Diffusion Modeling in Compacted Bentonite Based on Modified Gouy-Chapman Model
- PDF / 336,203 Bytes
- 7 Pages / 432 x 648 pts Page_size
- 97 Downloads / 208 Views
Diffusion Modeling in Compacted Bentonite Based on Modified Gouy-Chapman Model Kenji Yotsuji1, Yukio Tachi1 and Yuichirou Nishimaki2 1 Japan Atomic Energy Agency, 4-33, Muramatsu, Tokai, Ibaraki, 319-1194, Japan 2 Visible Information Center, Inc., 440, Muramatsu, Tokai, Ibaraki, 319-1112, Japan ABSTRACT The integrated sorption and diffusion (ISD) model has been developed to quantify radionuclide transport in compacted bentonite. The current ISD model, based on averaged pore aperture and the Gouy-Chapman electric double layer (EDL) theory can quantitatively account for diffusion of monovalent cations and anions under a wide range of conditions (e.g., salinity, bentonite density). To improve the applicability of the current ISD model for multivalent ions and complex species, the excluded volume effect and the dielectric saturation effect were incorporated into the current model, and the modified Poisson-Boltzmann equations were numerically solved. These modified models had little effect on the calculation of effective diffusivity of Sr2+/Cs+/I−. On the other hand, the model, modified considering the effective electric charge of hydrated ions, calculated using the Gibbs free energy of hydration, agreed well with the diffusion data including those of Sr2+. INTRODUCTION Diffusion and sorption of radionuclides in compacted bentonite are key processes in the safety of geological disposal of radioactive waste. The ISD model [1−4] gives consistent consideration to porewater chemistry, sorption and diffusion processes in compacted bentonite. The diffusion component based on the Gouy-Chapman EDL theory in the ISD model accounts consistently for cation De overestimation and anion exclusion in narrow pores. The key parameter of the diffusion model is an electrostatic constrictivity δel,i [-], related to De,i [m2 s−1] of species i by:
De,i
I
G g G el,i Dw,i W2
(1)
where ϕ is porosity [-], τ is tortuosity [-], δg is geometrical constrictivity [-] and Dw,i is tracer diffusivity of species i in bulk liquid water [m2 s−1]. The electrostatic constrictivity is the averaged ratio between the ionic concentration in the diffuse layer and in the bulk water, by taking into account the enhanced water viscosity by viscoelectric effects in the interlayers:
G el,i :
1 K 0 ni ( x) dx d ³0 K ( x) nb,i d
1 1 § e z \ ( x) · exp ¨ i ¸ dx d ³0 1 f ve (d\ dx) 2 kT ¹ © d
(2)
where ni(x), η(x) and ψ(x) are the local number density of ionic species i [m−3], the viscosity of the water [N s m−2] and the electric potential [V] in the interlayer at distance x [m] from the clay basal surface, respectively; nb,i and η0 are the corresponding number density and the viscosity of the water in the bulk, respectively; d is the interlayer width [m], zi is the valence of ionic species i [-], e is the absolute value of the elementary electric charge [C], k is the Boltzmann constant [J
123
K−1], T is the temperature [K], and fve is a viscoelectric constant (= 1.02×10−15 [m2 V−2], [5]). The Poisson-Boltzmann (P-B) equation, which describes the distribu
Data Loading...
