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

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11linearly with the NaCl concentration, in Muurinen’s data the increase flattens out. Thus,in Van Loon’s data the osmotic component is more important than in Muurinen’s, inwhich the DDL parameter predominates (Table 1). It may be that the preparation, or rather,the lack of preparation of the bentonite bears upon these results. The Volclay usedby Van Loon contains calcite and perhaps gypsum, which dissolve more when the ionicstrength increases. The increasing Ca 2+ concentration may cause the interlayer space tocollapse, thus causing the free porosity to increase with ionic strength (Dufey et al.1976). Muurinen washed MX80 bentonite with NaCl solution and may have removedthe more readily dissolving minerals. Muurinen (2007) also experimented withbentonite that was washed with distilled water, and observed that the Cl - -accessible porositieswere smaller than without washing.Table 1. Fit-parameters for the Cl - -accessible porosity measured by Muurinen (2006)and Van Loon et al. (2007) as a function of the dry density of bentonite. The fitparametersallow to obtain the internal planar, and total external surface of themontmorillonite, and to estimate the stacking number in the c direction.Muurinen(2006)Van Loon etal. (2007)ρ dry(kg/m 3 )a 0_IL(-)a osm(mol/L) -1a DDL(mol/L) -0.5A planar,int(m 2 /g)A ext(m 2 /g)1280 ± 80 0.162 -0.0106 0.0749 402 2371580 ± 40 0.192 -0.00856 0.0575 476 1471700 ± 70 0.299 -0.0128 0.0363 583 861300 0.478 -0.321 0.00312 1250 111600 0.388 -0.0632 0.00291 1073 81900 0.300 -0.0244 0.00157 921 4n c2.6>100
123 DIFFUSION IN BENTONITE: INTRODUCTIONThe diffusional flux of species i is given by:Jiuicii | z | F xi(14)where J i is the flux (mol/m 2 /s), u i is the mobility (m 2 /s/V), c i is the concentration(mol/m 3 ), z i is charge number (-), F is the Faraday constant (96485 J/V/eq), x is distance(m), and μ i is the thermodynamic potential, given by:μ i = μ i 0 + RT ln a i + z i Fψ (15)where μ i 0 is the standard potential (J/mol), R is the gas constant (8.314 J/K/mol), T isthe absolute temperature (K), a i is the activity (-), and ψ is the electrical potential (V).The activity is related to concentration by a i = γ i c i /c 0 , where γ i is the activity coefficient(-) and c i 0 is the standard state (1 mol/kg H 2 O, assumed equal to 1 mol/L in the following).Assuming an activity coefficient γ i = 1 and an electric potential gradient ∂ψ/∂x = 0, andusing the identities u i = D w, i |z i | F / (RT) and c d(ln c) = d(c), Equation (14) becomes:Jidci Dw,i(16)dxwhere D w,i is the diffusion coefficient in water (m 2 /s) and c i has units mol/m 3 . In a porousmedium, the porewater diffusion coefficient differs from the diffusion coefficientin free water (D w,i ) by tortuosity and constrictivity factors (Van Brakel and Heertjes,1974; Figure 5):D p ,i D2 w,i(17)The tortuosity factor (θ 2 ) expresses that diffusing molecules have to pass around solidgrains and take a longer path (L a ) than the straight line distance (L) (Figure 5). A tortuouspath at an angle of 45° with the straight line distance obviously gives a tortuosity θ= 2 / √2 = 1.4, and a tortuosity factor θ 2 = 2. The constrictivity factor (δ) encompasseseffects of pore narrowing and widening. A straight pore has a constrictivity factor of 1,if the pore narrows it becomes smaller than 1, and if it widens, larger than 1. Inert porousmedia have constrictivity factors slightly smaller than 1 (Van Brakel and Heertjes1974). However, in bentonite where DDL water occupies part of the pore space, porenarrowing that results in overlapping DDL’s has a different effect for cations and neutralspecies that still can pass through, and for anions for which the constriction becomesan obstruction that has to be circumnavigated. In that case the constrictivity issmaller for anions than for cations and neutral species, while at the same time, for anionsthe tortuosity increases.
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 and 10: 6t IL = 1.41×10 -9 - 4.9×10 -13
Page 11 and 12: 8data are few and not very precise
Page 13: 10Figure 4. (A): Anion-accessible p
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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