摘要: |
The transport and filtration of a particule-fluid mixture in porous media is a process of considerable importance in science and engineering. After nearly 100 years of intensive research, there are important theoretical and experimental aspects still unsolved. Not only is the complexity of the geometry of a porous medium a main problem, but, as recently discovered, the transport of mass or heat is strongly influenced by the presence of mechanisms that does not occur often. The purpose of this work is to analyze both theoretically and experimentally two mechanisms that are statistical improbable and one mechanism that is negligeable from the geometrical point of view. The first mechanism is related with the formation of arches between the grains of a porous matrix. The second mechanism is associated with the presence of preferential paths. The third and last mechanism is the leakage of an infinitely thin fracture in a earth dam. For each case the macroscopic flow was dramatically perturbed.
From the engineering point of view, the macroscopic description is in general the most interesting. However, the continuum approach is not adapted to describe mechanisms that involve a characteristic volume smaller than the representative elementary volume (REV). On the other side, the microscopic description is in general too complex for a direct analysis. This work is based on a mesoscale, also called mesoscopic, description of the flow of a particle fluid mixture through a porous matrix. The practical advantage of mesoscale experiments is obvious. However, the limited size of the experimental cell makes the extrapolation of the results to a macroscopic description more difficult.
Non-cohesive particles of mm-size were introduced at the top of a Hele- Shaw cell that contained cylindrical obstacles. An image analysis of the video frames, showed that a flow of the Darcy type still exists for the particles at mesoscale. The settling velocity is measured for different degrees of uniformity for the porous matrix. A maximum value of the settling velocity is identified with the formation of “trains” of particles that settle faster than single particles. Longitudinal and transversal velocities were measured and corrected from the settling velocity. The result is that there is no longitu dinal dispersion for the particles. One pore is filled before the next pore is invaded.
Particles that axe transported through a porous medium can be trapped in many different way^. The final outcome is usually the formation of clusters. Experiments show a subtle mechanism of trapping particles. The formation of arches between the grains of the porous matrix induces the formation of subclusters that finally agglomerate into large clusters. The growing rate of such clusters is mainly proportional to the number of subclusters.
Finally, a theoretical model of transport is applied to a pipe flow of a particle-fluid mixture. The velocity profiles for both phases are derived for the transverse and longitudinal directions of the flow for different fractions volume of particles. The velocity profiles in the transverse direction are similar with the experimental ones. On the other side, the velocity profiles in the longitudinal direction exhibit periodical oscillations located along the center line of the flow. This peculiar behavior should be validate experimentally.
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