Estimation of the Radionuclide Transport by Applying the Mean, the Standard Deviation and the Skewness of Permeability

Abstract

ABSTRACTA new method for estimating the mass transport by using the stochastic values (the arithmetic mean, the standard deviation and the skewness) of permeability is presented. Generally, detail of permeability distribution cannot be obtained except for moments of the distribution. Also, measurement results of permeability for the rock matrix including cracks or fast flowpaths do not always follow the log-normal distribution frequently applied. In such a situation, we must evaluate the characteristic permeabilities for the whole or some regions of the disposal site including the accessible environment.The authors have investigated the characteristic permeability on the basis of some probability density functions of permeability, applying the Monte Carlo method and FEM. It was found that its value does not depend on type of probability density function of permeability, but on the arithmetic mean, the standard deviation and the skewness of permeability [1].This paper describes the use of the stochastic values of permeability for estimating the rate of radioactivity release to the accessible environment, applying the advection-dispersion model to two-dimensional, heterogeneous media. When a discrete probability density function (referred to as ‘the Bernoulli trials’) and the lognormal distribution have common values for the arithmetic mean, the standard deviation and the skewness of permeability, the calculated transport rates (described as the pseudo impulse responses) show good agreements for Peclet number around 10 and the dimensionless standard deviation around 1. Further, it is found that the transport rates apparently depends not only on the arithmetic mean and the standard deviation, but also on the skewness of permeability. When the value of skewness dose not follow the lognormal distribution which has only two independent parameters (the mean and the standard deviation), we can replicate the three moments estimated from an observed distribution of permeability, by using the Bernoulli trials having three independent parameters.