Analytic Studies of Colloid Transport in Fractured Porous Media
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ANALYTIC STUDIES OF COLLOID TRANSPORT IN FRACTURED POROUS MEDIA
Y. Hwang, P. L. Chambrd, and W. W.-L. Lee, T. H. Pigford Department of Nuclear Engineering, University of California and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 ABSTRACT Mathematical models of coupled migration of colloids and solute in fractured, porous medium are presented, for two types of colloid-solute interaction. When the colloid-solute interaction is by dissolution, solute that normally has greater retardation than colloids is accelerated by colloid dissolutions. For sorption interaction, the apparent migration speed of pseudocolloids can be greater or less than the solute migration speed without interaction, depending on the choice of parameters. INTRODUCTION We analyze the interactive migration of radioactive colloids and solute in fractured rock. Two possible interactions between radionucides as colloids and as solute are considered: (1) solute sorption on nonradioactive colloids to form pseudocolloids, and (2) dissolution of radioactive colloids. Previous studies"'2 have discussed the formation and transport of colloids in porous media, including removal of colloids by filtration and sedimentation. Colloids can migrate faster than solute because of weaker sorption on stationary solids and because of hydrochromatography of colloid particles in flow channels. However, the migration of colloids and pseudocolloids can be retarded by the interaction of colloids with solute, and the migration of solute in local equilibrium with colloids can be more rapid than if colloids were not present. Here we present a new quantative analysis to predict the interactive migration of colloids and solute in porous and fractured media(Figure 1). PSEUDO-COLLOID MIGRATION Consider a radioactive solute at concentration C2(x, t) in water in the fracture of fractured porous rock. Also present in the fracture are natural colloids, on which solute can sorb to concentration C, (x, t) on the colloids to form pseudocolloids. We assume the onedimensional convective-diffusive transport within the fracture, and assume that colloids are too large to diffuse into the rock matrix. Neglecting possible colloid filtration within the fracture, the equation governing the transport of solute as pseudocolloids is: OC,(x,t)
el1loci
OCl(x,t)
+ f6Vac, X
,.O.,'C,(x,t)
+ eSi(X,t) + elS2(X,t)- e1 11D,2CX
+ el,6ACI= o, (1)
x>0, t>0 where el1 is the ratio of liquid volume to total volume in the fracture, C,(x, t) is the amount of species sorbed on the colloid per unit volume of solid colloid, v, is the colloid pore velocity, D, is the colloid dispersion coefficient, A is the decay constant, e1 is the porosity within the fracture, 61 is the constant volume fraction of colloids in fracture liquid, 61S,(x, t) is the rate of sorption to stationary solid, and ejS2(x,t) is the rate of desorption from the pseudocolloid. For the same species as solute in liquid in the fracture x > 0, el
OC2(x, t) at "EIV
2
0C2(Xt) .
t > 0
a C2(X,t) e,S2 (x, t) + elS3((x,
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