modelling reactive solute transport from groundwater to soil surface under evaporation

HYDROLOGICAL PROCESSESHydrol. Process. 24, 608–617 (2010)Published online 17 December 2009 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/hyp.7555

Modelling reactive solute transport from groundwater to soilsurface under evaporation

K. Nakagawa,1* T. Hosokawa,2 S.-I. Wada,3 K. Momii,1 K. Jinno4 and R. Berndtsson5

1 Department of Environmental Sciences and Technology, Kagoshima University, 1-21-24 Korimoto, Kagoshima 890-0065, Japan2 Department of Civil and Urban-Design Engineering, Kyushu Sangyo University, 2-3-1 Matsukadai, Higashiku, Fukuoka 813-8503, Japan

3 Department of Plant Resources, Kyushu University, Hakozaki, Higashiku, Fukuoka 812-8581, Japan4 Department of Urban and Environmental Engineering, Kyushu University, 744 Motooka, Nishiku, Fukuoka 819-0395, Japan

5 Department of Water Resources Engineering, Lund University, Box 118, SE-221 00 Lund, Sweden

Abstract:

Two-stage soil column experiments involving capillary rise and evaporation were conducted to improve understanding of saltand water movement from groundwater to soil surface. In total, 64 soil columns were placed in a tank partly filled with waterin order to mimic the groundwater table in soil. Each soil column was analysed by dividing it into 27 segments to analysepore water and ion distribution in both liquid and solid phases after prescribed time periods. The water and solute transportbehaviour in the columns was simulated by a one-dimensional numerical model. The model considers the cation exchangeof four cations (Ca2C, Mg2C, NaC and KC) in both dissolved and exchangeable forms and anion retardation for one anion(SO4

2�). The Cl� is treated as a conservative solute without retardation. The numerical results of the cation distributions inboth liquid and solid phases, anions in the liquid phase, and volumetric water contents were in relatively good agreement withthe experimental results. To achieve a better model fit to these experimental results, a variable cation exchange capacity (CEC)distribution may be required. When a simple calculation scheme for evaporation intensity was applied, better predictions interms of daily variation were achieved. The soil water profile displayed a steady state behaviour approximately 10 days afterthe start of the experiments. This was in agreement with numerical results and calculated distribution of velocity vectors. Thefinal model includes cation exchange, anion retardation, and unsaturated water flow. Consequently, the model can be appliedto study sequential irrigation effects on salt accumulation or reactive transport during major ion concentration changes ingroundwater. Copyright 2009 John Wiley & Sons, Ltd.

KEY WORDS soil column experiment; reactive transport modelling; evaporation; cation exchange; salinization

Received 19 June 2007; Accepted 2 April 2008

INTRODUCTION

Soil salinization is caused by a rise in groundwater,which brings naturally occurring salts to the soil surfaceand subsequent deposition. Because of global warming,evaporation intensity may increase significantly. Thiscauses growing concern about increased soil salinizationrisks and the need to develop better tools for simulatingsalt transport from groundwater to the soil surface byevaporation.

Much research has been devoted in recent years tosalt and water transport in soils. Fritton et al. (1967)examined the difference of water and salt distribution invarious soil types and evaporation intensities. Hassan andGhaibeh (1977) studied evaporation and salt movementin the presence of a groundwater table. They deducedthe relationship between pore water velocity and disper-sion coefficient from evaporation flux by means of thevariable thickness of sand and clay layers. Ghuman andPrihar (1983) investigated the effects of initial soil watercontent and application of water on the displacement anddistribution of surface-applied chloride in sandy soils for

* Correspondence to: K. Nakagawa, Department of EnvironmentalSciences and Technology, Kagoshima University, 1-21-24 Korimoto,Kagoshima 890-0065, Japan. E-mail: [email protected]

two evaporation rates. Nassar and Horton (1989a,b, 1992)and Nassar et al. (1992) conducted an experiment undernon-isothermal conditions and developed a model whichcan simultaneously consider transfer of heat, water andsolute in porous media. Fukuhara et al. (2001) developeda model to analyse heat, liquid water and water vapourmovement in a soil column under evaporation from soilpores at the interface between dry and wet capillary lay-ers. They compared model predictions with experimentalresults.

When not only prediction of the transport of waterand total amount of salts are warranted but also thetemporal change in pore water content near the soilsurface, accumulated salt species on the soil surfaceas well as chemical reactions among solutes and thesoil matrix have to be considered. Probably one ofthe most important processes affecting the major cationcomposition of pore water is the cation exchange reaction(Appelo and Postma, 2005). However, none of the abovestudies considered cation exchange reactions in theseexperiments or included these reactions in the model.

In this study, two-stage capillary rise and evaporationlab experiments were carried out using 64 soil columnsof 50 mm diameter and 580 mm length. Each columnwas divided into 27 segments to obtain the distribution

Copyright 2009 John Wiley & Sons, Ltd.

MODELLING REACTIVE SOLUTE TRANSPORT UNDER EVAPORATION 609

of water content and solute concentration. A numericalmodel was developed to describe transport and reactionprocesses occurring in the soil columns. In the model,a simple estimation procedure for evaporation intensityusing water content of the surface segment was applied.Pore water movement is solved by an implicit finite dif-ference method and solute transport is solved by themethod of characteristics (MOC). The model consid-ers cation exchange and anion adsorption as chemicalreactions. The solution algorithm for reactive transportfollows the theory outlined by Momii et al. (1997). Thecalculation results are compared to the laboratory exper-iments. The water movement and reactive transport dueto capillary rise and evaporation are discussed and weclose with a discussion of practical results of the study.

LABORATORY EXPERIMENT FOR SOLUTETRANSPORT UNDER EVAPORATION

Figure 1 shows the experimental apparatus used to inves-tigate the solute transport under evaporation in the 50-mmdiameter and 580-mm-long soil columns. The columnsconsisted of four parts. The upper part had ten segmentshaving a thickness of 10 mm each and the second part had15 segments of 20 mm. The third part had two segmentsof 50 mm and the lower part constituted a foundationto keep the column standing upright. All of the columnsegments were connected using watertight adhesive tape.Field soil was air dried and passed through a 2-mm sieveand then re-packed into the columns to approximatelythe original density. Then, the top of the columns wascovered with caps to prevent evaporation. In total, 64columns were used in the experiment. To make all ofthe columns uniform, they were all re-packed to havea constant soil density. The columns were then placedin a water tank to mimic groundwater conditions. Thewater tank was filled with groundwater containing 5 mMCa2C, 2 mM Mg2C, 20 mM NaC, 4 mM KC, 30 mM Cl�and 4 mM SO4

2�. These concentrations were defined byconsidering the following: (1) they mimic a realistic com-ponent concentration of saline groundwater; and (2) theywere adjusted to avoid clogging with the precipitated saltfrom the saline water. The groundwater table was kept atan 80-mm height from the bottom of the columns. The 64

columns were removed and divided into segments afterpredetermined time intervals and analysed for pore waterconcentrations of major ions Mg2C, Ca2C, NaC, KC, Cl�,SO4

2� and exchangeable cation composition.After this, the columns were again placed in the water

tank with covers at the top in order to reach a steadystate in terms of capillary rise for 7 days. Then, the cov-ers of the columns were removed and the evaporationprocess started. Temperature and humidity were mea-sured in the laboratory. The temperature tends to risein daytime, while the humidity does not change verymuch in the day and nighttime. From autumn to win-ter, there is a pattern in which the decline of humiditycorresponds with rise of the temperature in the daytime.Wind velocity and radiation were considerably lower inthe nighttime, because the laboratory was closed. Thereseems to be different factors which decide the evapo-ration rate between the day and nighttime. Therefore,the evaporation intensity was measured twice a day withone period representing daytime (9 : 00–17 : 00) and oneperiod representing nighttime (17 : 00–9 : 00). The day-time and nighttime evaporation was made dimensionlessby dividing with evaporation intensity near the water sur-face, which was measured beside the columns by usingan evaporating dish. The relationship between dimension-less evaporation and the water content of the soil surfacewas observed using the soil in the top column segment.Figure 2 shows the relationship between evaporation andwater content. The fitted evaporation models for daytimeand nighttime equations were as follows:

EV

EVWSD 0Ð957

(�ss � �r

�s � �r

)0Ð437

for daytime �1�

EV

EVWSD 0Ð984

(�ss � �r

�s � �r

)0Ð293

for nighttime �2�

where, EV (L T�1) is evaporation intensity from the soilsurface, EVWS (L T�1) is evaporation intensity near thewater surface, �ss �� is volumetric water content in thefirst soil surface column segment, �s �� is saturatedwater content, and �r �� is residual water content, whichwas obtained by using the model of van Genuchten(1980) to fit the measured soil water characteristics curve.From the figures, it is seen that the models are good

Figure 1. Experimental column setup

Copyright 2009 John Wiley & Sons, Ltd. Hydrol. Process. 24, 608–617 (2010)DOI: 10.1002/hyp

610 K. NAKAGAWA ET AL.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

(qss-r)/(qs-r)

Ev/

Evw

s

observed(night)model(night)observed(day)model(day)

Figure 2. Evaporation intensities depend on the water content of soilsurface

approximations of these observations. These equationswere used as a boundary condition for the top of thecolumn in the numerical soil water transport simulation.When �ss is equal to �s, both equations should takeEV/EVWS D 1, but our models take 0Ð957 and 0Ð984for the daytime and nighttime period, respectively. Themodels were obtained with the best fit curves using aleast square approximation. These differences were notproblems, because the uppermost part of the column didnot reach saturation during the experiment.

NUMERICAL MODEL

Water flow in the soil column

Successful numerical simulations of solute dynamicsrequire soil water flow to be modelled accurately. One-dimensional vertical soil water flow is described byRichard’s equation:

cw �h�∂h

∂tD ∂

∂z

[k�h�

(∂h

∂z� 1

)]�3�

where h is the pressure head (L), z represents verticalcoordinates which originate from the soil surface takenpositive downwards (L), t is time (T), k�h� is hydraulicconductivity as a function of the pressure head (L T�1),and cw�h� is the specific soil water capacity as a functionof the pressure head (L�1).

In order to obtain the functions for hydraulic conduc-tivity k�h� and specific soil water capacity cw�h�, theoret-ical formulas of van Genuchten (1980) were applied anddefined by:

Se D � � �r

�s � �rD

[1

1 C �˛jhj�n

]m

k�h� D ksSe

12

{1 �

(1 � Se

1m

)m}2

cw �h� D˛m��s � �r�Se

1m

(1 � Se

1m

)m

1 � m�4�

where Se is effective saturation (�), ks is saturatedhydraulic conductivity (L T�1), and ˛, n, m �D 1 � 1/n�are coefficients of the van Genuchten formula. As seenabove, water vapour transport was not considered inthis paper. Reasons for this were that the experimentalconditions represent low evaporation intensity and thuswater vapour movement is likely negligible. A prioritywas also to keep the simulation model simple. However,a future development of the model may include animprovement of the water vapour process.

Solute transport in soil column

The transport equation for cations is defined by:

∂ci

∂tC v0 ∂ci

∂z� 1

�

∂

∂z

(� D

∂ci

∂y

)D Si �5�

where ci is concentration of the i-ion in liquid phase(mol L�1), where i D Ca2C, Mg2C, NaC and KC. Thev0 is pore water velocity calculated as v0 D v/�, where vis the cross- sectional averaged velocity, Si is the reactionterm of the i-ion (mol L�1 s�1), and D is the dispersioncoefficient (L2 T�1). The dispersion coefficient, which isdependent on pore water velocity, is represented by:

D D ˛Ljv0j C DM �6�

where ˛L is dispersivity (L) and DM is the fluid moleculardiffusion coefficient, which include tortuousity effect(L2 T�1). The reaction term can be described as:

Si D �∂ci

∂t�7�

where ci is adsorbed concentration of the i-ion on thesolid phase (mol kg�1).

The transport equation for anions is defined by:

Rd∂ci

∂tC v0 ∂ci

∂z� 1

�

∂

∂z

(� D

∂ci

∂z

)D 0 �8�

where i D Cl� and SO42�, Rd is the retardation factor.

Equation (8) indicates instant equilibrium adsorption,which is the only difference as compared to Equation (5).In this paper, Rd is used only for SO4

2�, because Cl� isa non-adsorbed species. The reactive transport simulationfor SO4

2� (Equation 8) was solved with a retardation ofRd D 2. Finally, for simulation of Cl� (Equation 8) withretardation of Rd D 1 was solved.

Cation exchange

In our numerical model, only cation exchange andanion adsorption are included as chemical reactions,because the effect of other reactions such as complexationin the aqueous phase turned out to be negligible basedon ion speciation. The cation exchange reactions areexpressed as:

Ca2C C 2NaX D 2NaC C CaX2

Ca2C C MgX2 D Mg2C C CaX2

Ca2C C 2KX D 2KC C CaX2 �9�



where X� denotes a negatively charged cation exchangesite. The Gaines–Thomas selectivity coefficients forthese reactions are:

KCa

/Na

D ECa �NaC�2

E2Na �Ca2C�

KCa

/Mg

D ECa �Mg2C�

EMg �Ca2C�

KCa

/K

D ECa �KC�2

E2K �Ca2C�

�10�

where E is the charge fraction and () stands for theactivity of ions in the pore water. Ionic activities arecalculated as a product of the liquid-phase concentrationand activity coefficients �i that are calculated using theDavies equation:

log �i D �Az2i

( pI

1 Cp

I� 0Ð3I

)�11�

where A is a temperature-dependent parameter (here weuse 0Ð5116 for 25 °C) and zi is the valence of the i-ionand I is the ionic strength defined as:

I D 1

2

N∑iD1

ciz2i �12�

where N is the number of ionic species including bothcations and anions. The charge fraction has a relationwith adsorbed concentration expressed as:

Ei D zi�

Q �bci �13�

where �b is bulk density, Q is CEC (cmolc kg�1), and zi

is the charge of i-ion. In addition, the charge fraction ofthe exchangeable cations should satisfy:

ECa C EMg C ENa C EK D 1 �14�

0 0.1 0.2 0.3 0.4 0.5100

101

102

Volumetric water content

Suc

tion

/ cm

observedmodel

Figure 3. Soil water characteristics curve

Table I. Parameters used in the numerical simulation

Parameter Units Value

Dispersivity ˛L cm 0Ð074Saturated water

content�s — 0Ð48

Residual watercontent

�r — 0Ð102

Bulk density �b g cm�3 1Ð296

˛ cm�1 0Ð047VG

modelparametersm — 0Ð566

n — 2Ð304

Saturated hydraulicconductivity

ks cm s�1 9Ð63 ð 10�4

Retardation factor Rd — 2

KCa/Mg — 1Ð215Selectivity

coefficientsKCa/Na mol L�1 0Ð1504exp(34Ð3XNa)

KCa/K mol L�1 0Ð0112

Cation exchangecapacity

cmolc kg�1 7Ð1

Reactive transport modelling

To solve Equation (3) for soil water transport, animplicit finite difference method was applied. Thelower boundary condition was set to the groundwa-ter table by h D 0. Evaporation intensities given byEquations (1) and (2) were used as the upper boundarycondition.

When applying the numerical model to the evaporationcolumn experiments, the concentrations of ten chemicalspecies, Ca2C, Mg2C, NaC, KC, Cl� and SO4

2� inthe liquid phase and Ca2C, Mg2C, NaC and KC inthe solid phase must be evaluated so as to satisfyEquations (5), (8), (10) and (14). When all solutionconcentrations in the liquid phase are specified, thechemical reaction processes described by Equations (10)and (14) can be solved numerically or algebraically (e.g.Schulz and Reardon, 1983; Kinzelbach et al., 1991).Accurate estimation of the reaction term in Equation (5)will lead to concentrations of cations in the liquidphase simultaneously satisfying physical and chemicalprocesses such as convection, dispersion and reactions. Inthis study, the following procedure proposed by Momiiet al. (1997) was employed.

By applying MOC, the convective–dispersiveequations (Equation. 5) with unknown reaction termsSi, which are given as a constant value assumed inadvance, are numerically solved. These unknown butassumed terms Si are used as temporary values. Thisgives cation concentrations in the liquid phase. Theanion concentration in the liquid phase can be deducedfrom Equation (8), by MOC. Cation concentrations in thesolid phase are calculated by substituting temporary reac-tion terms Si into Equation (7). Equation (7) is solvedby the finite difference method. The charge fraction Ei

can be calculated from this cation concentrations in thesolid phase by Equaiton (13). The calculated cations



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epth

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observedcalculated

(a) (b)

(c) (d)

Figure 4. Comparison between measured and calculated water content profiles (a) 3 days, (b) 10 days, (c) 28 days and (d) 251 days after the startof the experiment

concentrations in the solid phase and charge fractionsneed to satisfy the selectivity coefficients (Equation 10).Equation (14) does also need to be satisfied and besides,satisfaction of electrical neutrality [see the last equationof Equation (15)] is desirable. To obtain a suitable reac-tion term Si, the following non-dimensional residual func-tions were introduced:

f1 D 1 � KŁCa

/Na

/K

Ca/

Na

f2 D 1 � KŁCa

/Mg

/K

Ca/

Mg

f3 D 1 � KŁCa

/K

/K

Ca/

K

f4 D 1 �4∑

iD1

Ei

f5 D 1 �4∑

iD1

jzijci

/ 4∑iD1

jzijci �15�

where KŁCa

/Na

, KŁCa

/Mg

and KŁCa

/K

are the tentative selec-

tivity coefficients, which are calculated by substitutingthe estimated cation concentrations in the liquid phaseand charge fractions in Equation (10). The first threeresidual functions are derived from Equation (10) and thefourth one from Equation (14). The last equation is for



-3 -2 -1 0 1

x 10-5

0

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Velocity Vector / cm s-1

Dep

th /

cm

Capillary rise stage

1day3day5day7day

8day10day12day14day

-1.4 -1.2 -1 -0.8 -0.6

x 10-6

0

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25

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40

45

50

Velocity Vector / cm s-1D

epth

/ cm

Evaporation stage

(b)(a)

Figure 5. Vertical distribution of velocity vector (a) capillary rise experiment and (b) evaporation experiment

the satisfaction of electrical neutrality, which is intro-duced to obtain better estimate for the reaction term.The denominator is for four cations (Ca2C, Mg2C, NaCand KC) and the numerator is for two anions (Cl�and SO4

2�). A nonlinear least-square estimate using theLevenberg–Marquardt method was adopted for obtainingsuitable values of the reaction terms to minimize the sumof squared error for residual functions f1 to f5.

In this study, numerical domains for calculation ofconcentrations were limited up to a height where watercontent was greater than twice the residual water contentduring the capillary rise. These positions were set to havea boundary condition of zero concentration flux.

APPLICATION TO THE COLUMN EXPERIMENT

Initial and boundary conditions

The parameters used in the numerical study are listedin Table I. Saturated hydraulic conductivity was obtainedby a permeability test. The van Genuchten model (VGmodel) parameters were determined by fitting data of thesoil water characteristic curve obtained from additionalsoil column experiments with the VG model curve.Figure 3 shows the soil water characteristic curve. Thedata for the uppermost part of the column differ from theVG model curve. However, since the numerical solutionof water content in the upper part of the column mimickedthe experimental one except for the initial stage, andsince evaporation intensity was small in this experiment,the effects of the difference are negligible. Howeverfor practical applications, the low water content partshould be determined more carefully since the resultsmay be important for a high evaporation intensity. Thedispersivity was adjusted referring to the mean diameterof the re-packed soils of the columns. Retardation of

Equation (8) was obtained from the results of Cl� andSO4

2� distributions a day after the experiment started. Bycomparing the difference between these two species, theretardation was determined equal to 2Ð0 (Dfront positionof Cl�/front position of SO4

2� D 33Ð8 cm/16Ð8 cm). Theselectivity coefficients, K

Ca/

Mgand K

Ca/

Kwere set to

1Ð215 and 0Ð0112, respectively, which were obtainedfrom the experimental result. The K

Ca/

Nawas given as a

linear function of the charge fraction of sodium that wasdetermined after linear regression analysis.

Initial conditions for pressure heads were calculatedfrom the residual volumetric water contents of soils filledin the columns using the VG model (Equation 4). Initialconcentrations for dissolved species were set equal tothose in the model groundwater and initial conditionsfor adsorbed species were calculated from dissolvedspecies with CEC and selectivity coefficients. The upperboundary condition for pressure head was set to zeroflux condition for the capillary rise stage and evaporationintensity evaluated by Equations (1) and (2) for theevaporation stage. The lower boundary for pressure headwere set to zero, because of the groundwater table. Theupper boundary for dissolved species concentration wasset to zero concentration flux. The lower boundary wasset as a constant groundwater concentration.

Numerical results of solute transport in soil columns

Figure 4 shows experimental and numerical results forthe volumetric soil water content profiles. Figure 4a andb is for capillary rise stage, and Figure 4c and d is forthe evaporation stage. Numerical results show rather goodagreement with experimental data. A day after the start ofthe experiment, the seepage front had risen 15 cm abovethe groundwater table. After 7 days, the seepage front hadreached the soil surface by capillary rise. After 10 days,



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Concentration / mM

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Concentration / mM

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Concentration / mM

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th /

cm

28day

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0

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Concentration / mM

Dep

th /

cm

252day

Cl(obs.)SO4(obs.)Cl(cal.),SO4(cal.)

(d)(c)

3day 10day(b)(a)

(d)

Figure 6. Comparison between measured and calculated concentrations of anions in the liquid phase (a) 3 days, (b) 10 days, (c) 28 days and(d) 252 days after the start of the experiment

i.e. 2 days after the start of the evaporation experiment,the water content profiles were stable. This means thatthe soil water transport had reached steady state after10 days.

Figure 5 shows the vertical velocity profile. The ver-tical axis represents the distance from soil surfaceto groundwater. Negative values thus indicate upwardvelocity. After 7 days, the velocity approached zerobecause the capillary rise had halted. After the start ofthe evaporation experiment, a high velocity was recordedclose to the soil surface. The velocity component becamevery close to the evaporation intensity at soil surface

after 14 days. After this, it attained a more or less con-stant value and the water content profile did not change,indicating that a stationary steady state was reached. Dur-ing the evaporation stage, small velocity change followedthose of the evaporation intensity change.

Figure 6 shows measured and calculated concentra-tions of anions in the liquid phase. During the initial stageof the experiment, there was some deviation betweenmeasured and predicted values for Cl� and SO4

2� inthe upper layer of the column. The same discrepancy canbe seen for the results of other cations. Since actual ini-tial concentration distributions were not known, it may



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Concentration / mMD

epth

/ cm

10day

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th /

cm

28day

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th /

cm

252day

Mg(obs.)Na(obs.)Ca(obs.)K(obs.)Mg(cal.),Na(cal.)Ca(cal.)K(cal.)

(a) (b)

(c) (d)

Figure 7. Comparison between measured and calculated concentrations of cations in the liquid phase (a) 3 days, (b) 10 days, (c) 28 days and(d) 252 days after the start of the experiment

be expected that some deviation would occur. The devi-ations were noticeable only at the initial stage. As shownin Figure 5, measured transport of both anions was fasterthan calculated. In the future, it may be possible to reduceerrors by running the numerical code in advance to geta more appropriate initial concentration distribution. Themeasured and calculated concentration distributions attaina similar general shape with time. The model repro-duced the delayed upward movement of dispersion frontof SO4

2� compared with Cl�.Figures 7 and 8 show the measured and calculated con-

centrations of cations in liquid and solid phases, respec-tively. Also, here there are some deviations between thecalculated and measured concentrations in the upper part

of the column at initial stage. Under assumed initialconditions, the calculated cation concentrations for boththe liquid and solid phases are in good agreement withthe measured data. Because of the high concentrationin the groundwater, NaC exchanged with other divalentcations such as Ca2C and Mg2C on the soil surface andconsequently the dispersive front displayed retardation.The KC is more retarded than NaC, which is also due tothe exchange with other cations. Desorption of Ca2C andMg2C produces higher concentration in the liquid phasethan in the groundwater. After being released into theliquid phase, the front for these cations started to movetowards the soil surface. At the evaporation stage of theexperiment, all cations had high concentration gradients



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epth

/ cm

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Concentration / cmolc kg-1

Dep

th /c

m

28day

Mg(obs.)Na(obs.)Ca(obs.)K(obs.)CEC(obs.)Mg(cal.),Na(cal.)Ca(cal.)K(cal.)CEC(cal.)

(c)

Figure 8. Comparison between measured and calculated concentrations of cations in the solid phase (a) 3 days, (b) 10 days and (c) 28 days after thestart of the experiment

near the soil surface. Also, the sum of calculated cationsin the solid phase [Equaiton (14)] agreed well with themeasured CEC. As seen from the figures, measured CECfluctuates slightly with depth. If a slight variation in theCEC distribution (Figure 8) would have been given prob-ably more accurate calculation results would have beenobtained (e.g. Momii et al., 1997). Initial condition of soilwater distribution and initial concentration distributionsin liquid phase should also be given more accurately inorder to obtain better results. As shown in Figure 8, sinceall observed cation distributions follow the CEC distribu-tion, the numerical simulation may be able to reproducethe concentration distributions for the solid phase accu-rately. For the solid phase, KC exchanged with Ca2C and

Mg2C in the lower layers of the column, close to thegroundwater table. The concentration distributions for allcations in the solid phase seem unchanged. This dependson the values of the selectivity coefficients and the CEC.These calculated concentration distributions more or lessagreed well with measurements.

To investigate the applicability of the Davies equation,calculated vertical distribution of ionic strength wasplotted for day 441 as seen in Figure 9. The Daviesequation is usually used for a solution having an ionicstrength below 0Ð5 M. Although calculated ionic strengthexceeded this upper limit in the upper layer of thecolumn, numerical results display realistic results asshown in this paper.



10-2 10-1 100 101

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Ionic strength / M

Dep

th /

cm

Ionic StrengthI=0.5M

Figure 9. Calculated ionic strength distribution in 441 days after the startof the experiment

SUMMARY AND CONCLUSIONS

To understand characteristics of solute movement fromgroundwater to soil surface under capillary rise andevaporative processes, unsaturated column experimentsand numerical simulation were conducted. The proposednumerical model accounts for cation exchange for fourcations (Ca2C, Mg2C, NaC and KC) in both dissolvedand exchangeable forms and anion retardation for oneanion (SO4

2�). The Cl� is treated as conservative solutewithout retardation. Numerical results of distribution ofcations in both liquid and solid phases, anions in theliquid phase and volumetric water contents were ingood overall agreement with experimental results. If amore realistic variable CEC distribution would have beenapplied to our simulation model, it would probably havegiven even better results, because all observed cation dis-tributions were seen to harmonize with the distribution ofthe CEC. To improve results further more accurate, initialdistribution of soil water content and initial concentrationdistributions in liquid phase should be given.

In the numerical simulation, a simple model for evap-oration intensity was applied as shown in Equations (1)and (2). This model uses dimensionless water contentchange at soil surface. This procedure gave reasonablepredictions for both daytime and nighttime evaporation.The vertical distribution of velocity became almost iden-tical to the evaporation intensity at soil surface about14 days after the onset of experiment. After this, itattained a straight distribution, which meant that the watercontent profile did not change with time and consequentlyhad reached a steady state.

For both cation and anion initial concentration dis-tributions, deviations between calculated and measuredvalues in the upper column layer were observed. In prac-tical terms, this could have been avoided by running thenumerical code in advance to obtain more appropriate ini-tial conditions. After about 10 days, however, these initialdeviations more or less disappeared. In practical termsthis depends on the values of the selectivity coefficientsand the CEC together with unsaturated soil parameters.

The developed numerical model includes cationexchange, anion retardation and unsaturated water flow.The model has a potential to be applied to experimentaldata from sequential irrigation effects on salt accumula-tion and/or reactive transport studies under groundwaterquality change. This will be studied in the future.

ACKNOWLEDGEMENT

We thank T. Matsuo, a graduate of Kyushu SangyoUniversity for assisting with experiments and numericalsimulations.

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modelling reactive solute transport from groundwater to soil surface under evaporation

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