Numerical Investigations on the Transport Properties of Fractally Fractured Media

Many authors have been trying to set up general formulas for the pressure behavior of fractally fractured porous media using fractal diffusion theory, fractional calculus, etc. For incorporating the aperture variations, the waiting-time distribution concept (sites disorder model) has been introduced. However, the validity of the sites disorder model for actual diffusion phenomena on fractal media is still being disputed. This paper reviews recent analytical results and investigates the validity of the sites disorder approach in comparison to bonds disorder using numerical simulations. By comparing the results, it is found that the diffusion coefficient that contains diffusional memory is successfully described by the analytic prediction by Park et al. (1998), except for small values of r(2)/t(2/dw). Through the research, we find that the sites disorder approach can be a good candidate for incorporating the effect of aperture variations, although the approach produces a little larger modified diffusion exponent.