Fluid Flow and Solute Transport in Fractal Heterogeneous Porous Media: Fid-Bau Portal

Fluid Flow and Solute Transport in Fractal Heterogeneous Porous Media

Wheatcraft, S. W. / Sharp, G. A. / Tyler, S. W.

Abstract We examine the nature of flow and transport in fractal porous media from an Eulerian point of view. The fundamental assumption is that the conventional advection-dispersion equation is valid on the local scale and that field-scale dispersion is a differential advection process driven by field-scale heterogeneity. This approach is common to most modern stochastic transport theories. Local diffusion is set to zero so that macrodispersion is caused entirely by differential advection. The Sierpinski carpet is used to simulate a deterministic binary hydraulic conductivity distribution that resembles low permeability “pebbles” embedded in a higher permeability matrix. Particle tracking experiments are conducted to determine the effect of scale and the effects of passing from a small scale of heterogeneity to a larger scale. Arrival time variances follow the fractal scaling relationships of simpler fractal models, with an exponent greater than two. Growth of dispersivity also follows a power law relationship with an exponent larger than one, as predicted by simpler fractal models. The fractal dimensions of tracks of individual particles are compared to the average fractal dimension of the entire particle swarm, as determined by the arrival time distributions and the fractal scaling relationships. The average fractal dimension agrees well with the individual fractal dimensions of particle tracks, as determined by ruler and box counting methods. The most important result is that a fractal hydraulic conductivity distribution used in a conventional transport model will produce results that are consistent with fractal scaling ideas.