one-dimensional inverse analyses of the synthetic data to optimize _w, using cumulative mass transfer data in the objective function. Since optimized values for the transfer coefficient depend somewhat on the characteristic time scale of the synthetic data (Young and Ball, 1995), we homogenized the different series by extending each set of data to well after equilibrium was reached.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Experimental Setup
A sandy loam (Typic Haploxeralf) with a small clay fraction (6%, mostly kaolinite) was used in this study because of its low shrink–swell capacity. The soil, collected from the Angeles National Forest (California) at 20 to 40 cm depth, was air-dried, sieved (2 mm), and packed into a large column in 3-cm increments to a dry bulk density of 1.56 g cm^-3. The column (Fig. 2) was made from an acrylic cylinder (75 cm deep; i.d. = 24 cm), resting on a specifically designed support for controlling the bottom boundary condition and collecting the drainage effluent (Fig. 3). The lower portion of the column was partitioned into six pie-shaped chambers using vertical dividers (Fig. 3). The dividers were made of 15-cm-high stainless-steel sheets, glued into grooves in the base plate and held rigidly by means of a vertical support placed in the center of the base plate. The base plate, also made of acrylic, housed six ceramic plates (bubbling pressure = 5 x 10⁴ Pa), one in each of the six chambers (Fig. 3). The ceramic plates were sealed into place with a system of rubber gaskets and removable cover panels. Drainage effluent from each chamber was collected separately in a system of six acrylic tubes (Fig. 2) that permitted automated measurement of the cumulative outflow using pressure transducers. The pressure head at the bottom of the soil column was regulated by adjusting the air pressure within the outflow tubes. A 3-cm layer of diatomaceous earth material (having a negligible hydraulic resistance) was placed in each chamber between the soil and the ceramic plates.

View larger version (98K): [in this window] [in a new window]   Fig. 2. Experimental setup.

View larger version (102K): [in this window] [in a new window]   Fig. 3. Partitioning of the bottom of the column in six pie sectors. The metal dividers are 15 cm high. The stainless-steel nets support the soil when the ceramics are removed.

Artificial Macropores
Different techniques for creating artificial macropores are described in the literature, depending on the objectives of the research, soil type, and column dimensions (Hu and Brusseau 1995; Li and Ghodrati, 1997; Czapar et al., 1992). In our study we created a single macropore by inserting a hollow stainless-steel tube (1-mm o.d.) from the surface into the soil matrix. The macropore was located approximately at the center of the column and reached the diatomaceous earth layer at the bottom of one of the chambers.

To help stabilize the artificial macropore, we applied a water-soluble polymer (polyacrylamide, PAM) along the macropore walls. This was done by pouring a PAM solution (75 g L^-1) into the stainless-steel tube once it was fully inserted into the soil. The tube was subsequently slowly removed from the soil such that the PAM left a coating on the macropore walls. To enhance diffusion into the surrounding matrix, the PAM was applied when the column was dry. After application, the column was left for 48 h before a new experiment was performed. While the technique proved effective, the macropore itself was not always perfectly stable, and new applications of the polymer were needed periodically between separate flow experiments.

Experimental Procedure
Using a 0.33 g L^-1 CaCl₂ solution, several infiltration and drainage experiments were performed before making the artificial macropore. These initial experiments were used to test the functionality of the experimental setup, especially the active drainage system, and to verify the uniformity of water flow through the soil column. A first-type boundary condition was imposed at the soil surface during the infiltration experiments by means of a tension infiltrometer (Ankeny et al., 1988; Perroux and White, 1988); this also permitted us to measure the infiltration rate. We used a disk (Soil Measurement Systems, Tucson, AZ) with the same diameter as the column, so that flow was always one-dimensional. A thin sand layer was placed on the soil surface to ensure perfect contact between soil and the infiltrometer. The head loss through the sand was measured by means of a very small tensiometer placed at the sand–soil interface.

One major challenge of the experimental setup was accurate control of the bottom boundary condition. When a tension is imposed through the ceramic plates, the presence of entrapped air, as well as the existence of fluxes greater than the conductivity of the ceramic plates, may cause the effective bottom tension to diverge from the applied one. Such a situation could lead to misinterpretations of the experimental results, particularly since the magnitude of the flux through the artificial macropore is not known a priori. We therefore designed the base of the column to allow us to remove or install different ceramic plates as needed. For example, to facilitate drainage from the column we applied tension at the bottom, whereas the ceramics were removed during the infiltration experiments to produce a seepage-type bottom boundary condition.

We present results for two infiltration experiments, one with and one without the artificial macropore, performed under identical initial and boundary conditions. The effects of the macropore on the overall flow regime were deduced by contrasting the measured inflow and outflow rates. In both experiments, the column was initially drained by applying suction at the bottom (h = -250 cm). Pressure head profiles during the drainage showed fairly uniform values in the upper three-quarters of the column, and a steep decrease in the pressure head in the lower portion. Once a nearly uniformly dry profile was obtained in the upper three-quarters of the column, the ceramic plates were removed and the column was left to equilibrate for about 1 wk. Having a relatively low initial water content distribution favored extensive lateral exchange of water during the macropore infiltration experiment. In both experiments, the top pressure head equaled zero, while a seepage boundary condition was applied at the bottom by removing the ceramic plates.

	RESULTS AND DISCUSSION

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Results from Numerical Simulations
Results from the two-dimensional simulations highlighted several factors affecting the water exchange between the macropore and matrix. In general, water flow in the two regions did not evolve independently (i.e., based on their specific hydraulic properties), but were very much affected by each other. For example, the wetting front in the macropore had a tendency to slow down because of diffusion of water into the surrounding matrix. This lateral exchange process is evident in Fig. 4, which shows snapshots (t = 0.05 h) of the infiltration process simulated for three values of K_f,sat. Notice that the relative position of the two wetting fronts determined the longitudinal extent of the region affected by transfer process (indicated with d in Fig. 4). Since this region is large for highly conductive macropores, the depth-integrated water exchange rate is higher for larger K_f,sat values. This result is also evident from Fig. 5, where the cumulative transfer flux integrated over the entire column is shown for the different scenarios. For each radius of the soil mantle, the water exchange rate is higher for higher macropore conductivity. Notice also that the total amount of exchanged water depends only on the size of the soil mantle for the smallest radius (Fig. 5b), whereas for larger mantles it also depends on K_f,sat (Fig. 5a). This is due to vertical flow of water entering the matrix region from the top. In general, the maximum value of the cumulative transfer rate is smaller when vertical flow in the matrix is relatively fast compared with that of the macropore (smaller K_f,sat), since the pressure difference between the two domains (i.e., the driving force for water exchange) will vanish sooner. This effect is negligible for the smallest radii, for which equilibrium is reached only in a relatively short time.

View larger version (69K): [in this window] [in a new window]   Fig. 4. Two dimensional simulations of pressure head distribution during infiltration processes for a 2.7-cm soil mantle. All figures show snapshots at 0.05 h.

View larger version (20K): [in this window] [in a new window]   Fig. 5. Summary of the cumulative water transfer for nine two-dimensional simulations.

View larger version (19K): [in this window] [in a new window]   Fig. 6. Cumulative water exchange predicted by the one-dimensional dual-permeability model (DPM) compared with the transfer calculated by HYDRUS 2-D.

View this table: [in this window] [in a new window]   Table 1. Optimized values of the scaling factor w for different soil mantle radii and macropore saturated hydraulic conductivities.

View larger version (13K): [in this window] [in a new window]   Fig. 7. Scaling factor dependency on the macropore saturated conductivity.

View larger version (24K): [in this window] [in a new window]   Fig. 8. Measured and fitted inflow and outflow curves during infiltration in the homogeneous soil column (without macropore). Simulated results are obtained using Richards' equation.

View larger version (29K): [in this window] [in a new window]   Fig. 9. Pressure head profiles during the infiltration experiments without the macropore. Simulated results are obtained using Richards' equation.

Infiltration Experiment with One Artificial Macropore
From capillary theory, a top boundary pressure head greater than -3 cm was needed to initiate flow through the 1-mm-diameter macropore. The occurrence of macropore flow was immediately evident, since the infiltration rate was considerably higher than that observed without the macropore (Fig. 10). Furthermore, after about 45 min a roughly constant flux was observed in the chamber where the macropore was located, while no outflow was observed in the other chambers (data not shown). This flux, 0.082 cm h^-1, was therefore assumed to be all macropore outflow (O_f). This experiment allowed us to discriminate between macropore flow and matrix flow, and to measure the interdomain exchange flux. We reproduced the same initial and boundary conditions as for the infiltration experiment without a macropore. In particular, a zero pressure head was maintained at the top. During infiltration, the following relationship holds:

[14]

where I_m is the flux of water infiltrating into the soil matrix, I_f is the flux entering the macropore, and I_tot represents the total infiltration rate, as measured with the tension infiltrometer. An analogous relationship can be written for the outlet flux:

[15]

where O_m and O_f are the contributions of matrix and macropore, respectively, to the total outflow (O_tot). Because of lateral diffusion, in general I_f > O_f, the difference between the two fluxes representing the total water flux exchanged between macropore and matrix:

[16]

View larger version (21K): [in this window] [in a new window]   Fig. 10. Cumulative infiltration rates measured with and without the macropore.

[17]

The cumulative lateral flux measured in this way is shown in Fig. 11, and will be discussed in more detail below. The experiment was repeated three times, with the three replications giving nearly identical results (not shown here). We emphasize here that steady-state conditions could never be reached completely because of slow, yet persistent clogging of the macropore during infiltration.

View larger version (17K): [in this window] [in a new window]   Fig. 11. Cumulative infiltration curves measured in the soil column with a macropore, and calculated using the dual permeability model, for w optimized and w = 1.

Since it was not possible to maintain macropore flow until steady-state conditions were reached, Eq. [4] could not be used to estimate the saturated hydraulic conductivity. We optimized K_f,sat by fitting this parameter to the inflow data using the parameter estimation feature of HYDRUS-1D. Cumulative infiltration rates were found to be sensitive to K_f,sat, but not affected by the other hydraulic parameters. Our measured data were closely reproduced when using K_f,sat = 25 000 cm h^-1 (Fig. 11). The contribution of the macropore to the composite soil saturated conductivity (K_sat) can now be estimated from Eq. [4]: for K_f,sat = 25 000 cm h^-1 and w_f = 1.8 x 10^-5, K_sat was found to be equal to 0.45 cm h^-1, as compared with a value of only 0.08 cm h^-1 as observed in the absence of the macropore. The scaling factor corresponding to this value was obtained from Fig. 7 (_w = 0.441). Three of the six VGM parameters for the macropore domain were fixed (_r = 0, _s = 0.5, l = 0.5), while the remaining parameters were determined by fitting lateral exchange and outflow data, on which they appear to have the largest impact. Least squares fitting gave = 0.1 cm^-1; n = 2.

To highlight the model sensitivity to the scaling factor, we compared the experimental data with the model results obtained with both the optimized value of the _w parameter, and for _w = 1. In both cases, the cumulative water exchange predicted with the DPM did not match the experimental data perfectly (Fig. 12). However, the calculated water transfer rate (given by the slope of the cumulative curve) reproduced the observations reasonably well when using the optimized scaling factor, while it persistently overestimated the experimental results with _w = 1. Even with the optimized _w, an offset of about 80 cm³ was still observed between the experimental and simulated cumulative curves. Assuming a porosity of 0.45 for the fine sand placed on top of the column, this amount corresponds to water adsorbed in about 0.4 cm of sand after infiltration started. Therefore, the disagreement between measured and calculated data in Fig. 12 may be attributed to a slight difference in the thickness of the sand layer between macropore and nonmacropore experiments.

View larger version (15K): [in this window] [in a new window]   Fig. 12. Observed vs. predicted cumulative water transfer between the macropore and matrix. In the dual permeability model, both w optimized and w = 1 were used.

View larger version (16K): [in this window] [in a new window]   Fig. 13. Observed vs. predicted cumulative outflow. In the dual permeability model, both w optimized and w = 1 were used.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

Similarly to the previous study by Gerke and van Genuchten (1993b), we derived the transfer rate coefficient for water from the equivalent coefficient for solute transfer through numerical simulations of the lateral diffusion process. Our analysis showed that the scaling factor _w, in general, is dependent on the hydraulic conductivity of the macropore domain.

	ACKNOWLEDGMENTS

 
The research was conducted at the George E. Brown Jr. Salinity Laboratory, Riverside, CA. P. Castiglione would like to acknowledge the financial support from the University of Naples, Italy, during his stay at Riverside as part of his Ph.D. research. The authors also acknowledge the technical support of J. Fargerlund and J.A. Jobes. This study was partially supported by NSF grant EAR-0106956.

	REFERENCES

TOP ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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