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LA-UR--89-3O95

DE90 001834

TITLE. LABORATORY STUDIES OF RAD1ONUCLIDE MIGRATION IN TUFF

AUTHOqS): R. S. Rundberg, A. J. Mitchell, N1. A. Ott, and J. L. Thompson

SUBMITTED TO: FOCUS 89-- Nuclear Waste Isolation in the Unsaturtited ZoneSeptember 18-21, 1989, Las Vegas, NV

DISCLAIMER

llm repml wu preperal m ● mxmunl of work npnwd by sn agency of Iha United SIaIoe

(kvernment. Neither Ihc (Jnild SIaIeI Governmm M wry ●#wncy dmrouf, nor any of Ihoir

employom, mthws wry wurrunty, cnpreu or Implied, or mmmos ●ny lqml Iitibihly or mqmmi.

hihly (or Ihe mxuracy, compfelem, or udulnas 0( mny in(ormulion, appemlus, product, or

pr~ didmd. or mpreuntn Ihml itn urn would noI Infringe privately ownaf rights. Rafor.

GM herein 10 ●y nmirw uommercml pork!. prucau, or acrvica hy Irdc rmme, I rulemark,

mmiuflciurer, or otherwlw dom no! rwxumrily Conniiiute or imply itc endureemont, mean-

mendalion, or fmvorq hy Ihe UmtA Slatec (kwcrnmenl or ●ny ●SWICy Ihemuf. rk wawt

and opinmnn af authum e~prd herein do not nawwdly mmIe or reflect Ihme of Ihe

(Jmtod Shlam (Jovernmenl or ●ny qwncy Iherouf.

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Laboratory Studies of Radicmuclide hligration in Tuff

R. S. Rundberg, A. ,J. hlitchell, il. A. Ott, J. L. ThOIIlpSOII,and 1, R. Triay, Los Alamos National Laboratory

The movement of selected radionuclides has been observed in crushed tu!T, intact tl~ff,and fractured tuff columns, Retardation factors and dispersivities were cktcrmincd fromthe elution profiles, Retardation factors have been compared with those predicted onthe basis of batch sorption studies. This comparison forms a basis for either validatingdistribution coefficients or providing evidence of speciation, including colloid format ioxl.Dispersivities measured as a function of velocity provide a means of determining the effect,of sorption kinetics or m~s transfer on radionuclide migration, Dispersion is also beingstudied in the context of scaling symmetry to develop a basis for extrapolating from thelaborator;~ scale to the field.

The alkali metals and alkaline earths eluted through crushed tuff columns yield retar-dation factors which are in agreement with batch sorption measurements. The actinidesyield more complex results. Anions including the pertechnetate ~ion have also been stU~-

ied in crl,shed tuff. The anion studies have been used to establish a relationship betweenthe crystallographic structure of zeolites and clays and the magnitude of the anion exclu-sion effect. This relationship S+.I1OWSthe prediction of retardation factors for pertechnetategiven the mineralogical composition of tuff. Ninety to ninety-five percent of the injectedneptmium and twenty to eighty percent of plutonium VI and V has been observed tomigrate through crushed tuff columns unretarded. This obserntion is in conflict with K~values for nc ptunium ranging from 1 to 5 ml/g as determined by the batch techni(luc.

This raises questions M to whether the aqueous species in Yucca Mountain groundwatcr+, A small fraction of americium tracers and pluto-is the expected neptunyl ion, Np02

nium colloid has been observed to migrate unretarded through crushed tuff columns. Apreliminary interpretation of the observed americium behavior is colloid or pseudocolloidformation. Significantly smaller retardation factors than expected were observed usingintact cuff columns for alkali metals and alkaline earths. The distribution of rcsidud ra-dioactivity in the t~df columns was measured by sectioning the column rtftm elutions wcrrcbserved, Thr distribution WIMfound to k nonuniform. The heterogeneous distribution ofsorbing nlinerals mrty be responsible, nt Ieaat i:l ~mrt, for the reduced retardation, Disl)cr-sivities of tritiated water and pertech Iletn:e are nmch greater than clispersivitics ol)w’rl’(’(1

in (.ru~he(l tuif columns, Diupersivitim for the sorbing tracers are Significantly grcntcr thm~dispersivitics for tritintcd water in the wktnc tuff coluIIms.

The migration of rndionuclides thro{lgh fractures in saturated tuff has IAN) b(*rII stu(l-

kd. Nommrbing trncer~ have ken f(JUlld to be in fair agreement with predictio]~ bmw(l 011imhq)rndrntly Inrm(lred diffusivitim and e~timutcs of fracture npmturc. The most r(’c(:lltwork with th(wc (x)lumn~ inv(dvr(l InmwIu-iIIg tile miglrdi(m of colloi(hd polystyrt’lw trnccrs.Polystyrmw c~)lloi(l:; with R al ~llicron (Iiwlwtcr wrrc foul~(l to IIavc the Iowtwt filtrutioll

r(wfiicicwt.Th(wr rx])(~ril~)ullt~ linvr INWI1 ])mforll~ml Ilmlvr tlw DyIlru~li(’ Trnnsport t:wk of tllv

grt)chcniistr}* i)rogrttt]] fi)r the YII(:cn ~lm~ll~tnill I)rojrct,

The theory of transport through porous media is well developed for chemical engi-neering [Sherwood, Pigford, and Willie]. The theoretical methods have been dcwclopcdwit h the principal purpose of designing efilcient separations processes for the chemicalindustry using chromatographic columns. Chrm-natographic columns are generally homo-geneous with respect to the both hydraulic properties, i.e., porosity and permeability, audchemical properties. Transport in geologic media is rm the other hand complex hy&ologi-cally and chemically. Some of difficulties which must be overcome in order to predict thehydrologic transport of radionuclides are: 1 ) the volubility of many of the radionuclidesis too low to allow the direct determination of the chemical stucture of solution speciesby spectroscopic methods. ~) ~1 of the &emic~ interwtions &tw@n radionuclides a[l(l

the minerals present in tuffaceaous rock have not been identified. 3) ah of the significantaqueous phase reactions occuring in groundwater have not been quantified. 4) The ctfcct ofheterogeneity, With respect to fourth difficulty hydrologists have successfully applied theprinciples developed for column chromatography by the use of the simplifying assumptionof a representative elementary volume, REV, [Bear]. However, the assumption of an REVis only valid under special circumstances. A general approach to modeling trmsport incomplex hydrologic systems haa yet to have ben developed.

The transport of solutes in porous media is most often considered a Fickian diffusiveprocms described by the convection-dMusion equation [Bear and Bachmat].

where

D

c

ue

Wdiv( D grad C - UC) = ~=

dispersion tensor;

concentration of solute;

Dsrcy’s velocity vector;

effective porosity.

(1)

The dispersion tensor representsdrodynamic dispersion in this context

both diffusion and hydrodynamic dispersion. Hy -refers both t~~dispersion cau~ed by the variation in

water velocity across pores and the dispersion causel by heterogeneity in the permeabilityof the hydrologic system, The use of a cliffusivr mechanism to describe dispersion wouldappear justifiable in light of the concept of represcntotive elementtuy volume.

Modern stochastic models [Matheron and dr Mamily, Gelhar, and Ncun~an] rnpnblrof calculating the transport of conservative tracmw describe the heterogeneity of quifrr~h terms of the covariance of the Pmmability distribution, If the probability clistrikltion

of the velocity field is is amurned to gaumian the transport equntion can be written M [(IcMarsily],

where

C C(wnriancr Ilmtrix of tlw vrkity firld;

ii velocity.

These approaches predict increasing dispersion with time. Spatial covnriancc is astatist ical property observed in Fract al geometry [Mandelbrot, 19S3] and other nonlinearphenomena, such as. cellular automata. This opens a number of practical methods for gen-erat ing realistic models of hydrologic transport. The spatial variation of the geochcmicaland/or sorptire properties with respect to mmsport has not been modeled. Of particularconcern in terms of making accurate predictions of radionuclide migration is the covarianccbet ween permeability and sorption. For example, if the highly sorptive minerals, such as,smectites, were correlated with zones of low permeability the fastest moving radionuclideswould in addition to having an above average water velocity would have a below averageretardation factor. This could greatly increase the observed dispersion and lead to earlybreakthrough of small quemtities of radioactive waste.

The Dynamic ~ansport task h= as its primary mission the task of testing the assump-tions made in the theory of chromatography and hydrologic transport by experimentallyobserving the tremsport of radionuclides in laboratory to field scale experiments. If therewere no technical difficulties in determining the chemical species (pefiorrned in the solubil-ity task ) and determining the mechanism of interaction between radionuclides and minerti(performscl in the sorption t~k) this would be the only purpoee for this task. This is notthe case however and the Dynamic ‘lhnsport task has M its secondcuy mission the vali-dation of sorption resul+.s in tufF columns of varying complexity. The simplest experimentsare performed with crushed tuff uniformly packed in acrylic columns. These expel imentsutilize crushed tuff prepared in the same rnsumer as the crushed tuff used by the sorptiontask. Significant discrepancies could indicate the presence of coexisting ehernicrd speciesof the same element, colloid formation, and/or pseudocolloid formation. The kinetics ofsorption can be studied by wuying the water velocity and measuring the dispersion of thebreakthrough curve as a function of velocity.

The radioactive tracers were prepared from commercially avaiable isotopes, NENand ICN corporations, diluted in J-13 water. All tuff columns wem pretreated with J-13 water, Colloidal tracers were fluorescent carboxylated polystyrene SOISavailable fromPOLY3CIENCES, INC. Radioactive tracers were assayed using standard Iadiochemicalprocedures in accordance with the Los Ahrnos National Laboratory YMP QA manuul.The methods used were gamma my tipect roscopy using hightors, aml liquid scintillation beta and alpha spectrometry.rrfmcucec! in the following 9L!cthJllS.

cd ‘IhKQ21J4WW

Tht= equatiwi ncmmdly used to predict the retardationhy Hristm nnd Vcmnmden,

I<dpn,., 1+—.

cm

resolution germmlium dt’trc-Fm more details me rq.mrts

of rndiouuclidc~ wm dc’rivw1

(3)

with the adsorbed phase. 2 ) the adsorption isotherm is linear. 3) the elution curve isconstant pattern. In addition it is assumed that a single aqueous chemical species is inequilibrium with a single adsorbed s@cies.

Crushed tti columns are suited to testing the above assumptions because the crushedtuff used in the column experiments are nearly identical in composition to the batch sorption measurements, the columns can be packed uniformly to minimize dispersion. and havea high porosities and permeabilities making the experiments simpler to perform.

The validity of batch ~(&S for the cations of sodium, strontium, and barium werechecked using short crushed tuff columns [Treher and Ray bold, 1982]. The results werefound to agree with the batch results if the the batch experiments were performed on wetsieved crushed tuff. This is illustrated in table 1. Samples G 1-2334, YM-22, and YM-38 were wet sieved to a size range of 75 to 500 micrometer diameter. This was necessarybecause the outlet frits in the crushed tuff columns have a pore diameter of 38 micrometers,The batch ~-@ from crushed tti treated in this manner yield retardation factors whichagree with the observed retardation factors within a factor of thr=. Sample G 1-3116 wasnot wet sieved and had a particle size ranging from O to 500 micrometers. The ~d forthis material yields a retardation factor which is one or more orders of magnitude greaterthan the observed retardation factor. This mult is due to the greater clay content in theunsieved material as compared with the column materiid which has been sieved by flushingthe column over the 38 micrometer frit.

Table I Comparison of Crushed Tuff Columns with Batch Sorption Experiments.

G1-2334 Sr 180 250 10213a 1400 1940 1180Cs 1200 1670 1630

YM-22 Sr 60 128 50Ba 890 1890 723Cs 255 540 2C6

YM-38 Cs 13000 54000 49000

G1-3116 Sr 2300 0146 1065Ba 120000 480000 8300cd 5900 23000 7100

IIydr(x@mmic dispersion in :rushed tuff columns WM examined in the context ofsorption kinetics or mass transfer, Figure 1 illustrates the dependm~cc of dispersivity onwntcr velocity. At low wntcr velwity !J~edisperuivity is dominated by Iongitudind diffusionam] thus increases with decreasing velocity, i.e., dispersivity increases w the rmidcnc tiuwincri’nms. At high water velocity mam transfer or rnorption kiuetics will duminato umlthr (li~pmt+ivity will immmm with il:crwwin~ velocity, The rrmdwd tuff coltmms di(l m~t

exhibit a significantly large dispersivity at velocities as high as 10-Z cm/s. The observed

dispersivit, as a function of velocity is shown in figure 2. The trend of the dispersivitieswere in general agreement with the thwretical curve in figure 1. Unfortunately there wereno data taken at velocities near 10-3 cnl/s where the minimum in the cur~w is expected.

Crushed tu5F columns were constructed for the specific purpose of determining theanion exclusion volume. These columns were 1S2 cm in length with an internal diameterof 0.7 cm. The dispersivities of these columns were on the order of 0.5 cm. Anion exclusionis the effect which cmwes anions to appear to migrate fsster than tritiated water. Thiseffect is clue to the large size of anions and repulsion by the negatively charged mineralsurfaces. The apertures of porous minerals such as zeolites and clays are on the orderof a few .~ugsttirn units making it sterically impossible for anions to diffuse into ~heintracrystalline pore space, The anion exclusion voiurnes for tuff samples having high

‘smTco~, diameter 6.3 ~, see Tableclay and zeolite contents wem determined usingII. These anion exclusion volunws were four,d to agnx with the estimated intracrystidinepore volumes based on the crystallographic data for the component zeolites and clays. Thepoorest agreement was for the sample USW-G2-33$. This sample contained principallysmectite clay. The intracrystalline pore volume was calculated for a monolayer of water ir.the clay interstices. If two layers of water Wexeassumed in the clay structure the agreementwould k within the experimental errors.

Table 11 Anion Exclusion Volumes

Sample Exclusion Volume Calculated Exclusion Volume

USW-G2-339 0.056 + 0.010 0.030 + 0.006USW-G2-1951 o.~(j ● 0,03 0.13 + 0.04USW-G2-2017 0,13 ● 0.01 0.12 ● 0.03USW-G2-2698 0.069 + 0.009 0.08 + 0.01USW-G3-4868 0.035 * 0.001 0.034 ● 0.004

The actinides neptunium, americium, and plutonium hnve exhibited unretarded break-through [Thumpoon, 1989]. For americium md plutonium colloid the amount which elutesearly is a small fraction usually a few percent of the total actinide injected. Plutoniumcolloid fig 3, and americium (open squares) eluted ahead of the tritiated water (filledcirclrs ). The difference in breakthrough volumes between the ccdloid and trit iated wateris equal to the anion exclusion volume. This im presumably due to size ●xclusion. Thepuzzling observation is that neptunium and putcmium in tht! V and VI oxidation states,see fig, 4, elute with the tritiated water, i.e., they are neither size excluded nor retarckl.One would expect the actinide moleculey to be size excluded from the intracryotnlline porevolume. It is concievable that actinidm are nctually being weakly sorbed by a limited nuln-

bcr of surface sites, Further ~tudy in needed to clarify this phenomenon before a mmunityretardation ftictor CM be n.ssigned to thcw elements.

One step closer to field conditions is achieved by performing radionuclide migrationexperiments with intact tuff columns. These columns will not have the hydrologic simplic-ity that the uniform packing of sieved crushed tuff provides. They will however be freefrom the uncertainty that crushing causes in terms of the surface properties of minerals,These samples retain the nat .md hydrodynamic dispersion (valid for the laboratory scale)for porous flow through the tu.ff matrix. These experiments hate produced interestingresults.

Samples of densely welded tuff from the Topopah Spring member, Yucca lMountain,Nevada have exhibited elution curves which cannot be fit to the conventional advection-dispersion equation, ADE [Bear and Bachrnat]. The curves can be fit however with a timedependent equivalent dispersion coefficient [Dieulin, 1979]. This effect has been previouslyobserved by Coats and Smith and more recently by Herr et al. These authors have at-tributed the effect to that of local heterogeneities or deadend pores (Coats and Smith).The el%ct of heterogeneity is more generally described by the methods advocated by DeMarsily and his coauthors, see for example [De Marsily, 1986] This phenomenon was the-oretically shown to be the result of the spatial distribution of permeability by Matheronand deMarsily [1980]. The most dramatic consequence of the time dependent dispersion isthe effect on the prediction of breakthrough times for sorbing tracers. If the conventionalADE is employed to predict the breakthrough of strontium the expected breakthrough inthe solid tti column would be at -1.5 years, based on batch sorption measurements. Theactual breakthrough, Fig. 5, occurs within a few weeks of the start of the experiment. Thisis a discrepancy of -U 2 orders of magnitude. If the dispersion is given a time dependencethe elution curve can be fit with the measured batrk sorption coefRcient, Fig. 6. The ob-ser~tion of time dependent in laboratory scale migration experiments has provided newinsight into the eff~t of heterogeneity on the retardation of sorbing radionuclides. In orderto calculate the time dependence a priori at the very least a stasticd characterization ofthe distribution of sorbing minerals and the distribution of hydraulic conductivity mustbe made.

This effect will have an even greater importance as the scale of the hydrologic systemincreases to field and repository scales. Time dependent dispersion has been obsemed inthe tritium and 3oC1 elutions from the CAMBRIC field test in tuffaceous alluvium on theNevada Tent Site for the HRMP project [Ogard et d. 1989]. The question which arisesfrom these column experiments is when can one ex~ct to observe the elution of sorbingradionuclic!es from CAMBRIC.

The next level of complexity is achieved with fractured tuff. In fractured rock thefluid flows through discrete fractures with a characteristic dispersion dominated by thevariation in permeability within the fracture. ‘Ihicers will difhse into the rock matrixperpendicular to the frncture as first pointed out by Neretnieks [1980]. Radionuclide mi-gration experiments in saturated tuff fractures have confirmed the importance of matrixdiffusion. Elutionrn of ronservntive tracers can be described adequately by the analyticsolution to the advection dispersion equati{ms of Tang et al. [], Early experiments exar.~-ining the movement of cationic tracers exhibited a small fraction eluting early [hmclbe’ g,

1983]. These observations may be attributed to pseudocolloid formation, chameling ortime dependent dispersion in the fracture.

The ~rmeabilities of th- fractures were measured to determine the cubic law aper-ture. This aperture was found to be adequate to fit the elution profiles of conservativetracers. A Topopah Spring member tuf sample taken from an outcropping at Fran Ridge,near Yucca Mountain was recently used as a fractured tuff sample. The fractures in thissample were originally filled with cal~ite. After the tti smple was cut and encapsulatedthe calcite was leaclml away with dilute hydrochloric acid. This was done in an effortto retained the insitu geometery of the fracture void. ‘Ihnsport in this fracture was notwell described using the cubic law aperture determined from the fracture permeability.Adjustment C! the fracture aperture was required to fit conserwtive tracer data.

Colloidal tracers have exhibited a peculiar shift in apparent fracture aperture withcolloid diameter. This phenomemm h a not been fully explained but is possibly the resuit of channeling. More transport experiments with tuil fractures and more detailedcharacterization of the water flow paths through the fkacture are required to advance theunderstanding of radionuclide migration in discrete fractures. One meter scale fractureflow experiments are p~ntly being planned to examine the effect of scale on migrationin fractures.

The next level of complexity to be examined is the migration of radionuclides in un-saturated solid and fractured tuf. These experiments will challenge both the experimentaland theoretical abilities of our project. Controlling tuff saturation over long periods of timeis experimentally difficult and the fluid movement through unsaturated fracturea may bea highly nonlinear problem, and may in fact be chaotic.

~ The results of crushed tuff columns have yielded the following conclusions.The observed retardation f~tors for alkali metals and alkaline earths have agreed withthose predicted from batch zorption me~urements of Kd using the eq. 3. The nctinidesdo not agree with the batch measurermmte. The elution curves observed for Pu colloid andamericium exhibit size exclusion. Neptunium and the higher oxidation states of plutoniumhave large bctions which migrate unretarded. ‘I he mechanism for sorption which leadsto a nonzero K~ for neptunium and the reason for the absence of sorption in the columnexperiment remain unknown. Ongoing experiments in the solubllity tazk and the sorptiontask will provide the explanation for these obsewations.

The solid tuff columns have exhibited time dependent dispersion. This observationpoints to the need for a more detailed characterization of the hydrologic and geochemicalproperties of Yucca Mountain tuff. The most important consequence of this obserwatimiis that without time dependent dispersion the elution of alkali metals and alakaline earthsdid not ag~ with batch sorption measurements. The apparant error in the predictedam lval time is greater than an order of magnitu&. fit ure experiments will utilize opticaland scanning electron microscopy along with microautoradiography to attempt to providea forward basin for predicting the time dependence of the dispersion in the radionucl.de mi.gration. One would expect dispel sion to increuw as saturation decreases because it seemsnatural that the tortuousity of connected flow paths should increase, hture experimentexamining migration in unsaturated tuE columns will tent this hypothesis and demonstrate

whether time dependent dispersion is more or less important in the unsaturated zone thanin saturated tuff.

The fractured tuff columns have provided good agreement between matrix diffusionmodels and the obser~ elution of nonsorbing (conservative) tracers. With the exceptionthat the aperture needed to ~ adjusted to fit the arrival time of the tritiated water in thecase of the sample from the Ran Ridge outcropping. !%rbing tracers have exhibited therelease of a small fraction appearing to unretarded. This result could b due to pseudo-ccdloid for~ation as was observed for americium in the crushed tuff columns or channelingdispersion in the fracture. The next phase of experiments with saturated fractures willdifferentiate between these possible mechanisms. Colloid trmsport was obsemed throughsaturated fracture t ti with carbxylated polystyrene SOISranging in size from 0.10 t~ 9.55micrometer in diameter. Only the 0.91 micrometer diameter sol eluted a significant frac-tion (24 percent ) of the input material. This is in general agreement with the predictedsize dependence of the Tien and Payatakes titration model.

In summary the crushed tuff columns have demonstrated a need for a better unders-tanding of the chemical speciation of actinides in Yucca Mountain groundwater and a needfor a mechanistic apprcmch to sorption of actinid=. Intact tti and h.ctured tuff columnshave demonstrated a need for the characterization of the distribution of hydrologic andgeochemical properties in Yucca Mountain. There is also a n-d for a better understandingof the efhct of heterogeneity on transport.

1. Sherwmd, T. K., Pigford, R. L., and Wilke, C. R., ‘Mass Thnsfer.”, McGraw-Hill,New York (1975).

2. Bear, J., “Hydraulics of Groundwater”, pp 29-30, McGraw Hill, New York (1979).

3. Bear, J. and Bachmat, Y., “A Generalised Theory on Hydrodynamic Dispersion inPorous Media,” Int, Ass. Sci. Mydml. PubL, 72, (1967).

4. Matheron, G., and de Marsily, G., “Is lhns~rt in Porous Media Always Diffusive?A Counterexample, “ Water Resour. Reg., 16(5), 901-917, (1980).

5. Gelhar, L. W., A, L. Gutjahr, and R. L. NafT, “Stochastic Analysis of Macmdispersionin a Stratified Aquifer, “ Water Resour. Res., 15(6), 1387-1397, (1979).

6. Neuman

7. de Mamily, G., “Quantitative Hydrogeology”, pp. 247-251, Academic Press, San Diego(1986).

8. Mandelbrot, B. B., “The Fhctal Geometry of Nature, “ W. H. We+man and Compnny,New York (1983).

9. Hiester, N. K. and T. Verm~ulen, “Saturation Performance of Ion Exchange and Ad-sorption Columns, “ Chem. fhg. Prog., 48(10), 505-516, (1952).

10. ~eher, E. N. and N. A. Ray bold, “The Elution of Radion’lclideu through Columns ofCrushed Rock from the Nevada Test Site, “ Los Alarnoa National Laboratory ReportJ.A-9329-MS (October 1982).

11. Ru.ndberg, R. S., “ Assessment Report on the Kinetics of Radionuclide Adsorption cnYucca Mountain TuR, “ Los Alagms National Laboratory Report LA-11026-NfS (July1987).

12. Thorn-peon, J. L., “Actinide Behavior on Crushed Rock Columns, “ J, Radioanal. andNUCL Chem., 130(2), 353-364, (19S9).

13. Bear, J. and Bachrnat, Y., op. cit.

14. Dieulin A., G. Matheron, and G, de Marsily, “Growth of the Dispersion Coefficientwith the mean Travelled Distance in Porous Media, “ Sci. Total. Environ. 21,319-328(1981).

15. Coats, K. H., and B, D. Smith, “Dead-End Pore Volume and Dispersion in PorousMedia, “ Sot. of Petroleum Engineers, hm, AIME 231,73-84 (1964).

16. Herr, M., G. Schafer, and K. Spitz, “Experimental Studies of Mus lhmsport inPorous Media with Local Heterogeneities, “ J. of Contaminant Hydrology 4, 127-137(1989).

17. A. E. Ogar~ J. L. Thompson, R. S. Rundberg, K. Wolfsberg, P. W. Kubik, D. Elmore,and H. W. Bentley, “Migration of ChlockIe-36 and ‘Eitium from an UndergroundNuclear Test,” Radiochimica Acts, 44/45, 213 (1988).

18. Neretnieks, I., “Diffusion in the Rock Matrix: An Important l%ctor i~ RadionuclideMigration? “ J. Geophys. Jles. 85(B8), 4379-4397 (1980).

19. Ihng. G. H., F. P, Rind, and E. A. Sudicky, “Contaminant ‘Ihnsport in IhcturedPorouIs Media: Analytical Solution for a Single Fhcture, “ Water Resour. Res. 17(3),55$564 (1981).

20. Rundberg, R. S., J. L. Thompson, and S. M=tas, “Radionuclide Migration: Lab-oratory Experiments with Isolated I%ctures, “ Scientific Basis for Nuclesx WsateManagement Vol. 6, pp. 239-248, North-Holland, New York (1982).

21. Tien, C. and A. C. Pqyatakes, “Advances in Deep Bed Filtration, “ AIChE Journal25(5) 737-759, (1979)

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