The present study consists of an experimental investigation of dispersion in inhomogeneous layered, isotropic porous media.
Thanks to an in situ method of measuring electrical conductivity, we have studied two layered models. We examine four different layouts. The first sample has three layers of different permeabilities. The second has only two layers. Furthermore. two models with layers oriented perpendicular to the flow are considered.
Besides normal "gaussian" dispersion, clear cut anomalies were observed. The experimental breakthrough curves are skewed as a consequence of tracer tailing.
Tailed breakthrough curves are known from displacement in cores with local heterogeneity. Good agreement has been obtained between the experimental results and the semiphenomenological model of Coats Smith. Thus~ the mechanism involved in this anomalous dispersion is not trapping in the so-called dead end pores, but rather is due to different residence times because of permeability difference.
The mixing of a tracer during flow through a porous medium involves the interplay between the two basic phenomena of dispersion, namely, molecular diffusion and mechanical (geometrical) dispersion. If two miscible fluids are in mutual contact. initially with a shaped interface, they will diffuse into one another because of random molecular motion according to the diffusion law of Fick1:: Equation (1) (Available in full paper)
To account for the tortuous path of a porous medium, equation (I) was modified by Klinkenberg2, who used the analogy with electrical conductivity, thus: Equation (2) (Available in full paper)
Do thereby corresponds to the bulk molecular diffusion coefficient for the fluid multiplied by the geometric factor (F Ø). The formation factor is F= σ o / σ, were σ denotes the electrical conductivity of a rock saturated with a fluid of conductivity σOØ. is the porosity of the rock.
Molecular Diffusion is the dominant factor at extremely low or zero flow rate. At a higher flow rates, fluid flow plays a key role: there is a competition between the dispersive effect of the velocity gradients in the flow, and the various processes that homogenize the tracer (diffusion and transverse dispersion) across the porous media. The dimensionless Peelet number, which is the ratio of convective velocity U to the average velocity of molecular diffusion over a distance I characterizes this competition. Thus: Equation (3) (Available in full paper)
This further mixing. which occurs in the direction of flow (axial) and perpendicular to it (transversal) is due to the combined action of three boundary effects:
- hydrodynamic dispersion: This mechanism was first described by Taylor3; the velocity is zero on the matrix surface. which creates a velocity gradient in the fluid phase. The characteristic time of homogenization - τ - (a2/D) - is associated with the molecular diffusion of the tracer across the width of the pore. Aris4 found the following for low velocities, where molecular diffusion is dominant: Equation (4) (Available in full paper)
- geometric dispersion: