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

17with increasing density of the bentonite. As noted by Bourg et al. (2003), the escalationof the tortuosity factor is due to the neglect of interlayer water which becomes the majorporosity type when density increases above 1800 kg/m 3 .Other models subdivide the effective diffusion coefficient in its components associatedwith free porewater, DDL water (usually denoted as surface diffusion), and interlayerwater (Eriksen et al. 1999; Bourg et al. 2006, 2007; Kozaki et al. 2008). The effectivediffusion coefficient becomes:D e, i = ε free D p, i + ε DDL D DDL, i + ε IL D IL, i (27)which for anions turns into (discussed in Section 5.1): freeD e ,i free D2 w,i(28)freeand for cations and neutral species:freeDDL ILD e ,i free DDL ILD 222 freeDDLILw,i(29)In these models, the concentration gradient in free porewater is used as the driving forcefor the diffusive flux. However, the concentration scales in the diffusion domains aredifferent, and, of course, the concentration gradient should be calculated in accordancewith that scale. Thus, as demonstrated in section 4.2, a fractional scale must be used forcalculating the concentration gradients for diffusion in interlayer water.Van Loon et al. (2007) measured the diffusion of 36 Cl - in bentonite at various NaCl concentrationand obtained anion-accessible porosities from the data, which are assumedhere to be equal to ε free . For a comprehensive dataset, they showed that the geometricalfactor for Cl - followed Archie’s law:1G 2 nfree(30)with n = 0.9 (Figure 7). Muurinen (1994) found a similar relation, but with n = 0.6. Theline given by Archie’s law in Figure 7 was forced to pass through the free water value,D w , Cl = 2.03×10 -9 m 2 /s. It can be seen that this forcing leads to a slight overestimate ofthe effective diffusion coefficient compared with experimental values and it may be thatthe real tortuosity is somewhat larger.