transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic...

Ž .Journal of Contaminant Hydrology 32 1998 313–331

Transport of reactive colloids and contaminants ingroundwater: effect of nonlinear kinetic interactions

H. van de Weerd ), A. Leijnse 1, W.H. van Riemsdijk 2

Department of EnÕironmental Sciences, Sub-department of Soil Science and Plant Nutrition, WageningenAgricultural UniÕersity, P.O. Box 8005, 6700 EC Wageningen, Netherlands

Received 1 August 1997; revised 5 December 1997; accepted 23 December 1997

Abstract

Transport of reactive colloids in groundwater may enhance the transport of contaminants ingroundwater. Often, the interpretation of results of transport experiments is not a simple task asboth reactions of colloids with the solid matrix and reactions of contaminants with the solid matrixand mobile and immobile colloids may be time dependent and nonlinear. Further colloid transportproperties may differ from solute transport properties. In this paper, a one-dimensional model for

Ž .coupled colloid and contaminant transport in a porous medium COLTRAP is presented togetherŽ .with simulation results. Calculated breakthrough curves BTC’s during contamination and

decontamination show systematically the effect of nonlinear and kinetic interactions on contami-nant transport in the presence of reactive colloids, and the effect of colloid transport properties thatdiffer from solute transport properties. It is shown that in case of linear kinetic reactions, the rateof exchange of mobile and immobile colloids have a large impact on the shape of BTC’s even ifthe solid matrix is saturated with respect to colloids. BTC’s during the contamination anddecontamination phase have identical shapes in this case. Moreover, the slow reactions ofcontaminants and colloids may lead to unretarded breakthrough of contaminants. Independent ofreaction rates, nonlinear reactions lead to BTC’s that are steeper during contamination than in thelinear case. A characteristic aspect of nonlinear sorption is that shapes of BTC’s differ during thecontamination and decontamination phase. It has been observed that shapes of some of the

) Corresponding author. Fax: q31-317-48-3766; e-mail: [email protected] Ž .National Institute of Public Health and the Environment RIVM , P.O. Box 1, 3720 BA Bilthoven, The

Netherlands. Fax: q31-30-229-2897; e-mail: [email protected] Also at: Department of Water Resources,Wageningen Agricultural University, Nieuwe Kanaal 11, 6709 PA Wageningen, The Netherlands.

2 E-mail: [email protected]

0169-7722r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0169-7722 98 00052-7

( )H. Õan de Weerd et al.rJournal of Contaminant Hydrology 32 1998 313–331314

simulated adsorption and desorption curves are similar as shapes found in experiments reported inliterature. This stresses the importance of incorporating both kinetics and nonlinearity in modelsfor coupled colloid and contaminant transport and the capability of COLTRAP to interpretexperimental results. Finally, to figure out whether nonlinear processes play a role, it is veryimportant to consider both contamination and decontamination in transport experiments. q 1998Elsevier Science B.V. All rights reserved.

Keywords: Kinetics; Nonlinear; Colloid; Contaminant; Modelling; Transport; Porous media; Groundwater;Sorption

1. Introduction

In natural groundwater, both inorganic and organic colloids are present. They differin origin and their concentration ranges from 108 to more than 1012 particlesrlŽDegueldre et al., 1989; Gschwend and Reynolds, 1987; Longworth and Ivanovich,

.1989; Short et al., 1988; Kim et al., 1987 . When these colloids are transported overlarge distances, they can act as a carrier for contaminants and enhance the transport of,

Že.g., trace metals. This has been observed in both laboratory experiments Dunnivant et. Žal., 1992a; Kim et al., 1994a,b; Saiers and Hornberger, 1996a and field situations von

.Gunten et al., 1988; Buddemeier and Hunt, 1988 .Due to their size and charge, colloids may be excluded from a part of the water-filled

void space and thus transport properties of colloids may differ from solute transportproperties. In experiments, the average velocity of inert colloids is found to be equal or

Žlarger than the average water velocity Enfield and Bengtsson, 1988; Pulse and Powell,.1992; Small, 1974 . Also, a fraction of the colloids may be immobile due to attachment

to the solid matrix. Consequently, colloids may travel faster or slower than inert solutesand multiple fronts of aqueous-phase contaminants, mobile colloids and contaminantsbound to mobile colloids may develop.

Sorption of contaminants to the solid matrix usually is described by nonlinearequilibrium isotherms, like the Freundlich and Langmuir isotherm. Sorption of contami-nants to colloids can be described by the same type of isotherms. However, oftendesorption of contaminants from colloids is found to be slow. According to BuffleŽ .1988 , dissociation of metal complexes is a slow process relative to other processes innature. Attachment of colloids to the solid matrix may be nonlinear and kinetic as well.

Ž .Saiers et al. 1994 showed that colloid interaction with the solid matrix can bedescribed well with a nonlinear kinetic model. Often colloid attachment is assumed to be

Žirreversible. However, experimental evidence shows that this is not always the case vande Weerd and Leijnse, 1997a; Dunnivant et al., 1992b; McCarthy et al., 1993; Saiers et

.al., 1994 , although detachment often is a very slow process.A model for coupled contaminant and colloid transport is based on the mass balance

equations for all colloid and contaminant species and equations for the interactionsbetween these species. In case of equilibrium between the different species, theequations can be simplified. In case of linear interactions, the introduction of retardationfactors leads to further simplification of the equations.

( )H. Õan de Weerd et al.rJournal of Contaminant Hydrology 32 1998 313–331 315

Different models describing coupled colloid and contaminant transport have beenŽreported Mills et al., 1991; Dunnivant et al., 1992b; Corapcioglu and Jiang, 1993; Jiang

.and Corapcioglu, 1993; Corapcioglu and Kim, 1995; Saiers and Hornberger, 1996b .Ž . Ž .Mills et al. 1991 and Dunnivant et al. 1992a assume colloids to be nonreactive with

the solid matrix. They assume the colloid concentration to be constant in time and spaceand take into account the effect of contaminant colloid interaction in the equation forcombined contaminant and colloid facilitated contaminant transport. Jiang and Corap-

Ž . Ž .cioglu 1993 and Corapcioglu and Jiang 1993 assume linear non-equilibrium attach-Ž .ment and Saiers and Hornberger 1996b assume nonlinear kinetic but irreversible

attachment of colloids to the solid matrix. They solve equations for both mobile andimmobile colloids.

All models for colloid facilitated transport account for interaction of contaminantsŽ .with colloids. Jiang and Corapcioglu 1993 assume linear equilibrium sorption of

contaminants to the solid matrix, and to mobile and immobile colloids. Saiers andŽ .Hornberger 1996b assume two-site kinetic sorption of contaminants to the solid matrix

and nonlinear equilibrium adsorption to mobile and immobile colloids. Corapcioglu andŽ .Jiang 1993 assume the sorption of contaminants to the solid matrix to be linear and in

equilibrium and to mobile and immobile colloids to be linear and kinetic. In their model,mass balance equations for contaminants bound to mobile colloids, contaminants bound

Ž .to immobile colloids i.e., colloids attached to the solid matrix and aqueous-phasecontaminants are solved. They assume adsorption of contaminants to colloids to be

Ž .independent of colloid concentration i.e., the mass of adsorbent , which is in contrastwith general formulations of linear adsorption reactions.

Interpretation of transport experiments in which colloid facilitated transport ofcontaminants occurs is often not a simple task. It is not always possible to determineinteraction processes of the different species independently. Further both reactions ofcolloids with the solid matrix and of contaminants with the solid matrix and mobile andimmobile colloids may be time dependent and nonlinear and transport properties ofcolloids may differ from contaminant transport properties.

The aim of this paper is to show the effect of nonlinear and kinetic interactions oncontaminant transport in the presence of reactive colloids and the effect of colloidtransport properties different from solute transport properties.

Ž .A one-dimensional model for coupled colloid and contaminant transport COLTRAPhas been developed. In this model, the attachment of colloids to the solid matrix and thesorption of contaminants to the solid matrix and to mobile and immobile colloids isdescribed by nonlinear kinetic interaction equations. Linear sorption and equilibriumsorption can be modelled by a proper choice of the interaction parameters.

The model has been used to simulate transport of contaminants and colloids withŽ . Ž .rates of interaction varying from high equilibrium to low almost inert and with

Žcontaminant concentrations ranging from low in the linear part of the interaction. Ž .equation to high in the nonlinear part of the interaction equation . Simulation results

show the effect of the various reaction rates, the degree of nonlinearity and of variousratios of colloid velocity and average water velocity and colloid and contaminantdispersion coefficients on the transport of free contaminants and contaminants bound tocolloids. Model results are qualitatively compared with experimental results from


literature. In an earlier paper, model results are quantitatively compared with data fromŽ .an experiment van de Weerd and Leijnse, 1997a .

2. Model description

Fig. 1 shows the six different species which are distinguished in the model. TheŽ .contaminant is distributed among four different species: 1 free contaminants in the

Ž . Ž . Ž . Ž .liquid phase S1 ; 2 contaminants sorbed to the solid matrix S2 ; 3 contaminantsŽ . Ž . Ž .sorbed to mobile colloids S3 ; and 4 contaminants sorbed to immobile colloids S4 .

Ž .Colloids in the porous medium are distributed among two species: 1 colloids inŽ . Ž . Ž .solution C1 ; and 2 colloids attached to the solid matrix C2 . Governing equations

are mass balance equations for mobile and immobile contaminant and colloid species,completed with constitutive equations for kinetic nonlinear interactions between colloidsand the solid matrix, colloids and contaminants and contaminants and solid matrix.

It is assumed that the properties of colloids are not affected by contaminants sorbedto them. However, the properties of colloids may change once they are attached to thesolid matrix; the interaction constants for contaminant sorption to mobile and immobilecolloids and the number of sites available for contaminant sorption on these colloidsmay differ. Furthermore, it is assumed that colloids attached to the solid matrix do notaffect the porous structure and colloid attachment does not compete with contaminantsorption to the solid matrix. Note that the term ‘immobile colloid’ is used for colloidsattached to the solid matrix, which may detach again depending on the reversibility ofthe interaction between colloids and the solid matrix.

Ž . Ž . Ž .Fig. 1. Speciation of colloids C and contaminants S ; free contaminants in the liquid phase S1 ;Ž . Ž .contaminants sorbed to the solid matrix S2 ; contaminants sorbed to mobile colloids S3 ; contaminants

Ž . Ž . Ž .sorbed to immobile colloids S4 ; colloids in the liquid phase C1 ; colloids attached to the solid matrix C2 .


In the system, mobile and immobile colloid and contaminant species are present.Describing the dispersive mass flux of all species by a Fickian type relation andassuming constant porosity, velocity and dispersion coefficient, the one-dimensionalmass balance equations for species W can be written as:

w x w x 2 w xE W E W E Wn qnÕ ynD sP 1Ž .W W W2E t E x E x

w x w x w x w y1 x w 2where t is time T , x is spatial position L , n is porosity y and Õ L T , D LW Wy1 x w y3 y1 xT and P M L T are average velocity, dispersion coefficient and productionW

term of species W, respectively. The production term P is the sum of all interactionWw xterms for species W. W indicates the concentration of species W per volume of pore

w y3 xwater M L . For the aqueous-phase contaminant, Õ and D are the averageW W

velocity of water Õ and the contaminant dispersion coefficient D, respectively. Forcontaminants sorbed to mobile colloids and for mobile colloids, Õ and D are givenW W

by the average velocity of colloids Õ and the dispersion coefficient for colloids D ,c c

respectively. For the immobile species, both Õ and D are zero. In this paper, theW W

mass balance equations are divided by the relative molecular or colloidal mass to obtainconcentrations in mole rather than in mass per volume of pore water.

Ž scm .Interaction processes considered are: contaminant sorption to mobile colloids P ,Ž sci.contaminant sorption to immobile colloids P , contaminant sorption to the solid

Ž s. Ž c .matrix P and colloid attachment to the solid matrix P . It is assumed that for allsorbing species a limited number of homogeneous binding sites exists and that variableelectrostatic potential effects and other interactions between adsorbed species can beneglected. In that case, the sorption reaction is given by an ideal Langmuir kineticreaction and can be described by the following reaction equation:

kaw x w x w xS q A ° SA 2Ž .

kd

w x w xwhere S is the activity of available binding sites for species A, A is the activity ofw xspecies A and SA is the activity of occupied binding sites. The activity equals the

concentration times an activity constant. The activity coefficient is assumed to be 1which implies that we consider low concentrations only. Note that both SA and A are

w y3 x w 3species and that their concentration is given in mole per liter pore water L . k Lay1 x w y1 xT and k T are the forward and backward reaction rate constants, respectively.d

When reaction rates are high compared to the time scale of other processes in the systemthe forward and backward reaction may be in equilibrium.

w 3 xThe equilibrium constant K L is defined as follows:

w x w xk SA SAaKs s s . 3Ž .w x w x w x w xk S A 1yu S AŽ .d t

w x w y3 x w xwhere S L is the total concentration of binding sites and u y is the fraction oftw xbinding sites which are occupied. Without competition uS s SA . A kinetic Langmuirt

Ž .interaction equation of the following form can be derived from Eq. 3 :i w x i w xE SA E A

i iw x w x w xsy sk A 1yu S yk SA . 4Ž . Ž .a t di iE t E t


the superscript i is used to indicate that the change in concentration due to interaction iis considered. The interaction equation consists of an adsorption term, representing theforward reaction rate, and a desorption term, representing the backward reaction rate. Inthe model COLTRAP, all interaction equations have the following form:

i i w x w x i w xP sn k A 1yu S yk SA . 5Ž . Ž .Ž .a t d

P is the sum of all P i that include species W. Other source or sink terms such asW

decay can also be included in P .W

Often sorption of contaminants is assumed to be linear. This is true only if thefraction of binding sites occupied, u<1. If equilibrium is assumed between sorptionsites and the aqueous solution, the forward and backward reaction are in equilibrium anda linear sorption isotherm can be defined:

w x w xSA sK A 6Ž .d

where K sk rk PS sKPS is the equilibrium distribution constant.d a d t t

The equilibrium assumption can be investigated by using the Damkohler number.This dimensionless characteristic is given by:

Li iD sk 7Ž .k d

Õ

Ž .and gives insight in the degree of non- equilibrium in a certain system during a certainŽ .dimensionless time after a change in the influent concentration. For each kinetic

Ž .reaction a Damkohler number exist. If Eq. 4 is rewritten in the following way:i w xE SA

i i i w x w x w xsk k rk A 1yu S y SA 8Ž . Ž .Ž .d a d tiE tit is evident that the rate of adsorption or desorption is determined by k i times thed

difference between what should have been adsorbed if the system was in equilibriumand what is really adsorbed. For all reactions, a range in the value of the Damkohler

Žnumber exists where the reaction changes from being insignificant lower limit of the. Ž .range to being in equilibrium upper limit of the range in the system. Above and below

this range, variations in Damkohler number will not change the effect of the reaction onthe system. Note that the degree of non-equilibrium also influences the net adsorption ordesorption rate. As the degree of non-equilibrium can change in time and place it cannot be included in the Damkohler number. Further note that the Damkohler number,like, e.g., the Peclet number is a characteristic of a certain system. Therefore, Damkohlernumbers of different experiments can not be compared without further research.

2.1. Complete set of goÕerning equations

Under the assumptions given above, the mass balance equations for mobile andimmobile colloids are given by:

E C c E C c E 2 C ccn qnÕ ynD syP 9Ž .c c 2E t E x E x

ESccn sP 10Ž .

E t


c c w y3 xwhere C and S L are the mobile and immobile colloid concentration. Theinteraction equation for colloid attachment to the solid matrix is given by:

P c sn k c C c Sc ySc yk c Sc 11Ž .Ž .Ž .a t d

c w y3 xwhere S L is the total number of sites available for colloid attachment. Note that intŽ . Ž .case of no competition Eq. 11 is equivalent to Eq. 5 . Mass balance equations for free

contaminants, and contaminants bound to the solid matrix are given by:

E C s E C s E 2 C ss scm scin qnÕ ynD syP yP yP 12Ž .2E t E x E x

ES ssn sP 13Ž .

E ts s w y3 xwhere C and S L are the contaminant concentration and the contaminant concen-

tration bound to the solid matrix. Contaminant sorption to the solid matrix is given by:s s s s s s sP sn k C S yS yk S 14Ž .Ž .a t d

s w y3 xwhere S L is the total number of sites available for contaminant sorption. The masst

balance equations for contaminants bound to mobile and immobile colloids are given by:

E C scm E C scm E 2 C scmscm scn qnÕ ynD sP yP 15Ž .c c 2E t E x E x

ES scisci scn sP qP 16Ž .

E tscm sci w y3 xwhere C and S L are the concentration of contaminants bound to mobile and

immobile colloids. C scm and S sci are products of the concentration of contaminantsadsorbed per mole of colloids and the concentration of the colloids. Note that thedispersion of contaminants bound to colloids is determined by the dispersion coefficientof the colloids. In case of constant colloid concentration in space, dispersion of colloidsis irrelevant for colloid transport. However, it is relevant for transport of contaminantsbound to colloids as concentration of contaminants bound to colloids may vary in space.

Ž . Ž .In contrast with this, Corapcioglu and Jiang 1993 , Jiang and Corapcioglu 1993 andŽ .Corapcioglu and Kim 1995 assume that the gradient of the colloid concentration is the

driving force for dispersion of contaminants bound to colloids. For constant colloidconcentration in space, they find dispersion of contaminants bound to colloids to bezero.

sc Ž . Ž .P in Eqs. 15 and 16 is a term accounting for mobilization or immobilization ofcontaminants bound to colloids due to interaction of colloids with the solid matrix. Thisinteraction term can be given by:

sc c scm c c c sciP sn k C S yS yk S 17Ž .Ž .a t d

Contaminant sorption to mobile and immobile colloids is given by:scm scm s scm c scm scm scmP sn k C C C yC yk C 18Ž .Ž .a t d

sci sci s sci c sci sci sciP sn k C S S yS yk S 19Ž .Ž .a t d


sci scm w xwhere S and C y are the total number of sites available per immobile and mobilet t

colloid, respectively. Note that the term for adsorption to mobile or immobile colloids inŽ . Ž .Eqs. 18 and 19 increases if the mobile or immobile colloid concentration increases.

Ž .In contrast, Corapcioglu and Jiang 1993 assume that sorption of contaminants tocolloids is independent of the colloid concentration.

2.2. Solution method

The governing equations together with boundary conditions for mobile species andinitial conditions for all species are solved numerically by a standard Galerkin finiteelement method where the time derivative is approximated by a backward finitedifference. Initial conditions for all species and boundary conditions for only the mobilespecies need to be defined. The resulting algebraic equations are solved simultaneously.A solution is obtained for the unknown concentrations C c, Sc, C s, S s, C scm, and S sci.Nonlinearities are solved by a Newton–Raphson iteration scheme.

In order to reduce round-off errors due to spatial discretization, an adaptive method isimplemented where the finite element grid is dynamically refined in areas with largeconcentration gradients.

The code has been verified by comparing numerical results with analytical solutionsŽ .van de Weerd and Leijnse, 1997b .

3. The simplified case of linear equilibrium sorption

In case of equilibrium between all sorption sites and the aqueous solution, linearsorption of contaminants and linear attachment of colloids to the solid matrix isdescribed by:

Sc sK c C c 20Ž .d

S s sK sC s 21Ž .d

with K c sk crk c PSc and K s sk srk s PS s. Sorption of contaminants to mobile andd a d t d a d t

immobile colloids is described by:

C scm sK scm C c C s 22Ž .d

S sci sK sciSc C s sK sciK c C c C s 23Ž .d d d

scm scm scm scm sci sci sci sci Ž . Ž .with K sk rk PC and K sk rk PS . Combining Eqs. 12 , 13 ,d a d t d a d tŽ . Ž . Ž . Ž .15 , 16 , 21 – 23 , the mass balance equation for contaminants can be written as:

E E C s E 2 C ss s scm c sci c cn C 1qK qK C qK K C synÕ qnDŽ .Ž .d d d d 2E t E x E x

24Ž .2E E

scm c s scm c synÕ K C C qnD K C CŽ . Ž .c d c d2E x E x


the terms at the left hand side reflect respectively: free contaminants, contaminantsbound to the solid matrix, contaminants sorbed to mobile colloids and contaminants

Ž . Ž . Ž .sorbed to immobile colloids. Combining Eqs. 9 , 10 and 20 , the mass balance forcolloids is given by:

E C c E C c E 2 C cc1qK n synÕ qnD 25Ž .Ž .d c c 2E t E x E x

Ž .Eq. 24 can be rewritten as:

E C s E C cs scm c sci c c scm sci c s1qK qK C qK K C n q K qK K nC sŽ . Ž .d d d d d d dE t E t

E C s E 2 C sscm c scm cy 1qÕ rÕK C nÕ q 1qD rDK C nDŽ . Ž .c d c d 2E x E x

E C c E 2 C c E C s E C cscm s scmqK C ynÕ qnD q2nD K 26Ž .d c c c d2ž /E x E x E xE x

Ž .If the colloid concentration is constant in time and space, Eq. 26 reduces to:

E C s E C s 1qD rDK scm C c E 2 C sc d

)R n synÕ q nD 27Ž .scm c 2E t E x 1qÕ rÕK C E xc d

where the retardation factor R) is given by:

1qK s q K scm qK sciK c C cŽ .d d d d)R s 28Ž .scm c1qÕ rÕK Cc d

Ž .Eq. 27 is the conventional advectionrdispersion equation with an adapted retardationfactor and dispersion term. The factor multiplying the conventional dispersion term isdue to the contribution of contaminants bound to colloids to the dispersion. Corapcioglu

Ž .and Jiang 1993 do not consider dispersion of contaminants bound to colloids in case ofconstant colloid concentration in time and space. Therefore, the dispersion term in theirequation is given by:

nD E 2 C s

29Ž .scm c 21qÕ rÕK C E xc d

with this definition, the dispersion of contaminants decreases with increasing colloidŽ .concentration. In Eq. 27 , however, dispersion of contaminants decreases or increases

depending on the ratio of D rD and Õ rÕ. If D rD)Õ rÕ the dispersion termc c c c

increases if contaminants bound to colloids are present. If D rD-Õ rÕ the dispersionc cŽ .term decreases in these circumstances. It can be shown that for Õ rÕsD rD Eq. 27c c

reduces to the conventional advectiverdispersion equation with an adapted retardationfactor.

For equal colloid and contaminant velocities the retardation factor R) reduces to:

1qK scm C c qK s qK sciK c C c K s qK sciK c C cd d d d d d d

)R s s1q 30Ž .scm c scm c1qK C 1qK Cd d


if the distribution coefficient for sorption of contaminants to immobile colloids andŽ scm sci.sorption of contaminants to mobile colloids are the same K sK and thed d

distribution coefficients for attachment of colloids to the solid matrix equals theŽ c s.coefficient for sorption of contaminants to the solid matrix K sK , the retardationd d

factor R) equals the conventional retardation factor Rs1qK s.d

4. Modelling results and discussion

COLTRAP has been used to investigate the effect of nonlinearity, reaction rates andthe effect of varying ratios of colloid and contaminant velocities and dispersion

Ž .coefficients on the breakthrough curves BTC of contaminants in a column experiment.Ž .In all simulations the following assumptions have been made. 1 We consider transport

Ž .of 10 pore volumes of contaminated water with colloids in equilibrium through a cleansoil column saturated with colloids, followed by transport of uncontaminated water with

Ž .colloids. Note that in Figs. 2–4 only a part of the breakthrough curve is shown. 2Interactions of contaminants with the solid matrix is assumed to be in equilibrium.Ž .3 The interaction constants for sorption of contaminants to mobile and immobilecolloids are assumed to be equal in all simulations.

Interaction parameters are chosen in such a way that in equilibrium and in the linearpart of the sorption isotherm the distribution of colloids among the solution and the solid

Žmatrix is in a ratio of 1:1. The distribution of contaminants among solution free.contaminants , mobile colloids, immobile colloids and the solid matrix is in the ratio

1:1:1:2. The standard choice of model parameters and initial conditions are listed inTable 1. If deviant model parameters or conditions are used this will be noted explicitly.

Fig. 2. Simulated breakthrough curves varying the Damkohler numbers for interaction between contaminantsŽ scm sci. Ž . Ž .and colloids D s D between 0.01 S0.01 and 1000 S1000 together with analytical solutions for thek k

Ž .extreme cases: equilibrium interaction between contaminants and colloids A1 , no interaction betweenŽ .contaminants and colloids A2 .


Fig. 3. Simulated breakthrough curves varying simultaneously the ratio of colloid and contaminant velocityŽ . Ž . Ž .and dispersion coefficient. Õ r Õs D rDs1 , 1.2 - - - , 1.4 P P P .c c

4.1. Linear sorption

First we will focus on the equilibrium situation. As was previously derived, in case ofequilibrium, a BTC calculated with COLTRAP should be identical to a BTC calculatedwith the conventional advection dispersion equation using parameters from Table 1 and

Ž . ŽEq. 28 for the retardation factor analytical solution A1 in Fig. 2; Parker and van.Genuchten, 1984 . From Fig. 2, it is obvious that equilibrium exists if the Damkohler

Ž scm sci.numbers for contaminant colloid interaction D sD G1000. Note that the ex-k k

change rate between mobile and immobile colloids does not affect simulation results ifequilibrium exists between contaminants and colloids. Fig. 3 shows the effect of varyingratios of colloid and contaminant velocities and dispersion coefficients. According to

Ž . Ž . Ž .Eqs. 27 and 28 , the retardation factor changes from 2.5 Õ rÕsD rDs1 to 2.08c cŽ .Õ rÕsD rDs1.4 but the shape of the curves remains identical. Fig. 4 shows thec c

effect of varying the ratio of the colloid and contaminant dispersion coefficient with a

Ž .Fig. 4. Simulated breakthrough curves with a constant ratio of colloid and contaminant velocity Õ r Õ of 1.2,cŽ .varying the ratio of colloid and contaminant dispersion coefficient D rD from 0.24 to 6.c

()

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Table 1Non-zero boundary and initial conditions and default parameters used for model simulations

s s y6 s y3wŽ . Ž .xwŽ . Ž .x Ž .C y D r nÕ EC r Ex xs0,t 0F tF t 1.0=10 M S 2.0=10 molrlpuls t

scm scm y6 s s q3wŽ . Ž .xwŽ . Ž .x Ž .C y D r nÕ EC r Ex xs0,t 0F tF t 1.0=10 M k rk 1.0=10 lrmolc c puls a d

c c y10 s q3wŽ . Ž .xwŽ . Ž .x Ž .C y D r nÕ EC r Ex xs0,t tG0 1.0=10 M D 1.0=10 yc c k

c y10 c y7Ž .C x,ts0 0F xF L 1.0=10 M S 1.0=10 molrlt

c y10 c c q7Ž .S x,ts0 0F xF L 1.0=10 M k rk 1.0=10 lrmola d

c y3L 25 cm D 1.0=10 yk

scm sci q7n 0.33 y C sS 1.0=10 molrmolt t

scm scm q3Õs Õ 2.62 cmrh k rk 1.0=10 lrmolc a d

2 sci sci q3Ds D 0.22 cm rh k rk 1.0=10 lrmolc a d

scm sci q3t 95.4 h D s D 1.0=10 ypulse k k


constant ratio of the colloid and contaminant velocity. As can be expected from Eqs.Ž . Ž .27 and 28 , the retardation factor remains the same but the overall dispersion

Ž . Žcoefficient increases from 0.56 D rDs0.24, Õ rÕs1.2 to 3.18 D rDs6, Õ rÕsc c c c.1.2 times the contaminant dispersion coefficient. Hence, for colloid facilitated transport,

the colloid dispersion coefficient affects contaminant transport even if colloid concentra-tions are constant in time and place.

The opposite of equilibrium between contaminants and colloids is that contaminantsdoes not adsorb to or desorb from colloids which leads to uncoupled transport ofcontaminants and colloids. For uncoupled transport in the assumed model system, ananalytical solution can be constructed by adding the analytical solution for inert

Ž .transport of colloids Rs1 and the transport of contaminants with the conventionalŽ . Ž .retardation factor Rs3 analytical solution A2 in Fig. 2 . From Fig. 2, it is obvious

that transport of colloids and contaminants is uncoupled with Damkohler numbers forŽ scm sci.contaminant colloid interaction D sD F0.01. If the interaction rate and thus thek k

Damkohler number increase, transport becomes more and more coupled, the BTCŽ .becomes more symmetrical around the center of mass CrCos0.5 and in the

neighborhood of equilibrium slower reaction rates have the same effect as diffusionrdis-persion. The intermediate BTC has a larger tail than the extreme BTC’s. This is due to

Ž .contaminant adsorption on immobile colloids. In case this is negligible i.e., very slowthe breakthrough of contaminants is dominated by the equilibrium sorption of contami-nants to the solid matrix. Increasing rates of contaminant sorption to immobile colloidsresults in an increasing effect of immobile colloids on breakthrough of contaminants. Aslong as equilibrium is not reached between immobile colloids and contaminants, theconcentration is affected and a tailing effect results. From Fig. 2, we can conclude thatvery slow desorption of contaminants from colloids, may result in inert transport ofcontaminants bound to colloids. Note that for all simulations in Fig. 2 the exchange rate

Ž c .of mobile and immobile colloids is assumed to be negligible D s0.01 . Results ofkŽ .experiments performed by Kim et al. 1994b show unretarded breakthrough of eu-

ropium, americium, neptunium and protactinium in the presence of humic colloids.Breakthrough curves of experiments with neptunium and protactinium show a plateaufollowed by breakthrough of a second front. Since in these experiment a pulse isinjected, it is not easy to interpret results. Results of experiments of Saiers and

Ž .Hornberger 1996a show unretarded breakthrough followed by a plateau and break-through of a second front of cesium in the presence of kaolinite colloids. The height ofthe plateau increases with increasing colloid concentration. This indicates that kineticinteraction of contaminants and colloids may play an important role in practice.

Fig. 5 shows the effect of various exchange rates of mobile and immobile colloids.The BTC’s show the breakthrough of contaminated water followed by the breakthroughof uncontaminated water. Note that the simulation in Fig. 5A and B with Dc s0.001 arek

the same simulations as S1 and S0.01, shown in Fig. 2, only now the breakthrough ofuncontaminated water is shown as well. From Fig. 5, we can conclude that the exchangerate between mobile and immobile colloids has a high impact on the simulation results.With increasing exchange rate, equilibrium between mobile and immobile colloids isreached faster and thus the effect of kinetics on the simulation results will be more andmore limited to non-equilibrium between colloids and contaminants. Fig. 5B with


Fig. 5. Simulated breakthrough curves during contamination and decontamination, varying the DamkohlerŽ c . Ž .number for colloid solid matrix interaction D from 0.001 to 1000, for intermediate 5A and low interactionk

Ž .rates between colloids and contaminants 5B .

Ž c .intermediate exchange D s1 shows extensive tailing both during breakthrough ofk

contaminated and uncontaminated water. This is due to the slow exchange betweenimmobile and mobile colloids. During contamination mobile colloids with contaminants

Žexchange slowly with clean immobile colloids, during decontamination breakthrough of.uncontaminated water the immobile colloids with contaminants exchange slowly with

Ž .the clean mobile colloids. van de Weerd and Leijnse 1997a showed that theseexchange processes may be responsible for the extensive tailing of low contaminantconcentrations and the incomplete recovery within the timeframe of the experiment,found in the experiment with americium and numic colloids performed by Kim et al.Ž .1994b . Extensive tailing like this is also found in an experiment performed by

Ž .Grolimund et al. 1996 . Possibly the exchange process may play a role in thisexperiment. However, since the colloid concentration in that experiment is not constant,this is not totally evident. The results of Fig. 5 show clearly that even if the solid matrixis saturated with respect to colloids, the assumption of colloids being nonreactive withthe solid matrix is only true in case of very slow exchange of mobile and immobile

Ž .colloids i.e., irreversible attachment .


Fig. 6. Simulated breakthrough curves during contamination and decontamination varying the duration of theinjected pulse. Dscm s Dsci s1.k k

Fig. 5A and B also shows that the shape of the BTC during decontamination afterŽ .reflection in the time-axis x-axis is the same as the shape of the BTC during

contamination. This is generally the case when all sorption reactions are linear and thecolumn is in equilibrium with the contaminated water before decontamination starts. Fig.6 shows that when equilibrium is not reached before decontamination starts, this is notalways the case. In Fig. 6, it is shown that the shape of the reflected BTC’s duringdecontamination does not equal the shape of the BTC during contamination if theduration of contamination pulse is decreased. However, a steep initial breakthrough ofcontaminated water will be followed by a steep initial breakthrough of uncontaminated

Ž .water in all cases. The results of Saiers and Hornberger 1996a show difference inshape between the BTC during contamination and the reflected BTC during decontami-nation. Even the initial steep breakthrough of contaminated water is not followed by asteep initial breakthrough of uncontaminated water.

4.2. Nonlinear sorption

To show the effect of nonlinearity, simulations with higher total contaminant influentconcentrations are compared with simulations with lower concentrations. Fig. 7 showsthat the ratios between the contaminant species are equal up to a total contaminantconcentrations around 2=10y5. Above this concentration, the ratios changes withincreasing concentration and we have nonlinear sorption. We define the concentration ofmaximum nonlinearity to be that concentration where the difference between thedisplacement velocity of the influent concentration and the mean front velocity ismaximal. Nonlinearity is found to be highest around a total concentration of 2=10y3.Therefore, simulations with a total contaminant influent concentration of 2=10y6 arecompared with simulations with influent concentrations of 2=10y4 and 2=10y3. Fig.

Ž .8 shows the effect of nonlinearity on the BTC’s with equilibrium 8A , almost noŽ . Ž .interaction 8C and intermediate interaction 8B between free contaminants and

contaminants bound to colloids. Fig. 8A shows that with increasing degree of nonlinear-


Fig. 7. Contaminant species concentration as a function of the total contaminant concentration; freeŽ s. Ž s. Ž scm .contaminants C , contaminants sorbed to the solid matrix S , to mobile C and immobile colloids

Ž sci.S .

ity the front is more steep during contamination. With increasing nonlinearity highŽconcentrations tend to travel faster than low concentrations but this is physically

.impossible and thus the effect of dispersion will be decreased and the front will tend tobe a block front. During decontamination high concentrations will travel faster than lowconcentrations and thus the front will be flatter with increasing nonlinearity. Further,with increasing total contaminant concentration, the mean retardation factor will de-crease.

At low reaction rates, part of the contaminants bound to colloids do not desorb in thetime frame of the experiment and nonlinearity does not affect their inert transport. InFig. 8B and C, we see a steep initial breakthrough during contamination, independent ofnonlinearity. During decontamination, part of the contaminant binding sites on colloidswill not be occupied due to slow adsorption. This results in the steep initial breakthroughof uncontaminated water, independent of nonlinearity. Due to nonlinearity, the other partof the BTC’s will be steeper in case of contamination and flatter in case of decontamina-tion and the mean retardation factor will decrease as a result of higher total contaminantconcentration. In the nonlinear non-equilibrium case the concentration plateau disap-pears during decontamination and we get a dispersed front.

In case of nonlinearity, the reflected part of the BTC during decontamination does nothave the same shape as the BTC during contamination anymore. This might be anexplanation for the differing shape of the BTC during contamination and decontamina-

Ž .tion found by Saiers and Hornberger 1996a .In this paper, nonlinear sorption is represented by a Langmuir isotherm and also

certain parameters are assumed. It is not sure that the same effect of nonlinearity will befound with different parameters, since the effect of changing parameters in nonlinearsystems is not always predictable. Often Freundlich or Langmuir–Freundlich typeisotherms are used to represent sorption in situations with sorption site heterogeneity. Itmight be interesting to study the effect of introducing these nonlinear isotherms.However, in this paper, we want to show the importance and possible effects ofnonlinearity, we do not intend to put general statements.


Fig. 8. Simulated breakthrough curves during contamination and decontamination with different total contami-y6 Ž . y4 Ž . y3 Ž .nant influent concentration 2=10 linear , 2=10 intermediate and 2=10 M nonlinear for 8A:

high, 8B: intermediate and 8C: low interaction rates between colloids and contaminants.

In this paper, we use only mass balance equations of the contaminant and colloidspecies considered. It is assumed that all other conditions will stay constant. In practice,however, e.g., the pH may change upon introduction of contaminants. Meeussen et al.


Ž .1996 stressed the importance of multi-component sorption. They showed that a pHfront may develop and lead to multiple fronts after introduction of fluoride in a soilcolumn.

5. Conclusions

Ž .A model is developed for coupled colloid and contaminant transport COLTRAP .Model simulations show the effect of variation in the ratio’s of the colloid andcontaminant velocities and dispersion coefficients. Using model simulations the effect ofkinetics and nonlinearity on the shape of breakthrough and desorption curves is studied.Model results indicate that with slow reaction kinetics, unretarded breakthrough ofcontaminants facilitated by colloids may occur. As a result of nonlinearity breakthroughcurves become more steep during contamination.

It is very important to consider both contamination and decontamination in transportexperiments as this gives insight in adsorption processes. It is shown that in case oflinear sorption the BTC’s during contamination have the same shape as the BTC’s

Ž .during decontamination reflected in the x-axis if complete breakthrough occurs.Different shapes indicate nonlinear sorption or incomplete breakthrough. It is shown thatshapes of simulated adsorption and desorption curves correspond with shapes of

Žadsorption and desorption curves found in experiments e.g., unretarded breakthrough.followed by a plateau and a new front, asymmetrical curves, large tailings . This stresses

the importance of incorporating both kinetics and nonlinearity in models for coupledcolloid and contaminant transport. Finally, it is shown that it is not correct to assumethat colloids are nonreactive only by stating that the solid matrix is saturated withrespect to colloids. Exchange between mobile and immobile colloids can have a large

Ž .impact on the shape of the BTC during contamination and decontamination.

References

Buddemeier, R.W., Hunt, J.R., 1988. Transport of colloidal contaminants in groundwater: radionuclidemigration at the Nevada test site. Appl. Geochem. 3, 535–548.

Buffle, J., 1988. Complexation reactions in aquatic systems: an analytical approach. In: Chalmers, R.A.,Ž .Masson, M.R. Eds. , Ellis Horwood Series in Analytical Chemistry, Ellis Horwood, Chichester, UK.

Corapcioglu, M.Y., Jiang, S., 1993. Colloid-facilitated groundwater contaminant transport. Water Resour. Res.Ž .29 7 , 2215–2226.

Degueldre, C.A., Baeyens, B., Goerlich, W., Riga, J., Verbist, J., Stadelmann, P., 1989. Colloids in water froma subsurface fracture in granitic rock Grimsel test site, Switzerland. Geochim. Cosmochim. Acta 53,603–610.

Dunnivant, F.M., Jardine, P.M., Taylor, D.L., McCarthy, J.F., 1992a. Cotransport of cadmium and hexachloro-biphenyl by dissolved organic carbon through columns containing aquifer material. Environ. Sci. Technol.

Ž .26 2 , 360–368.Dunnivant, F.M., Jardine, P.M., Taylor, D.L., McCarthy, J.F., 1992b. Transport of naturally occurring

Ž .dissolved organic carbon in laboratory columns containing aquifer material. Soil Sci. Soc. Am. J. 56 2 ,437–444.

Enfield, C.G., Bengtsson, G., 1988. Macromolecular transport of hydrophobic contaminants in aqueousŽ .environments. Groundwater 26 1 , 64–70.


Grolimund, D., Borkovec, M., Barmettler, K., Sticher, H., 1996. Colloid-facilitated transport of stronglyŽ .sorbing contaminants in natural porous media: a laboratory column study. Environ. Sci. Technol. 30 10 ,

3118–3123.Gschwend, P.M., Reynolds, M.D., 1987. Monodisperse ferrous phosphate colloids in an anoxic groundwater

plume. J. Contam. Hydrol. 1, 309–327.Jiang, S., Corapcioglu, M.Y., 1993. A hybrid equilibrium model of solute transport in porous media in the

presence of colloids. Colloids Surf. A Physicochem. Eng. Aspects 73, 275–286.Kim, J.I., Buckau, G., Klenze, R., 1987. Natural colloids and generation of actinide pseudocolloids in

Ž .groundwater. In: Come, B., Chapman, N.A. Eds. , Natural Analogues in Radioactive Waste Disposal.Graham and Trotman, London, pp. 289–299.

Kim, J.I., Delakowitz, B., Zeh, P., Probst, T., Lin, X., Ehrlicher, U., Schauer, C., 1994a. Appendix I. In:Colloid Migration in Groundwaters: Geochemical Interactions of Radionuclides with Natural Colloids,RCM 00394, Institut fur Radiochemie, Technische Universitat Munchen, pp. 16–61.

Kim, J.I., Delakowitz, B., Zeh, P., Klotz, D., Lazik, D., 1994b. A column experiment for the study of colloidalradionuclide migration in Gorleben aquifer systems. Radiochim. Acta 66–67, 165–171.

Longworth, G., Ivanovich, M., 1989. The Sampling and Characterization of Natural Groundwater Colloids:Studies in Aquifers in Slate, Granite and Glacial Sand, NSSrR165, Harwell Laboratory, Harwell, UK.

McCarthy, J.F., Williams, T.M., Liang, L., Jardine, P.M., Jolley, L.W., Taylor, D.L., Palumbo, A.V., Cooper,Ž .L.W., 1993. Mobility of natural organic matter in a sandy aquifer. Environ. Sci. Technol. 27 4 .

Meeussen, J.C.L., Scheidegger, A., Hiemstra, T., van Riemsdijk, W.H., Borkovec, M., 1996. Predictingmulti-component adsorption and transport of fluoride at variable pH in a Goethite–Silica sand system.

Ž .Environ. Sci. Technol. 30 2 .Ž .Mills, W.M., Liu, S., Fong, F.K., 1991. Literature review and model COMET for colloidrmetals transport in

porous media. Groundwater 29, 199–208.Parker, J.C., van Genuchten, M.T., 1984. Determining transport parameters from laboratory and field tracer

experiments, Bulletin 84-3, Virginia Agricultural Experiment Station.Pulse, R.W., Powell, R.M., 1992. Transport of inorganic colloids through natural aquifer material: implications

Ž .for contaminant transport. Environ. Sci. Technol. 26 3 , 614–621.Saiers, J.E., Hornberger, G.M., 1996a. The role of colloidal kaolinite in the transport of cesium through

Ž .laboratory sand columns. Water Resour. Res. 32 1 , 33–41.Saiers, J.E., Hornberger, G.M., 1996b. Modelling bacteria-facilitated transport of DDT. Water Resour. Res. 32

Ž .5 , 1455–1459.Saiers, J.E., Hornberger, G.M., Liang, L., 1994. First- and second-order kinetics approaches for modeling the

Ž .transport of colloidal particles in porous media. Water Resour. Res. 30 9 , 2499–2506.Short, S.A., Lowson, R.T., Ellis, J., 1988. Uranium-234rUranium-238, and Thorium-230rUranium-234

activity ratios in the colloidal phases of aquifers in lateritic weathered zones. Geochim. Cosmochim. Acta52, 2555–2563.

Small, H., 1974. Hydrodynamic chromatography, a technique for size analysis of colloidal particles. J. ColloidŽ .Interf. Sci. 48 1 , 147–161.

van de Weerd, H., Leijnse, A., 1997a. Assessment of the effect of kinetics on colloid facilitated radionuclidetransport in porous media. J. Contam. Hydrol. 26, 245–256.

van de Weerd, H., Leijnse, A., 1997b. Development of a model for coupled colloid and contaminant transportŽ .COLTRAP . In: Development of a model for radionuclide transport by colloids in the geosphere. Nuclear

Ž .Science and Technology EUR 17480 EN, Commission of the European Communities CEC , pp. 123–180.von Gunten, H.R., Waber, U.E., Krahenbuhl, U., 1988. The reactor accident at Chernobyl: a possibility to test

colloid-controlled transport of radionuclide in a shallow aquifer. J. Contam. Hydrol. 2, 237–247.

transport of reactive colloids and contaminants in groundwater: effect of nonlinear kinetic...

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