download pdf version of PhD book - Universiteit Utrecht
download pdf version of PhD book - Universiteit Utrecht
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4.6 Conclusions<br />
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br />
4.6 Conclusions<br />
The transport <strong>of</strong> adsorptive solutes in porous media is a scale dependent process.<br />
We need to apply effective adsorption parameters at different scales.<br />
In our previous study [Rao<strong>of</strong> and Hassanizadeh, 2010a], we have shown that,<br />
starting from equilibrium at the local scale (at the wall <strong>of</strong> pores), the effective<br />
form <strong>of</strong> adsorption at the pore scale could be kinetic. In this study, using<br />
a MDPN model for simulating adsorptive solute transport, we have extended<br />
upscaling to the core scale for the case <strong>of</strong> saturated porous media with homogenous<br />
local-scale adsorption. In particular we have challenged the conventional<br />
view <strong>of</strong> reactive transport where a single adsorption parameter is used for the<br />
whole network. The model allows us to investigate how various micro-scale<br />
parameters affect transport properties <strong>of</strong> a medium.<br />
Different combinations <strong>of</strong> local-scale distribution coefficient and pore-scale velocity<br />
have been used to obtain upscaled adsorption parameters. Through this<br />
procedure, we found relationships between core-scale adsorption parameters<br />
and local-scale transport coefficients, including the molecular diffusion coefficient,the<br />
grain specific surface area, and average pore-throat size. We have<br />
shown that even if there is equilibrium adsorption at the pore wall (or at the<br />
grain surface), one may need to employ a kinetic description at larger scales.<br />
In contrast to some other studies, which reported dependency <strong>of</strong> reaction parameters<br />
on flow rate, we have shown that these kinetic parameters are only a<br />
weak function <strong>of</strong> velocity; in this aspect, our result is more in agreement with<br />
the study done by Zhang et al. [2008] and Zhang and Lv [2009] who have shown<br />
that adsorption parameters are not dependent on flow rate.<br />
Natural porous media are most likely to be heterogeneous with correlated spatial<br />
distributions. Therefore, treating adsorption as homogenous is an idealization.<br />
Quantifying adsorptive heterogeneity and also dependencies <strong>of</strong> adsorption<br />
parameters on velocity for the case <strong>of</strong> unsaturated porous media are areas that<br />
still need to be investigated.<br />
We should state that the statistical distributions (pore sizes, k d , coordination<br />
number, and etc) in this study have been uncorrelated, and under correlated<br />
distributions one may need more statistical parameters to define upscaled coefficients.<br />
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