A review of porosity and Diffusion in Bentonite (pdf) (2.4 MB) - Posiva

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71) the interlayer thickness decreases gradually with the dry density (Muurinen et al.,2007); the interlayer porosity depends on unit-cell stacking in the c-direction (n c ) andis shown for n c = 1.5, 3 and 25 (lines);2) the interlayer thickness changes from 0.9 to 0.55 nm between dry densities of 1420and 1570 kg/m 3 and all the planar surfaces are bordering the interlayer space (n c = ∞;Bourg et al. 2006, dotted line);3) the interlayer porosity is a constant fraction of the dry density of 0.16 (Bourg et al.2003, dashed line).First, figure 2 illustrates that the interlayer porosity is a very significant part of the totalporosity when dry density increases above 1000 kg/m 3 . This is reached in all practicalapplications of bentonite. At a dry density of 1800 kg/m 3 almost all the porosity residesin the interlayers of Na-montmorillonite. Since anions are excluded from the interlayers(Bolt and De Haan, 1982), the anion-accessible porosity becomes zero, and aniondiffusionis minimized (Bourg et al. 2003).Second, the number of stacks in the c-direction has considerable influence on the interlayerporosity. The interlayer porosity increases with n c . The maximum is reached whenn c ≈ 25 and it remains almost the same with higher n c . The interlayer porosity halveswith n c when n c is smaller than 3, and it becomes zero for n c = 1. Thus, a well washedand completely dispersed Na-montmorillonite in distilled water will have zero interlayerporosity.The DDL porosity can be calculated by multiplying the external surface area with thethickness of the DDL. The thickness of the DDL can be expressed in Debye-lengths:t10DDL f DDL3.0910 m(8)IWhere I is the ionic strength (mol/L), and f DDL is the number of Debye-lengths. TheDDL porosity is:ε DDL = A ext × t DDL × w mm × ρ dry (-) (9)Defined in this way, f DDL also corrects the decrease of external surface area by grain tograin contacts.Finally, the free water porosity becomes:ε free = ε tot - ε IL - ε DDL (-) (10)2.3 Calculating the porewater distribution from experimental dataMuurinen (2006) and Van Loon et al. (2007) have measured the anion accessible porosityof bentonite as a function of the dry density and the concentration of NaCl in theexternal solution. In principle, the experimental data permit to obtain the coefficients n c ,f I_IL , f dens and f DDL . However, the coefficients were found to be highly correlated and the
8data are few and not very precise (cf. Van Loon et al. 2007). Thus, the model was simplifiedto derive the effect of the NaCl-concentration for a given bentonite dry density.According to Equations (5) and (8), the external solution concentration affects the anionaccessible porosity in two ways. The interlayer porosity decreases linearly with concentrationby the osmotic effect, and the DDL porosity decreases with the square root ofconcentration. Or, in Equation (10), assuming that DDL-water and interlayer water aredevoid of anions:aDDL free tot a0 _ IL aosm I NaCl (11)INaClwhere a 0_IL , a osm and a DDL are variables that lump the effects of the ‘f’’ parameters fromthe previous section.The parameters were optimized to obtain the smallest sum of the squared deviations (usingPEST, Doherty 1994) and the resulting Cl - -accessible porosities (assumed equal toε free ) are shown in Figures 3 and 4, together with the data. Muurinen used MX80 andwashed it in NaCl, while Van Loon et al. used Volclay as received from the manufacturer.The Cl - -accessible porosities were measured for different dry densities of 1300,1600, and 1700 or 1900 kg/m 3 , and different concentrations of NaCl in the external solution.At the same ionic strength and dry density, Van Loon et al. found a smaller Cl - -accessible porosity than Muurinen, possibly a result of the different origin of thebentonite and the different preparation. However, both datasets show the expected trendof a decreasing Cl - -accessible porosity with increasing dry density of the bentonite andwith decreasing NaCl concentration, and the data are closely matched by the modellines.Parts B, C and D in figures 3 and 4 illustrate the model’s distribution of the porosityover free porewater, interlayer and DDL- water, where the latter two are given by the2 nd and 3 rd terms of the right-hand side of Equation (11). In both datasets, the fraction ofinterlayer water increases, as expected, with decreasing NaCl concentration and withincreasing dry density. The fraction of DDL-water is substantial in Muurinen’sbentonite, but fairly small in the bentonite used by Van Loon et al. For NaCl concentrationsbelow 0.4 M, the fraction of DDL porosity increases markedly with decreasingNaCl concentration. Concomitantly, the anion-accessible porosity diminishes to verysmall values.
Page 1 and 2: Working Report 2013-29A Review of P
Page 3 and 4: 2Katsaus bentoniitin huokoisuuteen
Page 5 and 6: 21 INTRODUCTIONBentonite is foresee
Page 7 and 8: 42 POROSITY IN BENTONITELaboratory
Page 9: 6t IL = 1.41×10 -9 - 4.9×10 -13
Page 13 and 14: 10Figure 4. (A): Anion-accessible p
Page 15 and 16: 123 DIFFUSION IN BENTONITE: INTRODU
Page 17 and 18: 14Dp,iDa,i (22)Rwhere R is the reta
Page 19 and 20: 16In Equation (26) it is assumed th
Page 21 and 22: 18Figure 7. The effective diffusion
Page 23 and 24: 20The equivalent fraction of an exc
Page 25 and 26: 22Table 3. Concentrations, concentr
Page 27 and 28: 24Table 4. Specific volume and rela
Page 29 and 30: 26Furthermore, if the flux of Cs +
Page 31 and 32: 286 ACKNOWLEDGMENTSComments of Urs
Page 33 and 34: 30Doherty, J., 1994. PEST, Model-in
Page 35 and 36: 32Muurinen, A., Karnland, O. and Le

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