download pdf version of PhD book - Universiteit Utrecht

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
pore-scale adsorption coefficient and corresponding upscaled attachment and
detachment adsorption parameters. The upscaled adsorption parameters are
found to be only weak functions of velocity; they strongly depend on geometry
of the pore and diffusion coefficient in the solution as well as the pore-scale distribution
coefficient. Results of two approaches (i.e., theoretical averaging and
numerical upscaling) agree very well. The upscaling relations from this chapter
are appropriate to be used within models in which subpore scale concentration
gradients are neglected.
Chapter 4 continues the upscaling process, going from effective pore scale
to the core scale where Darcy-scale flow and transport parameters are applied.
This is done by utilizing the upscaling relations developed in Chapter 3 and
applying them to the MDPN model developed in Chapter 2. This enabled us to
scale up from a simplified but reasonable representation of microscopic physics
to the scale of interest in practical applications. This procedure has resulted
in relationships for core scale adsorption parameters in terms of micro-scale
parameters. We found relations between core-scale adsorption parameters and
local-scale transport coefficients, including molecular diffusion coefficient, specific
surface area, and average pore-throat size. Results of Chapter 4 show that,
even if there is equilibrium adsorption at the pore wall (i.e., grain surface), one
may need to employ a kinetic description at the larger scales. In contrast to
some other studies that reported dependency of reaction parameters on flow
rate, we found that that these upscaled kinetic parameters are only a weak
function of velocity.
Part III: Upscaling under partially-saturated conditions
Part III (Chapters 5 through 7) deal with pore-scale modeling of adsorptive
transport under partially saturated conditions.
Chapter 5 presents a new formulation for pore-network modeling of twophase
flow. Pore-network models of two-phase flow in porous media are widely
used to investigate constitutive relationships between saturation and relative
permeability as well as capillary pressure. Results of many studies show discrepancy
between calculated relative permeability and corresponding measured
values. An important feature of almost all pore-network models is that the resistance
to flow is assumed to come from pore throats only; i.e., the resistance
of pore bodies to the flow is considered to be negligible compare to the resistance
of pore throats. We have shown that the resistance to the flow within
filaments of fluids in drained pore bodies is comparable to the resistance to the
197