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III. Analysis of Process Assumptions

III. Analysis of Process Assumptions

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2=50 crn















TIME (days)






TIME (days)

Figure 3. Normalized solute outflow concentrations predicted at 150-cm depths by the

CDE and CLT models after common calibration at 2 = 50 cm. Reproduced with permission,

from Jury and Roth (1990).

shapes are virtually indistinguishable when the two functions are fitted to

each other, or to a single outflow record, even though they model the

dispersion process in completely different ways. This demonstrates that a

soil column experiment monitored only at the effluent end cannot be used

to test the validity of a dispersion model. However, the travel time pdfs

of these two models calibrated at 50cm have very different shapes at

z = 150 cm, even though the mean breakthrough times of each model concentration pulse are still the same. Therefore, the appropriate type of

experiment to evaluate a dispersion hypothesis is one in which the spreading rate is studied as a function of the distance from the inlet end.



This procedure was followed in the study of Khan and Jury (1990), who

measured solute outflow concentrations in repacked and undisturbed soil

columns 90, 45, and 22.5 cm in length (created by cutting off part of the

column at the end of a series of experiments) at several column widths and

flow rates. Their study showed that the CDE description of dispersion

[Eq. 251 was generally valid in the repacked soil, but only at the lowest

flow rate in the undisturbed columns. At higher flow rates in the undisturbed soil, the apparent dispersion coefficient increased with distance

from the source, as it would for a stochastic-convective process.



The effects that solute adsorption can have on solute concentrations in

soil can be somewhat subtle, depending on the details of the process

hypotheses. Some of the principal findings of researchers studying adsorptses will be summarized below for the main adsorption representations

introduced in Section II,G,l.

1. Nonlinear Adsorption Models

a. Freundlich Adsorption

The Freundlich isotherm shape, Eq. (35b), is a common form for the

equilibrium partitioning of many organic chemicals. The major effects that

this isotherm shape can have on transport compared to the simple linear

model, Eq. (38), are to alter the symmetry of the spreading process and to

make the travel time of a pulse or front concentration dependent. In a

simulation study, Van Genuchten and Cleary (1979) demonstrated the

effect of nonlinearity on concentration pulse shape by using Freundlich

adsorption isotherms, Eq. (35b), with different powers of 1 / N . Using a

numerical model that assumed equilibrium adsorption between dissolved

and adsorbed phases, they predicted the concentration-depth curves of a

pulse of solute whose adsorption was described by Freundlich isotherms

that agreed at the initial pulse concentration, but that had Freundlich

power coefficients 1/N ranging from 0.4 to 1.0. Their results showed that

within the same concentration range, solute undergoing nonlinear adsorption caused the solute pulse to be more asymmetric than the one representing a solute undergoing linear adsorption. For example, with 1/N = 0.4,

the partitioning to the sorbed phase is higher at low concentrations, which

restricts the compound from penetrating in the forward direction in the soil

and retains it more in the surface layers than when N = 1, in which case the

pesticide partitions equally at all concentrations.



Nonlinear adsorption can have significant effects on mean travel time, as

was demonstrated by Rao and Davidson (1979). These authors measured

concentration outflow curves for the pesticide 2,4-D added at 50 and

5000 g ml-'. If the pesticide was linearly adsorbed to equilibrium, then the

two outflow curves would have been identical. In contrast 2,4-D, which

had a nonlinear Freundlich isotherm in the soil in which the experiments

were performed (1/N = 0.7), had much greater mobility per unit of water

applied at the higher concentration than at the lower one, arriving at the

outflow end after about 2 and 6 pore volumes, respectively. This result

illustrates that one should be careful to use linearized forms of nonlinear

isotherms that represent the actual concentration range to be encountered

in the soil, rather than to use standard linear forms of the isotherm from

the literature, which might have been measured at significantly different

concentrations. As shown in Table I, nonlinear isotherms are common for

pesticides, which indicates that this procedure should be generally followed

when simulating pesticide movement. Even when correctly linearized

isotherms are used, however, the resulting model will not reproduce the

assymmetry of the breakthrough curve (Jury and Ghodrati, 1989).

b. Hysteretic Adsorption Models

Because of the extreme difficulty in simulating hysteresis in adsorptiondesorption reactions, very little information has been obtained about the

importance of this process on transport of solutes. Van Genuchten et al.

(1974) used a Freundiich adsorption-desorption model with different

parameters for the two cases to describe hysteresis in simulating the transport of picloram in a soil column. By comparing the predicted transport to

a model using a single Freundlich isotherm, they were able to show that the

main feature of hysteresis is to retard desorption, producing a longer

effluent tail on a column breakthrough curve. Unfortunately, this effect is

also characteristic of rate-limited nonequilibrium adsorption, so that the

importance of hysteresis is difficult to establish experimentally (Van

Genuchten et al., 1977).

2. Rate-Limited Adsorption

Figure 4, taken from Jury and Roth (1990), shows the calculated outflow

curve for a chemical undergoing rate-limited linear adsorption (with R = 3)

according to the mass transfer model, Eq. (40), as a function of the value

for the rate constant a. For extremely small values of a, the compound

moves as if it is completely mobile, except for a small amount of tailing

(that persists to very long times) due to the limited sorption and subsequent desorption that occurred during the residence time of the molecules







= aL/V =0.005







s3 0.













Figure 4. Outflow concentrations for a solute undergoing rate-limited adsorption as a

function of the value for the rate constant a. Reproduced with permission, from Jury and

Roth (1990).

in the transport volume. When the rate coefficient a is large, the compound

nearly adsorbs to equilibzium, and the breakthrough is delayed nearly

proportionally to the retardation factor R = 3. At an intermediate value of

the rate coefficient, the solute pulse shows both early breakthrough and

pronounced tailing.

3. Stagnant Water Phase Models

The division of the liquid pore volume into a mobile region and an

immobile region is at best an approximate representation of the true state

of nature. This framework is likely to be most successful in describing

transport through a medium containing distinct aggregates in a narrow size

range that hold water within small pores. For such a system, the interaggregate transport may be approximated by a single flow velocity if the aggregates are packed into a uniform configuration, and diffusive transport into

the aggregates can be modeled either with an explicit, radial diffusion sink

term representing flow into the aggregates (Rao et al., 1980a,b), or by

representing the transfer into the immobile region with a mass transfer

coefficient (Coats and Smith, 1956; Van Genuchten and Wierenga, 1976).

These two approaches are not equivalent (Rao et af.,1980a), but the mass

transfer coefficient can be adjusted to produce nearly the same mass

exchange properties by analyzing the geometry of the region between the

two water phases (Van Genuchten, 1985; Villermaux, 1987).

When the aggregates have a distribution of pore sizes, the exchange

process becomes more smeared out than for the case of a single aggregate geometry. This effect can be modeled if the distribution function is



known (Moharir et al., 1980; Rasmuson, 1985). An excellent review of

mass transfer models and their characteristics is presented in the article of

Brusseau and Rao (1990).

The mobile-immobile water models described above have been used

successfully to model solute transport in aggregated media prepared with

a specified geometric configuration (Rao et al., 1980ab), and have been

used to interpret rate-limited solute adsorption in a groundwater experiment in an aquifer containing relatively homogeneous sediments (Goltz and

Roberts, 1986). However, other explanations based on completely different assumptions can produce similar effects when applied to the same

problem. Nkedi-Kizza et al. (1984) showed that a model with an immobile

and mobile water fraction assuming instantaneous sorption produced a

mathematical equation with the same form as that of model wtih uniformly

mobile water carrying solute that adsorbed on two types of sites, one of

which was limited by diffusive mass transfer. Kabala and Sposito (1991)

reanalyzed the aquifer problem studied by Goltz and Roberts (1986) with a

stochastic continuum model, and demonstrated that the effective retardation factor was time dependent when equilibrium adsorption was assumed

to occur on adsorption sites that were spatially distributed and correlated

with the spatial variations of the water flow velocity. Thus, there are

alternate mechanisms capable of reproducing a solute transport event that

may not be resolvable with the given experimental information.

An additional limitation to applying stagnant water-phase models to the

field regime is the possibility that water partitions into a number of distinct

phases having different relative motion under the influence of an external driving force. In such a circumstances, there will be many rate coefficients operating locally, which when integrated up to the field scale by

volume averaging will have transport properties that differ from those of a

model with a single rate coefficient between a mobile and stagnant phase.

An extreme case of such behavior is encountered when the solute partitions into a rapid or preferential flow region and a slower but still mobile

matrix flow region, each of which may embody a smaller but still significant

degree of water flow variability (Roth et al., 1991). There are also significant complications introduced for model identification when more than

one rate process is limiting solute movement and reactions in soil

(Brusseau et al., 1989).

4. Preferential Flow of Solute

The mechanisms that can create preferential flow are understood for the

most part, but cannot be predicted from an a priori analysis of the field

characteristics. Preferential flow may arise from true fluid instabilities



created by density or viscosity differences between the resident and invading fluids (Krupp and Elrick, 1969; see review by Hillel and Baker, 1988).

It can be induced by structural voids that have extremely high permeability

when filled with water (Kissel et af., 1974; Beven and Germann, 1982). It

can develop at the interface between two soil layers of different permeability (Hill and Parlange, 1972). It can also occur in sandy soils having high

matrix permeability, and which also contain discrete coarse or fine lenses

of porous material. When water moves through such soils, these lenses can

act as barriers to downward flow and cause focusing or funneling of water

(Kung, 1990a,b). White (1985) reviewed a number of studies of water and

solute transport through soil containing a pronounced macrostructure.

Although each of these situations results in extremely rapid transport

through a portion of the wetted cross-section, they have very different

attributes and cannot be described by a single process hypothesis. Structural voids can cause preferential flow if they transmit water, even if the soil

water flux is spatially uniform. The physical properties of the preferential

flow region in this case are very different from those of the surrounding

matrix, creating extremely high velocities when the flow channels are

saturated. Moreover, sorbing chemicals moving in solution in a water-filled

structural void may largely bypass the reduced number of adsorption sites.

In fine-textured soils containing structural voids, the permeability of

the surrounding matrix may be so low that virtually all of the convective

transport occurs within the void region (Beven and Germann, 1982). In

this case, the matrix acts as a stagnant water zone through which solute

may move only by diffusion.

The situation is quite different when preferential flow is caused by lateral

movement and funneling of water flow into smaller cross-sections, or when

fluid instabilities produce fingering along the direction of flow. Here the

physical properties of the preferential flow region may be quite similar to

those of the surrounding matrix; only the flow velocity is different.

Moreover, substantial water flow may be occurring in the surrounding matrix as well as in the preferential flow region; consequently, the

transport problem cannot be characterized in terms of a mobile and an

immobile water region, but must include a description of transport through

each zone as well as mass transfer between them.


Despite the abundance of agricultural and environmental applications

for solute transport modeling, very little field-scale research on transport

has occurred until recently. In the few comprehensive experiments that



have been performed over a large surface area, only the most basic of

the process assumptions can be evaluated. Several of these are discussed




When a mobile anionic tracer such as bromide or chloride is added as a

pulse to the surface of a field and is subsequently leached by irrigation or

rainfall, the mean velocity V , of the area-averaged pulse can be estimated

by monitoring the downward movement of the chemical with solution

sampling or soil coring. If the field is receiving water at a net flow rate q ,

then the observed field-mean velocity should be comparable to the socalled piston flow velocity V, = q / 8 , where 8 is the mean volumetric water

content, provided that all of the water is participating in the transport.

However, field studies that have made this comparison have come to

somewhat contradictory conclusions, as shown in Table 11.

The study by Biggar and Nielsen (1976) took place on 20 continuously

ponded plots located within a 150-ha field area. The chloride tracer was

added to each plot as a pulse and was monitored by solution samplers to

1.8 m. The measured solute velocity was calculated by fitting the breakthrough curve from a given sampler to the solution of the convection

dispersion model. The 20 calculated solute velocities averaged over all of

the samplers at a given site compared favorably with the piston flow

velocity (slope = 1.09; r 2 = 0.84) estimated from the steady infiltration rate

and the saturated water content of each site.

The studies by Butters et ai. (1989) and Ellsworth et aZ(l991) took place

on the same field at different times. Butters’ study involved applying a

bromide pulse to the entire surface and leaching it downward by spatially

uniform bidaily sprinkler irrigation, while monitoring the pulse with solution samplers in a 4 x 4 grid at different depths between 0.3 and 4.5 m. He

calculated the solute velocity as the ratio of the depth of observation to the

mean solute pulse arrival time, and found it to be substantially less than the

net applied water flux divided by the volumetric water content in the top

1.8 m, below which the estimates agreed. When the arrival time of the

peak concentration rather than the mean arrival time was used to estimate

the solute velocity, the agreement with piston flow was much closer, but

still was about 30% slower near the surface.

The study by Ellsworth et aZ(1991) involved leaching massive plumes of

solute under bidaily irrigation, after the plumes had been injected in the

soil slowly in an approximate cubic configuration 1.5 or 2.0 m on a side.

The plumes were sampled by soil coring at various times after application

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