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We investigate colloid-facilitated contaminant advection in strongly heterogeneous geological medium with fractal properties. Transport regimes and asymptotic behavior at large distances are studied for different relationships between sorption parameters and characteristics of percolation medium. Crossover times between transport regimes are determined.

The problem of tracer advection in random self-similar (fractal) media with strong anisotropy is solved. Transport regimes and concentration tails are described depending on the rate of velocity correlation function decay and on the degree of anisotropy. The influence of the finite correlation length of the fractal medium on transport regimes is analyzed. The derivation is conducted by means of scaling analysis.

We investigate tracer advection in fractal media with finite correlation length. The process is superdiffusive at early times and transforms to a classical diffusion regime later. At large time the spatial tail of the concentration has a two-stage structure with a long-distant part corresponding to superdiffusive regime.

The problem on passive scalar advection in random (statistically homogeneous) self-similar media is solved. Even in superdiffusive mode the solution is found not to possess "heavy" power tails. Instead, they are exponential (not Gaussian). The derivation is conducted by means of the scaling analysis.