Scale-Dependent Porous Dispersion

This research monograph presents a new model to explain why the dispersion of solutes carried by flow through a porous medium, is observed to depend on the scale of the flow path, unlike predictions from simpler diffusion-like models. Stochastic partial differential equations are used to describe how microscopic displacements caused by pore walls, and macroscopic variations in flow velocity, interact. An analytic solution for accelerating flow is followed by a detailed analysis, first for velocity steps and then for stepwise velocity fluctuation profiles. Fluctuations enhance dispersion, and the cumulative effect of a long series of fluctuations causes a complex behavior of dispersion with the traversal length. A significant concept arising from the work is that of a natural length scale associated with velocity fluctuations, and which separates distinct short and long range dispersivity trends. Emphasis is placed throughout on formulating analytical models rather than numeric ones, to exploit their power to explain and interpret, rather than merely mimic measurements. The book endeavours to transmit insight into the underlying mechanisms, not just reproduce observations.