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

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21The tortuosity factor for the combination of free porewater and DDL water is δ/ θ 2 = ε =0.1. The same factor is used for interlayer water as well, in accordance with estimatesfrom MD calculations for 2-layer hydrated montmorillonite.The concentrations and gradients in the 3 water types can be calculated with PHREEQCand are given at x = 1 m in Table 3. The steady-state fluxes then follow using Equations(35, 36 and 40), for example for Cs:3152210 4 1410mol/m /s19free Cs 0.01 2.0710.(35a)10J ,J DDL , Cs219 2 43 10 0 09 2 07 10 . . . 31010. 3132210 90510mol/m /s(36a)197142IL Cs 0.3 2.071049383.2310 9.9110mol/m /s (40a)10J ,The fluxes are also listed in Table 3.The concentration gradient of Cs + in free porewater is -2×10 -3 mol/m 4 , and near-zero ininterlayer water. Thus, most diffusive transport of Cs + takes place through freeporewater and DDL water. The flux in DDL water is 219 times higher than in freeporewater because the porosity is 9 times, and the concentration 24 times higher forDDL water. On the other hand, the flux of I - in DDL water is 2.7 times smaller than infree porewater because the concentration is 24 times smaller than in free porewater. Theconcentration gradient of Sr 2+ in free porewater is also -2×10 -3 mol/m 4 (negative), but ininterlayer water the gradient of the exchange fraction is positive. Thus, transport of Sr 2+through interlayer water is in opposite direction of transport through interlayer water.The different behavior of Cs + and Sr 2+ is a consequence of the law of mass action,which favors higher charged cations on exchange sites when the free porewater solutionis diluted. The Sr 2+ concentration gradient is also positive in DDL water, but compensatedthere by the negative potential gradient which results in a positive flux. Overall,the flux through interlayer water dominates, and the flux of Sr 2+ is predicted to be negative.
22Table 3. Concentrations, concentration gradients and fluxes in porewater, DDL waterand interlayer water in a column filled with bentonite packed to a dry density of 1700kg/m 3 with a steady state flux of background NaCl (gradient of -200 mol/m 4 ) and oftrace concentrations of I - , Cs + and Sr 2+ . Calculations with PHREEQC (Parkhurst andAppelo, 1999).0.1 M NaCl1 μM I - , Cs + , Sr 2+ gradient ε 2D w(10 -9 m 2 /s)Flux(mol/m 2 /s)Free porewater mol/m 3 mol/m 4I - 10 -3 -2×10 -3 0.01 0.1 2.03 4.06×10 -15Cs + 10 -3 -2×10 -3 0.01 0.1 2.07 4.14×10 -15Sr 2+ 10 -3 -2×10 -3 0.01 0.1 0.794 1.59×10 -15DDL water mol/m 3 mol/m 4 or V/mI - 4.12×10 -5 -1.65×10 -4 0.09 0.1 2.03 1.50×10 -15Cs + 2.43×10 -2 -2.36×10 -5 0.09 0.1 2.07 9.05×10 -13Sr 2+ 0.59 +1.18 0.09 0.1 0.794 8.43×10 -12ψ / V 0.082 -0.051Interlayer water β (-) 1/mCs + 1.99×10 -4 -3.23×10 -7 0.3 0.1 2.07 9.91×10 -14Sr 2+ 8.11×10 -4 +1.62×10 -3 0.3 0.1 0.794 -9.51×10 -11
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 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: 20The equivalent fraction of an exc
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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