Effects Of Matrix Diffusion Research Articles

Migration of radionuclides in fissured rock: The influence of micropore diffusion and longitudinal dispersion

The migration of radionuclides in the fissures in the bedrock surrounding a repository is discussed. A one‐dimensional transport model is presented. It includes diffusion of the nuclides into the microfissures of the rock, and linear sorption, and longitudinal dispersion in the bedrock. An analytical solution to the model is given in terms of an infinite integral. The integrand is a sometimes highly oscillatory function of the system parameters. A special integration method is developed to evaluate the infinite integral. The method utilizes the oscillatory behavior of the integrand. The assessment of input parameters is discussed in some detail. Dimensionless breakthrough curves are given for the approximate range of variation of the input parameters. Calculations are made for a repository of spent fuel surrounded by fissured but fairly good rock (Kp = 10−9 m/s and fissure spacing S = 50 m). Longitudinal dispersion may significantly affect the amount of radioactive material reaching the biosphere. Radionuclides, which would decay completely without longitudinal dispersion, may arrive in nonnegligible concentrations. Dispersion effects of the magnitude considered in this study can significantly diminish the retardation effects of matrix diffusion.

Solute transport through fractured media: 1. The effect of matrix diffusion

Solute transport through fractured media is described by numerically combining advective‐dispersive transport, which is dominant in the fractures, and diffusive transport, which is usually dominant in the unfractured matrix. Transport is considered in a manner conceptually similar to ‘double‐porosity’ or ‘intra‐aggregate’ transport models. A finite element model is developed for simulating nonreactive and reactive solute transport by advection, mechanical dispersion, and diffusion in a unidirectional flow field. The effect of the value of the solute diffusion coefficient in the matrix (termed the matrix diffusion coefficient) is illustrated by solute breakthrough curves and concentration profiles in the fracture as well as in the matrix. The illustrated conditions are similar to the laboratory tracer study on fractured till described in the accompanying paper (Grisak et al.). The effects on solute transport of fracture aperture size, water velocity in the fracture, matrix porosity, matrix distribution coefficient, and dispersivity in the fracture are illustrated with breakthrough curves and concentration profiles. The net effect of large matrix diffusion coefficients and/or large distribution coefficients in the matrix is to reduce significantly the effective solute velocity in the fracture. Reduction in the effective solute velocity can also be seen to be possible in materials with low matrix porosities such as crystalline rocks. The aperture size, matrix porosity, matrix diffusion coefficient, and distribution coefficient, all are important in determining the relative amounts of solute transported in the fracture and stored in the matrix. Implications with regard to aquifer recharge, groundwater chemistry, contaminant transport, tracer tests, and groundwater age dating in fractured media are discussed. The numerical model and the laboratory tracer test data provide considerable insight into the processes controlling solute transport in fractured media.