Intrapore dispersion

Figure 25.1 Heterogeneity is one of the main properties of porous media it not only characterizes the scales shown in the figure, but also occurs on larger scales up to the size of the whole porous system. Three important mechanisms of transport and mixing in porous media are (a) interpore dispersion caused by mixing of pore channels (b) intrapore dispersion caused by nonuniform velocity distribution and mixing in individual channels (c) dispersion and retardation of solute transport caused by molecular diffusion between open and dead-end pores as well as between the water and the...

In porous media the flow of water and the transport of solutes is complex and three-dimensional on all scales (Fig. 25.1). A one-dimensional description needs an empirical correction that takes account of the three-dimensional structure of the flow. Due to the different length and irregular shape of the individual pore channels, the flow time between two (macroscopically separated) locations varies from one channel to another. As discussed for rivers (Section 24.2), this causes dispersion, the so-called interpore dispersion. In addition, the nonuniform velocity distribution within individual channels is responsible for intrapore dispersion. Finally, molecular diffusion along the direction of the main flow also contributes to the longitudinal dispersion/ diffusion process. For simplicity, transversal diffusion (as discussed for rivers) is not considered here. The discussion is limited to the one-dimensional linear case for which simple calculations without sophisticated computer programs are possible. 

Edis combines the effects of the different processes causing dispersion. For the case of inter/intrapore dispersion it is usually written as (Freeze and Cherry, 1979) ... 

The following assumptions were made in formulating this model 1) there is no solute adsorption to the stationary phase, 2) the porous particles which form the stationary phase are of uniform size and contain pores of identical size, 3) there are no interactions between solute molecules, 4) the mobile phase is treated as a continuous phase, 5) the intrapore diffusivity, the dispersion coefficient and the equilibrium partition coefficient are independent of concentration. The mobile phase concentration. Cm, is defined as the mass (or moles) per interstitial volume and is a function of the axial coordinate z and the angular coordinate 0. The stationary phase concentration, Cs, is defined as the mass per pore volume and depends on z, 6 and the radial coordinate, r, of a spherical coordinate system whose origin is at the center of one of the particles. 

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