longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
longitudinal dispersion in nonuniform isotropic porous media
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155<br />
CHAPTER 6<br />
SUMMARY AND CONCLUSIONS; SUGGESTIONS FOR FUTURE RESEARCH<br />
Longitud<strong>in</strong>al <strong>dispersion</strong> <strong>in</strong> flow through <strong>nonuniform</strong> <strong>porous</strong> <strong>media</strong><br />
has been studied theoretically and experimentally. An analysis to<br />
<strong>in</strong>clude the effect of <strong>nonuniform</strong> gra<strong>in</strong> size was developed from<br />
Saffman's (1959) random capillary tube model for passive solutes<br />
flow<strong>in</strong>g through homogeneous, <strong>isotropic</strong>, unconsolidated <strong>porous</strong><br />
materials. Miscible displacement experiments were carried out on two<br />
sands <strong>in</strong> order to test the theoretical model. The experiments also<br />
demonstrated asymmetrical breakthrough curves which could not be<br />
described by advection-diffusion theory.<br />
6.1 SU,tqrqary and, CO,Ilc.1us,ipIlI:!. .fu.!. lli Invest,i,gat,io,Il .Qi L,o,n,git,lJ,d"<strong>in</strong>al<br />
Di,s,pers,ion<br />
The theoretical model of <strong>longitud<strong>in</strong>al</strong> <strong>dispersion</strong> developed here<br />
may be used to predict the asymptotic <strong>longitud<strong>in</strong>al</strong> <strong>dispersion</strong><br />
coefficient based on the measured permeability, pore radius<br />
distribution, gra<strong>in</strong> size distribution, and Peclet number of the flow<br />
(v diD).<br />
s g<br />
No free parameters are used to fit the calculated<br />
<strong>longitud<strong>in</strong>al</strong> <strong>dispersion</strong> coefficients with the measured values.<br />
Therefore, this <strong>dispersion</strong> theory is based on measurable structural<br />
features and the permeability. The permeability is required to fix a<br />
parameter; the junction connectivity, to obta<strong>in</strong> a proper flow<br />
distribution through the various sized pores. The follow<strong>in</strong>g features<br />
have been added to the Saffman (1959) model:
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