Comparison of transport persistence and dispersion length for strongly heterogeneous conductivity fields

When modelling transport in fractured and other strongly heterogeneous media, the classical ADE-approach with a continuum dispersion coefficient is usually not applicable. This has led to the development of alternative approaches, often based on particle tracking. When upscaling travel time information by means of particle travel time distributions, it is, however, not obvious how the distributions of travel times among neighbouring elements should be spatially correlated. In our earlier works (Öhman et al, WRR 2005, WO3016, Oden at al. WRR 2008, WO2421) we have introduced the concept of transport persistence to account for this 'memory' of travel times. Transport persistence is a distance that, for example, a fast particle remains fast. The present study investigates the nature of transport persistence for different characteristics of the underlying hydraulic conductivity field - defined through the standard deviation and correlation length of K - and compares it to the classical dispersion length that can also be determined based on the statistical characteristics of the conductivity field. Flow and particle tracking simulations are carried out for heterogeneous conductivity fields for ten different combinations of standard deviation and correlation length values. Sixty realizations are considered for each combination, and for each realization a large number particles are released. The relationship between the transport persistence distance and the dispersion length is examined. Preliminary results indicate that the correlation between the two concepts depends on the values of the standard deviations of hydraulic conductivity, i.e., the degree of heterogeneity and transport channelling. Implications of these results will be discussed.