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Dynamics of two-fluid interfaces in porous media

Shankar Ghosh

23 June 2011

Experimentally obtained 3-D images of oil (shown in red) displacing a more viscous immiscible fluid (not shown) in a porous medium for increasing flow rates from left to right.

A porous medium is a material containing large number of randomly located voids (pores) of sizes greater than the microscopic interatomic scale such as wood, sponge, rocks etc. Flow of fluids through such porous media is of interest to many scientific and engineering disciplines. For example, petroleum engineers study the flow of water through rocks containing oil and gas, chemical engineers are interested in separation processes in packed-bed reactors, hydrologists are concerned with flow of water and contaminants through soil, geologists and geophysicists study the flow of molten magma in the mantle. We have studied the motion of two-fluid interfaces in a model porous media made by packing spheres in a pipe during the displacement of one fluid by another. If a less viscous fluid displaces a more viscous one in a pipe or in a porous medium, an initially flat two fluid interface spontaneously develops finger-shaped protrusions which grow unstably with time to result in a macroscopically fingered interface, known as the Saffman-Taylor instability. The images show the transformation of a flat two-fluid interface into a fingered one with increasing flow rates (left and middle panel). Our results additionally show that at still higher flow rates, the two-fluid interface further fragments in the form of droplets (right panel).

In general, a porous medium is opaque to light and hence flow visualization in three dimensions (3-D) is usually not possible. We overcome this difficulty by using liquids whose refractive indices are the same as that of the solid matrix which makes the medium transparent to light. Visualization can be achieved by dissolving fluorescent dyes in liquids and illuminating a two-dimensional (2-D) plane of the medium with a light sheet. The liquids appear bright with characteristic colors and solid matrix remains dark resulting in visual contrast. By scanning the sheet across the system, one can map a 3-D medium as a set of 2-D planes. Using this technique, called light sheet imaging, we have shown that at low flow rates, fragmentation is mainly localized near the leading edge of the front. However, for higher flow rates, the break-up occurs all along the length of the finger which disrupts the fingered phase and promotes the formation of the droplet phase instead.

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