Longitudinal Dispersion in Porous Media

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Longitudinal Dispersion in Porous Media

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1. Longitudinal Dispersion in Porous Media A. G. Hunt and T. E. Skinner Department of Physics Wright State University

2. What is “longitudinal dispersion?” It is what causes contaminant plumes to spread out in the direction of flow. The spreading is due to heterogeneity in the medium. Consider a (saturated) medium that is, at the pore scale, homogeneous in the mean. Heterogeneity comes from distribution of pore sizes (and shapes).

3. For such systems we know already K (the hydraulic conductivity) ? (the electrical conductivity) ka (the air permeability) D (the diffusion constants, solute and gas) Electromechanical properties Thermal conductivity (?) as functions of saturation.

6. Important Percolation Input Saturated K K (S) ? (S) kA (S) dispersion Competition Geometry (except very near threshold) Topology (almost all) Topology exclusively both

8. Two inputs to t(g)

17. Work left to do Tortuosity cannot actually diverge in a finite system. Compare and contrast with Stanley’s group, which uses a distribution of arrival times other than the optimal one, but does not use distribution of controlling conductances. Other?

18. Conclusions We have made an interesting start on a complicated problem. It is widely believed that the saturated hydraulic conductivity and dispersion are closely related: note that g value for which t has a local minimum is closely related to the optimal g value which defines the saturated hydraulic conductivity – it also produces a spike in solute arrival Whether specific results at this point are compatible with experiment is a little doubtful – the tail is probably not fat enough and it is not clear if such a spike as predicted has been observed.

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