A 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.