Ž .Journal of Contaminant Hydrology 35 1999 389–407

Modelling tritium and phosphorus transport bypreferential flow in structured soil

Archana Gupta a,), Georgia Destouni a, Marina Bergen Jensen b

a Department of CiÕil and EnÕironmental Engineering, Royal Institute of Technology, BrinellÕagen 32, S-100¨44 Stockholm, Sweden

b Department of Agricultural Sciences, Royal Veterinary and Agricultural UniÕersity, ThorÕaldsensÕej 40,DK-1871 Frederiksberg, Denmark

Received 14 August 1997; accepted 8 July 1998

Abstract

Subsurface solute transport through structured soil is studied by model interpretation ofexperimental breakthrough curves from tritium and phosphorus tracer tests in three intact soilmonoliths. Similar geochemical conditions, with nearly neutral pH, were maintained in all theexperiments. Observed transport differences for the same tracer are thus mainly due to differencesin the physical transport process between the different monoliths. The modelling is based on aprobabilistic Lagrangian approach that decouples physical and chemical mass transfer andtransformation processes from pure and stochastic advection. Thereby, it enables explicit quantifi-cation of the physical transport process through preferential flow paths, honouring all indepen-dently available experimental information. Modelling of the tritium breakthrough curves yields aprobability density function of non-reactive solute travel time that is coupled with a reactionmodel for linear, non-equilibrium sorption–desorption to describe the phosphorus transport. Thetritium model results indicate that significant preferential flow occurs in all the experimental soilmonoliths, ranging from 60–100% of the total water flow moving through only 25–40% of thetotal water content. In agreement with the fact that geochemical conditions were similar in allexperiments, phosphorus model results yield consistent first-order kinetic parameter values for thesorption–desorption process in two of the three soil monoliths; phosphorus transport through thethird monolith cannot be modelled because the apparent mean transport rate of phosphorus isanomalously rapid relative to the non-adsorptive tritium transport. The occurrence of preferentialflow alters the whole shape of the phosphorus breakthrough curve, not least the peak mass fluxand concentration values, and increases the transported phosphorus mass by 2–3 times relative to

) Corresponding author. E-mail: archana@ce.kth.se

0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0169-7722 98 00107-7

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407390

the estimated mass transport without preferential flow in the two modelled monoliths. q 1999Elsevier Science B.V. All rights reserved.

Keywords: Phosphorus; Tritium; Macropores; Preferential flow; Tracer transport; Sorption kinetics; Immobilewater

1. Introduction

In commercial agriculture, large quantities of nutrients in the form of fertilizers andmanure may be applied on or incorporated into the soil. With the infiltration of rain orirrigation water, part of the nutrients move into the root zone and are taken up by plants,whereas some part may be transported to underlying groundwater systems. Leaching offertilizers to lakes and other water bodies is of great environmental concern and it is ofinterest to characterize their possible transport and fate in the subsurface system.Phosphorus, for instance, is the main cause of eutrophication to fresh waters. Due toimproved control of point sources, the phosphorus load to aquatic environment fromnon-point sources becomes more and more important. Subsurface transport of phospho-rus has often been discounted due to its strong adsorption to soil particles. However, ithas been reported by several studies that transport of pollutant in subsurface environ-

Žments may be affected significantly by flow through preferential flow paths e.g.,.Luxmoore et al., 1990; van der Zee and Boesten, 1991; Gaber et al., 1995 .

Preferential flow is a term for describing the process whereby much of the water andchemical movement through a porous medium follow favored flow paths, bypassingother parts of the medium. As a consequence of the hydrological balance, in theremaining parts of the medium water must flow considerably slower, or not at all. Thisconcept does neither exclude nor imply advective transport in the regions of less mobilewater; it only implies that advective travel times in the relatively immobile water zonesare significantly greater than in the preferential flow paths, and approach infinity if thewater is truly immobile. Field soils are usually structured by containing large continuousmacropores, such as interaggregate pores, earthworm burrows, drying cracks andrordecayed root channels. These macropores are generally characterized by distinctlydifferent hydraulic properties than the soil matrix and may result in significantly morerapid solute movement through the unsaturated zone than indicated by average flowestimations, due to preferential flow. Preferential flow leads to an apparent non-equi-

Žlibrium situation with respect to pressure head or solute movement or both Brusseau.and Rao, 1990; Wang, 1991a,b , which may severely limit our ability to predict flow

and transport processes in undisturbed media. The degree to which the resulting effectcan be quantified and predicted depends upon our ability to characterize and model thesephenomena in complex subsurface systems. The accuracy with which we need to modelthese phenomena is expected to be case specific, depending on which transportmechanisms dominate the solute spreading process, such as the physical transportmechanisms for a non-reactive tracer, or, for instance, the sorption kinetics for sorptivesolute transport.

Various models that use two-domain or multi-domain concepts have been used toŽdescribe water flow andror solute transport in macroporous soils e.g., Hoogmoed and

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 391

Bouma, 1980; Beven and Germann, 1981; Davidson, 1985; Bruggeman and Mostaghimi,.1991 . Most of these models are limited to steady-state flow, because the solute

transport quantification becomes more complicated and requires extensive input data fortransient flow conditions. The solute transfer between the different flow domains iscommonly assumed to be diffusion controlled and described either by a first-order rate

Žexpression e.g., Gerke and van Genuchten, 1993; Harvey et al., 1994; Wilkins et al.,.1995 , or by Fick’s law if the geometry of the macropores can be specified explicitly

Ž .van Genuchten and Dalton, 1986 . Unfortunately, models that are based on well-definedgeometry are difficult to apply to actual field situations since they require an extensiveamount of information about the geometry of the structural units; this type of informa-tion is seldom available.

In this paper, we study and attempt to quantify solute transport through structured soilŽ3 . Žby model interpretation of experimental results from tritium H O and phosphorus as2

32 y.H PO tracer tests in three undisturbed soil monoliths. Specifically, we aim at2 4

quantifying the possible existence of preferential flow and its effects on transport of bothŽ .a non-reactive tracer tritium and a solute that undergoes non-equilibrium sorption–de-

Ž .sorption phosphorus . Geochemical conditions, such as pore water pH and ionicstrength, are similar in the different experiments, implying that differences in effluentbreakthrough curves for the same tracer can be expected to result mainly fromdifferences in the physical transport mechanisms within the different soil monoliths.Geochemical problems, such as the pH dependence of phosphorus behaviour need thusnot be considered here, and phosphorus sorption can be quantified by a relatively simplemodel, thereby enabling the desired focus on physical transport mechanisms associatedwith the possible existence of preferential flow paths.

For the model interpretation of experimental results, we use a probabilistic La-grangian approach that is based on the assumption that the spreading of solute is

Žprimarily an effect of variability in solute advection and thereby solute residence or.travel time both along and among different streamlines. Application of such an

approach to the scale of laboratory soil monolith experiments follows the line ofprevious transfer function analysis of sorbing solute transport on the laboratory scalethat have been based on the concept of a residence time distribution within the transport

Ž .domain e.g., Villermaux, 1974; Sardin et al., 1991; Roth and Jury, 1993 . Recenttheoretical developments have helped in clarifying the conceptual basis of a stochastic

Ž .Lagrangian approach to reactive subsurface transport Cvetkovic and Dagan, 1994 ,enabling better understanding of its application to different spatial scales. On the fieldscale, both molecular diffusion and local dispersion within the mobile water arecommonly neglected. On the laboratory scale, it is only molecular diffusion within themobile water that needs to be neglected, whereas the effect of hydrodynamic localdispersion and possible other physical spreading mechanisms, such as preferential floweffects, are explicitly described by stochastic advection variability along and amongdifferent streamlines through the transport domain. The main advantage of using such aLagrangian approach for model interpretation of tracer tests in soil monoliths is thatphysical, chemical and biological mass transfer and transformation processes can bedecoupled from pure advection, which may simplify the modelling significantly. Fur-thermore, it enables us to explicitly quantify the possible effects of transport of both

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407392

non-reactive and sorptive solute through preferential flow paths, which is the mainobjective of this paper.

2. Materials and methods

2.1. Soil characteristics

Three intact soil monoliths were excavated in an agricultural loamy-sand field nearFarre, Jutland in Denmark. The monoliths were sized 0.5 m in diameter by 1.0 m long,0.5 m in diameter by 0.73 m long, and 0.5 m in diameter by 0.5 m long and are in thefollowing referred to as C1, C2 and C3, respectively. The identified horizons of the

Ž .monoliths are A , E , B and B Table 1 . Monolith C1 contained all the soilp g t1 g t2 g

horizons. To investigate the subsoil, the A -horizon was removed in the laboratory forp

monolith C2. For C3 the top soil was investigated by removing the B-horizons in theŽlaboratory. The subsoil contained two distinct types of macropores: biopores earthworm

.burrows and some decayed root channels and fractures. In the subsoil the number ofburrows with diameter)1–2 mm decreased from 300–450rm2 in the E -horizon tog

2 Ž 2 .only 20–25rm in the B -horizon. A few of these 5–15rm had diameters in thet 2 g

range 5–8 mm and were continuous throughout the monolith length. The fractures wereeasily localized due to their bleached color of reddish, iron oxide rich soil material.When viewed horizontally the fractures formed a net of polygons with an approximatemesh size of 15 cm. The fractures originated in and continued downward from the lowerpart of the E -horizon.g

The soil monoliths were excavated from the soil surface by manually removing theŽ .surrounding soil to allow an edged steel cylinder 0.5 m in diameter by 1 m long to

slide down the outside of the monolith. The steel cylinder was replaced by a rubbermembrane overlaid by a steel mantle. A fluid rubber, that hardened within 24 h, ensuredcontact between the soil monolith and the rubber membrane. Bulk samples from theidentified horizons were air dried and passed through a 2 mm sieve. Bulk porosityestimation was based on 0.05 m diameter samples, horizon depths and an average

3 Ž .mineral density of 2.65 grcm Table 1 . The texture was determined by sieving andŽ .sedimentation Bouyoucos, 1927 . The total phosphorus content was estimated as the

Ž .amount of phosphorus extracted from ignited samples 5508C, 1 h with 6 M H SO for2 4Ž10 min at 708C. The pH of the samples was determined in 0.01 M CaCl soil:solution2

.ratio 1:2.5 .

Table 1Characteristics of the field soil as determined from standard soil samples

Ž .Horizon cm Bulk density Porosity Clay diameterF Silt diameter Fine sand diameter Ptot3 y1Ž . Ž . Ž . Ž . Ž .grcm 2 mm % 2–20 mm % 20–200 mm % mg P kg

A 0–25 1.33 0.50 15 15 44 744p

E 25–45 1.40 0.47 19 14 43 272g

B 45–73 1.56 0.41 19 11 44 284t1 g

B 73–108 1.78 0.33 20 13 42 314t 2 g

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2.2. Laboratory setup

In the laboratory, the monoliths were insulated and cooled to 1–28C, which is themean temperature measured under the field conditions, controlled by a thermocoupleinserted 15 cm into the soil in the middle of the monolith. The experimental setup isshown in Fig. 1. Top and bottom surfaces of the monolith were vacuum-cleaned in orderto remove any air present in the pores. A full cone nozzle fed from a pressurized carboyapplied influent uniformly to the surface of the soil monolith, at a rate regulated with atimer-controlled magnetic valve. To avoid dispersion of the soil from influent droplets, a2 mm grid of stainless steel was placed on the soil surface. Under application of tracer

Ž .pulses, a secondary tracer carboy replaced by turning of a three-way stop-cock theordinary influent carboy.

Effluent was collected from four openings in the bottom cover, placed in a squarepattern at equal distance from the center and the periphery of the cover, and combined ina single effluent line running to a fraction collector. The effluent flow rate wascontrolled by means of a peristaltic pump. To maintain free drainage from the fullcross-sectional area of the monolith, two grids of stainless steel with mesh sizes of 63and 2000 mm were inserted between the lower soil surface and the bottom cover, thefinest grid being closest to the soil. For flow control the influent and effluent carboyswere placed on automatically recorded balances. The pressure head was measured byconnecting an open-ended vertical tube to the bottom cover. Saturated hydraulicconductivity of the soil monoliths were determined according to the constant head

Ž .method Jury et al., 1991 .

2.3. Solute applications

Radioactive tracer experiments were carried out in all the three monoliths undersaturated, and generally steady-state flow conditions. The monoliths were pre-leached

Žfor 5 days before tracer application. Pulses of influent spiked with both tritium as3 . Ž 32 y 32 .H O and phosphorus as H PO and denoted by P were applied at the sixth day2 2 4

Ž .to all the soil monoliths Table 2 . The pulse application rate was identical to the flowŽ y1 .rate. In all the experiments the influent consisted of distilled water 0.003 mS cm and

the electrical conductivity was measured with a conductivity meter. The mean saturated

Fig. 1. Schematic representation of laboratory setup.

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407394

Table 2Experimental results

Ž Ž .Monolith Q mlr Tracer u % Ponding Input pulse Mass recovery Peak arrival. Ž . Ž . Ž . Ž .min volume ml activity MBq % time min

3C1 8.92 H O 42 500 2.31 97 700232 yH PO 500 7.56 1.0 5002 4

3C2 8.42 H O 38 670 15.98 81 600232 yH PO 670 1.83 0.78 3502 4

3C3 4.21 H O 48 243 1.86 76 20002Ž .pulse-13H O 246 1.77 91 21002Ž .pulse-2

32 yH PO 243 8.91 7 5002 4

hydraulic conductivity was measured to be 1.8=10y5 mrs. Continuous measurementsof effluent pH were obtained on-line with a combined glass electrode inserted directlyinto the effluent line. During all the experiments the pH was rather stable with valuesbetween 6.8–7.2. In C1 and C2, only one pulse of tritium and phosphorus tracers wereapplied while in C3, two pulses of tritium and one pulse of phosphorus tracers wereapplied. In C3, phosphorus pulse was applied with the first pulse of tritium and secondtritium pulse was applied at the eleventh day, i.e., when the concentrations from the firstpulse were low to measure.

Effluent fractions of 15 ml were sampled continuously for the first 4 h after pulseapplication, followed by discrete sampling at a frequency steadily decreasing to onesampling per 2 h. All discrete samples consisted of two 15 ml effluent samples taken ina row. The samples were analyzed for 3H O and 32 P by scintillation counting. Aliquots2

Ž .of the applied pulse solutions Table 2 were also analyzed by scintillation counting.

3. Modelling approach

3.1. Non-reactiÕe tracer tests

The probabilistic Lagrangian transport formulation that was discussed in Section 1Žsee also Cvetkovic and Shapiro, 1990; Destouni and Cvetkovic, 1991; Destouni, 1993;

.Cvetkovic and Dagan, 1994 will in the following be used for the model interpretation ofŽ3 . Ž .the tritium H O breakthrough curves BTCs . As discussed previously, application of2

this approach to the laboratory scale of the soil monoliths implies that we neglect theeffect of molecular diffusion within the mobile water and assume that, for non-reactivesolute, spreading is primarily an effect of stochastic variability in solute advection

Ž .between different streamlines leading to local hydrodynamic dispersion , coupled withpossible diffusional solute mass transfer between mobile and immobile water zones. Foran instantaneous uniform pulse injection at the soil surface and steady-state vertical

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 395

Ž .flow, the mass flux s t, z of non-reactive solute per unit cross-sectional area throughwhich the flow takes place can then be expressed as

s t , z rr s f t ; z 1Ž . Ž . Ž .A

where r is the surface density, defined as mass of injected solute per unit cross-sec-AŽ .tional area, and f t; z is the probability that the solute originating from an arbitrary

position at the soil surface will be advected to the effluent at depth z, at the elapsed timet after solute injection. In the absence of possible preferential flow and immobile waterzones, a relevant mechanistic solute transport model for a laboratory monolith experi-

Ž .ment is the advection–dispersion equation ADE . For instantaneous flux injection andflux detection of non-reactive and non-sorptive solute, and under steady-state flow

Ž . Ž .conditions, the travel time probability density function pdf f t; z may be expressedŽ .from the consistent solution to the ADE as Kreft and Zuber, 1978

21 1y trTŽ .

f t ; z s exp y 2Ž . Ž .1r23 4 lrz trTŽ . Ž .T 4p lrz trTŽ . Ž .where Tszurq, is the mean advective solute travel time to the monolith effluent at z, u

is the total water content expressed as the fraction of unit soil volume occupied bywater, q is the specific discharge and l is the local dispersivity defined from the localdispersion coefficient, Dslqru , in which molecular diffusion is neglected.

When accounting for preferential flow and transport, one possible conceptualizationis to use a two-region model, assuming advection in the region of preferential flow pathsonly and immobile water in the other region, with diffusional mass transfer taking placebetween the mobile and the immobile water zones. For pulse injection at the soil surface

Ž̃ .a modified solute travel time pdf described by f t; z accounting for linear, reversible,non-equilibrium diffusional mass transfer, can be expressed from the results of the work

Ž .of Destouni and Cvetkovic 1991 asa t

f̃ t ; z sexp y t f t ; z q c t ,T f T ; z dT 3Ž . Ž . Ž . Ž . Ž .Hu 0m

2 2a a a a aˆc t ,T s Texp y Ty tq T P I T tyT H tyTŽ . Ž . Ž .1

u u u u u u um im m im im m im

4Ž .ˆ ˆŽ . Ž . Ž .where H t is the Heaviside step function and I W is defined as I W s1 1

Ž 1r2 . 1r2I 2W rW , with I being a modified Bessel function of first kind of order one.1 1

Further, u and u are the volumetric content of mobile and immobile water respec-m im

tively with a being the mass transfer coefficient between the mobile and the immobilewater zones.

Another possible two-region model of preferential flow and transport is to considermobile water and solute advection in both regions, with a bimodal pdf of solute travel

Ž .time, f t; z used to quantitatively handle solute advection variability through bothŽpreferential and slow flow paths. The soil water is then distributed as u water content1

. Ž .in slow flow paths and u water content in preferential flow paths , i.e., usu qu .2 1 2

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ŽThe bimodal pdf may be expressed as e.g., Destouni, 1993; Destouni et al., 1994;.Eriksson and Destouni, 1997

f t ; z sn f t ; z q 1yn f t ; z 5Ž . Ž . Ž . Ž . Ž .1 2

2G1 1 ln t y ln TŽ . Ž .Ž .if t ; z s exp y 6Ž . Ž .i 1r2 22 2 sit 2psŽ .i

Ž . Ž .where f t; z is a log–normal distribution of solute travel time T z , evaluated ati

elapsed time t, with T G being the geometric mean and s 2 the variance of ln T withini i

the population of slow flow paths for is1 and the population of preferential flow pathsfor is2. Furthermore, n is a weighting coefficient expressing the water flow fractionthrough slow flow paths such that

QsQ qQ sn Qq 1yn Q 7Ž . Ž .1 2

where Q is the total water flow, which is the sum of the water flowing through slowflow paths and preferential flow paths, designated as Q and Q , respectively. It is noted1 2

Ž Ž .. Ž Ž ..that the model Eq. 3 may be viewed as a special case of the bimodal model Eq. 5Žwith the coefficient ns0 i.e., no flow through the slow flow paths, implying immobile

.water there , u su and u su , and with an additional quantification of the1 im 2 m

diffusional mass transfer between the extreme mobile and immobile water zones; such aŽ Ž ..quantification of diffusional mass transfer could also be added to the model Eq. 5 ,

however it has been shown to have only a small effect in the case of n)0 and isŽ .therefore neglected here Destouni, 1993 .

From the definition of volumetric water content

u'V rV su qu 'V rV qV rV 8Ž .w tot 1 2 w1 tot w 2 tot

where V and V are the volume of soil water and the total soil monolith volume,w tot

respectively. Furthermore, V and V are the volumes of water in the slow flow pathsw1 w2

and in the preferential flow paths, respectively, which may be expressed as

V sn QT ; V s 1yn QT 9Ž . Ž .w1 1 w 2 2G 2Ž . Ž .where T sT exp s r2 is the mean travel time, for is1,2. Combining Eqs. 8 andi i i

Ž .9 yields

T Q T Q1 2usu qu sn q 1yn 10Ž . Ž .1 2 V Vtot tot

which puts an experimental restriction on the possible choice of the unknown modelparameters n and T , based on the independently observed parameters u , Q and V .i tot

3.2. ReactiÕe tracer tests

Ž32 .For model interpretation of the phosphorus P BTCs, the non-reactive probabilisticLagrangian transport formulation is extended to couple with chemical mass transferprocesses by quantifying sorption–desorption as it takes place along the advection flow

Ž . Ž .paths e.g., Cvetkovic and Dagan, 1994 . The reactive solute mass flux, s t, z , in theeffluent of the soil monolith can then be expressed as

s t , z sr H`g t ,T f T ; z dT 11Ž . Ž . Ž . Ž .A 0

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 397

Ž .where f T ; z is given by the model of the corresponding non-reactive tracer BTC, andŽ .the function g t,T depends on the considered linear sorption–desorption process;

possible extension to non-linear sorption processes by a similar methodology is de-Ž . Ž .scribed by Dagan and Cvetkovic 1996 and Cvetkovic and Dagan 1996 .

Considering instantaneous solute input and non-equilibrium linear sorption–desorp-Ž . Žtion within the soil monolith, the function, g t,T , may be expressed as Lassey, 1988;

.Shapiro and Cvetkovic, 1990; Destouni and Cvetkovic, 1991

g t ,T sexp yk t d tyT qk k T exp yk Tyk tqk TŽ . Ž . Ž . Ž .1 1 2 1 2 2

ˆ= I k k T tyT H tyT 12Ž . Ž . Ž .1 1 2

where k and k are the sorption and desorption rate coefficients, respectively, and d is1 2Žthe Dirac delta function. For a given travel time T , the behaviour of the function g Eq.

Ž ..12 can be separated into two parts. The first part, which contains the Dirac deltafunction, expresses the solute arrival at time tsT. The second part, which contains themodified Bessel function, expresses the delayed mass arrival due to sorption at times

Ž . Ž .t)T. For a non-reactive solute with k sk s0, g t,T reduces to d tyT ; hence the1 2Ž .complete mass arrival occurs at tsT and Eq. 11 reduces to the non-reactive

Ž Ž ..expression Eq. 1 .

4. Interpretation of experimental results

The variation of accumulated water flow with time is shown in Fig. 2 for the threesoil monoliths. All the monoliths show steady-state flow conditions, but in C1 there is asudden change in the slope of the accumulated flow curve after 2200 min due to air

Fig. 2. Accumulated flow during the tracer experiments as a function of time and for monolith C1 also as afunction of flow corrected time.

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407398

entry in the influent system. In order to account for this change in flow rate and to beable to compare it with the other monolith BTCs, the accumulated water flow for C1 has

t Ž X. X F Ž .been plotted on a flow corrected time scale, G , defined as G'FH Q t d t rH Q t d t0 0Ž .Eriksson et al., 1997 , where F is the total observation period of the tracer test andŽ .Q t is the measured flow of water.The experimental BTCs from the tracer experiments have been analyzed in terms of

the normalized mass flux, srr , where the total injected mass of tracer divided byA

column cross-sectional area has been used for normalization as in the case of modelledŽ . Ž . Ž . Ž . Ž . Ž .BTCs. In real time s t, z is calculated as s t, z sc t, z q t , where c t, z and q t are

the measured tracer concentration and specific discharge of water, respectively. In theŽ . Ž . Ž .flow corrected time s G , z sc G , z q where c G , z is the measured solute concentra-˜

F Ž . Ž .tion at the flow corrected time G and q'H Q t d tr AF is the steady-state water˜ 0

flux that corresponds to the flow corrected time G with A being the cross-sectional areaŽ .of the soil monolith Eriksson et al., 1997 .

Table 2 shows the mass recovery in the individual tracer tests for all the threemonoliths. The mass recovery is then defined as the accumulated mass at the end of theexperiment. For the sorptive tracer 32 P the mass recovery in C1, C2 and C3 was 1%,0.78% and 7%, with a peak arrival time of 500, 350 and 500 min, respectively. In the

Ž3 . Ž32 .following, the tritium H O and phosphorus P BTCs are modelled based on2

available independently measured parameters, namely total water content u and waterflux qsQrA, with A(0.20 m2 for all monoliths and with u and Q values as listed inTable 2.

4.1. 3H O BTCs2

Ž Ž ..The advective–dispersive pdf Eq. 2 alone, which implies neglect of preferentialflow paths, could not be fitted to any of the observed 3H O BTCs honouring the2

Ž . Ž Ž ..independently available parameter values. Eq. 3 combined with the pdf Eq. 2 , couldbe fitted to the 3H O BTC in monolith C1, with fitted parameter values ls0.75 m,2

u s0.16 and as0.000009 miny1. Even though this fitted model showed goodmŽagreement with observations in terms of both normalized mass flux and accumulated

.mass fraction , the resulting fitted dispersivity, l, value was almost equal to the wholemonolith length, which implies that an advective–dispersive transport process is not aphysically meaningful model interpretation of the transport process in monolith C1.Thus, a different model was required to interpret the experimental results in a more

Ž . Ž .meaningful way and we used Eqs. 5 and 10 for this purpose. The agreement betweenŽ Ž . Ž . Ž ..the experimental and modelled Eqs. 1 , 5 and 10 tritium BTCs in C1 is shown in

Fig. 3a in terms of the normalized mass flux. The agreement is in our view sufficientlygood not to require use of a more complex model, in particular since the fitted parameter

Ž Ž ..values, shown in Table 3, are consistent with the experimental restriction Eq. 10 andthereby physically meaningful. The model implies water content values u s0.32 and1

u s0.10 in the slow flow paths and preferential flow paths, respectively. This implies2Žthat in C1 water flows preferentially through 24% of the total water content obtained as

.u ru .2Ž Ž .. Ž Ž ..The modified pdf Eq. 3 combined with the advective–dispersive pdf Eq. 2

Ž . 3provided the best fit least squares method to the H O BTCs in monoliths C2 and C3.2

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3 Ž .Fig. 3. Comparison between experimental and modelled H O BTCs in terms of normalized mass flux for: a2Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .C1 according to Eqs. 1 , 5 and 10 ; b C2 according to Eqs. 1 – 3 ; C3 according to Eqs. 1 – 3 : c

Ž .pulse-1; d pulse-2.

The agreement between the experimental and modelled BTCs, in terms of normalizedmass flux, are shown in Fig. 3b for C2 and Fig. 3c and d for C3, pulse-1 and pulse-2,respectively. The fitting parameters were the dispersivity, l, the mobile water content,u and the mass transfer rate coefficient, a , the values of which are listed in Table 3.m

Table 3Fitted parameter values for 3H O BTCs2

Monolith

C1 C2 C3

Pulse-1 Pulse-2

n s0.4 ls0.11 m ls0.12 m ls0.12 m2 2s s0.4, s s0.7 u s0.10 u s0.19 u s0.201 2 m m mG y1 y1 y1T s9460 min, a s0.00008 min a s0.00002 min a s0.000007 min1GT s1644 min2

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407400

For monolith C2, the ratio u rus0.26, which implies that water flows preferentiallym

through 26% of the total water content. The corresponding value for C3 is u rus0.40m

and u rus0.41 for pulse-1 and pulse-2, respectively, which implies that water flowsm

preferentially through about 40% of the total water content. This consistent result andŽ .the consistency of the fitted parameter values for pulse-1 and pulse-2 Table 3 indicate

that the 3H O BTC experiments in monolith C3 are reproducible and can be interpreted2

by the same transport model, even though we had a less satisfactory mass recovery forŽ . Ž .pulse-1 76%; Table 2 as compared to pulse-2 91%; Table 2 .

The model consistency for the two tritium pulses in C3, honouring all the indepen-dently available experimental parameter values and minimizing the use of fitted parame-

Žters, also supports the decision not to introduce additional model complexity beyond the.models discussed in Section 3.1 for non-reactive transport , even though model fits to

observations are less than perfect, particularly for monoliths C2 and C3. Increasedmodel complexity does namely imply more flexibility to obtain better fit to observations,however without more input data available to restrict this flexibility in an independentway there is not much more reliable information to be gained from an extended fittingexercise.

4.2. 32P BTCs

32 Ž . Ž .The P BTCs were modelled by Eq. 11 coupled with the corresponding pdf f T ; z˜Ž Ž . .or modified pdf f T ; z to account for potential diffusional mass transfer for each

monolith, as obtained by modelling of the 3H O tracer tests. The only required fitting2

parameters were the sorption–desorption rate coefficients, k and k . The comparison1 2

between the experimental and modelled 32 P BTCs in terms of normalized mass flux andaccumulated mass fraction is shown in Fig. 4 for monoliths C1 and C2. The resulting fitis in our view sufficiently good not to require use of a more complex phosphorussorption–desorption model, in particular since this would require more input data that

Žare not available and would have to be calibrated. The experimental BTC for C1 Fig..4a exhibits two small peaks that are not captured with our model. Furthermore, the peak

Ž .arrival time for the BTC in C2 Fig. 4c differs somewhat between model results andobservations. However, the small peaks in Fig. 4a contain a negligible amount of masscompared with the main peak that is captured by the model, which can be seen in the

Ž .associated cumulative BTC Fig. 4b . Furthermore, the peak time discrepancy in Fig. 4calso has very small effect in terms of the main mass arrival time, as can be seen in the

Ž . y1cumulative BTC Fig. 4d . The fitted kinetic parameter values are k s0.010 min ,1

k s0.004 miny1 for C1 and k s0.007 miny1, k s0.002 miny1 for C2, which2 1 2

shows consistent k and k values, of the order of 10y2 miny1 for k and 10y3 miny11 2 1

for k , for both soil monoliths. Such consistency between rate coefficients is to be2

expected for consistent geochemical conditions between the different experiments. Theobtained results thus indicate an insignificant compensation effect in the fitting of thesorptive transport model for the relatively poor fit of the underlying non-reactiveŽ .tritium model, which describes the physical transport process through preferential flowpaths. This does in turn imply that the kinetics of the sorption–desorption processdetermine the spreading of the 32 P BTCs to such a degree that quantification of all the

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 401

32 Ž . Ž . Ž .Fig. 4. Comparison between experimental and modelled P BTCs; for C1 according to Eqs. 5 and 11 : aŽ . Ž .in terms of normalized mass flux; b in terms of accumulated mass fraction; and for C2 according to Eqs. 3

Ž . Ž . Ž .and 11 : c in terms of normalized mass flux; d in terms of accumulated mass fraction.

details of the physical transport process is not required, as long as the dominating effectof transport through preferential flow paths is described adequately.

For monolith C3, however, the experimental 32 P BTC exhibits a much earlier peak3 Žarrival time than the corresponding non-sorptive H O BTCs 4 times earlier; see Table2

. 322 , and a much higher mass recovery than the P mass recovery in the other twoŽ . Ž Ž ..monoliths about an order of magnitude higher; see Table 2 . The model Eq. 11

Ž̃ . Ž Ž ..combined with a relevant pdf f T , z Eq. 3 already accounts for the early break-Ž .through and physical non-equilibrium behaviour asymmetrical BTC with long tailing

caused by the occurrence of preferential flow and transport, and diffusional masstransfer between mobile and immobile water. There is therefore no way that the modelŽ Ž .. 32Eq. 11 can be made to fit to the observed P BTC, based on the independentlyobserved 3H 2 O BTC. This is illustrated in Fig. 5 by using consistent kinetic parametervalues as for C1 and C2, i.e., k s0.0085 miny1 and k s0.003 miny1, obtained as the1 2

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407402

32 Ž . Ž . Ž .Fig. 5. Comparison between experimental and modelled P BTCs according to Eqs. 3 and 11 for C3: a inŽ .terms of normalized mass flux; b in terms of accumulated mass fraction.

average parameter values for monolith C1 and C2. Fig. 5a and b show the comparisonbetween the experimental and the modelled BTCs in terms of both the normalized mass

Ž Ž ..flux and the accumulated mass fraction, which is obtained by integrating Eq. 11 overtime. As expected, the modelled BTCs that honour independent parameter values andunderlying physical transport mechanisms, predict much later 32 P arrival in comparisonto the observations. This difference indicates either some unexplained mechanism thatincreases the transport velocity of 32 P 4 times in comparison to 3H O, or some2

32 Žexperimental error. Accounting for a possible P acceleration mechanism unknown to.us since we have already accounted for preferential flow by modifying the underlying

Ž̃ . Žpdf f T ; z through a reduced value of the mobile water content to u s0.05 4 timesm.smaller than the best fitted value in Table 3 yields a 1.2% mass recovery, to be

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 403

compared to the extremely high experimental value of 7%. Thus, even by reducing um

to get the observed increase in transport velocity of 32 P we still cannot model the high32 Ž Ž ..percentage of P mass transported through the monolith C3 with model Eq. 11 and

kinetic parameter values consistent with those for C1 and C2; in fact, acceptable modelfitting could not be obtained even for other values of the kinetic parameters. The factthat the 3H O experiment in C3 was shown to be reproducible, along with the2

inconsistently high 32 P mass recovery in C3, relative to C1 and C2, indicates anexperimental error in the 32 P BTC in soil monolith C3. Unfortunately, this could not bechecked by repeating the experiment because the soil monolith was destroyed directlyafter the tracer tests to facilitate other measurements.

At any rate, it was not possible for us to model the 32 P BTC in C3 based onindependent parameter values and possible transport mechanisms that are known to us.In the following, we will therefore concentrate on explicitly quantifying the effect ofpreferential flow paths on phosphorus transport through monoliths C1 and C2.

4.3. Effect of preferential flow on 32P transport

The existence of preferential flow paths implies that a large part of the totalinfiltrating water flows through a small part of the cross-sectional area of the porousformation. In the present study we have saturated flow conditions that are unlikely toprevail as a steady-state situation in an actual field situation. Under transient flowthrough a macroporous soil, however, the macropore sequences will primarily conductwater when near-saturated conditions exist. It is therefore of general interest to evaluatethe effect of preferential flow paths for the 32 P transport in the considered monolithexperiments under saturated flow conditions.

To evaluate the effect of preferential flow paths in C1 and C2, we wish to comparethe observed 32 P BTCs with a corresponding transport situation in the absence of

Ž .preferential flow paths. We thereby use Eq. 11 combined with the purely advective–Ž . Ž Ž ..dispersive pdf f T ; z Eq. 2 , a dispersivity, l, value that is 10% of the monolith

length, the kinetic parameters evaluated in the above section and the observed totalŽ .water content, u , value summarized in Table 4 . For C1, the percentage of mass that

would be transported through the monolith during the experimentation period in absenceof preferential flow is 0.3%, as compared to the value of 0.9% in the modelled 32 P BTC

Ž .with preferential flow paths and the observed 1%; Table 2 . Corresponding results forŽmonolith C2 is 0.35% without and 0.77% with preferential flow paths 0.78% observed;

.Table 2 . Fig. 6 shows the comparison between the obtained modelled BTCs in

Table 4Model parameter values and results in the evaluation of the effect of PFP

32 32Ž .Monolith l m u k k P mass P mass1 2y1 y1Ž . Ž .min min transported transported

without PFP with PFPŽ . Ž . Ž . Ž .modelled % modelled %

C1 0.10 0.42 0.010 0.004 0.3 0.9C2 0.07 0.38 0.007 0.002 0.35 0.77

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32 Ž .Fig. 6. Modelled P BTCs with and without preferential flow paths; for C1 in terms of: a normalized massŽ . Ž . Ž .flux; b accumulated mass fraction; and for C2 in terms of: c normalized mass flux; d accumulated mass

fraction.

monoliths C1 and C2, with and without preferential flow paths, in terms of bothnormalized mass flux and accumulated mass fraction, illustrating that preferential flowpaths significantly affect the 32 P transport through the soil.

5. Discussion and conclusions

In this paper, a stochastic Lagrangian approach has been used to model tritium andphosphorus transport in controlled laboratory experiments. The approach is consistentwith the concept of a residence time distribution within the transport domain thatunderlies a transfer function analysis of sorbing solute transport on the laboratory scale.The main advantage of using the stochastic Lagrangian approach for model interpreta-tion of laboratory experiments is that recent theoretical developments have helped inclarifying the conceptual basis for decoupling pure and stochastic advection from

( )A. Gupta et al.rJournal of Contaminant Hydrology 35 1999 389–407 405

physical, chemical and biological mass transfer and transformation processes. Thisdecoupling simplifies the modelling considerably and enables us to explicitly quantifythe physical transport process through preferential flow paths, honouring all indepen-dently available experimental information.

Our model analysis indicates that significant preferential flow and transport occurredin all the experimental soil monoliths. Monolith C1 included all the soil horizons fromA to B . The modelling results on this monolith indicate that all the water is mobile,p t2 g

Ž Ž ..however about 60% obtained from the value of 1yn ; see Table 3 and Eq. 7 of thetotal water flow moves through preferential flow paths that hold only 24% of the total

Ž .water content u ru under saturated conditions. For monolith C2, which excludes the2

top A -horizon of the soil, the modelling results indicate that only 26% of the totalpŽ .water content is mobile u ru , implying that 100% of the water flow moves throughm

preferential flow paths under saturated conditions. For C3, which includes only the topA - and E -horizons of the soil, the modelling results indicate that about 40% of thep g

Ž .total water content is mobile u ru . Thus in all three monoliths, cracks and macrop-m

ores in the structured soil appear to act as channels for preferential flow and transport.Where immobile water appears to exist, the rapid transport in the mobile region isaccompanied by diffusive mass transfer of solute between the mobile and immobilewater regions, yielding the characteristic physical non-equilibrium behaviour of earlyinitial breakthrough and long tailing in the BTCs. Comparison between the monolithsindicate that the different soil horizons play important roles for the water movement,with the top A - and E -horizons of the soil containing more cracks that are continuousp g

and more conductive as compared to the lower horizons of the soil.The model results of 32 P transport in monoliths C1 and C2 yielded consistent

sorption and desorption rate coefficients, k and k of the order of 10y2 miny1 and1 2

10y3 miny1, respectively, for both soil monoliths. Such consistency between ratecoefficients for consistent geochemical conditions between the different experimentsŽ .pH of 6.8–7.2 and similar ionic strength in all experiments indicates that the fittingprocedure of the sorptive transport model did not compensate for the poorer fit of the

Ž .underlying non-reactive tritium model, which quantifies the physical transport processthrough preferential flow paths. This does in turn imply that the kinetics of thesorption–desorption process determines the spreading of the 32 P BTCs to such a degreethat quantification of all the details of the physical transport process is not necessary, aslong as the dominating effect of transport through preferential flow paths is describedadequately.

32 Ž .For the P tracer BTC in monolith C3, the observed concentration or mass fluxpeak arrived 4 times faster than for the observed non-sorptive 3H O tracer BTC. Since2

we already accounted for preferential flow and physical non-equilibrium effects in the3H O transport model, we could not find any additional acceleration mechanisms to2

explain the 4 times more rapid 32 P transport. This inability to model the phosphorustransport while honouring the independently quantified and reproducible physical trans-port process may be indicative of experimental error in the 32 P tracer test in monolithC3.

In the present experiments, the total transport of 32 P mass through the soil wasincreased by 200% in monolith C1 and 120% in monolith C2 by the occurrence of

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preferential flow and transport. Furthermore, not only the total transported phosphorusmass but also the whole shape of the phosphorus BTC, not least the peak mass flux andconcentration values, were very much affected by the rapid phosphorus transport

Ž .through preferential flow paths Fig. 6 . These are important effects that may havesignificant environmental implications also in real field situations. The modellingapproach used in this paper enables quantification of such effects of preferential flow,using non-reactive tracer BTCs as hydrological transport models that are based on andhonour all independently available experimental information. With such an underlyinghydrological model, a consistent model interpretation of reactive tracer tests in the samesoil domain can be used for estimation of reaction parameter values that are relevant forthat domain.

Acknowledgements

We are grateful to Jakob Masid of the Royal Veterinary and Agricultural Universityof Denmark for initiating the experiments and for his help with the data transfer to theSwedish group. Financial support for this work was provided by the Swedish Council

Ž .for Forestry and Agricultural Research SJFR through the Nordic Research project onLosses of Dissolved and Particulate Phosphorus from Agricultural Land to the Aquatic

Ž .Environment NORPHOS . The second author also acknowledges the financial supportŽ .of the Swedish Natural Science Research Council NFR .

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