Taylor dispersion in porous media. Determination of the dispersion tensor

Abstract

In homogeneous porous media, the analytical expression of the dispersion tensor D* can be calculated by the method of moments and by a multiple scale expansion; the symmetric component of this tensor is identical in both cases. Numerically, D* can be computed by two methods, namely the B equation and random walks. The porous media are modeled as being spatially periodic; D* is determined as a function of the Péclet number for four types of unit cells: deterministic, fractal, random, and reconstructed. A systematic comparison is made with existing numerical and experimental data. The long time behavior, and its Gaussian limit, is documented.

The impact of inertial effects on solute dispersion in a channel with periodically varying aperture

“…This includes, but is not limited to micro fluidic systems, 2, 3 nutrient transport in bloodflow, 4,5 single and multiphase transport in porous media, [6][7][8][9][10][11][12] and transport in groundwater systems. [13][14][15][16] The basic idea behind Taylor dispersion is simple.…”

Influence of Stagnant Zones on Transient and Asymptotic Dispersion in Macroscopically Homogeneous Porous Media

“…In particular, the influence of stagnant zones with respect to the actual mesoscopic and macroscopic flow field heterogeneity of the medium has found little attention in theory and experiment, and furthermore, the additional length and time scale associated with transport in stagnant regions complicates numerical simulations. Therefore it leaves the controversy about the dominating contribution to dispersion and the origin of long-time tails in residence-time distributions unresolved [3,7,14], let alone the question whether hydrodynamic dispersion coefficients exist at all [13]. In this Letter, we are able to resolve this issue experimentally and numerically for a macroscopically homogeneous medium by considering transient and asymptotic dispersion in a random packing of porous spheres, i.e., in a medium with bimodal porosity and associated length scales that differ by orders of magnitude.…”

“…For example, natural and industrial materials such as soil, rock, filter cakes, or catalyst pellets often contain lowpermeability zones with respect to hydraulic flow of liquid through the medium or even stagnant regions which then remain purely diffusive. The relevance of stagnant zones stems from their influence on dispersion: Fluid molecules entrained in the deep diffusive pools cause a substantial holdup contribution and thereby affect the time scale of transient dispersion, as well as the value of the asymptotic dispersion coefficient (if the asymptotic long-time limit can be reached at all) [2][3][4]. Consequently, the associated kinetics of mass transfer between fluid percolating through the medium and stagnant fluid becomes rate limiting in a number of dynamic processes, including the separation and reaction efficiency of chromatographic columns and reactors, or economic oil recovery from a reservoir.…”

“…In many situations, however, both a macroscopic flow heterogeneity and solute trapping in stagnant zones contribute to transient and asymptotic dispersion [3,7,9].…”

Influence of the disorder on solute dispersion in a flow channel

“…In some specific configurations such as flow in a capillary tube [14,15], in a periodic square array of beads [9,16] or in a fracture [5,6,7], the velocity field has long range correlations. In such media, the flow velocity difference between the walls bounding the open space and its center stretches the tracer front and creates concentration gradients: The latter are balanced by molecular diffusion across the gradient.…”