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

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13Figure 5. (Left:) The tortuosity is the ratio of traveled and straight-line distance,squared in the tortuosity factor (Appelo and Postma, 2005). (Right:) Overall picture ofthe porosity in clay, showing changes in pore-width (constrictivity). Overlapping doublelayers at pore constrictions increase the tortuosity for anions (Appelo et al. 2008).The quotient of the constrictivity and tortuosity factors is assembled in the geometricalfactor (G i ) which is related by Archie law to the accessible porosity (ε a,i ) (Van Loon etal., 2007; Grathwohl 1998): 12Gi na,i(18)where n is an empirical factor (≈ 1).In the flux equation, the porewater diffusion coefficient of the porous medium (D p,i ) iscorrected for the surface area that is accessible for the solute. Thus:D e, i = D(19)a,ip, iCombining Equations (16-19) gives the flux in terms of the known diffusion coefficientin free water and accessible porosity as:Ji1 n dci a,iDw,i(20)dxOften in experiments, the concentration profile in the bentonite is measured and interpretedin terms of an apparent diffusion coefficient:citDa,i2ci2x(21)where D a,i is the apparent diffusion coefficient (m 2 /s), and where c i can be the concentrationin porewater as before, or the concentration in the bulk volume (= ε a, i c i ) asmeasured easily when i is a radioactive tracer. The apparent diffusion coefficient includesthe effects of retardation by sorption, ion-exchange, and/or precipitation and dissolution:
14Dp,iDa,i (22)Rwhere R is the retardation (-), given by:Rddsi 1(23) dca,iiwhere ρ d is the dry density of solid (kg/m 3 ) and s i the concentration in the solid(mol/kg). Usually for tracers, the slope of the isotherm (ds i / dc i ) is constant and can beestimated. For Na-montmorillonite it is (Appelo and Postma 2005):z idsiCEC KI\KdcizNa i a(24)d 1000 Na where K d is the distribution coefficient (m 3 /kg), CEC is the cation exchange capacity (≈1 eq/kg for montmorillonite), K I\Na is the exchange constant (-), and a Na is the activity ofNa + in free porewater, in the first instance about equal to the NaCl concentration. Valuesof K I\Na are given by Appelo and Postma (2005).Altogether, Equations (21-24) relate the changing concentration of a tracer with timeand the porewater diffusion coefficient as:cita,ia,iDdp,iKd2ci2x(25)The apparent diffusion coefficient in Na-montmorillonite can be found from:Da,ia,i d1na,i10z3iDw,i K aI\ NaNaz i(26)Equation (26) contains terms that should be known for the experiment or can be lookedup, and is useful for obtaining first estimates.Figure 6 compares measured apparent diffusion coefficients of Na + , Cs + and Sr 2+ withvalues estimated by Equation (26), using the parameters listed in Table 2. The values forArchie’s exponent n, and the sodium activity a Na were adapted to obtain a visual agreement(the Na + concentration is unknown). The Na + and Cs + data are from Kozaki et al.(1998) who removed excess salt from the (Kunipia) bentonite by dialysis after having itwashed with NaCl solution, while the Sr 2+ data stem from Sato et al. (1992) who useddistilled water for saturation only and did not prepare the bentonite. This could explainthe higher activity of Na + in the experiments of Sato, but it may be that also other cationsare present in the porewater. The values for Archie’s n are low (meaning that thetortuosity is small).
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 and 14: 10Figure 4. (A): Anion-accessible p
Page 15: 123 DIFFUSION IN BENTONITE: INTRODU
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

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

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