Kari Cook and Dr. Hugh Hales, Chemical Engineering

Purpose

Computerized simulation of the flow in underground petroleum reservoirs is widely used by oil companies to optimize the production of oil and gas. Such simulations are known in the Industry as “reservoir simulation”. They are based on Darcy’s Law, smoothly varying flow potentials, and the assumption that all phases move uniformly through the pore spaces. It seems possible that at low flow rates, such as those resulting when gravitational forces predominate, a different mechanism applies. The more dense phases may move downward in some pores, while the lighter fluids move upward through others. This would result in much more rapid phase velocities than predicted by traditional reservoir simulations. Segregation of the phases when wells are shut in or when well rates are reduced would be in error and optimal reservoir management would not be achieved. The purpose of this research is to understand the mechanism of gravity induced, counter-current flow of oil and water in reservoirs. Thus, this research is an experimental study of the patterns of oil and water movement in water wetted glass beads, an environment approximating natural oil reservoirs.

Experimental Design

The first step was discovery of a fluid that flows at an observable rate, with repeatable flow observation. Trial and error experimentation of several different oils through water and air along with preliminary observations of their flow yielded that octane and water is the best oil/water combination, as shown by the 1-4 ranking (1 being the best) in Table 1. The Vegetable Oil/Water set-up proved especially poor, because an apparent hydrate formed. The hydrated vegetable oil/water interface allowed for no additional flow after hydration. The surfactants in motor oil increased the miscibility motor oil/water mixtures. Mineral oil/water mixtures showed similar flow limitations. The theoretical flow velocities for the two hypothesis mechanisms were much the same for mixtures containing air because of its very low viscosity and thus there was no calculable differentiation between the velocities even if there was differentiation between homogenous and segregated flow.
The experimental set up shown in Figure 2b used a bottle with square cross-section of 4 cm by 4 cm and a height of 12. This bottle was chosen to allow for more quantitative velocity determinations through better optic properties so that a more accurate view of the flow was obtained. In addition experiments were performed with horizontal orientations to investigate the cross-sectional area scale dependence of fingering. See Figure 2c.

Experimental Results and Statistics

Fifty total experiments were performed, 25 in each orientation, to determine velocity for the octane and water. The experimental velocities were 2.91 cm/s with a standard deviation of .961 for horizontal orientation and 2.45 cm/s and .0956 for vertical orientation based on sample means from sets of 5 experiments for a total of 25 experiments (5 sets of 5) for each orientation or 50 total. These flow rates are much closer to the theoretical velocity resulting from the fingering mechanism, 2.08 cm/s, than to the.

These experimental results also show an increased velocity for the horizontal orientation suggesting that the fingering mechanism may be even more dominant in the horizontal orientation as a result of the increased flow cross-section. However, it might also be simply the results of the increased difficulty of obtaining accurate velocity data in the horizontal position as suggested by the large standard deviation of these data.

Conclusions

The observed, gravity-induced velocities of oil (octane) and water in a packed bed of glass beads closely corresponded to the theoretical velocities predicted for segregated flows in which one phase moves upward through some pores and the other moves downward through other pores. Reservoir simulators generally assume that the saturations are homogeneous in each of the finite difference cells, and that the flow velocities are the same in all the pores. Gravity induced flows are assumed to occur counter-currently in all the pores. This mechanism provides significantly smaller velocities. These results suggest that simulators should be modified to include the segregated mechanism for flow when gravity forces predominate and the flow directions of the phases are substantially different.
It seems likely that accurate, segregated flow could also be modeled by reduced cell sizes. However, cell sizes would have to be substantially smaller than the size of these flow experiments, i.e. a few centimeters. Such cell sizes are unfeasible for most reservoir simulations.

References

• Buckley, S. E. and M. C. Leverett, Mechanism of Fluid Displacement in Sands,” Trans. AIME, v146, p 107, 1942