Are We Describing Dispersion Correctly? Some Concerns

Abstract

There are many observations that the dispersion length increases with the observation distance in fractured rocks. This is contrary to the common assumption on which the advection-dispersion equation is based and casts doubt on its usefulness in extrapolation to longer distances. There are several mechanisms which can cause the observed effect. Three such mechanisms are discussed. In systems with strong channeling i.e. where the flow paths are essentially independent until their waters are mixed in the collection well the dispersion of the collected waters from the different paths will depend on the velocity distribution along the path ways. The “dispersion length” evaluated for this system will be proportional to the distance. Another mechanisms which will have similar effects is the matrix diffusion in a dual porosity system. The tracer diffuses in and out of the stagnant waters in the rock matrix. The larger contact surface between the flowing water and the rock in the longer paths will increase the interaction and cause “dispersion” in addition to the hydrodynamic dispersion. A third cause can be that in a self similar system the dispersion length also will be self similar and be a constant fraction of the scale of observation. There are observations indicating that there are self similar structures in fractured rocks.