Joel Koplik and German Drazer,
City College of the City University of New York
Jean Pierre Hulin, Laboratoire FAST, Orsay, France
Jysoo Lee, Korea University, Seoul

Research Objectives

We are concerned with two related topics involving the motion of particulate matter in porous media formations of relevance to transport in industrial and geological porous media: (1) A quantitative study of the dynamics of deep bed filtration-filtering suspended particles from a solvent when the mixture passes through a porous medium. We aim to determine how the parameters of the process such as flow rate, filtrate concentration, and porous medium structure control the efficiency of filtration, the time scales for the process, and the spatial distribution of the deposit. (2) A study of flow, passive tracer dispersion, and depositional processes in the self-affine fractures often observed in naturally fractured rock. In such systems the rock surfaces have long-range correlations which have been shown to significantly enhance and modify the dynamics of passive tracers used as diagnostic tools. We further wish to examine the motion of rock suspended in flowing fluid in fractured geological formations, and in particular study the evolution of the fractured pore space as deposition occurs.

Computational Approach

In statistically isotropic and homogeneous porous media, transport properties are readily obtained from an equivalent network description in which the pore space is modeled as a "ball and stick" network with appropriately sized elements and connection topology. The relevant network-scale simulations of particle deposition may then be formulated as a time-sequence of analog resistor network problems, and amount to averaging over solutions of large sets of linear algebraic equations. The problem of flow and particle deposition in self-affine fractures occurs at a different scale, and the problem here is to efficiently solve for the flow in a highly irregular and evolving geometry. This case is treated using the lattice Boltzmann method, which is optimal for flow problems in complicated regions because only a geometrical specification of the solid region is needed.

Accomplishments

We have completed and published the initial work needed for both problems. In porous medium filtration, we have determined the junction rules for particle motion around grains in a porous medium, and can now abstract the local geometry into a suitable random network. In fracture flow, we have performed the initial (approximate) simulations showing that self-affine fractures lead to enhanced dispersion, and have modified a borrowed lattice Boltzmann code for the purpose of systematically studying passive tracer dispersion as well as the behavior of suspended particles large enough to modify the flow field.

Examples of flow in a self-affine fracture. A granite rock is fractured to produce a self-affine surface which is used as a mold for a transparent plastic copy. The rock and its copy are placed in register and then separated vertically to give a self-affine fracture. Fluid is injected through the center and flows out to the boundaries, and images of the front at two successive times are taken from above. The difference in the images indicates the location of the moving front. In Figure 1, the surfaces are simply separated vertically, producing a roughly circular outgoing fluid front. In Figure 2, however, the surfaces are shifted laterally, leading to a surprisingly strong anisotropic flow. (Figures provided by Harold Auradou and Jean Pierre Hulin, Laboratoire FAST.)

Significance

The efficient extraction of water and hydrocarbon resources from underground reservoirs, as well as the use of underground formations as waste disposal sites, requires a full understanding of the dynamics of the flow of fluids and various suspended matter in the disordered porous media which comprise geological formations and reservoirs. This research studies the transport and deposition of solid particulates which may clog or perhaps break open new flow channels in these systems, and the effects of subtle correlations resulting from fracture processes on tracer tests. In addition, some of the results are relevant to commercial filtration processes used in purification and manufacturing.

Publications

J. Lee and J. Koplik, "Microscopic motion of particles passing through a porous medium," Phys. Fluids 11, 76 (1999).

F. Plouraboue, J. Koplik, J. P. Hulin, and S. Roux, "Numerical study of geometrical dispersion in self-affine rough fractures," Phys. Rev. E 58, 3334 (1998).

S. Rojas and J. Koplik, "Nonlinear flow in porous media," Phys. Rev. E 58, 4776 (1998).