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PFG NMR study of hydrodynamic dispersion in porous media

Aimin Ding, University of Massachusetts Amherst


We have studied hydrodynamic dispersion in plastic bead packs using the pulsed field gradient (PFG) NMR technique. The bead diameter was varied from 15 to 138 $\mu$m and the Peclet number Pe varied from 0 to 10$\sp3$ (the Peclet number is a dimensionless measure of the flow velocity). We studied the time dependence of both the longitudinal dispersion coefficient $D\sb{\vert\vert}$ and the transverse dispersion coefficient $D\sb{\perp}.$ We observed transitions from decreasing with time at low Pe to increasing with time at high Pe for both $D\sb{\vert\vert}$ and $D\sb{\perp}.$ We used our data to find the transition time $t\sb0$ the time required for dispersion coefficient to reach its long time value. For both $D\sb{\vert\vert}$ and $D\sb{\perp}$, we found a power-law dependence of $t\sb0$ on Pe, as has been predicted by Koch and Brady. The Pe dependence of $t\sb0$ provides information on the operative dispersion mechanisms. Our results show that both convection dispersion and boundary layer dispersion contribute to longitudinal dispersion in our experiments. However, the Pe dependence of $t\sb0$ for transverse dispersion does not agree with the theoretical prediction of Koch and Brady. We measured $D\sb{\vert\vert}$ and $D\sb{\perp}$ as a function of Pe. Our experimental results are consistent with previous results measured using conventional methods. We found that the results for longitudinal dispersion agree with Saffman's capillary tube model in our observation range. The results for transverse dispersion agree with Koch and Brady's fixed bed model to some extent, but at low Pe, the disagreement is significant. We obtained the wave-number and frequency dependent nonlocal dispersion coefficient ${\buildrel{\approx}\over{D}}\sb{\vert \vert,\perp}(q,\omega)$ from our PFG NMR data. In the local (long time and distance) limit, our results agree with previous results obtained with conventional methods and for no flow they agree with a simple model of restricted diffusion. Our results for nonlocal dispersion with flow are in reasonable agreement with Koch and Brady's calculation based on a dilute-sphere approximation to the medium.

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Recommended Citation

Ding, Aimin, "PFG NMR study of hydrodynamic dispersion in porous media" (1997). Doctoral Dissertations Available from Proquest. AAI9809328.