ABSTRACT
Two approaches to the subject of transport in fractal porous media have been derived using minimal assumptions. One is derived from a thermodynamics and statistical mechanics, and the other utilizes a continuum mechanics approach where the divergence of the velocity is a random function. This chapter explores three additional models of transport in fractal media. The Lagrangian perspective on fractional Brownian motion with a nonlinear clock can be clearly understood from the perspective of fractional Brownian motion combined. The primary purpose of the dispersive component in a transport model is to represent the unresolved portion of the velocity. The chapter presents a number of approaches for modeling transport in highly-heterogeneous, fractal velocity fields. The main drawback of these two approaches is that the transport equations are complex and involve integral kernels that cannot be readily estimated in many applications except through curve fitting.
