Submitted to: Water Resources Research
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: February 1, 2005
Publication Date: May 1, 2005
Citation: Jimenez-Hornero, F.J., Giraldez, J.V., Laguna, A., Pachepsky, Y.A. 2005. Continuous time random walks for analysing the transport of a nonsorbing tracer in a single fissure. Water Resources Research. 69:1-5.
Interpretive Summary: Choosing the correct model to predict contaminant transport in fractured media remains a challenging problem in subsurface hydrology. Transport depends on structure of media, and the arrangement of solid matter defines the shape of pores and relative mobility of contaminant particles in the pore space. Fissure-like pores are seemingly simple conduits of water and solutes. However, even in such simple conduits, differences in flow velocities near walls and in the middle of fissures may create differences in mobility of particles relative to the average flow velocity. Those differences would manifest themselves as non-Brownian movement of particles relative to the mean velocity flow. The objective of this work was to test the hypothesis that the solute transport in a fissure is a non-Brownian process, and therefore the applicability is limited for the classic advective-dispersive equation derived for Brownian movement hypothesis. To test this hypothesis, we applied the continuous random walk model. This novel transport model includes the advective-dispersive transport as a special case, and is also capable to simulate a broad class of non-Brownian transport. Fitting the CTRW to published experimental data showed that the solute transport in the fissure is indeed non-Brownian transport. We interpret this phenomenon as a result of the existence of sticking regions near the fissure walls where the diffusion is enhanced with respect to the advection.
Choosing the correct model to predict contaminant transport in fractured media remains a challenging problem in subsurface hydrology. In this work, the experimental data corresponding to nonsorbing tracer runs in natural fissures are analysed. The Advection Dispersion Equation (ADE) yields a relatively poor fit in the late time regions of the breakthrough curves denoting the existence of 'anomalous' or 'non Fickian' transport for the diffusive component of the flow. The objective of this work was to determine whether the Continuous Time Random Walks (CTRW) model can produce better fits to the observed breakthrough curves compared with the ADE model. Better performance of the CTRW model was found compared with ADE. In all simulations done with the CTRW model, superdiffusion is found which is interpreted as a result of the existence of sticking regions near the fissure walls where the diffusion is enhanced with respect to the advection.