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Published as: Raoof, A. and Hassanizadeh S. M., “Upscaling Transport of Adsorbing
Solutes in Porous Media: Pore-Network Modeling”, Vadose Zone Journal, vol. 9, pp.
624-636, 2010.
CHAPTER 4
UPSCALING TRANSPORT OF ADSORBING
SOLUTES IN POROUS MEDIA: PORE-NETWORK
MODELING
Experience is a good school. But the fees are high.
Heinrich Heine
Abstract
The main objective of this research is to enhance our understanding of, and obtain
quantitative relationships between, Darcy-scale adsorption parameters and
pore-scale flow and adsorption parameters, using a 3D MDPN model. This involves
scale up from a simplified but reasonable representation of microscopic physics to
the scale of interest in practical applications. This upscaling will be carried out in
two stages: i) from a local scale to the effective pore scale, and ii) from effective the
pore scale to the scale of a core. The first stage of this upscaling, from local scale to
effective pore scale, has been discussed in Chapter 3. There, we found relationships
between local-scale parameters (such as the equilibrium adsorption coefficient, k d , and
the Peclet number, P e) and effective parameters (such as the attachment coefficient,
k att, and the detachment coefficient, k det ). Here, we perform upscaling by means of a
3D MDPN model, which is composed of a large number of interconnected pore bodies
(represented by spheres) and pore throats (represented by tubes). Upscaled transport
parameters are obtained by fitting the solution of the classic advection-dispersion
equation with adsorption to the average concentration breakthrough curves at the
outlet of the pore network. This procedure has resulted in relationships for upscaled
adsorption parameters in terms of micro-scale adsorption coefficient and flow velocity.