Estimation of dispersion coefficients from particle tracks

The rate of growth of variance (RGV) method and the integral of the velocity covariance function (ICF) method may both be used to estimate dispersion coefficients from particle tracks. It has been demonstrated that, in statistically homogeneous velocity fields, the ICF method of estimating the dispersion coefficient uses all available information on the particle- velocity autocovariance structure. In contrast, RGV method is shown to be equivalent to using only a limited, and less precise, estimate of the Lagrangian-velocity autocovariance function to estimate the dispersion coefficient. A typical example of dispersion in porous media is presented in which it is demonstrated that the ICF approach significantly improves estimation of the dispersivity tensor, for a given number of particle tracks. Finally, the results presented in this paper reinforce the fact that dispersion coefficients in nonhomogeneous velocity fields can only legitimately be estimated via the RGV method.