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Published online 16 August 2005
Published in Vadose Zone J 4:866-880 (2005)
DOI: 10.2136/vzj2004.0111
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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ORIGINAL RESEARCH

Mini Suction Cups and Water-Extraction Effects on Preferential Solute Transport

J. Maximilian Köhne*

Dep. of Biological and Agricultural Engineering, Texas A&M Univ., Scoates Hall, College Station, TX 77843-2117
Currently at: Univ. of Rostock, Institute for Land Use, Justus-von-Liebig Weg 6, D-18059 Rostock, Germany
* Corresponding author (max.koehne{at}uni-rostock.de)

Received 23 July 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soil water suction cups used in laboratory solute transport studies may cause undesired perturbations of the flow field. The twofold objective of this study was to test mini suction cups, and to assess the effects of pore water-extraction rate and cup size on preferential water flow and bromide (Br–) breakthrough. Porous ceramic cups of 0.25-cm outer diameter and 1-cm length could extract 1 cm3 of pore water within 17 (34, 38) min from 100% (85%, 70%) saturated loam soil by applying 0.1 (0.3, 0.5) bar suction. The corresponding sampling times for larger cups (0.6-cm diam., 2-cm length) were 3.3, 4.6, and 5.7 min. The smaller cups were subsequently tested for solution extraction of 1-cm3 samples every 20 min out of the matrix and preferential flow path (PFP) of a large soil column (24-cm diam., 80-cm high) during a Br– transport experiment. Numerical simulations were used (i) to describe the Br– transport experiment and (ii) to evaluate how preferential Br– transport would be affected by pore solution extraction at different locations in the matrix and the PFP of a loam soil block (20 by 20 by 20 cm3) subject to wet and dry initial conditions. Three-dimensional water flow and solute transport were simulated using the Richards and convection–dispersion equations. The experimental and simulation results revealed a dilemma: while fast solution extraction using larger cups altered the flow field and preferential Br– breakthrough for wet and particularly for dry initial conditions, slower solution extraction using small cups caused negligible perturbation of the flow field, but yielded insufficient resolution of the preferential Br– breakthrough. Sampling in the matrix did not considerably affect Br– transport, and gave sufficient resolution of the matrix Br– peak. This study showed that the use of suction cups for measuring solute transport may be problematic in case of preferential flow.

Abbreviations: CV, doefficient of variation • IC, ion chromatography • HPLC, high-pressure liquid chromatography • PFP, preferential flow path • TDR, time domain reflectometry


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
EXPERIMENTAL ANALYSIS of physical nonequilibrium transport processes in the laboratory suffers from inadequate techniques to monitor local pore water chemistry in the soil or sediment during a column experiment. For example, resident solute concentrations in a soil column are typically only obtained at the end of a solute transport experiment by destructive sampling of the soil. On the other hand, time domain reflectometry (TDR) probes require time-consuming calibration to convert measured values of soil bulk electric conductivity into concentration values of a single salt solution, and cannot measure several tracers simultaneously. Moreover, the TDR technique cannot provide local, "point"-scale solute concentrations. Local concentration measurements may provide valuable information for the analysis of, for example, physical nonequilibrium transport with locally variable concentrations.

Ceramic suction cups have been frequently used to withdraw pore water samples from soil in field studies (e.g., Starr et al., 1986, Patterson et al., 2000, Ahmed et al., 2001, Ridley et al., 2001, Su et al., 2004). More rarely, cups have also been employed for solute transport studies in the laboratory. For instance, Starr et al. (1986) used an array of up to 40 cups to measure chloride transport during unstable flow in fine over coarse soil placed in a 30-cm wide and 150-cm deep plexiglass chamber. They successfully measured the chloride transport process within the soil, even if the number of samplers apparently was still not sufficient for accurate mass recovery calculations (Starr et al., 1986).

Current suction cups are relatively large with a diameter of several centimeters, and may, therefore, cause considerable perturbations of the flow pattern, particularly in small soil columns and/or when high suctions for fast water extraction were applied. Warrick and Amoozegar-Fard (1977) demonstrated in detail how suction cup water samplers may affect water flow in a porous medium. For various combinations of hydraulic properties and cup radii, they calculated the maximum distance for which flow can be intercepted by the cup. Further results of this study involve the water flow rate through soil into the cup as a function of the applied suction. Most calculations were based on analytical solutions for the hydraulic head and the stream function of the axially symmetric steady- state water flow equation, in which the cup was represented either as a point or a line sink. An exponential form of the unsaturated hydraulic conductivity function was assumed (Warrick and Amoozegar-Fard, 1977).

However, the effects of different water-extraction rates and porous cup sizes on solute transport, and particularly on preferential solute transport, have not been analyzed in detail. Aiming at minimum flow disturbance suggests the use of small extraction rates, corresponding to large time intervals between pore water samples of a particular volume. However, the sampling intervals should at the same time be short enough for sufficient temporal resolution of solute breakthrough at the point of interest. Interestingly, modern standard analytical devices for determining concentrations of ions or organic molecules such as ion chromatography (IC) and high-pressure liquid chromatography (HPLC) require only small sample volumes of <1 cm3.

In view of the above considerations, a sampling technique for laboratory solute transport studies is needed for sampling small pore water volumes within small time intervals with minimal disturbance to the soil and the water flow pathways. Furthermore, a quantitative assessment of the sampling effect on (preferential) solute transport is desirable. The objectives of this study were (i) to build and test mini laboratory suction cup samplers for extracting a small volume of 1 cm3 pore water from soil and (ii) to assess the combined effect of porous cup size and extraction rate on conservative solute breakthrough in a soil block with a cylindrical preferential flow path filled with coarse sand. The scope of this study is limited to conservative solute. Therefore, suction cup designs for solutes undergoing reactions such as sorption or volatilization, and sampling effects on reactive solute transport processes, are not discussed.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Mini Suction Cups
The sampler (Fig. 1) consisted of a porous ceramic cup (no. 0652X03-B1M3, Soilmoisture Equipment Corp., CA) that was attached to a hollow 0.3-cm diam. stainless steel tube (Popper & Sons, Inc., New York) using glue (Quiktite super glue, Loctite). The ceramic porous cups (0.3-cm inside diam., 0.6-cm outside diam., cut to 2-cm length) had an air-entry pressure of 1.3 bar, a porosity of 45%, pore size of 2.5 µm, and saturated hydraulic conductivity of 0.75 cm d–1. The sampler was connected to a vial of 5-cm3 capacity, which in turn was connected to a vacuum pump that supplied adjustable suctions between 0 and 0.5 bar pressure difference with the atmospheric pressure (Fig. 1). Moreover, in an attempt to further reduce cup dimensions, ceramic cups were built using plate fragments of the same ceramic type as described above (B1M3). The fragments were filed into cylindrical shape of approximately 0.25-cm diam. and 1-cm length, and a 1-mm diam. hole was drilled into the small cylinders. The resulting small ceramic cups were attached to 1-mm stainless steel needles (Popper & Sons).



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  		Fig. 1. Schematic of the laboratory suction sampler consisting of a porous ceramic cup attached to a hollow stainless steel tube and sample vial. Numbers in parentheses indicate dimensions of "small" and "large" mini porous ceramic cups.

 
A total of 10 samplers were constructed; 5 with porous ceramic cups of 0.25-cm diam. and 1-cm length (henceforth denoted small cups) and 5 with cups of 0.6-cm diam. and 2-cm length (large cups). Since all ceramic was pre-used, the ceramic cups were left in hydrochlorid acid (10% concentration) for 15 h to remove clogging soluble particles and to restore the permeability. To test the samplers, 10 loam soil columns (7.5 cm in height and diameter) were packed to an average bulk density of 1.49 g cm–3 with a coefficient of variation (CV) equal to 1.1%, and were saturated with tap water to a saturated water content of 0.391 (CV = 2.0%). Soil properties are summarized in Table 1. One sampler was inserted into each of the soil columns. A water-extraction test was initiated by applying a suction of 0.1 bar to the 10 samplers. For each sampler, the weight of the water extracted after 20 min was measured using a precision balance. The soil cores were subsequently left to evaporate from both sides until reaching 85% of their saturated water content (0.335, CV = 4.2%), after which they were put into plastic bags and left for 2 d to reach static hydraulic equilibrium conditions. Then, the water-extraction test was repeated using a suction of 0.3 bar. The procedure of drying and subsequent hydraulic equilibration was repeated until soil columns reached 70% saturation (0.276, CV = 4.5%), when water was extracted at 0.5 bar suction.


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  		Table 1. Physical properties of the fine sandy loam soil used in the suction sampler tests.

 
Bromide Transport Experiment
The feasibility of using the small (0.25-cm diam.) suction cups in laboratory solute transport studies was tested in a Br– transport experiment. A large soil column (80-cm height, 24.4-cm diam.) was packed with dry-sieved and graded fine sandy loam soil (referred to as matrix), in which a cylindrical preferential flow path of 2.4-cm diam. (PFP) was prepared by using a 2.4-cm inside diam. metal tube, into which well-sorted coarse sand was poured. Conceptually, the loosely filled preferential flow path may represent, for instance, a large vertical earthworm (Lumbricus terrestris) burrow or decayed root channel partially refilled with loose soil. The sand-filled PFP has continuous water retention and hydraulic conductivity functions as required by the model analysis (see below). Using soil cores (7.5 cm in diam. and height), the saturated water content, {theta}s (L3 L–3) of the loam matrix was measured to be {theta}s = 0.39, and the saturated hydraulic conductivity, Ks (LT–1) was determined during saturated steady-state flow to be equal to Ks = 0.29 cm h–1. The corresponding values for the coarse sand were {theta}s = 0.35 and Ks = 500 cm h–1.

After packing the column, the metal tube was cautiously pulled out of the column. At 20, 35, 50, and 65 cm, mini suction cups were inserted into the PFP, and into the matrix at 4-cm distance from the PFP wall. Column outflow at the bottom boundary subject to atmospheric pressure was monitored separately for matrix and PFP regions.

Before the experiment, the entire column was saturated from the bottom with deionized water. Infiltration of deionized water under zero-head boundary condition was initiated and maintained during several hours using a tension infiltrometer of a matching diameter, until steady-state flow conditions with equal rates of inflow and outflow were achieved. The experiment then consisted of two steps. (i) Bromide transport was started by exchanging the infiltration plate of the tension infiltrometer carrying the deionized water with the infiltration plate of another tension infiltrometer filled with an aqueous solution of 3 g L–1 Br–. The exchange was performed quickly within 5 s to maintain the saturated steady-state flow conditions at zero-applied suction. The Br– solution was continuously applied for 22.5 h. (ii) Infiltration plates were switched back and deionized water was applied until the end of the experiment at 40 h. During the experiment, the Br– concentration in the effluent of matrix and PFP was continuously monitored using two Br– specific electrodes (NICO2000, Great Britain) that could be employed for measurement of small Br– concentration in small volumes of water. A suction of –0.1 bar was continually applied to the porous ceramic cups. Every 20 to 30 min for the PFP and every 60 min for the matrix, samples of 1 to 2 mL were quickly collected by replacing the vials attached to the porous cup samplers with empty vials. The Br– concentrations in the small sample volumes were also measured with the Br– specific electrodes. Since the internal volume of cup and attached needle was very small ( <0.2 mL), any remnant solution present in the sampling system appeared to be insignificant, such that it seemed justified not to implement a design for discarding remnant cup solution before sampling.

Numerical Simulations
Numerical simulations of preferential solute transport through a porous medium containing a PFP were performed to describe (i) the effects of different cup sizes and different water-extraction rates in the PFP or in the matrix (Fig. 2) , and (ii) the Br– concentrations in the suction cup samples and column effluent of the Br– transport experiment (Fig. 3) .



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  		Fig. 2. Schematic of the three-dimensional mesh for numerical simulation of solution extraction effects on Br– transport in a porous medium with a preferential flow path (PFP) at its center: (a) reference case with no cup, (b) small cup in PFP, (c) large cup in PFP, (d) small cup in matrix (at 2-cm distance from PFP), (e) large cup in matrix (at 2-cm distance from PFP).

 


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  		Fig. 3. Schematic of the soil column employed in the Br– transport experiment with position of suction cups in preferential flow path (PFP) and matrix, and pseudo three-dimensional, axially symmetric mesh used for numerical model simulation.

 
Modeling of Water-extraction Effects on Preferential Solute Transport
Five scenarios were assumed to assess the combined effect of sampler size and water-extraction rate, and the effect of sampling position (in the PFP or in the matrix) at 10-cm depth: (i) a reference case with no cup (Fig. 2a), (ii) the small cup (0.25-cm diam., 1-cm length) in the PFP (Fig. 2b), (iii) the large cup (0.6-cm diam., 2-cm length) in the PFP and intersecting the adjacent matrix (Fig. 2c), (iv) the small cup at 2-cm distance between its end and the PFP wall (Fig. 2d), and (v) the large cup at 2-cm distance between its end and the PFP wall (Fig. 2e).

To evaluate the effect of initial soil moisture, all scenarios were simulated for both saturated and relatively dry initial conditions. Since dry initial conditions were expected to enhance lateral water and Br– transfer from PFP into matrix, the cups in the scenarios (iv) and (v) were moved to 4-cm distance from the PFP to better separate flow and transport in matrix and PFP.

A three-dimensional model is best suited for comprehensive evaluation of how the suction sampler affects solute transport: in a two-dimensional vertical domain, the impervious tube of the sampler cannot be accounted for since it would essentially block vertical flow across its entire length. The model SWMS-3D (Simunek et al., 1995) was used to simulate three-dimensional Darcian water flow and convective–dispersive solute transport. The governing equation to describe water flow in an isotropic, variably saturated rigid porous medium without significant effect of the air phase on water flow was given by the following modified form of the Richards' equation:

[1]
where {theta} is the volumetric water content (L3 L–3), h is the pressure head (L), S is the sink term to account for water extraction by the suction cup (T–1); xi (i = 1,2,3) are the spatial coordinates (L), t is time (T), and K is the unsaturated hydraulic conductivity(L T–1), which is a function of pressure head and location, K = K(h,x1, x2, x3).

The internal sink S represents the volumetric extraction rate of water, Q (L3 T–1), per unit volume of soil, V (L3), as follows

[2]
where the Qi are the individual volumetric water-extraction rates (constant in time) at the nodes in the numerical grid representing the suction cup, and Lx1, Lx2, and Lx3 are the model domain dimensions representing the soil block.

For scenarios involving initially saturated conditions, Eq. [1] was solved subject to the following initial and boundary conditions:

[3]

[4]
where {Gamma}N denotes a Neumann type (constant flux) boundary segment, {sigma} (L T–1) is the prescribed water flux as a function of x1, x2, x3; {sigma} was here assumed to be constant in time at the upper and lower boundary segments and zero at the sides of the block, and ni are the components of the outward unit vector normal to {Gamma}N. Equation [4] represented both the upper and the lower boundary. In case of a homogeneous soil block, values for {sigma} were the same (equal to Ks) throughout the upper and lower boundaries, whereas for a soil block containing a PFP at its center, values for {sigma} were depending on the x1, x2–location and were equal to Ks of either matrix or PFP.

For the simulations of water infiltration into relatively dry soil, the following initial and boundary conditions were invoked:

[5]

[6]
where {Gamma}D denotes a Dirichlet type (constant head) boundary segment which here represents both the upper and the lower boundary, whereas the sides of the block were once again characterized by a zero flux boundary condition (Eq. [4] with {sigma} = 0).

Three-dimensional convective–dispersive conservative solute transport in a porous medium at variable saturation, with or without PFP, was described with the following partial differential equation (Simunek et al., 1995):

[7]
where c is the solute concentration (ML–3), qi is the i-th component of the water flux (L T–1), S is the sink term in the water flow Eq. [1], cS is the solute concentration in the sink term (M L–3), and Dij is the dispersion coefficient tensor (L2 T–1) calculated as shown below (Bear, 1972)

[8]
where D0 is the ionic diffusion coefficient in free water (L2 T–1), D0 is the transversal dispersion coefficient (L2 T–1), {tau} is a tortuosity factor, |q| is the absolute value of the Darcian fluid flux density (L T–1), {delta}ij is the Kronecker delta function ({delta}ij = 1 if i = j, and {delta}ij = 0 if i!=j), and {lambda}L and {lambda}T are the longitudinal and transversal dispersion lengths, respectively (L). Further details regarding the calculation of the dispersion tensor can be found in Simunek et al. (1995).

Equation [7] was solved subject to the following initial condition [9] and pulse-type (Cauchy) boundary condition [10] along a boundary segment {Gamma}C:

[9]

[10a]

[10b]
in which qini represents the water flux in the directions of the orthogonal coordinates xi (i = 1,2,3), and c0 is the concentration of the incoming water during times between zero and tC, assumed to be a unit concentration with an arbitrary unit of mass per volume (c0 = 1). The application duration tC was 10 min and the total simulation time was 15 h. Equations [1] and [7] subject to the above initial and boundary conditions were numerically solved using the Galerkin finite element method (Simunek et al., 1995).

For the various scenarios, a smaller soil sample was assumed than in the soil column experiment. This was done not only to save computation time, but also to analyze the "worst case" for sampling effects of the cups. A numerical grid was constructed to represent a soil cube of 20-cm edge length with a preferential flow path (1 cm by 1 cm by 20 cm) at its center (Fig. 2). The grid consisted of 8820 numerical elements constrained by 10 164 nodes. Internodal distances were between 2 cm at the boundaries and 0.1 cm at the suction sampling location. The soil matrix and the preferential flow path were represented by van Genuchten (1980) model parameters for "loam" texture and "sand" texture, respectively (Table 2), that were obtained from the database of Carsel and Parrish (1988). The Ks value of the PFP (29.7 cm h–1) was 28.5 times higher than that of the soil matrix (1.04 cm h–1). For saturated initial conditions where flux-type boundary conditions [4] were employed, this approach resulted into the same PFP-to-matrix water flux ratio (28.5) at the top boundary, since boundary water fluxes were set to the Ks values of PFP and matrix. The PFP occupied 1 cm2 of the total cross-section area perpendicular to the main flow direction and the matrix occupied 399 cm2. The Br– transport parameters are also shown in Table 2. The longitudinal dispersivity was set to 0.5 cm for both matrix and PFP, which is within the range of values typically found in column studies with homogeneous loam soil or sand (e.g., Maraqa et al., 1997). The transversal dispersivity (0.1 cm) is typically several times smaller than the longitudinal dispersivity (e.g., Dullien, 1972), and the molecular diffusion coefficient of Br– in water (0.075 cm2 h–1) was calculated as described in Atkins and Depaula (2001).


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  		Table 2. van Genuchten (1980) parameters and solute transport parameters (longitudinal dispersivity, {lambda}L, transversal dispersivity, {lambda}T, molecular diffusion coefficient, D0) for numerical simulations of Br– transport.

 
The small cup (0.25-cm diam. and 1-cm length) was represented by 20 nodes in the three-dimensional numerical mesh. For the scenarios with initially saturated conditions, to simulate the total volumetric extraction rate of Q = 4 cm3 h–1 comparable to the value measured with the small cups in the saturated loam soil columns (Table 2), individual sink fluxes of Qi = –0.08 cm3 h–1 were applied continuously throughout the numerical experiment to each of the 20 nodes. The fast water-extraction rate of the large cup (0.6-cm diam., 2-cm length) of Q = 20 cm3 h–1 was represented by individual nodal sink rates of Qi = –0.09434 cm3 h–1 applied to 212 nodes. The stainless steel tube was represented by a single line of nodes for the small sampler and a 0.3-cm diam. region for the large sampler, with zero Ks values between cup and side wall (Fig. 2). The large extraction rate of Q = 20 cm3 h–1 reduced the total volumetric flow rate by 4.5% (i.e., 20 cm3 h–1/444.6 cm3 h–1 x 100%), while the small extraction rate of Q = 4 cm3 h–1 reduced the total flow by <1%. For the scenarios with initially dry conditions, a constant suction of –500 cm was imposed at the nodes representing the suction cups. The hydraulic conductivity values at the suction cup nodes were adjusted to yield the same respective water-extraction rates at saturation as assumed above, that is, Q = 20 cm3 h–1 for the large cup and 4 cm3 h–1 for the small cup, respectively.

Modeling of the Bromide Transport Experiment
For simulating the experiment of Br– transport through the 80-cm long soil column, a pseudo three-dimensional axisymmetric numerical model approach was used, based on the Richards' equation in cylindrical coordinates and the convection–dispersion equation as implemented in HYDRUS-2D (Simunek et al., 1999). The suction cups were similarly implemented as described above, except that the impervious sampling tubes were not considered assuming that potential effects of flow restriction caused by the impervious sampling tubes were negligible in the large column. A fully three-dimensional numerical model grid with accurate spatial resolution near the matrix-PFP interface and the various suction cups would have required an excessive number of numerical nodes resulting into a disproportionately large simulation time. Apart from the flow symmetry and dimensionality, the pseudo three-dimensional approach was similar to the fully three-dimensional one, that is, flow and transport equations as well as initial (saturated) and boundary conditions were comparable to those described above. According to the experiment, the pulse duration (Eq. [8]) was tC = 22.5 h, and the total simulation time was 40 h. A two-dimensional rectangular numerical grid of 80-cm length and 12.2-cm width represented a half cross-section through the axisymmetric soil column with central cylindrical PFP of 1.2-cm radius surrounded by the matrix mantle of 11-cm radius (Fig. 3). As in the three-dimensional model described above, the node spacing varied between a maximum value of 2 cm and a minimum of 0.1 cm at the matrix–macropore interface and at sampler locations. Hydraulic model parameters were fixed based on measurements mentioned above to {theta}s = 0.39 and Ks = 0.29 cm h–1 for the loam matrix, and to {theta}s = 0.35 and Ks = 500 cm h–1 for the coarse sand. The transport parameters were assumed as described in Table 2. The grid consisted of 4830 numerical elements.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Experimental Results for the Water-Extraction Test
The results of the water-extraction test are summarized in Table 3. After 20 min of applying 0.1 bar suction to the saturated soil, the small (0.25-cm) ceramic cups extracted 1.2 cm3 and the large (0.6-cm) cups extracted 6.0 cm3 of solution (Table 3). The extraction rates for the cups with 0.25-cm (0.6-cm) diam. gradually decreased to 0.7 (4.3) cm3 per 20 min at 85% saturation and to 0.5 (3.5) cm3 per 20 min at 70% saturation. Using the 0.25-cm diam. cup, volumes of 1 cm3 water were sampled after 17 min (100% soil saturation, 0.1 bar), 34 min (85%, 0.3 bar), and 38 min (70%, 0.5 bar). The respective sampling times for the 0.6-cm diam. cup were 3.3 min, 4.6 min, and 5.7 min. All water samples at all applied suctions were clear and free of particles. The time for exchanging a vial, that is, unscrewing the cap and replacing the filled vial by an empty one, required only a few seconds.


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  		Table 3. Sample volumes of pore water extracted during 20 min from a loam soil at 100, 85, and 70% water saturation for 0.1, 0.3 and 0.5 bar of applied suction, respectively, and corresponding times to obtain 1-cm3 solution samples.

 
Experimental and Modeling Results for the Br– Transport Study
The observations obtained in the Br– transport experiment are illustrated in Fig. 4 together with the corresponding simulation results. The Br– concentration in the effluent (Fig. 4a) increased within 10 min to the input concentration, after which it fluctuated around this level. More than 99% of the total outflow came out of the PFP, such that the fast Br– concentration increase was entirely caused by preferential flow through the PFP. In response to the water infiltration starting at 22.5 h, Br– effluent concentrations quickly declined back to low values. However, zero concentrations were only reached after several hours indicating considerable Br– diffusion from the matrix back into the PFP. The forward model simulation approximated the observed Br– effluent concentrations relatively well suggesting that the main transport processes were captured by the model (Fig. 4a). The observed Br– concentrations at 35- and 65-cm depths obtained by using the small suction cups in the PFP (Fig. 4b) showed a similar pattern as in the effluent (Fig. 4a), while concentrations in the matrix (Fig. 4c) varied at values below 0.01 of the input concentration, and only at late times slightly increased at 35-cm depth (note the different scaling of the y-axes in Fig. 4b, 4c). The suction cup derived data clearly demonstrate the physical nonequilibrium between local Br– concentrations in PFP and matrix. The agreement between data and the corresponding numerical simulation results (Fig. 4b, 4c) was comparable to that obtained for effluent concentrations (Fig. 4a). This suggests that the Br– concentrations derived from mini suction cup samples were at least fairly accurate. However, the sampling interval (20 min) was not small enough to precisely describe the increasing and decreasing limbs of the Br– breakthrough curve. The effect of different water-extraction rates (or sampling intervals) in PFP and matrix on preferential Br– breakthrough is given below as based on numerical simulations for various scenarios.



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  		Fig. 4. Experimental observations of the Br– transport soil column experiment and numerical simulation results for Br– concentrations in (a) effluent, (b) preferential flow path (PFP), and (c) the matrix. The small 0.25-cm diam. cups were used for slow Br– solution sample extraction of 1 cm3 per 20 min.

 
Simulation Results for the Five Scenarios Assuming Saturated Initial Conditions
The numerical model simulation results for both the reference case without water extraction and the cases with slow (4 cm3 h–1) extraction using a small cup (0.25-cm diam., 1-cm length) produced saturated water contents and zero pressure heads in the entire domain. The simulations with fast (20 cm3 h–1) extraction using a large cup (0.6 cm, 2 cm) gave slightly negative pressure heads above –1.5 cm, with unsaturated flow near the respective sampling location in matrix or PFP, and saturated flow conditions elsewhere in the model domain. Steady-state flow was established within the first minute of all simulations.

For each of the five scenarios (no extractor, slow or fast water extraction in matrix or PFP at the 10-cm depth), the lines of equal hydraulic heads H = h + x3 and the flow velocity vectors v = q/{theta} are shown in Fig. 5 for the central vertical cross-section through the cube at x2 = 10 cm, cut across the cup's long axis. It is noted that the lines of equal hydraulic head and the velocity vectors form an orthogonal set just as they would for a flow net made of streamlines crossing lines of equal hydraulic head. The reference case without suction cup (Fig. 5a) shows horizontal lines of equal hydraulic head and vertical flow vectors, which are elongated in the central region indicating faster flow in the PFP. Only the large cups and extraction rates in PFP and matrix produced a notable perturbation of the uniform flow field close to the cup, in form of a local deflection of the equal hydraulic head lines from the horizontal. For all cases, the effects were substantially smaller than in the examples given by Warrick and Amoozegar-Fard (1977). The main two reasons for these deviating findings are (i) that Warrick and Amoozegar-Fard assumed unsaturated steady-state flow conditions (h = –100 cm), at which their hydraulic conductivity was four times smaller than the matrix Ks value assumed here, and (ii) that they chose a pressure head internal boundary condition (h = –400 cm) to represent the cup sink term, without considering flow resistance of the porous cup material. Hence, the extraction water flux of 41 cm3 h–1 was twice as large as even the larger extraction flux assumed here, while the water flux toward the cup was restricted by the fourfold lower hydraulic conductivity. The combined effect of both these differences was one of much stronger deflection of the lines of equal hydraulic head, and of flow toward the cup from 8 cm below the cup (Warrick and Amoozegar-Fard, 1977). In the present study, assumed (and measured) water-extraction rates were on the small side, with the intention to rather limit the effect on water flow.



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  		Fig. 5. Simulated hydraulic head distributions and flow velocity vectors at steady-state flow conditions for the five cases: (a) without suction cup (Reference), (b) small cup in preferential flow path (PFP), (c) small cup in matrix, (d) large cup in PFP, and (e) large cup in matrix.

 
The lines of equal relative Br– concentrations for the central cross-section at x2 = 10 cm are shown in Fig. 6 for the five scenarios at three different times. Compared to the reference case (Fig. 6a), the Br– concentrations in the case of having a large cup in PFP somewhat lagged behind (Fig. 6b). In all other cases, the Br– concentrations appeared unaffected by water extraction. However, Br– concentrations at the matrix cup position remained close to zero and hence information on potential effects of water extraction on Br– concentrations in the matrix cannot be derived from Fig. 6d and 6e.



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  		Fig. 6. Simulated Br– concentration distributions at 0.166, 0.3, and 0.5 h for the five cases assuming initial water saturation: (a) without suction cup (Reference), (b) large cup in preferential flow path (PFP), (c) small cup in PFP, (d) large cup in matrix, and (e) small cup in matrix.

 
The simulated extraction rates of dimensionless Br– mass, calculated as dimensionless Br– concentrations multiplied with the extraction water flux, are shown in Fig. 7 for the fast (large cup) and slow (small cup) extraction rates from PFP and matrix. The log time axis in Fig. 7 was chosen so as to properly display the two time scales of preferential Br– movement as captured by simulated continuous solution extraction in the PFP, and of slower Br– transport measured by simulated solution extraction in the matrix. The Br– mass extraction from the PFP peaked around 0.25 h and was by and large finished after 0.5 h for both samplers. Because steady-state flow was established almost immediately after the start of simulation, the Br– mass extraction peaks corresponded to the narrow Br– concentration peaks passing the sample cup location in the PFP at 10-cm depth (see below, Fig. 9a). The Br– mass extraction out of the matrix at 2-cm distance from the PFP wall more gradually increased and decreased between 1 and 10 h, with the peak at 4 h being 10-fold lower than in the PFP (Fig. 7).



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  		Fig. 7. Simulated Br– extraction rates from the preferential flow path (PFP) and the matrix assuming the large and the small extraction rate associated with the 0.6-cm diam. and 0.25-cm diam. cup, respectively, assuming initially saturated conditions.

 


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  		Fig. 9. Simulated region-specific Br– concentrations at different positions without (reference), slow (small cup in preferential flow path, PFP) and fast (large cup in PFP) solution extraction: (a), (b) in the PFP; (c), (d), (e) in the matrix at 0.5-cm dislocation from the PFP; (f), (g) in the matrix at 2-cm distance from the PFP, for initially saturated conditions. In (a) discrete Br– concentrations values calculated by averaging simulated values representing 1-cm3 samples taken from the PFP at 10-cm depth are provided.

 
In Fig. 8 , the reference simulation results for the Br– effluent concentrations at the lower boundary are compared with corresponding results for the scenarios with slow and fast water extraction from the PFP (Fig. 8a) and from the matrix (Fig. 8b). In all cases, the preferential Br– peak left the lower boundary between 0.2 and 0.7 h, followed by the matrix peak between 4 and 15 h (Fig. 8). While there was hardly any effect of the slow solution extraction from the PFP, the fast extraction caused the preferential Br– peak to decline by about 20% (Fig. 8a). This is because more Br– mass was removed by the fast than by the slow extraction. The simulations showed only minimal effects even of the larger extraction rate and cup size on the Br– breakthrough curve when extracting from the matrix (Fig. 8b).



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  		Fig. 8. Simulated Br– effluent breakthrough curves at the bottom of the soil block assuming zero (reference), slow (small cup in PFP), and fast (large cup in PFP) solution extraction from the preferential flow path (PFP), for initially saturated conditions.

 
For the cases of no, slow, and fast extraction from the PFP, Fig. 9 compares the simulated Br– breakthrough concentrations at different locations in the PFP and in the matrix. The Br– concentrations in the PFP at the 10-cm depth (Fig. 9a) and at the 20-cm depth (Fig. 9b) were almost similar without and with slow continuous extraction. By contrast, the fast extraction caused an apparent retardation of the breakthrough along with slight decrease of the peak concentrations (Fig. 9a, 9b). Additionally, discrete Br– concentration values are shown which were obtained by averaging the simulated continuous concentrations over assumed 1-cm3 samples. In Fig. 9a, the discrete Br– concentration values were plotted against the times at the midpoints of the sampling intervals between either 4 (slow extraction scenario) or 20 (fast extraction) 1-cm3 samples per hour. These simulated discrete concentrations more realistically reflect experimental sampling conditions. It can be readily seen that the 10 discrete concentrations obtained by the fast extraction gave an accurate representation of the corresponding continuous preferential Br– breakthrough. However, both the continuous and the 10 discrete concentrations lagged behind the simulated reference Br– breakthrough. The slow sample extraction, on the other hand, provided merely two Br– concentration values insufficient for characterizing the preferential Br– peak. At best, the two samples could be used to constrain the time-frame for the passage of the preferential Br– peak.

In the transition region, that is, the matrix at just 0.5-cm distance from the PFP, Br– breakthrough curves displayed a double-hump shape at depths of 10 cm (Fig. 9c), 10.5 cm directly below the sampling position (Fig. 9d), and 20 cm (Fig. 9e). The first peak of the double-hump shaped breakthrough curves can be explained with Br– transfer out of the PFP into the matrix, while the second peak was related to vertical Br– transport in the matrix. The fast extraction (large sampler) markedly affected Br– breakthrough. It caused the peak to drastically rise at the sampling depth of 10 cm (Fig. 9c), because the high extraction rate of the large sampler (2-cm length), located in PFP and adjacent matrix, increased Br– transfer into the matrix. Immediately below the cup, the high Br– concentration peak had already reduced due to the Br– solution extraction (Fig. 9d). At 20-cm depth, the net effect of fast extraction was a lower first and higher second peak of Br– breakthrough concentrations. The small extraction rates with the small sampler located entirely within the PFP had minor effects on concentrations at 10- and 10.5-cm depths and no effect at the lower boundary (Fig. 9c, 9d, 9e). Already at 2-cm distance from the PFP wall, the Br– concentrations were essentially no longer affected by the solution extractions (Fig. 9f, 9g).

For the cases of no, slow, and fast solution extraction from the matrix at 2-cm distance from the PFP, Fig. 10 shows the simulated local Br– concentrations at various locations in the PFP and in the matrix. The individual Br– breakthrough curves in PFP (Fig. 10a, 10b) and matrix (Fig. 10f, 10g) were not substantially affected by either small or large solution extractions, and could be accurately determined even by slow extraction of discrete 1-cm3 samples (Fig. 10f). The Br– concentrations in the transition region (Fig. 10c, 10d, 10e) showed some deviations from the reference curve.



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  		Fig. 10. Simulated Br– breakthrough curves at different positions without (reference), slow (small cup in matrix), and fast (large cup in matrix) solution extraction from the matrix at 2-cm distance from the preferential flow path, assuming initially saturated conditions.

 
Simulation Results for the Five Scenarios Assuming Dry Initial Conditions
Figure 11 illustrates the flow field as defined by the lines of equal hydraulic head and flow velocity vectors in a vertical half cross-section at x2 = 10 cm; at 0.25 h for no, large, and small cup in PFP (Fig. 11a, 11b, 11c); and at 0.75 h for no, large, and small cup in matrix (Fig. 11d, 11e, 11f). In the reference case, the curved lines of equal hydraulic head and orthogonal velocity vectors illustrate that infiltration was not only vertical as in the initially saturated case, but there was considerable water transfer directed from the PFP laterally into the matrix (Fig. 11a, 11d). The effect of cups on the lines of equal hydraulic head was stronger during the first hour of transient, variably saturated flow (Fig. 11) than at steady-state saturated flow (Fig. 5). As could be expected, the larger cup with higher extraction rates caused more perturbation in the flow field than the smaller cup, both in the PFP (Fig. 11b, 11c), and in the matrix (Fig. 11e, 11f).



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  		Fig. 11. Simulated hydraulic head distributions and flow velocity vectors for the five cases assuming dry initial conditions: at 0.25 h for (a) no suction cup (Reference), (b) large cup in preferential flow path (PFP), (c) small cup in PFP; and at 0.75 h for (d) no suction cup (Reference), (e) large cup in matrix (at 4-cm distance from the PFP), and (f) small cup in matrix (at 4-cm distance from the PFP).

 
The succession of simulated pressure head increases at the lower boundary, in the PFP and at successively larger distances in the matrix, is displayed in Fig. 12 for the reference case and the cases of having a small or large cup in the PFP. The pressure head reactions in the reference scenario started in the PFP after about 0.66 h, and in the matrix occurred increasingly later with growing distance from the PFP. Moreover, the time gap between the reference pressure head values and the corresponding values of the scenarios of small or large cup in PFP gradually decreased in the matrix with increasing distance from the PFP. The results demonstrate the pronounced effect of the larger cup in the PFP on the pressure head propagation.



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  		Fig. 12. Simulated pressure heads along the lower boundary of preferential flow path (PFP) and matrix for the scenario without cup (Reference), small cup in PFP, and large cup in PFP assuming dry initial conditions. Matrix (3.5) signifies matrix domain at 3.5-cm horizontal distance from the PFP.

 
Figure 13 shows the simulated water contents at the lower boundary in PFP, together with matrix water contents averaged over the boundary nodes along the entire matrix width. The comparison is made for the reference scenario vs. small or large cup in PFP (Fig. 13a), or vs. small or large cup in matrix (Fig. 13b). The large cup in the PFP caused a marked 0.5-h delay of water content increase in the PFP and some delay in the matrix, whereas the small cup in the PFP invoked very minor delays in both, PFP and matrix (Fig. 13a). The simulation results suggest that both cups in the matrix had negligible effect also on water content increase (Fig. 13b).



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  		Fig. 13. Simulated water contents at the lower boundary separately averaged over preferential flow path (PFP) and matrix for dry initial conditions, (a) no cup (Reference), small cup in PFP, and large cup in PFP; and (b) no cup (Reference), small cup in matrix (at 4-cm distance from the PFP), and large cup in matrix (at 4-cm distance from the PFP).

 
The simulated seepage flux rates across the lower boundary are given in Fig. 14 together with the water-extraction rates during the first 3 h of the simulation. In response to the infiltration, the large cup in PFP at 10-cm depth started to extract water after 12 min and reached its steady-state value of 20 cm3 h–1 after 1.7 h. The extraction flux caused some delay of the seepage water flux as compared to the reference case (Fig. 14a). In the remaining cases, simulated seepage water flux was not significantly affected by either large or small cup in the matrix.



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  		Fig. 14. Simulated seepage water flux at the lower boundary and extraction water flux for the scenarios with dry initial conditions: (a) no cup (Reference) vs. large cup in the preferential flow path (PFP), and (b) no cup (Reference) vs. small cup in PFP.

 
The lines of equal relative Br– concentrations are shown in Fig. 15 at 0.25 h for no, large, and small cup in PFP (Fig. 15a, 15b, 15c); and at 0.75 h for no, large, and small cup in matrix (Fig. 15d, 15e, 15f). Bromide traveled farther into the matrix, both vertically from the infiltration boundary and laterally from the PFP, than it did for initially saturated conditions (cf. Fig. 15 and 6). This can be explained with the enhanced advective transport by water flux which was accelerated by large pressure head gradients directed from the saturated into the relatively dry regions. The cup-induced deflection pattern of the lines of equal Br– concentrations was comparable to that of the simulated hydraulic heads (Fig. 11).



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  		Fig. 15. Simulated Br– concentration distributions assuming dry initial conditions; at 0.25 h for the cases (a) without suction cup (Reference), (b) large cup in preferential flow path (PFP), (c) small cup in PFP; and at 0.75 h for the cases (d) no cup (Reference), (e) large cup in matrix (at 4-cm distance from the PFP), and (f) small cup in matrix (at 4-cm distance from the PFP).

 
Finally, the Br– breakthrough curves for initially dry conditions are illustrated in Fig. 16 . The cases of no, large, and small cup in PFP are compared in Fig. 16a for the cup position at 10-cm depth and in Fig. 16b for the lower boundary. Compared to saturated initial conditions, the Br– breakthrough for low initial water content showed higher peak Br– concentrations, and the two peaks for PFP and matrix were less separated. Furthermore, for dry initial conditions, the large cup's retarding effect on preferential Br– breakthrough in the PFP appeared somewhat more pronounced, with peak concentrations being even slightly higher than for the reference case (Fig. 16b, Fig. 8a). The latter result can partly be explained by the extraction water Br– concentration being lower for dry than for wet initial conditions (Fig. 16a, Fig. 9a).



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  		Fig. 16. Simulated Br– breakthrough concentrations assuming dry initial conditions; for the case without suction cup (Reference) vs. large and small cup in the preferential flow path (PFP), respectively; (a) at the assumed sampling position in the PFP at 10-cm depth, and (b) in the effluent at the lower boundary, and for the case without suction cup (Reference) vs. large and small cup in the matrix, respectively; (c) at the assumed sampling position in the matrix (10-cm depth, 4-cm distance from the PFP), and (d) in the effluent at the lower boundary.

 
The cases of no, large, and small cup in matrix are compared at the cup position at 10-cm depth (Fig. 16c) and at the lower boundary (Fig. 16d). Only the larger cup with faster water extraction in the matrix somewhat reduced and retarded Br– concentrations in the matrix part of the breakthrough curve (Fig. 16d), as opposed to wet initial conditions where there was no such effect of either cup (Fig. 8b).


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Small laboratory suction samplers with ceramic cups of 0.25- and 0.6-cm diam. were constructed and experimentally tested for extraction of pore water out of soil columns. In water-saturated soil, the 0.25- and 0.6-cm diam. ceramic cups allowed for extraction of 4 cm3 h–1 (0.25-cm diam. cup) and 20 cm3 h–1 (0.6-cm diam. cup), respectively, at the applied suction of 0.1 bar. The use of the smaller cup type for solution extraction out of matrix and PFP of an 80-cm long soil column during a Br– transport experiment did not disturb the preferential transport, based on qualitative comparison with the observed effluent Br– breakthrough curve and with results from a numerical model simulation. Furthermore, the cups were useful in demonstrating the differences in local Br– concentrations between PFP and matrix involved in physical nonequilibrium transport as caused by preferential flow. However, the temporal sampling interval of one sample per 20 min was not sufficient for the accurate delineation of the short preferential Br– breakthrough, even when using several cups staggered along the column. This limitation may become more severe with smaller size of the soil column, since then the time scale of preferential solute transport becomes even smaller.

The effects of suction sampling on preferential Br– transport in a smaller soil block (20 by 20 by 20 cm3) with a preferential flow path was assessed by means of three-dimensional numerical model simulations using the experimentally determined water-extraction rates. The results revealed that both the small and the large extraction rates may provide accurate monitoring of Br– transport in the soil matrix without disturbing the breakthrough curve in the bottom effluent. When the large sampler was intersecting the preferential flow path, the large extraction rate accurately measured the sharp preferential Br– peak. However, the large extraction rate changed this preferential Br– peak itself, and even modified the Br– effluent breakthrough curve at the bottom boundary. These effects were more pronounced for initially dry than wet conditions, and they would result in biased interpretation of a transport experiment, if the effects could not be somehow quantified and accounted for in the analysis. On the other hand, the simulations also demonstrated that slow water extraction by a cup in the preferential flow path neither disturbed Br– concentrations at the sampling location nor the Br– breakthrough curve at the lower boundary. However, the information gained by the small sampler was constrained to the approximate duration of breakthrough. Using continuous tracer application as done in the bromide transport experiment might give more favorable conditions for capturing breakthrough than the pulse-type application assumed in the model simulation scenarios.

This study suggests that mini porous cup samplers with small water-extraction rates can be used for monitoring conservative solute transport in a homogeneous porous medium. For preferential flow conditions, even if the location of the preferential flow path is exactly known and the cup can be accurately placed, the problem of optimizing the water-extraction rate between too large (perturbation of the observed transport) and too small (insufficient temporal resolution of the observed transport) appears challenging.

A possible solution to this dilemma might lie in the use of advanced analytic devices such as capillary electrophoresis, which requires only minimal solution volumes of about 0.1 mL. Such small sample volumes could be extracted more frequently without disturbing the preferential flow pattern. However, the current sampling system would need to be modified to further reduce its remnant solution volume of presently about 0.2 mL. Additional work is also necessary to extend this study to natural soils where locations of preferential flow paths are generally unknown.


   ACKNOWLEDGMENTS
 
The financial support by the National Science Foundation (grant EAR 0296158) is gratefully acknowledged. I am thankful to Binayak Mohanty for his support. Furthermore, the critical comments of three anonymous reviewers and of Nobuo Toride as Associate Editor of this manuscript are greatly appreciated.


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




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L. Weihermuller, R. Kasteel, and H. Vereecken
Soil Heterogeneity Effects on Solute Breakthrough Sampled with Suction Cups: Numerical Simulations
Vadose Zone J., July 26, 2006; 5(3): 886 - 893.
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