colloid-facilitated transport of radionuclides through fractured media

$: Colloid-facilitated transport of radionuclides through fractured media$
Journal of Contaminant Hydrology, 13 (1993) 143-166 Elsevier Science Publishers B.V., Amsterdam

143

Colloid-facilitated transport of radionuclides through fractured media

P.A. Smith and C. Degueldre Paul Scherrer Institute, Wiirenlingen and Villigen, Switzerland

(Accepted for publication January 8, 1993)

ABSTRACT

Smith, P.A. and Degueldre, C., 1993. Colloid-facilitated transport of radionuclides through fractured media. In: J.I. Kim and G. de Marsily (Editors), Chemistry and Migration of Actinides and Fission Products. J. Contam. Hydrol., 13: 143-166.

The sorption of radionuclides on natural colloids may significantly modify their transport behaviour through fractured media, since radionuclides bound to colloids may not be subject to the important retardation mechanisms of matrix diffusion and sorption onto pore surfaces. This paper reports on theoretical and experimental work aimed at assessing the relevance of colloid-facilitated transport to repository safety analyses, with specific reference to the Swiss case. Transport models are presented, developed in conjunction with field- and laboratory- based studies of deep groundwater in the crystalline basement of northern Switzerland, in which colloid size distributions, composition and sorption properties have been measured. Various potential mechanisms giving rise to both reversible and irreversible sorption are discussed. In the first case, a simple approach is examined which is based on previously reported models of colloid transport and assumes reversible, linear sorption on colloids, for which experimental data have been obtained. It is shown that transport of radionuclides would not, in general, be significantly enhanced because of this process. A more recently developed and more complex model is then described incorporating irreversible sorption, in which case the transport of radionuclides tends to be strongly dependent on the extent of colloid-fracture wall interaction.

1. INTRODUCTION

In Project "Gew/ihr 1985", which aimed to demonstrate the feasibility of deep disposal of radioactive waste in Switzerland, the potential rrle of colloids in enhancing or diminishing transport through the geosphere of radionuclides released from a waste repository was not assessed (NAGRA, 1985):

"the effect of colloids on nuclide transport in the far-field .. . is not modelled .. . as no data are available for calculations".

Since then, considerable effort has been expended in the Swiss programme

0169-7722/93/$06.00 O 1993 Elsevier Science Publishers B.V. All rights reserved.

] 4 4 P \ ",MIIH \~ , l~ i q~,! i i l ~ k J

and this paper reports the results of a collaborative programme of experimen.- tal and modelling work aimed at clarifying how the presence of colloids may influence the effectiveness of the geosphere as a migration barrier, with reference to the disposal of high-level radioactive waste in Switzerland.

Several potential sources of contaminated colloids (associated colloids or radiocolloids) have been identified (Avogadro and de Marsily, 1983). Colloids may be broadly divided into two classes: those formed in the near-field, for example during the leaching of radionuclides from the glass matrix or from the corrosion of canister material, and those formed in the far-field by the sorption of dissolved radionuclides on naturally occurring colloids in groundwater. Transport models have been proposed for both classes of colloids through porous (B.J. Travis and Nuttall, 1985: Mills et al., 1989; Light et al., 1990) and fractured (Hwang et al., 1989: Grindrod, 1990: Castaing, 1991) media. The present work is concerned with the transport of contaminated natural colloids through a fractured medium, specifically the crystalline basement of northern Switzerland. Natural colloids are present in all groundwater and an extensive characterisation programme has been carried out in order to determine the concentration, size distribution and speciation of colloids in groundwater from relevant systems.

In the transport of solutes through fractured rock, important retardation mechanisms are diffusion into regions of connected porosity adjacent to the fractures and sorption on pore surfaces (Hadermann and R6sel, 1985). In modelling transport, it is generally sufficient to consider only reversible, linear sorption. Neglection of irreversible sorption gives model predictions erring on the side of conservatism and nonlinearity can be accounted for conservatively using a retention factor corresponding to the highest concentrations encoun- tered along the flow path. Reversible, linear sorption is also assumed for the solute-colloid interaction in previously reported colloid transport models (Hwang et al., 1989; Grindrod, 1990). However, if colloids migrate over long distances and are excluded from wall-rock pores due to their size, irreversible sorption would increase the rate of transport through the geosphere and furthermore a sorption constant calculated from a nonlinear isotherm at high solute concentrations would, in general, be non-conservative. The incorpora- tion of more complete models of solute-colloid interaction, supported by parallel experimental studies, is therefore an important aspect of the present work.

Firstly, the physical and chemical processes to be modelled are discussed. The mathematical formulation of a general model is then given, with particular emphasis on radionuclide sorption on colloids. Following this, the determination of parameters characterising the processes within the model is discussed. The perturbations produced by colloids on the Project "Gewfihr" base case are then examined. Where possible, experimental values for the

COLLOID-FACILITATED TRANSPORT OF RADIONUCLIDES THROUGH FRACTURED MEDIA 145

parameters describing the effects of colloids are used. Otherwise, parameter variations are made over a broad range. Results are presented using a succession of models of increasing complexity for solute-colloid interaction, showing how experimental work feeds into the modelling work at each stage.

2. TRANSPORT PROCESSES

The modelling work presented in this paper for colloid-facilitated transport generalises the dual-porosity model for solute transport through fractured rock, the assumptions and approximations of which are discussed in detail in Hadermann and R6sel (1985). This model was taken as a starting point for reasons of compatibility with previous Swiss safety assessments (NAGRA, 1985) and because it has been successfully applied to a number of test cases at both laboratory (SKI, 1987; Jakob and Hadermann, 1990; Smith et al., 1990) and field scale (Herzog, 1991).

Following the model for solute transport, different zones within the rock are distinguished:

(1) A water-conducting zone of length, X (m), in which transport of radionuclides, both dissolved and sorbed on colloids, is governed by advection and dispersion. The zone is a parallel-walled fracture of half-width, b (m), which is equal to the ratio of the volume of water-conducting fractures within the rock to their surface area. Radionuclides may sorb onto the walls of the fracture. Colloids may become incorporated into fracture coating material through filtration or are generated through scouring.

(2) A porous matrix surrounding the water-conducting zone. Radionu- clides in solution are transported through the pores by diffusion and may sorb onto their surfaces. Colloids are assumed to be excluded from the matrix pores due to their size. Since matrix diffusion is a mechanism for retardation, this is a conservative assumption.

(3) Rock adjacent to the porous matrix lacking interconnected porosity, within which radionuclide transport is neglected.

The physical and chemical processes relevant to colloid-facilitated transport of radionuclides, in addition to radioactive decay, are illustrated in Fig. 1 and listed below:

(1) Advection of radionuclides, dissolved and sorbed on colloids. (2) Dispersion of radionuclides, dissolved and sorbed on colloids. (3) Colloid-wall interaction: colloid generation and filtration (or sorption). (4) Solute-rock interaction: diffusion into and sorption onto the porous

matrix and sorption on fracture walls by dissolved radionuclides. (5) Solute-colloid interaction: sorption of dissolved radionuclides on

colloids. Each of these processes is discussed separately below.

146 I~A SMI|H A N I ) ~ IIi:(H [li)I~.i

~ radionucl ide ~ in solution i

ii ItlItIlI'i. [ o II'I'llllIIIll " : "

7__0 o , . . .o 1 1 1 l l W / 1 t ~ _ ."

)/ o

o o

o o

o o o

o

o o

-" ] - -

1

Fig. 1. Colloid transport processes in fractured media. Uncontaminated natural colloids, indicated by open circles, are shown passing through a migrating pulse of dissolved radionuclides, the concentration of which is illustrated qualitatively by shading, and forming radiocolloids indicated by solid circles~ Radionuclide concentration profiles along the fracture length, dissolved and sorbed on colloids, are also illustrated. Profiles resulting from irreversible sorption on colloids are characterised by a sharp "trailing-edge" (Section 5.4).

2.1. Advection

Advection of dissolved radionuclides takes place with a mean water velocity v (m s I ). Radionuclides sorbed on colloids are advected with a mean velocity v c (m s-~), which may be greater than the mean velocity of the water in which the particles are suspended. This phenomenon is more pronounced for large particles and is employed in hydrodynamic chromatography (Dodds, 1982). Qualitatively, small particles moving along the fracture and subject to Brownian diffusion sample more of the parabolic velocity profile than large particles, which are excluded from the slowest parts of the profile near the walls due to their size. This effect cannot exceed Vc/v = 1.5. since the particles cannot travel faster than the maximum water velocity, no matter how they are distributed across the fracture, and has been calculated to be around Vc/V = 1.3 for a wide range of situations Vc/V, although the precise value may be colloid-size dependent (Grindrod. 1990). In the present work. vc/v = 1.5 is taken as a conservative value.


2.2. Dispersion

Dispersion of migrating radionuclides is described by a P6clet number Pe [-] = X/aL, where aL (m) is the longitudinal dispersion length. In the calculations of radionuclide transport through the geosphere carried out for Project "Gew/ihr" (NAGRA, 1985), the transport model for a single fracture is generalised to fracture networks through an appropriate choice of longitudinal dispersion length aL. Dispersion is believed to be dominated by the differing transit times through the fracture network and aL is thus a function of the fracture network geometry only, and does not depend on the smaller- scale mechanisms determining dispersion in single fractures. Therefore, aL is assumed to be colloid-size independent and is assigned the same value for solutes and colloids.

Although this assumption may be justified for a network of fractures, as in the extensively fractured rock mass considered in NAGRA (1985), it would not be applicable to migration along single fractures. Dispersion of transported solute in a single, uniform, parallel-walled fracture is described by Taylor's (1953) dispersion theory, which, in a generalised form, has recently been applied to the dispersion of radionuclides sorbed on colloids (Grindrod, 1990). In this case, dispersion results from diffusion across the velocity profile within the fracture. The diffusivity of colloids is different to that of truely dissolved species, which gives rise to different dispersivities. In the case of a single, natural fracture, the dominant mechanism for dispersion is the differing solute or colloid transit times along various flow paths, arising from heteroge- neities in the properties of the fracture, such as aperture width and sorption (Gelhar, 1987). The latter would again result in dispersivities which are different for solutes and colloids (and also different for sorbing and non- sorbing solutes).

2.3. Colloid-wall interaction

An equilibrium is considered to exist between colloids and material comprising the fracture walls, giving a colloid concentration which is constant in space and time. Colloids are mobilised continuously by scouring of the wall material at a rate which is assumed equal to that of filtration. A retention factor Rc [-] is defined as the fractional time during which a particle is mobile. Theoretical work has been carried out by several authors on the filtration of particles in laminar flow through parallel-walled channels (Bowen and Epstein, 1979; Adamczyk and van der Ven, 1981, 1984; Grindrod, 1990). Without an accompanying scouring model, however, these cannot be used to obtain R c . Furthermore, use is made of DLVO (Derjaguin-Landau-Verwey- Oberbeek) theory in the filtration models. In this theory, the motion of a

1 4 ~ ] ) ' k < . M I l I t ~\NI'* ( i i t ( ; I l : l . l ' qe t

particle as it approaches a fixed surface is dominated by the force generated by the interface, consisting mainly of the London-Van der Waals force and the electric double layer. On comparison with experimental data, tor negative particles and negative fracture walls, the measured deposition rates are always much greater than those predicted theoretically on the basis of DLVO theory (Bowen and Epstein, 1979). The shortcomings of DLVO theory have been reviewed by Grauer (1990), quoting Christiansen (1988):

"'... DLVO-theory is completely inadequate (to put it gently) in almost every system so far investigated".

A series of experiments have therefore been carried out to obtain experimental values of R c (see Sections 4 and 5).

2.4. Solute-rock interaction

Sorption on the surfaces of the water-conducting zone and the matrix pores is assumed to be rapid, reversible and linear: The former gives rise to a retardation, described by a retention factor Rr [-]. In the present work, for simplicity, it is assumed that solute concentration in the matrix pore water adjusts rapidly to that in the fractures (with respect to the time-scale of migration). The processes of diffusion and sorption in the porous matrix and sorption on the surfaces of the water-conducting zone are then described by a modified retention factor R [-] (Jakob et al., 1989). This reduces the problem to one dimension in space. For a porous matrix with porosity e,~ [-], density p (kg m-3) , volume-based sorption constant Kd (m 3 kg -~) and thickness y~ (m):

R = Rr+[~ +PKd(l --E~)](y~/b) (1)

2.5. Solute-colloid interaction

In a general modelling approach to solute-colloid interaction. L types of sorption sites are considered on colloids, each having different sorption characteristics. The following definitions are made:

C: concentration of dissolved radionuclides in fracture water (mol m -3 ): Si: concentration of radionuclides sorbed on colloids occupying sites of

type i (i = 1 . . . . . L) (mol m -3); SMi: concentration of sites of type/carr ied by colloids (Si <~ SM~) (mol m - 3 );

c S = Y' Si: total concentration of radionuclides sorbed on colloids (mol

I - - I

m-3);

aAi: rate of sorption from solution onto sites of type i (mol m --~ s-I);


- - aoi: rate of desorption from sites of type i into solution (mol m -3 s -I ); L

- - aA = ~ aA~: total rate of sorption from solution onto colloids (mol m -3 i = 1

s - I ) ;

- - O " D

L

~_, ao~: total rate ofdesorption from colloids into solution (molm -3 I = 1

s-l);

- - ki: kinetic constant for desorption onto sites of type i (s). Various mechanisms have been identified giving rise to both reversible and

irreversible sorption on colloids. Reversible sorption may take place by cation exchange or surface complexation and irreversible sorption by dehydration, a colloid "reorganisation" reaction, or sorption together with a masking reaction (Hamilton, 1986).

Calculations have been made using an sorption model in which each particle possesses two types of sorption sites (L = 2). This is applicable, for example, for cations where the sorption mechanism is one of surface complexation. In the two-layer, surface complexation model of Dzombak and Morel (1990), which has been applied extensively to hydrous ferric oxide systems, sorption can occur on two types of surface sites, "strong sites" and "weak sites". The sorption sites considered here are: - - type 1, at which sorption is irreversible; - - type 2, at which sorption is rapid and reversible.

It has been suggested that these may be regarded as internal sites and surface sites (Hamilton, 1986; Degueldre et al., 1989). A modified bilinear sorption model (with the term accounting for desorption set to zero; C.C. Travis and Etnier, 1981) and a first-order linear sorption model with a maximum capacity (Bear, 1979; C.C. Travis and Etnier, 1981) are used to describe sorption at type- /and -2 sites, respectively. Both models take into account the finite number of sites of each type available.

kl C, C < SMI - - S 1

aA~ = kI(SM~-S~), C>~SM~--SI (2)

o'D1 = 0 (3)

k C, C< SMz/Kc

0"/12 = 0 , C>/SM2/Kc (4)

I k2S2/K c, C< SM2/Kc (5)

am = ( 0, C >~ SM2/Kc

K c [-] is an sorption constant for type-2 sites on colloids. Since sorption on

1 5 0 I ' A S b l l I H , \ N I ) ( i )] ( ,~ ~ I l ) t ' , i

type-2 sites is considered rapid (with respect to the time-scales for advection - dispersion processes within the geosphere), the sorption and desorpt ion rates may be equated, giving:

I Kc (', (" < ,S'M2/K(. S, = ~6)

(SM2, C>/SM2/Kc In eqs. 2 and 4, the sorpt ion models for type-1 and -2 sites, no sorption can

take place when C = 0 (no source of radionuclides) or when S, = SM,, i = 1, 2 (all sites occupied). No desorpt ion takes place from type-/ sites (irreversible sorpt ion or very slow desorpt ion kinetics) and desorpt ion takes place f rom type-2 sites only when C < SM2/Kc.

3. MATHEMATICAL FORMULATION

3.1. Transport equations

To derive t ransport equat ions for a single radionuclide, the mass balance in a representative elementary section of the fracture, taking into account each of the processes listed above, is considered. The time derivatives of radionuclide concentrat ions, dissolved and on sorption sites on colloids, are given in the following expressions:

R SC 8C 8 2 C = - - v - - - - +crD- -~A- -2RC (7) 8t ~X +aL V sx2

8& 8Sg 8 2 & Rc 8t - Vc--ff-f + a e v c 8x-------~ --Rc(aDi --~Ai +2S~), i = 1 . . . . . L (8)

These are advect ion-dispersion equations with addit ional terms for radioactive decay and exchange of nuclides between solution and the L types of sorpt ion sites, x (m) is distance, in the direction of water flow, from the upstream end of the conduct ing zone and 2 (s ') is the radioactive decay constant. In-growth from a parent radionuclide is not considered in the present model. It is assumed that radionuclide concentrat ions are initially negligible, so that:

C = 0: Vx, t <~0 (9)

Si = O, i = 1 . . . . ,L; Vx,t<~O (10)

At the downst ream end of the conduct ing zone, a zero-concentration gradient boundary condit ion is assumed:

t,~C ~ x ( X , t ) = 0; Vt (11)

COLLOID-FACILITATED TRANSPORT OF RADIONUCLIDES THROUGH FRACTURED MEDIA 15 |

OSi (X, t ) : O, i = 1 , . . ,L ; Vt (12) ~3x

F(t) (mol s-~), the radionuclide flux leaving the system, is then given by:

F(t) _ C(X,t)+Vc ~ S;(X,t) (13) Q 'V i = l

where Q (m 3 s -~) is the water flux through the system. The general model for sorption of radionuclides onto colloids given by eqs.

2, 3 and 6 completes the specification of transport equations (7) and (8). Eliminating aA2 and %2 from eqs. 7 and 8 and using eqs. 3 and 6:

/~ ~ C ~ 0 C ~ 0 2 C Ot - v ~ +aLV~x 2 -a~ I -R2C-A (14)

Rc(~SI OSI ~ 2 S 1 Ot - Vc--~x +aLVC-~x 2 +Rc(trAl -2S1) (15)

In eqs. 14 and 15, aA; is given by eq. 2 and the following definitions have been used:

t v[l +(vc/v)(Kc/Rc)], C <SM2/Kc = (16)

l v, C >/SM2/Kc

= l R + K c ' C<SM2/Kc (17) ( R, C >/ SM2 / K c

0, C < SM2/Kc A = (18)

2SM2 , C > a M 2 / K c

Fo(t) (mol s - t) is the radionuclide flux entering the geosphere from the near-field. If the type-/sorption sites are initially saturated [v c SM~/V < Fo(t)/ Q], the boundary conditions for eqs. 14 and 15 at the upstream end of the conducting zone are given by:

l + K c (C(O,t)--aL (0,t) = Q SM,-- ,V C<SM2/Kc (19)

OC Fo(t) s u - Vc C(O,t) -- aL-ff~x (O,t) - -~ -- SM2 ~ ,

Sl(O,t)--aL~-~(O,t) = SM1

C >~ SM2/Kc (20)

(21)

If vcSm,/v>~Fo(t)/Q, all radionuclides are carried on type-/sites, so that:

] 5 ~ I 'A ~ M I I H -'~NI), ) ! t , t t I.i)~,rl

?C C(0,t) - a~ ~ ( 0 , t ) = () (22')

v~-L(S,(O,t)-at S' (O,t)) f~' v ~ Q (23t

Finally, from eq. 13, at the downstream end of the conducting zone:

F(t) vc IC(X,t)[I + Kc(vc/v)], C < SM2/K c -~ - - S D , - - = (24)

v (C(X,t)+SM2(vc/v), C>~SM2/K,-

3.2. Numerical technique

The coupled partial differential equations (7) and (8) are solved using the computer code MOLCH. This is a subprogram in the MATH/LIBRARY of IMSL, Inc., in which a set of time-dependent, ordinary differential equations is obtained using cubic Hermite polynomials and in tegra ted by Gear's variable order predictor-corrector method. For the special case SM~ = 0, SM2 = ~ (see Section 5), the model takes the same form as that for solute transport and comparison can be made with results from the two-dimensional solute transport code RANCHMD. No difference has been found between the results from the two codes; MOLCr~ was used for the work presented in this paper.

In the case of a solubility-limited release to the geosphere from the near- field, the radionuclides are assumed to enter the geosphere as a pulse of duration At, the "leach time":

0, t < 0

Fo(t) = QC~,t, O>.t~nt (25)

O, t>At

where C~ t (tool m -3) is the solubility limit. Such a discontinuous boundary condition cannot be computed by code MOLCH. Instead, F 0 is approximated by the function:

0, t < 0

F°(t) ~- ½QC~,,[l-tanh{ko(t-At)}], t>~O (26)

The choice of k0 (s ~) must satisfy the condition koAt << 1 so that eq. 25 is well approximated.

Laboratory experiments indicate that the time-scale for sorption, k~--~, is of the order of seconds or minutes and therefore much smaller than the time-scales of the advection-dispersion processes. Very large CPU times would be required to compute a systea'n c h a r a c t e r i ~ by such greatly differing


time-scales. However, results are insensitive to the value of the time-scale for irreversible sorption as long as it is small in comparison to those of advection- dispersion and therefore, where this insensitivity can be demonstrated, a convenient value of k 1 can be chosen.

4. PHYSICAL-CHEMICAL PARAMETER DETERMINATION

Colloid concentrations and speciations have been determined in sampling and characterisation campaigns on groundwater systems relevant to the crystalline option for high-level waste disposal in Switzerland as well as other analogous systems. Sampling has been performed in such a way as to avoid artefact generation, which may arise through degassing and pH changes (Degueldre and Wernli, 1987; Degueldre et al., 1991) contamination by trace oxygen and pe changes (Degueldre et al., 1991), or by aggregation and sticking to vessel walls during off-line characterisation. Characterisation combines on-line (on site) separation (micro-/ultrafiltration) and off-line (laboratory) chemical analysis of the fluid samples or dried colloid membranes.

A typical micrograph of the colloid samples is shown in Fig. 2. Analysis of the micrographs (Quantimeter ®) yields size distributions which are translated to those of groundwater colloids. Normalised size distributions [normalised concentrations as a function of size • (m)] have been obtained and are seen to follow a Pareto law (Buffle, 1988) (Fig. 3), given by:

log (dx/d(I)) = a + b log (I) (27)

where d;~/d(I). 6~ is the number of particles in the size range q) to (~ + 6(I)) per unit volume of fluid; and the parameters a and b are dependent on colloid generation and stability in the groundwater (aggregation) (Buffle, 1988). This result has been found to apply to the total colloid population and to the elemental composition when the colloid concentration is not so small that the given element falls below the detection limit.

Since the sorption behaviour of the colloids with respect to sorbing radionuclides is fundamental to the transport model, tests have been performed to study both sorption and desorption. The tests were carried out mainly by combining on-site (where applicable) separation techniques (micro-/ultrafiltration) and analytical/radioanalytical techniques. Tables 1 and 2 give the results obtained for groundwater colloids (mix of colloidal phases) under natural conditions and pure colloidal phases, respectively (analogous).

The constant Ke (m 3 kg -I ) is obtained from the sorption tests:

l ie = (S /C) (pw[co l l ] ) - ' (28)

where [coil] [-] is the mass-based colloid concentration for the sorption test (the product of particle mass and the number of particles per unit mass of

154 1',~ SMl l i lANI )~ i ) i G [ I I I J R t

Fig. 2. Micrograph of Grimsel colloids. Conditions: volume of filtered water 35 mL, active filtration surface 1.2 cm~', pore size 3 nm. Membrane: polyacylamide. Fillration performed December 1~)86,


10 ~ --2-

~o ° --

10 7

=

, 10'

10'

1 0 4 - -

\

o MF12

o Morkhom

~e Gohy 214

A Eglisou III

3 FLG/MI

10 3 I I I I i l i l I I I 1 I I l l | I I I 1 I I l l l I

n W

0 0 0 0 -- 0 0 0

0 0 -- 0

~ / n m

Fig. 3. Normalised size distribution. Conditions: volume of filtrated water small enough to yield a membrane coverage < 0.33, pore size 3 nm, on-site filtration. Data from Miekeley et al. (1990) (Morro do Ferro, MF 12), Longworth et al. (1989) (Markham), Degueldre et aL (1988) (Gorleben, Gohy 214), Briitsch and Degueldre (1990) (Eglisau III) and Degueldre et al. (1991) (Grimsel, FLG/MI). [coll] using eq. 29 with q~m--q~M = 40-450nm: Markham, 0.5 ppb; Gorleben, 5 ppb; Grimsel, 50 ppb; Morro do Ferro 12~ 250 ppb; Eglisau, 250 ppb.

[ 50 P.A SMll H \ N I ) ( i ~[ f 1 ! DRI

"FABLE 1

Results derived from size distributions and sorpt ion tests on groundwater colloids for specilic etcments

Ion species Concentrat ion [coil] K t, K~ q),~ (ppb) ( × 10 ~) (nil kg i) [.] (nm)

Site. Grimsel, Switzerland (pH 9.6, composit ion: clay-silic):

1 I 200 100 2"10 :' 2 .10 ~' t0 Sr 2~ 150-1.500 100 6-10 i 6" I0 ~ 10 Cs 4 1-200 100 2 2- I 0 ~ I (1 Am(I l l ) 0. I 100 1(1 ~ I0 i 10 U(VI) 0.03 100 10: 10 ~ 10

Site. Morro do Ferro, Po¢os de Caldas, Brazil (pH 6.0, composition: iron hydroxide-organics)~

Th(IV) 0.03 250 10 !-104 0.25-2.5 I 0 Re(Il l) 0.1 1 250 (0.7-1.5)- 103 0.175-0.375 10 U(VI) 1.1 250 10" 2.5.10 2 10 Sr-' + 126 250 7.7 1 .9 .10 ~ 10 Cs ' 1.0 250 16 4 .10 ~ 10 Pb(lI) (1.7 250 102 2.5.10 : 10

Site: Eglbau HI, Switzerland (pH 8.0, composition: iron hydroxide-organics):

Pb(ll) 100 300 10: 3.10 " 10 Bi(Ill) 100 300 102-103 0.03-0.3 10 Po(IV) < 1 0 3 300 10:- 103 0.03 - 0.3 10

[coil] = colloid concentration; Ke = sorption constant (defined in eq. 28); K c = p,[coll]Ke; ~m -- minimum colloid size. Data from Vilks and Degueldre (1991) (Grimsel), Miekeley et al. (1990) (Morro do Ferro) and Briitsch and Degueldre (1990) (Eglisau III).

fluid); and Pw (kg m-3) is the density of the fluid. Colloid concentrations are determined by integrating the normalised size distributions (Flg. 3) from a minimum size Om (m) (Table 11 to a maximum size ~M (m) (i.e. 1 pm), on the assumption of single, spherical colloids:

/ t p p I ~(i)3d(i) (29) [coll] 6 Pw 3,~,~

where pp is the particle density. In Table 1. where the tests have been performed on groundwater colloids, the sorption constant Kc for transport in the groundwater has also been given. On the assumption that sorption is rapid, linear and reversible (Section 5.1 ), Kc = Pw [coll]Ke. In Table 2, where tests have been performed on pure colloidal phases, values of Ke enable Kc to be calculated using [col!] of the particular groundwaters of interest.

It has been noted that sorption is generally relatively rapid (in the order of seconds or minutes) compared to desorption (in the order of days, weeks or longer). Desorption experiments are therefore considered important to inves- tigate whether desorption is complete or an irreversible component is present.

COLLOID-FACILITATED TRANSPORT OF RADIONUCLIDES THROUGH FRACTURED MEDIA

TABLE 2

Results derived from size distributions sorption tests on pure colloidal phases for specific elements

157

Ion species Concentration [coil] K e ~,, (ppb) ( x 10 -9) (m 3 kg -I ) (nm)

Composition: Colloidal montmorillonite:

Pb(II) (pH = 8) 21 5,000 6-30 30 Pb(lI) (pH = 8) 21 200 1.3.10 z 30 Pb(ll) (pH = 8) 21 105 60 30 Am(Il l ) (pH = 5-10) 0.24 4,000 2.102-3 • 104 30

Composition: SiO 2 (quartz):

Am(Il l ) (pH = 10) 0.001-0.24 102-105 102 30 Am(Il l ) (pH = 5-12) 0.001-0.24 104 2-200 30

Composition: SiO 2 (amorphous):

Am(Il l) (pH = 6) 0.001-0.24 104-106 0.1-1 3 Am(Il l ) (pH = 6-9) 0.001-0.24 106 0.1-200 3

Data from H.J. Ulrich (pers. commun., 1991) (montmorillonite) and Degueldre and Wernli (1993) (SiO2).

Colloid sorption tests and colloid resuspension/filtration tests are used to determine both the sorption and desorption kinetic constants.

The transport model also takes account of the interaction between colloids and fracture walls. Two kinds of experimental investigations may be performed to quantify this. Static contact tests, which are currently being carried out, consist of placing a small volume of colloidal suspension on the surface of a non-porous rock sample. On the assumption that all sorption is rapid, linear and reversible, the retention factor Rc for colloid-wall interaction is given by:

Rc = 1 + KA/b (30)

where KA (m) is the ratio of the mass of colloids per unit area attached to the rock surface to the mass of colloids pur unit volume in the contacting fluid.

Kinetic adsorption/desorption tests have, however, been carried out and again it has been found that adsorption kinetics are much more rapid than desorption. Classical tests for estimating the sorption behaviour of colloids onto rock surfaces are dynamic (Champ, 1988; Rosta et al., 1991). However, such experiments are generally carried out with high flow velocities (e.g., 10-4-10-3 m s -I) and may be relevant only to the unsaturated zone, for example, after heavy rainfall. Velocities in the saturated zone are, however, orders of magnitude slower [e.g., 10-Sm s -~ in NAGRA (1985)] and the results of dynamic tests may not be directly applicable.

155 I ' A SMIIH ,~NI)( J3~ , , i i l lDRi

5. C O M P U T A T I O N A L R E S U L T S

5.1. Fixed parameters

The parameters defining the geosphere, used as a test case for the transport model in the following computations, are based on data from Project "Gewfihr" (NAGRA, 1985) for water flow through aplite/pegmatite dykes and are given below:

Q = 1.331-10 7 m 3 s -I ( 4 . 2 m 3 yr -~) b = 5" 10 -5 m Pe = 10p = 2616 kg m -~ E~ = 3"10 -2 ),~ = 1-10 -3 m

X = 500 m v = 1.5.10 - S m s

The following nuclide-specific parameters, which are those of 237Np in N A G R A (1985), are used for a generic long,lived, sorbing radionuctide, with a solubility-limited release from the repository:

At = 1.603" 10 j4 S

2 = 1.026"10 -I s -j K a = 0.1 m 3 kg -I

In order to examine individually the effects of sorption reversibility and a limited number of sorption sites on colloids, three simplified descriptions of solute-colloid interaction, derived from the generai model of Section 2.5, are considered in turn. For each description, it is shown how experiments produce data for modelling work.

5.2. Model I

Reversible, linear sorption onto an unlimited number of type-2 sorption sites is considered first, with no irreversible sorption on type- / s i t es (SM~ = O, SM2 = ~ ) and no colloid-watt interaction (Rc = 1). F rom eq. 2, trAz = 0 and, from eq. 18, A = 0. Under these conditions, the model is d e s c r i ~ by a single t ransport e q ~ t i o n (oq. I4), which isidenticai in form to the transport equation for dissolved radionuclides, but with redefined velocity and retention factors:

= v[1 + (v c/v)(K c /R c)] (31)

= R + Kc (32)


10 e 10"

0

Fig. 4. Model I. Sorption on colloids is assumed reversible and linear, with an unlimited number of sorption sites. There is no colloid-wall interaction. ~, the eflSciency of the geospbere as a barrier to radionuclide migration, is plotted as a function of Q, the water flux through the system, and sorption constant K c . tl

= 0 means that radionuclide flux is undiminished by passage through the geospbere and ~ = I that there is zero radionuclide flux from the geosphere.

The model is essentially the same as that of Hwang et al. (1989). The assumption that solute concentration in matrix pore water adjusts rapidly to that in the fracture (Section 2.4) may, if desired, be relaxed and matrix diffusion calculated explicitly using the RANCHMD code.

In order to demonstrate the potential r61e of colloid transport, a measure of the barrier efficiency of the geosphere, t/[-], is defined:

~l = 1 - Fmax/QCsat (33)

where Fm,x is the maximum radionuclide flux from the geosphere. ~/ = 1 therefore corresponds to a zero flux from the geosphere and a high barrier efficiency. ~/ = 0 corresponds to a solubility-limited flux from the geosphere and an ineffective barrier. In Fig. 4, r/is plotted as a function of both Q and K c. For a given value of K c, r/behaves as a smoothed step function as Q is varied, with a transition from 1 to 0 as transit time through the geosphere (ATR ~) becomes smaller than the half-life. Values of K c are given in Table 1 for a number of elements in different groundwaters. In Fig. 4, however, K c has been extended beyond the range of values found in the table in order to display a broad range of behaviour: for small values of Kc (+ 1), breakdown of the geosphere occurs at flow rates orders of magnitude above the Project "Gew/ihr" base case value of 4.2 m 3 yr -~ , whereas, for K c >> 1, breakdown of the geosphere occurs at lower flow rates. For most of the cases given in Table 1, K c < 1 and radionuclide transport would not be greatly enhanced by the presence of colloids. The exception is the case of Th(IV) for the colloids at Morro do Ferro (Poqos de Caldas, Brazil), where K c ranges from 0.25 to

1 0 0 P A SMII tt \ N I ) ~ l )k ( i l I I.DR[

2.5. Th(IV) may be used as an analogue for Sn(IV), Zr(IV), U(IV), Np(IV) and Pu(IV), which would be expected to behave in a similar way. However, in the Morro do Ferro system, it has been found that colloids are likely to be filtered by the rock and not transported for long distances (Miekeley et al.. 1990).

5.3. Model II

Model II allows for a limited number of type-2 sorption sites, but again with no irreversible sorption on type-/s i tes (SM~ --- 0) and no colloid-wall interaction (R c = 1). Again, from eq. 2, aA~ - 0. The model is described by a single transport equation (eq. 14), similar in form to the transport equation for dissolved radionuclides, with redefined velocity and retention factors given by eqs. 16 and 17, but with an additional term, A, given by eq. 18.

In addition to Kc, the model requires values for the concentration of sorption sites SM2. These may be obtained from experimental data by integrating the normalised size distributions (e.g., Fig. 3), using an estimated surface site density (James and Parks, 1982) and assuming single, spherical colloids. Preliminary results give values in the range (0.005-50)'10 6 tool m -~ However, it is the ratio SM2/Csat which determines the behaviour of radionuclides in solubility-limited release. Rather than retrict the results to a particular radionuclide, with a particular value of Csat, results are presented for a broad variation of SM2/C,, ~, the limits of which have been selected to display a complete range of breakthrough behaviour.

In Fig. 5, F/QCsat, the flux from the geosphere normalised to the solubility- limited flux, is plotted as a function of both t and SM2/C~,~. A value of K c of 1.0 is taken so that, on the basis of the results for model I. the presence of colloids would be expected to affect transport if sufficient sorption sites are available. For high values of SM2 (SM2 >1 Csa~), model II is equivalent to model I and, as SM_~ tends to zero, the model approaches that for solute transport alone. Fig. 5 shows the transition between the two limits: at intermediate values of SM2, a plateau appears in the breakthrough curves due to colloid- facilitated transport, with the peak representing transport m solution occurring later. The figure also shows that the breakthrough curves are characterised by a sharp "trailing edge", with the plateau giving an elongated "leading edge"; colloids passing through the migrating pulse of solution interact with radionuclides most strongly from the trailing edge, giving rise to the characteristic shape of the breakthrough curves.

5.4. Model I II

Finally, irreversible sorption onto a limited number of type- /sorpt ionsi tes is considered, with reversible linear sorption onto an unlimited number of

COLLOID-FACILITATED TRANSPORT OF RADIONUCLIDES THROUGH FRACTURED MEDIA | 61

F/QC,ot[-]

10 ° - 109

10%

10-L

10 -6 -

100 ~ r ~ 02

Rc[-] I0 ~

Fig. 5. Model II. Sorption on colloids is reversible and linear, but with the number of sorption sites is limited. There is no colloid-wall interaction. F, the radionuclide flux from the geosphere, normalised to the solubility-limited solute flux, QCsat, is plotted as a function time t and normalised concentration of sorption sites carried by colloids SMflQa t. K c = 1.0

type-2 sites (aM2 = O0). Transport is governed by the coupled eqs. 14 and 15, with a~, defined by eq. 2. In this case, the transport of radionuclides is strongly dependent on the extent of colloid-fracture wall interaction, described by the retention factor Rc.

In Fig. 6, F/QCsat, the flux from the geosphere normalised to the solubility- limited flux, is plotted as a function of both t and Rc. As R c is varied, the product SM1Rc is held constant (and equal to Csat); SMI Rc is the concentration of sites for irreversible sorption on both mobile colloids and colloids attached to the fracture walls. Preliminary results from the contact tests give a KA for the sorption of montmorillonite colloids on muscovite of (2.0-t-0.6). 10-3m (pH = 7-10), giving Rc ~40. However, in the absence of data for other relevant minerals and for other colloids, results are presented for a broad variation of Rc, the limits of the parameter variation again being selected to display a complete range of breakthrough behaviour: for low values of Rc (Rc ~ 1), virtually all transport is on colloids, whereas, as Rc becomes large (R c ~ 104), the model approaches that for solute transport alone. Fig. 6 shows the transition between these limiting cases: as in Fig. 5, at intermediate values of Rc, a plateau appears in the breakthrough curves due to colloid-facilitated transport, with the peak representing transport in solution occurring later. In Fig. 6, however, the height of the plateau decreases and the time at which the plateau value is first reached increases with

1~3~ PA. SMI 114 -~NI) ( !)[d.;l I I!)RI

:: / (- I ~CsatL-- j ~_10 °

] I

I0 -6

aF- r tL'/r_ 10 o ~ u L)/ _

s~JC,o,[-]

Fig. 6. Model Ili. Irreversible sorption occurs on a limited number of type-/s i tes and reverible sorption on an unlimited number of type-2 sites. F, the radionuclide flux from the geosphere, normalised to the solubility-limited solute flux, QC~,t, is plotted as a function time t and colloid-wall retention factor Re: SMaRt., the concentration of sites for irreversible sorption on both mobile colloids and those attached to fracture walls, is held constant at the solubility limit C~,,.

increasing Rc. Again, the breakthrough curves are characterised by a sharp trailing edge.

6. D I S C U S S I O N A N D C O N C L U S I O N S

The dual-porosity transport model for solute transport through fractured porous media has been generalised to include colloid-facilitated transport. A description of solute-colloid interaction, which includes the effects of finite numbers of sorption sites and irreversible sorption, has been employed. Since slow desorption kinetics or irreversible sorption would increase the rate of radionuclide transport through the geosphere, these features cannot be neglected in a conservative model.

A general transport model was used to examine three simplified cases of increasing complexity. The least conservative of the cases are models I and II: those in which all sorption is reversible. The degree to which colloids facilitate radionuclide transport may be judged from the magnitude of the sorption parameter Kc. In most cases, Kc < 1 is to be expected (see Table 1) and colloid-facilitated transport will not significantly perturb the transport of radionuclides through the geosphere for the Project "Gew~ihr" base case. The most conservative of the cases is model III: further experimental work on the degree of sorption irreversibility and the magnitude of colloid-wall interaction (Rc) will be needed to decide whether colloid-facilitated transport is significant in this instance.


Irreversible or linear reversible sorption, with a limited number of sites, used in models II and III, may be described in terms of discontinuous, nonlinear sorption isotherms; continuous sorption isotherms, such as the Langmuir and Freundlich isotherms, may prove to be better representations of sorption on colloids when sufficient experimental data are available to define them. As in the Langmuir and Freundlich isotherms, sorption is greatest at low solute concentrations. The limited number of sorption sites is a feature of the Langrnuir isotherm, as is the linear behaviour at low concentrations of model II. The high gradient of the Freundlich isotherm at low concentrations, tending to infinity as concentration tends to zero for Freundlich exponents less than unity, is reproduced by model III. The breakthrough curves in Figs. 5 and 6, with nonlinear sorption on colloids, showing sharp trailing edges and elongated leading edges, contrast with those for nonlinear sorption of solute onto thefixed fracture walls, in which case it is the leading edge of the breakthrough curves which becomes sharp, with an elongated tailing part (Jakob et al., 1989).

The following conclusions may be drawn from this work: (1) On the basis of combined experimental and modelling work, where

reversible, linear sorption on colloids is assumed, colloid-facilitated transport through the geosphere should not generally be significant for the specific case of a high-level waste repository in the crystalline basement of northern Swit- zerland, where colloid concentrations are < 1 ppm and the sorption constant does not exceed unity.

(2) The assumption of rapid, reversible linear sorption is non- conservative. Preliminary experimental results suggest that the time-scales for desorption greatly exceed those for sorption. Further experimental work, together with literature evaluation, is required to assess the extent of reversibility and the form of sorption isotherms.

(3) Modelling work accounting for irreversible sorption shows again that it is important to determine the extent of colloid-wall interaction. It is still necessary to show that this interaction may be described using the KA concept.

(4) Although filtration models are available for fracture flow, they are of limited applicability and there is a lack of an accompanying generation model. This shows again that the colloid-wall interaction must be quantified experi- mentally.

(5) Modelling work indicates that, where irreversible sorption on colloids takes place, or where a limited number of reversible sorption sites becomes occupied, the resulting breakthrough curves have distinctive forms. In both cases, there is an elongated leading edge or plateau region and a sharp trailing edge.

(6) Each of the transport models requires additional experimental input. Experimental work has also guided the way in which the model has been

164 r ' a S M I I H A N D ( DI:GIq~LI )Ri

developed. F o r example , desorp t ion tests have p rov ided evidence o f very slow desorp t ion kinetics. An in terac t ion between the exper imenta l and model l ing aspects o f the work has thus p roved useful.

ACKNOWLEDGEMENTS

Several col leagues have con t r ibu ted to this work t h r o u g h helpful discussion. In par t icular , the au tho r s would like to t hank J. H a d e r m a n n , R. Graue r , T. Karap ipe r i s (all PSI) and W.R. Alexander (Univers i ty o f Berne). T h a n k s for co l l abora t ion in the exper imenta l w o rk go to H. Silby (Her io t Wat t Universi ty): col loid sorp t ion , H,J. Ulr ich (PSI): col loid sorpt ion , R. Brfitsch (PSI): SEM, as well as H. B a u m a n n (Ciba Geigy) and B. Wernl i (PSI): ICPMS. Part ia l f inancial suppor t by N A G R A is grateful ly acknowledged .

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