An effective scale-dependent dispersivity deduced from a purely convective flow field

Abstract

In the case of straight flow but with hydraulic conductivity varying in a transverse direction, the distribution of hydraulic conductivity has been determined for which the breakthrough curve due to convection only will have the same analytical form as the onedimensional convection/dispersion equation solution at the outlet end of a porous medium. That distribution is found exactly and it is very similar to the lognormal distribution. This result is significant since field evidence indicates that the logarithm of hydraulic conductivity is normally distributed. For the case considered, a simple relation between dispersivity and the coefficient of variation of hydraulic conductivity is found. One can thus determine very simply dispersivity in terms of the parameters of the distribution of hydraulic conductivity. This is particularly useful to estimate dispersivity in various cells of finite difference or finite element models when the distribution of hydraulic conductivity is not stationary, i.e. varies in space. © 1992 Taylor & Francis Group, LLC.