It is known that dispersion in porous media results from an interaction
between convective spreading and diffusion. However, the nature and
implications of these interactions are not well understood. Dispersion
coefficients obtained from averaged cup-mixing concentration histories have
contributions of convective spreading and diffusion lumped together. We
decouple the contributions of convective spreading and diffusion in core-scale
dispersion and systematically investigate interaction between the two in
detail. We explain phenomena giving rise to important experimental observations
such as Fickian behavior of core-scale dispersion and power-law dependence of
dispersion coefficient on Péclet number.
We track movement of a swarm of solute particles through a physically
representative network model. A physically representative network model
preserves the geometry and topology of the pore space and spatial correlation
in flow properties. We developed deterministic rules to trace paths of solute
particles through the network. These rules yield flow streamlines through the
network comparable to those obtained from a full solution of Stokes' equation.
Paths of all solute particles are deterministically known in the absence of
diffusion. Thus, we can explicitly investigate purely convective spreading by
tracking the movement of solute particles on these streamlines.
Then, we superimpose diffusion and study dispersion in terms of interaction
between convective spreading and diffusion for a wide range of Péclet numbers.
This approach invokes no arbitrary parameters, enabling a rigorous validation
of the physical origin of core-scale dispersion. In this way, we obtain an
unequivocal, quantitative assessment of the roles of convective spreading and
diffusion in hydrodynamic dispersion in flow through porous media.
© 2010. Society of Petroleum Engineers
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- Original manuscript received:
8 July 2008
- Meeting paper published:
22 September 2008
- Revised manuscript received:
11 February 2010
- Manuscript approved:
4 May 2010
- Published online:
4 October 2010
- Version of record:
15 March 2011