Unstable Oil Displacement by Water in a Two-Dimensional Porous Medium
Authors: Cruz-Hernandez J. , Perez-Rosales C. , Samaniego-V. F. 
Published: December 2007

Abstract
The analytical description of oil displacement by water in porous media is a complex problem of interest in secondary oil recovery by waterflooding. Due to its complexity, most of the studies in this area are restricted to one-dimensional cases. In this paper, the radial two-dimensional case is treated. For the experimental work, a transparent porous cell built with two ground circular glass plates was used. This cell has the advantage of allowing direct visualization of the movement of fluids.
Based on the experimental results, a theoretical model was developed to explain the radial displacement of oil by water in a porous medium. The theory considers that:water tends to follow preferential paths where the motion is essentially longitudinal and of the convective type;at the same time, there is a lateral motion of dispersive type which tends to widen the preferential paths.

Introduction
Oil displacement by water within porous media is a very complex process that has been studied by reservoir engineers for more than fifty years. The complexity of the process is due to the simultaneous action of several factors, primarily viscous forces, capillary forces and pore volume geometry. For describing this process, some simple theoretical models have been proposed. Frequently, these models do not represent in a reasonable way the reservoir behavior.
Recently, immiscible displacement of oil by water within a porous medium has had a renewed interest at some research centers. For the study of this flow problem, besides conventional techniques, some non-conventional such as X- and gamma-ray tomography and nuclear magnetic resonance have been used. Because of its transparency, that allows direct visualization of fluid movement, the use of two-dimensional transparent cells has been of particular interest.
The purpose of this paper is to describe a new two-dimensional transparent porous cell, which has proved to be a versatile research tool. Based upon experimental results obtained with this cell, a theoretical model that explains in a reasonable way the mechanics of oil displacement by water through porous media is proposed.

Experimental Work
Experimental work was carried out with a two-dimensional porous cell. This cell is constructed with two glass plates. One of the faces of each plate is roughened by using an appropriate abrasive. Upon placing one roughened surface against the other, we obtain a two-dimensional porous medium whose matrix has a random distribution of pores. Fig. 1 shows the components of a circular cell, with an inlet port at the center of the cell.
The operation of the cell is as follows: when the porous space is occupied by air, the cell is translucent, but when it is saturated with oil it becomes transparent, because the refraction indices of the glass and of the oil used in the experiments are similar. However, when water is injected to displace oil, the invaded area becomes translucent because water has a refraction index smaller than that of glass. In this way, the water front can be followed in detail.
The experiments of this paper were carried out with circular, square and hexagonal cells. The circular cell has 20 cm (7.9 in) in diameter. The glass plates, 0.6 cm (0.24 in) thick, were treated with an abrasive that yielded 0.01 cm (0.0049 in) pores. The inlet port consists of a stainless steel tube of 0.05cm (0.020 in) of interior diameter.
To carry out the displacements runs, the cell was saturated completely with heavy oil of 100 cp (0.1 Pa.s) viscosity; then it was placed on the arrangement shown on Fig. 2. Afterwards, water was injected at the center of the cell, at a constant rate of 0.23 cm3/min (0.014 in3/min). Fingering effects appeared immediately.
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