effectiveness of equilibrium and physical non-equilibrium approaches for interpreting solute...

Ž .Journal of Contaminant Hydrology 50 2001 121–138www.elsevier.comrlocaterjconhyd

Effectiveness of equilibrium and physicalnon-equilibrium approaches for interpreting solute

transport through undisturbed soil columns

V. Comegna a, A. Coppola a,), A. Sommella b

a DITEC Department, UniÕersity of Basilicata, Potenza, Italyb Department of Agricultural Engineering, UniÕersity of Naples A Federico II B , 80055 Portici, Italy

Received 1 December 1999; received in revised form 19 December 2000; accepted 24 January 2001

Abstract

This study observes the dispersion process of chloride through three undisturbed soil columnsŽ .sabA, sabB and arg of different texture under both saturated and unsaturated conditions.Overall, 17 leaching experiments were conducted by means of an equipment designed and built inPortici together with the DITEC of the University of Basilicata.

During the experiments, both symmetric and positive asymmetric breakthrough curves of thechloride anion were measured. As expected, manifest asymmetry was obtained especially for soilcolumns labeled as sabA and arg. In such columns, it was also noted that the degree ofasymmetry increased as the flow density increased at the sample surface. The experimentsconducted on soil column labeled as sabB resulted in more symmetric BTCs.

The experimental data were firstly analysed using the classical two-parameter CD model. Thevariation of the dispersion coefficient, D, with pore water velocity, Õ , and porous medium0

characteristics was explored in detail. The application to all experimental data of the four-parame-ter MIM model, which compartmentalises the pore water in the mobile-stagnant domains providedan insignificant different description of BTCs, even of the asymmetric ones. Furthermore, itresulted in ill-defined parameters, especially those related to the partitioning in the mobile-immo-bile phases. However, for all the three soils examined the two parameter CD model proved to bevery powerful even in interpreting asymmetric BTCs. In any case, it should be emphasised that theagreement of outflow experimental data with a mechanistic model does not unequivocally identify

) Corresponding author.Ž .E-mail address: [email protected] A. Coppola .

0169-7722r01r$ - see front matter q2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-7722 01 00100-0

( )V. Comegna et al.rJournal of Contaminant Hydrology 50 2001 121–138122

the mechanism of solute transport in the soil. In fact, when we applied the CLT model, which isbased on a stochastic approach, the BTCs were comparably well predicted. q 2001 ElsevierScience B.V. All rights reserved.

Keywords: Outflow tracer experiments; Physical non-equilibrium; Transport models

1. Introduction

In the last decade, many problems related to soil and groundwater conservation,tackled by recovering non-conventional resources and through rational, coordinatedmanagement of various resources, have led to increased awareness of processes involved

Ž .in natural systems Rifkin, 1992; Cavazza, 1989 .Particular attention has been focused on the hazards posed by widespread pollution of

groundwater resources, which are especially vulnerable due to the extent of the surfaceŽ .area directly affected by land use Jury et al., 1991; Carravetta, 1996 .

Major progresses have been achieved through parallel studies in setting up experi-mental techniques for monitoring inorganic, organic and biological substances to be

Ž .found in soils and aquifers Kachanosky et al., 1992; Comegna et al., 1999 , usingŽmathematical tools and having widespread recourse to numerical calculations Santini,

. Ž1992 , as well as characterizing natural systems on a statistical basis Jury et al., 1987;.Kutilek and Nielsen, 1994; Comegna and Vitale, 1993 .

From the theoretical point of view, there are insuperable difficulties in giving adetailed and thorough definition, by direct analytical means, of the salient properties ofsolute transport in the soil layer affected by the above phenomena, especially when thereis the filtration of liquids that transport, in solution or in suspension, substances thatinteract with one another, with the liquid phase and with the soil matrix. Thesesubstances, whose toxicity renders them hazardous, penetrate the soil, with someremaining in the root zone and the rest moving towards deeper layers. The tortuosity and

Žconsiderable irregularity of the very fine flow paths, the presence of channels biopores,.dead end pores, cracks whose size and continuity depend on the geometry and

management of the porous media within which the flow occurs, slows or increases theŽ .diffusion rate of the pollutant Beven and Germann, 1982 ; precipitation and release of

the transported parts is facilitated, as well as dispersion; exchange and mass reductionŽprocesses occur, caused by chemical and biochemical reaction Jury et al., 1991; Selim,

.1992 .The most commonly used research techniques currently involve setting up mathemat-

Žical models for simulating flow, transformation and root adsorption Addiscott and. Ž .Wagenet, 1985 . Along these lines, Nielsen and Biggar 1962 were the first to set up a

Ž .straightforward convective–dispersive CD mathematical model to simulate the flow ofy y Ž .Cl and Br ion tracers. Davidson et al. 1977 also simulated one-dimensional flow in

the soil of water containing nitrogen compounds similar to those normally found inŽ y y.run-off NH , NO and the connected ion exchange processes. Convection and4 3

dispersion processes, together with root adsorption and microbiological transformationŽ .of nitrogen nitrification, denitrification and absorption have also been taken into

consideration.

( )V. Comegna et al.rJournal of Contaminant Hydrology 50 2001 121–138 123

However, according to most recent studies, it is becoming increasingly clear that suchmodels fail to exhaustively describe the phenomena in their totality and are also difficultto apply on a regional level because of the heterogeneity of natural porous media and the

Žlarge number of chemical, physical and biological parameters to be considered Jury and.Fluhler, 1992 .¨

Ž .A more complex model MIM for including the preferential flow of solutes inŽ .heterogeneous media, first proposed by Coats and Smith 1964 and subsequently

Ž . Ž .applied by van Genuchten and Wierenga 1976 , Gaudet et al. 1977 and by Schulin etŽ .al. 1987 to describe the solute transport process in soil monoliths, represents the

porous space affected by the circulating solution as divided into two fields or domains,with a mobile water content u and an immobile water content u suyu , respec-m im m

tively. For this system, the solute concentration can, in turn, be subdivided into anaverage concentration C in the mobile phase and a second concentration C in them im

immobile phase. The solute is transported by convection–dispersion in the first phaseand exchanged by diffusion with first-order kinetics in the second. Griffioen et al.Ž .1998 provided an exhaustive review of MIM applications. The model is generallymore powerful and versatile in modelling experimental data obtained on undisturbed soil

Ž .samples. Brusseau and Rao 1990 also showed that the MIM model might betterexplain the flow of water and solutes in structured porous media. However, the problemof the independent estimate of the larger number of parameters involved in the model

Ž .remains unsolved Kool et al., 1987 .The heterogeneity of natural porous media may limit the applicability of the CD

equation in the field. In such conditions, an alternative path to describe the transport ofsolutes is the stochastic–convective approach, SC, in which the solute is assumed to

Žmove in isolated stream tubes at different velocities without any lateral mixing Dagan.and Bresler, 1979 . The effectiveness of this approach in the field has been amply

Ždemonstrated Jury et al., 1982; Butters and Jury, 1989; Heuvelman and McInnes,.1999 . The SC approach was also applied successfully at a laboratory scale on

Ž .undisturbed soil columns Khan and Jury, 1990 . The complex heterogeneity of soil hasencouraged the development of transport theories based on conceptual models, such as

Ž .the transfer function approach Jury, 1982 . A transfer model can predict the flux densityfrom a system with definite boundaries depending on the input flux without any need to

Ž .describe the complex process that takes place within the porous system. Jury 1982suggested a log-normal travel time probability density function and set up the convective

Ž .log-normal transfer function model CLT . This model was shown to supply an accurateŽ .prediction of solute transport in field experiments. Khan and Jury 1990 suggested that

also in laboratory experiments, when working with undisturbed columns whose length iscomparable to the diameter, the SC assumptions are most likely to be valid. The reasonfor the success of the CLT model may be sought in the limited lateral mixing of thesolutes in accordance with the stochastic–convective theory formulated by Jury and

Ž .Roth 1990 .Against a background of considerable practical interest in the issues concerned, in

this paper we refer to applications of CD, MIM and CLT models to typical southernItalian soils. In Section 2, the structure of the models will be illustrated; Section 3 will


describe the experiments, which provided data on the model parameters. Lastly, inSection 4, some conclusions will be drawn and comments made.

2. Theory

2.1. CD model

The widespread use of CD models in interpreting chemical transport phenomena innatural porous media is well documented in the Proceedings of the International

ŽConference on AValidation and Transport Models in the Unsaturated ZoneB Wierenga.and Batchelet, 1988 .

The convective–dispersive flow of an inert solute in a homogeneous, isotropic porousmedium, within a permanent one-dimensional flow domain with no source andror

Ž .sinks, may be described according to the following five adimensional variables: iŽ . Ž . Ž .relative concentration C, ii Peclet number P, iii pore volume number T , iv relative

Ž .distance X, and v retardation coefficient R.These variables may be defined as follows:

Õ t0Ts 1Ž .

Lz

Xs 2Ž .L

Õ L0Ps 3Ž .

D

C yCŽ .e iCs 4Ž .

C yC0 i

rkRs1q 5Ž .

u

Ž y1 . Ž .where Õ sqru LT is the effective pore water velocity, q LrT is Darcy’s0Ž 3 3. Ž .velocity, u L rL is the volumetric water content, L L is the length of the flowŽ . Ž . Ž y3 .system, z L the distance, t T the time, C and C ML are, respectively, thee i

Ž y3 .concentrations of the effluent and initial solution, and C ML is the influentoŽ y3 . Ž 3 y1.concentration, r ML the soil bulk density k L M the distribution coefficient of

Ž 2 y1.the linear isotherm of adsorption and D L T is the dispersion coefficient, whichhas commonly been expressed as DslÕ nqD , where l and n are constants. l is a0 0

characteristic property of the porous medium usually referred as dispersivity and n isŽ .commonly taken as a value between 1 and 2 Kutilek and Nielsen, 1994 .

Hence, the convection–dispersion equation may be expressed in the following way:

EC 1 E2 C ECR s y . 6Ž .2ž / ž / ž /ET P EXEX


Ž .Eq. 6 is based on the assumption that the porous medium and water content arehomogeneous and isotropic, and that dispersion converges rapidly toward a symmetricalhomogeneous mixing process, which may be described by the constant parameter l.

2.2. MIM model

Ž .Eq. 6 implies that all the pore water is involved in convective solute transport andthat all the adsorption sites are equally accessible to the solute if adsorption is also to

Ž . Ž .occur. Moreover, Eq. 6 predicts breakthrough curves BTCs that are typically sigmoidor symmetric in shape, at least for low Peclet number values. Many experiments, asmentioned above in Section 1, have supplied BTCs with considerable deviations fromthe symmetric distribution curves. Such BTCs are indicative of new mechanisms forshowing tailing and early appearance of tracer in the effluent, mechanisms that cannot

Ž .be described by analytical solutions supplied by Eq. 6 .Several authors have used the MIM model, which is based on the conceptual

approach of solute transport from a domain with mobile water content to another withŽ .immobile water content van Genuchten and Wierenga, 1976; Gaudet et al., 1977 .

As with the CD model, the MIM model may be described according to dimensionlessvariables:

u q frKmbs 7Ž .ž /uqrK

aLvs 8Ž .

q

C yCm iC s 9Ž .1 ž /C yC0 i

C yCim iC s 10Ž .2 ž /C yC0 i

where C and C are the concentrations relative to the mobile and immobile regions,m im

respectively, u is the mobile water content; f is the adsorption site fraction in themŽ y1 .mobile region and a T is a mass transfer coefficient expressing in its most

simplified form the law of diffusive transport of the solute between the two regions.Therefore, the MIM model in the case of one-dimensional flow and in a permanent flowregime may be written in the following form:

EC EC 1 EC EC EC1 2 1 1 2bR q 1yb R s y 1yb R sv C yCŽ . Ž . Ž .1 22ž / ž /ž /ET ET P EX ETEX

11Ž .

where variables P and T are defined in terms of actual pore water velocity Õ sqru ,m mŽ . Ž .which differs from velocity Õ found in Eqs. 1 and 3 .0


2.3. CLT model

The CLT model is based on the concept of stochastic–convective transport. Thisconcept means that solutes move at different velocities in isolated stream tubes withoutlateral mixing. The probability that a solute applied at the soil surface zs0 at time

Ž .ts0 will reach a given depth zs l in the time range, ty tqD t, is given by f t d t inŽ . Ž . Žwhich f t is the probability density unction pdf . The pdf of the CLT model flux

. Ž .concentration mode is a log-normal density function Jury and Roth, 1990 :

21 ln tymf t s exp y 12Ž . Ž .2ž /' 2s2p s t

Ž .with the corresponding cumulative density function cdf :

1 ln tymP t s 1qerf 13Ž . Ž .ž /'2 2 s

Ž .in which m and is s are the CLT model parameters. When the parameters of Eqs. 12Ž .and 13 are determined for the reference depth, l, the solute concentration may be

measured for an arbitrary depth z using:

f z ,t s lrz f l ,tlrz 14Ž . Ž . Ž . Ž .P z ,t sP l ,tlrzŽ . Ž .

.Ž .The processes that obey Eq. 14 are called stochastic–convective. The mean and

variance of stochastic–convective models at any distance z are calculated by:

zE t s E tŽ . Ž .z lž /l

2zVAR t s VAR t 15Ž . Ž . Ž .z lž /l

.

3. Materials and methods

Miscible flow experiments were carried out on three undisturbed soil samples 150mm in diameter and 170 mm in length from different sites of southern Italy. Thesamples were collected by means of steel samplers guided by an appropriate hydraulicdevice, ensuring the simultaneous removal of surrounding material so as to reducealterations and compaction of the samples.

The main physical characteristics of each sample, as determined in the laboratory, arereported in Table 1. Samples were identified as sabA, sabB and arg, respectively.

In the laboratory, the samples were saturated slowly from the bottom. Subsequently,the saturated hydraulic conductivity K was determined by the constant head method.s


Table 1Physical properties of the soils examined

Soil Sand Silt Clay Bulk Organic DescriptionŽ . Ž . Ž .% % % density matter

y3Ž . Ž .g cm %

Sandy 80.00 12.00 8.00 1.29 3.1 Horizon A:Ž .sabA granular structure Site:

Ž .Napoli ItalySandy 73.84 19.00 7.16 1.48 1.1 Horizon B:Ž .sabB glomerular structure Site:

Ž .Napoli ItalyClayey– 39.72 25.43 34.85 1.24 1.9 Horizon A:

Ž .sandy arg subangular prismatic structure;Ž .Site: Potenza Italy

Ž .Subsequently, in a thermoregulated chamber 20"0.58C , the samples to be charac-terised were subjected to very simple one-dimensional flow processes with a specificallyconstructed experimental leaching configuration. The leaching unit shown in Fig. 1

Ž . Ž . Ž .Fig. 1. Schematic diagram of the laboratory apparatus showing: 1 rain simulator; 2 soil monolith; 3Ž . Ž . Ž . Ž . Ž . Ž .fraction sampler; 4 Mariotte vessel; 5 vacuum pump; 6 computer; 7 TDR tester; 8 multiplexer; 9

Ž . Ž . Ž . Ž .tracer vessel; 10 peristaltic pump; 11 tensiometer; 12 pressure transducer; and 13 coaxial cable.


consists essentially of a soil column, a rain simulator, a vacuum unit and allowssaturated and unsaturated flow experiments to be conducted.

The bottom end cap of the column supports a nylon cloth of 25 mmesh-wire with abubbling pressure of f2.5 kPa. A bubble tower with a movable air entry tube allowsthe pressure potential, h, of water to be imposed at the bottom of the sample. Thecolumn is then equipped with a vertically installed bifilary TDR probe for measuring thewater content u , and with two tensiometers for measuring the water potential h.

The laboratory-built TDR probe consists of two 5-mm-diameter steel rods, 50 mmapart, 150-mm long extending from a perspex head enclosing a 1:1 matching ferrite

Ž .balun Spaans and Baker, 1993 and is connected to the measuring device by a 2-m-longŽ .coaxial cable RG 58U with a characteristic impedance of 50 V. Porous fritted glass

Ž .plate tensiometers 10 mm in diameter and with a bubbling pressure of f50 kPa areinserted horizontally 5 and 15 cm down the soil column and are connected to pressure

Ž .transducers. The leaching unit is completed by other basic components, namely: i aTektronix Mod. 1502C metallic TDR cable tester equipped with an RS 232 interfaceŽ . Ž . Ž .Tektronix ; ii a personal computer for control, acquisition and data analysis; iii a

Ž . Ž .50-needle id. 0.6 mm rainfall simulator; iv a peristaltic pump serving the simulator;Ž . Žand v an automatic fraction collector to collect the effluent in small fractions 10–15

3.cm .In order to conduct the experiments in question, each soil column thus underwent a

preliminary conditioning phase by feeding, with different steady water flux densities, theflow system with a 0.01-N CaSO solution until the steady flow and initial chloride4

concentration C s0 were reached. Contemporaneous measurements of u , h and qi

allowed us to determine the onset of steady-state. At steady-state, the solution wasshifted with a step feeding by another solution containing 1.86 grl of KCl correspond-

Table 2Experimental conditions for the columns examined

Ž . Ž . Ž .Soil column Experiment u y k cmrmin q cmrmins

sabA sabA-1 0.452 0.0923 0.098sabA-2 0.416 0.025sabA-3 0.406 0.020sabA-4 0.398 0.018sabA-5 0.322 0.006sabA-6 0.318 0.005sabA-7 0.318 0.002

sabB sabB-1 0.432 0.0854 0.096sabB-2 0.430 0.095sabB-3 0.420 0.09sabB-4 0.406 0.028sabB-5 0.410 0.027sabB-6 0.406 0.024sabB-7 0.402 0.017sabB-8 0.387 0.003

arg arg-1 0.489 0.0343 0.019arg-2 0.400 0.005


ing to 25 meqrl of Cly. KCl was selected as tracer because of the low backgroundlevel, the conservative nature of the Cly ion, the low hydration level of the Kq ioncompared with the Naq ion and the mineralogical nature of the clay in the vertisol

Ž . Ž .investigated arg consisting of kaolinite )70% and sodium smectite of marineorigin. During leaching tests, the leachate was periodically collected. The chloride ionconcentration at the outlet boundary was determined by titrating 10 ml of aliquot against

Ž .standard AgNO using 5% K CrO as an indicator Richards, 1968 .3 2 4

Overall, seven tests were carried out on sabA sandy soil, eight on sabB sandy soiland two on arg clayey soil according to procedures summarised in Table 2.

4. Results and discussion

Some experimental BTCs for the soils examined are represented by Fig. 2. GraphssabA-1, sabB-1 and arg-1 refer to the experiments conducted on respective columns atlargest Õ value. SabA-4, sabB-7 and arg-2 graphs are examples of breakthroughs0

obtained under unsaturated conditions.Ž Ž ..The experimental BTCs were first modeled with the CD model Eq. 6 . The model

Ž .parameters were determined using the CXTFIT program Toride et al., 1995 , whichminimises the sum of the squares of the residuals between the measured values andthose calculated with an analytical solution of type A1 proposed by van Genuchten and

Ž .Wierenga 1976 . So as to reduce the number of iterations, the actual velocity Õ was0

set equal to the qru ratio and initial estimates used of parameters R and D werereasonably close to optimal values, obtained with the deterministic methods proposed by

Ž .Fried and Coubarnous 1971 .The obtained parameters, which refer to all the experiments, are supplied in Table 3,

together with 95% confidence intervals. Seemingly, a good agreement between calcu-lated and measured BTCs was achieved at all q values, as confirmed by the high r 2

obtained.Ž .Inspection of the shape of all C t distributions allowed for grouping examined soils

into two series.Ž .a sabA and arg soils whose BTCs show tailing and asymmetry, the extent of which

increases with saturation of the medium and average pore water velocity. Earlyappearance of tracer in the leachate and tailing was apparent especially for sabA-1 andarg-1 experiments and would reflect a type of transport, which typically occurs when thesolute is conducted relatively rapidly through more permeable regions in the soil matrix.The increasingly asymmetric breakthrough as pore water velocity increases is usuallyattributed to a decrease in residence time of solute in the rapidly conducting fraction ofthe porous system that would limit the transfer by diffusion into the stagnant region.BTCs at low Õ values were markedly more symmetric presumably because at slower0

flux the residence time in the column is long enough to allow diffusion to bring themobile and immobile regions closer to physical equilibrium.

Thus, at slow flux, the conceptual assumption of the CD model that all water in theŽ .porous medium is in physical equilibrium is satisfied Anamosa et al., 1990 . Fre-

quently, discrepancies between observed asymmetric BTCs and CD predictions are


Fig. 2. Measured and CD, MIM and CLT simulated breakthrough curves.

attributed to the inability of the model to take account of the existence of a supplemen-tary liquid phase consisting of stagnant water.

Ž .b sabB soil whose BTCs appear to be symmetrical with no noticeable tailing, evenŽ .at high average pore water velocity and at saturation. As mentioned in point a , sigmoid

BTCs would reflect a type of transport consistent with the CD model, which implies awholly mobile pore water and a completely miscible solute.

Fig. 3 shows the relationship between the parameter R and average pore watervelocity Õ . From inspection of Table 3 and of Fig. 3, the behaviour typical of a0

macroporous soil seems suggested for the sabA and arg soils, though with some


Table 3CD model parameters, 95% confidence intervals and goodness of fit

2 2Ž . Ž .Experiment Õ cmrmin D cm rmin R r0

sabA-1 0.216 0.887"0.052 0.449"0.052 0.997sabA-2 0.061 0.054"0.026 1.128"0.026 0.999sabA-3 0.048 0.028"0.055 1.175"0.054 0.997sabA-4 0.045 0.035"0.089 1.091"0.089 0.993sabA-5 0.019 0.026"0.051 1.408"0.050 0.997sabA-6 0.015 0.012"0.033 1.698"0.034 0.998sabA-7 0.006 0.009"0.056 1.107"0.056 0.997sabB-1 0.222 0.197"0.073 0.898"0.072 0.992sabB-2 0.220 0.159"0.097 0.895"0.097 0.986sabB-3 0.215 0.203"0.093 0.929"0.093 0.987sabB-4 0.070 0.045"0.080 0.924"0.080 0.991sabB-5 0.067 0.043"0.139 0.919"0.139 0.974sabB-6 0.060 0.038"0.092 0.963"0.092 0.992sabB-7 0.042 0.065"0.056 0.931"0.056 0.996sabB-8 0.009 0.004"0.030 0.932"0.030 0.999arg-1 0.039 0.159"0.075 1.439"0.074 0.997arg-2 0.013 0.015"0.220 1.032"0.220 0.953

Ždistinction between them. With the series of experiments conducted on sabA soil from.experiments sabA-1 to sabA-7 , a fairly close link between R and Õ was evidenced. It0

is worth noting that R decreases as Õ increases, reaching the value of 0.45 when Õ is0 0

at its maximum of 0.216 cmrmin. This value is considerably less than unity, which maybe attributed to the anion exclusion of the negatively charged Cly. Thus, it is not

Fig. 3. Retardation factor R as a function of the effective pore water velocity Õ .0


possible to set Rs1 as would be the case for a AnonreactiveB or ideal tracer. vanŽ .Genuchten 1980 highlighted the similarity between anion exclusion and phenomena of

non-equilibrium due to the presence of stagnant regions. Early breakthrough occurs inboth cases but the BTC is symmetric in the case of pure anion exclusion. Parameteroptimization may be hampered by non-uniqueness if both anion exclusion and non-equi-

Ž .librium occur. The higher values of R e.g., 1.698 for sabA-6 can be attributed to errorsof this type besides the uncertainties due to evaluation errors of velocity Õ , which is set0

in the procedure of optimization. Although asymmetry in arg-1 breakthrough is to belikely attributed to a similar mechanism, it results in a value of parameter R of 1.44,implying sorption. Thus, a verification of the existence of chemical non-equilibriumwould be also necessary. With R)1, it is difficult to ascribe any non-equilibriumsituation and asymmetry to either a slow chemical interaction with sites of the solidmatrix or to a slow solute diffusion to and out of relatively stagnant water regions.Values larger than unity for chloride were already observed. For example, Nkedi-Kizza

Ž .et al. 1982 noted a sorption of chloride in an aggregated oxisol depending on pH valueand solution concentration of the carrier solution.

The R values observed for the sabB experiments are uniformly close to 0.9, whichwould justify the fairly symmetrical relevant BTCs.

Ž .By virtue of Eq. 3 , Peclet’s number ties the sample length and actual solute velocityto the dispersion coefficient D. The variation of the dispersion coefficient, D, with porewater velocity, Õ , and porous medium characteristics was explored in detail. Assuming0

Ž y6 2 y1negligible molecular diffusion 10 cm s is a typical value for molecular diffusiv-.ity , which is plausible given the field of velocities surveyed, the theoretical relation

between D and Õ is as follows:0

DslÕ n 16Ž .0

where n is an empirical constant and l is the soil dispersivity reflecting the scale ofmechanical dispersion caused by the variation in the local velocities of the water flowdomain around the average value.

The dispersivity is usually considered a characteristic fundamentally tied to soilŽ .structure and may be better compared if n is set equal to 1 linear relation . The n

Ž .parameter involved in the theoretical relation 16 was found to be of 1.012 when all theŽ .series of D and Õ values were considered Fig. 4 , thus, allowing such an assumption.0

The l value of 0.73 would suggest a relatively homogeneous nature of the exploredmedia. Nevertheless, values of 2.83 and 1.22 were obtained for l and n, respectivelywhen D and Õ series pertaining sabA and arg experiments were considered and the0

Ž .theoretical power law in Eq. 16 seems suitable. The average value of ls2.83, whichŽis higher than that commonly observed for uniform soils or for disturbed soils Biggar

.and Nielsen, 1976 , would appear to reflect the field behaviour represented by the soilcolumns considered. Their relatively high D values together with the lower P valuesobserved at high q and u values are indicative of a greater weight of dispersive flow

Ž .compared with convective flow, which justifies C t distributions consistent with thepreferential flow paths of the solute. It could be argued that desaturation in these soilswith presence of macropores produces a narrowing of the effective pore-size distributionthus resulting in a decreased dispersion and in breakthroughs approaching a symmetrical


Fig. 4. Relationship between dispersion coefficient D and the effective pore water velocity Õ .0

shape with decreased water content. On the contrary, the l and n values concerning thesabB experiments, again illustrated in Fig. 4, would suggest a more homogeneousporous system. Such results are consistent with the symmetric shape of pertaining BTCsat all q values.

The BTCs were subsequently modeled with the MIM model, which required theoptimization of two more parameters, b and v. Parameter b represents the solutefraction present in the mobile domain under equilibrium conditions, and may still beused to calculate the fraction of mobile water u using the following expression:m

umFs sbRy f Ry1 17Ž . Ž .

u

where f is the fraction of solute adsorption sites in the mobile water domain.Ž .Following the approximations of Nkedi-Kizza et al. 1982 , we assume that Fs f so

Ž .that from Eq. 17 results bsu ru .m

Parameter v relates the first-order mass-transfer coefficient, a , to the column lengthand solution flux. While the interpretation of this model parameters is relativelystraightforward when the model is applied to soil columns packed with soil aggregatesŽ .Brusseau and Rao, 1990; Nkedi-Kizza et al., 1982 , it is not as clear when the MIM isapplied to intact columns. Anyway, low values of b and a are indications ofpreferential flow. It has been demonstrated in the literature that v increases with the

Ž .increase in flow density q Anamosa et al., 1990 . Furthermore, the coefficient v in theMIM model implies a solute exchange with first order kinetics, a hypothesis that would

Žonly hold in the case where there are dead-end pores in the matrix Coats and Smith,.1964 .

The first trial was conducted fitting the solution of the MIM model to all the BTCs byŽ .simultaneous optimising of all model parameters R, D, b and v . Since the solution

was very dependent on the initial values of parameters, especially b and v, a set of


different combinations of starting values of this parameters was used. The resultsobtained from this trial run are shown in Table 4, which again refers to all theexperiments, and include also 95% confidence intervals for the parameter estimates. Therelationship between D and D is DsbD , although the value for D is notm m

particularly meaningful as it is averaged over the entire flow domain.From inspection of Tables 3 and 4 and Fig. 2 emerged that, albeit its added

complexity, the MIM model resulted in r 2 values comparable with those obtained fromCD model application. Furthermore, values of b , especially when this parameter is quitebetter defined, would indicate large values of u ru , which eliminates the need to makem

a distinction between mobile and immobile regions. Obviously, in this case D valuesfrom MIM model result comparable to those from CD model and the uncertainidentification of parameter b and v produces also uncertain identification of Dparameter. Indeed, comparison of D as well as R values for sabA and arg experimentseries appear always better defined in CD than in MIM. No specified trend wasencountered in parameter v, which assumes occasionally well-defined values. In anycase, due to the general poor definition of parameters involved in the MIM model, it isvery arduous and hazardous to attach them any physical meaning.

For sabB series and for the unsaturated experiments of sabA series such a result wassomeway expected, due to symmetrical shape of breakthrough. Seemingly, the increasednumber of parameters invoked to represent additional processes produced unreliableestimates and unimproved goodness of fit when nothing clearly corroborated theexistence of those processes.

Table 4MIM model parameters, 95% confidence intervals and goodness of fit

2Experiment Õ D R b v r02Ž . Ž .cmrmin cm rmin

sabA-1 0.216 0.917"0.077 0.471"2.7eq06 0.963"2.7eq06 1.0ey07"0.070 0.997sabA-2 0.061 0.042"0.122 1.118"0.034 0.063"1.225 75.650"1.290 0.999sabA-3 0.048 0.029"0.098 1.220"0.134 0.960"0.171 1.0ey07"10.600 0.997sabA-4 0.045 0.035"1.490 1.131"3.796 0.986"1.185 100.000"4.600 0.993sabA-5 0.019 0.026"0.104 1.741"785.959 0.796"785.000 0.003"0.257 0.997sabA-6 0.015 0.012"0.088 1.371"2.202 1.000"2.293 3.8ey04"0.168 0.998sabA-7 0.006 0.000"0.071 1.094"0.058 0.006"0.041 12.580"0.030 0.999sabB-1 0.222 0.001"26.679 1.110"0.084 0.000"1.408 24.530"27.810 0.995sabB-2 0.220 0.004"47.266 1.108"0.106 0.000"5.589 29.290"52.700 0.991sabB-3 0.215 0.002"32.098 1.143"0.097 0.000"1.775 17.760"33.650 0.992sabB-4 0.070 0.047"0.134 1.172"0.304 0.990"0.360 1.0ey07"21.920 0.991sabB-5 0.067 0.046"0.226 1.157"1.3eq07 0.998"1.3eq07 1.0ey07"0.277 0.974sabB-6 0.060 0.039"0.124 1.207"0.219 0.993"0.267 1.0ey07"11.700 0.992sabB-7 0.042 0.066"0.096 1.169"0.135 1.000"0.158 1.0ey07"13.290 0.996sabB-8 0.009 0.000"0.030 1.081"0.043 0.045"0.365 29.290"0.370 0.999arg-1 0.039 0.160"0.114 1.424"2.5eq06 1.000"2.5eq06 1.0ey07"0.108 0.997arg-2 0.013 0.015"2.320 0.993"4.915 0.986"1.344 100.000"5.000 0.953sabA-1 0.216 0.917"0.074 1.000 0.454"0.085 1.0ey07"0.067 0.997arg-1 0.039 1.0ey07"0.191 1.000 1.0ey04"0.962 10.540"0.960 0.955


Conversely, it could be expected the asymmetrical shape encountered in sabA-1 andarg-1 be better interpreted using an approach explicitly accounting for a form ofnon-equilibrium. Nevertheless, again asymmetry is uncertainly explained using theMIM, at least for these cases, probably because of difficulties to associate it to a distinctnon-equilibrium, and the additional mathematical complexity appear not justified. Onecould speculate that in these cases the usefulness of additional parameters in the MIMmodel could be to keep Rs1 for accommodating the theoretical non-adsorbing ofchloride.

For the sabA-1 experiment such an assumption produces acceptable results, with amuch better defined value of parameter b. In this case, a more reliable physical meaningcan be ascribed to the D value.m

Concerning the arg-1 experiment, a poor fit of experimental breakthrough wasobtained, thus suggesting the key role to be attached to parameter R. In effect, thenon-equilibrium could be a result of some sorption-related mechanism Nkedi-Kizza et

Ž .al. 1982 and a non-linear sorption kinetics could also be hypothesised. Furthermore,the non-equilibrium could be even caused by more than one process and a modelaccounting for a multiple sources of non-equilibrium could be required to appropriately

Ž .represent such systems Brusseau and Rao, 1990 . The results of the two trials forRs1, which refer to experiments sabA-1 and arg-1, respectively, are shown at the endof Table 4. With the same assumption MIM failed in interpreting symmetrical curves

Ž .and poor goodness of fit were obtained results not shown here .Ž Ž ..Finally, all BTCs were fitted with the CLT model Eq. 13 . Transport parameters m

and s were obtained by using a conventional optimization algorithm. Relevant graphi-cal results are shown again in Fig. 2. Table 5 shows the best fitting results of the

Table 5CLT model parameters as estimated by simultaneously fitting m and s

2Experiment m s r

sabA-1 3.208 0.687 0.998sabA-2 5.569 0.337 0.999sabA-3 5.868 0.275 0.998sabA-4 5.847 0.315 0.993sabA-5 6.927 0.417 0.996sabA-6 7.385 0.325 0.999sabA-7 7.837 0.424 0.998sabB-1 3.775 0.294 0.993sabB-2 3.783 0.265 0.988sabB-3 4.052 0.337 0.988sabB-4 5.253 0.306 0.986sabB-5 5.274 0.280 0.986sabB-6 5.442 0.287 0.992sabB-7 5.711 0.446 0.998sabB-8 7.316 0.255 0.999arg-1 6.094 0.704 0.998arg-2 7.008 0.384 0.959


transport parameters in CLT. For each outflow experiment, the CLT and CD modelsfitted the data equally well, as indicated by the high coefficient of determination, r 2,between the log-transformed data and the calculated concentrations.

The overall analysis performed above highlights the problems connected with identi-fying the parameters of models CD and MIM based on curve-fitting. Given that theBTCs contain only limited information, it is difficult to establish what process should beincluded in the transport model. Moreover, when several parameters are optimizedsimultaneously, the problem of non-uniqueness arises, because of correlation betweenparameters. However, it should be recalled that when the number of parametersdecreases, the optimization technique allows us to identify unique parameter values and,in all cases, the estimated parameter set is robust in prediction. This observation is

Ž .confirmed by Kool et al. 1985 .Another question concerns the impossibility of making any process hypothesis

Ž .convective–dispersive, stochastic–convective from outflow experiments. Jury andŽ . Ž .Roth 1990 and Khan and Jury 1990 showed that determining whether the governing

Ž . Ž .transport process is stochastic–convective CLT or convective–dispersive CD, MIMrequires BTCs observed at different depths in the soil profile.

5. Conclusions

Seventeen leaching experiments were conducted through three undisturbed soilcolumns of different texture under both saturated and unsaturated conditions. From theshape of the breakthrough curves, together with other curve parameters, it could behypothesised the establishment of a non-equilibrium during experiments carried out athighest q values on columns labeled as sabA and arg. Nevertheless, curve-fitting MIMmodel and CD model to experimental breakthrough produced equivalent goodness of fit.Furthermore, MIM model yielded parameter estimates quite reliable only when asymme-try was evident and could be connected to a physical non-equilibrium identified by an Rvalue less than unity. In any case, deducting physical meanings from the uncertainlyparameters obtained by MIM model can be hazardous.

As a result, a good agreement between CD-fitted and measured curves was obtained,comparable to that obtained with the four-parameter MIM model, even when non-equi-librium could be supposed from the asymmetrical shape of BTC. As long as parametersinvolved in the MIM model will be estimated through curve-fitting alone and withunsatisfactory confidences, good agreement between measured and calculated curveswill be worthless and not sufficient for model verification. In such circumstances, themodel selection should be governed by parameter parsimony.

However, based also on the analysis carried out by using a stochastic–convectiveŽ .approach CLT model , it was also concluded that with the outflow experiment data

used to calibrate the various models it is not possible to identify the most plausibleprocess hypothesis, which may be deduced only through observations of transport atdifferent depths. All the models in question supply equivalent and indistinguishableinterpretations when applied at only one depth.


References

Addiscott, T.M., Wagenet, R.J., 1985. Concept of solute leaching in soils: a review of modeling approaches. J.Soil Sci. 36, 411–424.

Anamosa, P.R., Nkedi-Kizza, P., Blue, W.G., Sartain, T.B., 1990. Water movement through an aggregatedgravelly oxisol from Cameroun. Geoderma 46, 263–281.

Beven, K., Germann, P., 1982. Macropores and water flow in soils. Water Resour. Res. 18, 1311–1325.Biggar, J.W., Nielsen, D.R., 1976. Spatial variability of leaching characteristics of a field soil. Water Resour.

Res. 12, 78–84.Brusseau, M.L., Rao, P.S.C., 1990. Modeling solute transport in structured soils: a review. Geoderma 46,

155–192.Butters, G.L., Jury, W.A., 1989. Field scale transport of bromide in an unsaturated soil: 1. Experimental

Ž .methodology and results. Water Resour. Res. 25 7 , 1583–1589.Carravetta, R., 1996. Il degrado della circolazione sotterranea nel meridione d’Italia. Pubbl. Dpt. Ing. Civile, II

Universita degli studi di Napoli. p. 7.`Cavazza, L., 1989. Agricoltura e Ambiente. L’aspetto tecnico del problema visto nel suo insieme. Genio

Rurale 11, 56–69.Coats, K.H., Smith, D.B., 1964. Dead end pore volume and dispersion in porous media. Soc. Pet. Eng. J. 4,

73–84.Comegna, V., Vitale, C., 1993. Space–time analysis of water status in a volcanic Vesuvian soil. Geoderma 60,

135–158.Comegna, V., Coppola, A., Sommella, A., 1999. Nonreactive solute transport in variously structured soil

Ž .materials as determined by laboratory-based time-domain reflectometry TDR . Geoderma 92, 167–184.Dagan, G., Bresler, E., 1979. Solute dispersion in unsaturated heterogeneous soil at field scale: 1. Theory. Soil

Sci. Soc. Am. J. 43, 461–467.Davidson, G.M., Rao, P.S.C., Selim, H.M., 1977. Simulation of nitrogen movement, transformation and plant

uptake in the root zone. Proc. of National Conference AIrrigation Return Flow Quality ManagmentB,Colorado St. University.

Fried, J.J., Coubarnous, M.H., 1971. Dispersion in porous media. Adv. Hydrosci. 7, 169–282.Gaudet, J.P., Jegat, H., Vachaud, G., Wierenga, P.J., 1977. Solute transfer, with exchange between mobile and

stagnant water, through unsaturated sand. Soil Sci. Soc. Am. J. 41, 665–670.Griffioen, J.W., Barry, D.A., Parlange, J.-Y., 1998. Interpretation of two-region model parameters. Water

Resour. Res. 34, 373–384.Heuvelman, W.J., McInnes, K., 1999. Solute travel time distributions in soil: a field study. Soil Sci. 164, 2–9.Jury, W.A., 1982. Simulation of solute transport using a transfer function model. Water Resour. Res. 18,

363–368.Jury, W.A., Fluhler, H., 1992. Transport of chemicals through soil: mechanisms, models and field application.¨

Adv. Agron. 47, 141–201.Jury, W.A., Roth, K., 1990. Transfer Function and Solute Movement through Soil: Theory and Applications.

Birkhauser, Basel, p. 26.Jury, W.A., Stolzy, L.H., Shouse, P., 1982. A field test of the transfer function model for predicting solute

movement. Water Resour. Res. 18, 368–374.Jury, W.A., Russo, D., Sposito, G., 1987. The spatial variability of water and solute transport properties in

unsaturated soil. Hilgardia 55, 1–31.Jury, W.A., Gardner, W.R., Gardner, W.H., 1991. Soil Physics. 5th edn. Wiley, New York, p. 328.Kachanosky, R.G., Pringle, E., Ward, A., 1992. Field measurement of solute travel time using time domain

reflectometry. Soil Sci. Soc. Am. J. 56, 47–52.Khan, A.U.H., Jury, W.A., 1990. A laboratory test of the dispersion scale effect in column outflow

experiments. J. Contam. Hydrol. 5, 119–132.Kool, J.B., Parker, J.C., van Genuchten, M.Th., 1985. Determining soil hydraulic properties from one-step

outflow experiments by parameter estimation: I. Theory and numerical studies. Soil Sci. Soc. Am. J. 49,1348–1354.

Kool, J.B., Parker, J.C., van Genuchten, M.Th., 1987. Parameter estimation for unsaturated flow and transportmodels—a review. J. Hydrol. 91, 255–293.


Kutilek, M., Nielsen, D.R., 1994. Soil Hydrology. Catena, Verlag, Geoscience Publisher, Cremlingen-Destedt,Germany, p. 370.

Nielsen, D.R., Biggar, J.W., 1962. Miscible displacement in soils: theoretical considerations. Soil Sci. Soc.Am. Proc. 26, 216–221.

Nkedi-Kizza, P., Rao, P.S.C., Jessup, R.E., Davidson, J.M., 1982. Ion exchange and diffusion mass transferduring miscible displacement through an aggregated Oxisol. Soil Sci. Soc. Am. J. 46, 471–476.

Richards, L.A., 1968. Diagnosis and improvement of saline and alkali soils. USDA Handbook, vol. 60, U.S.Government Printing Office, Washington, DC.

Rifkin, J., 1992. Entropia. A. Mondadori, Milano, p. 366.Santini, A., 1992. Modeling water dynamics in the soil–plant–atmosphere system for irrigation problems.

Excerpta 6, 133–166.Schulin, R., Wierenga, P.J., Fluher, H., Leuenberger, J., 1987. Solute transport through a stony soil. Soil Sci.¨

Soc. Am. J. 51, 36–42.Selim, M.H., 1992. Modeling the transport and retention of inorganics in soils. Adv. Agron. 47, 331–385.Spaans, E.J.A., Baker, J.M., 1993. Simple baluns in parallel probes for time domain reflectometry. Soil Sci.

Soc. Am. J. 57, 668–673.Toride, N, Leij, F.J., van Genuchten, M.Th., 1995. The CXTFIT Code for Estimating Transport Parameters

from Laboratory or Field Tracer Experiments. Version 2.0, Research Report No. 137, U.S. SalinityLaboratory Agricultural Research Service. U.S. Department of Agriculture, Riverside, California.

van Genuchten, M.Th., 1980. Determining transport parameters from solute displacement experiments.Research Rep. 118, U.S. Salinity Laboratory, riverside, CA, 37 pp.

van Genuchten, M.Th., Wierenga, P.J., 1976. Mass transfer studies in sorbing porous media: I. Analyticalsolutions. Soil Sci. Soc. Am. J. 40, 473–480.

Wierenga, P.J., Batchelet, D., 1988. Validation and transport models for the unsaturated zone. Ruidoso, NM,Res, Rep. 88-SS-04, New Mexico State Univ., Las Cruces, p. 545.

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