This paper presents the results of a numerical simulation study aimed at evaluating the effect of rock anisotropy on water invasion and oil bypassing in edge-water-drive reservoirs. A complete set of dimensionless groups for 3D immiscible displacement of oil by water in an anisotropic reservoir is selected using inspectional analysis. The dimensionless groups are validated using numerical simulation. Numerical simulation and statistical analysis are also used to evaluate the effect of each group on water invasion.
The results show that the end-point mobility ratio (i.e., mobility contrast for oil and water) has the strongest effect on water invasion, followed by the aspect ratios, the dip angle group and the buoyancy number. Also, it has been found out that rock anisotropy controls the geometry of displacement, resulting in water underruning or overriding the oil, which in some cases may lead to substantial bypassing of the oil reserves.
Oil bypassing is a significant problem in the U.S. reservoirs. Of the 582 billion barrels of estimated oil in-place, 208 billions have been already produced or proven, leaving behind 374 billion barrels, or 64.3% of the oil in place(1). Water invasion is known to be a major contributor to this problem. On one hand, from the reservoir standpoint, water invasion is needed to recover oil, on the other hand - at the well, water becomes a reason for oil bypassing.
Displacement of oil by water in side-water systems is controlled by viscous forces, gravity forces, capillary forces, rock heterogeneity and/or anisotropy. These forces may interact with each other during the displacement, forming multiple fingers, water channeling and/or gravity underrunning (formation of a water tongue). In the homogeneous systems producing at low flow rates, gravity forces tend to dominate the displacement and a stable (constant slope) interface occurs(2). A stable front is desirable because it results in high recovery factors. However, the required flow rates must be below the critical production rate and would not be economical. Generally, production rates needed for economical recovery exceed the critical rates. Therefore, even in homogeneous sands the oil-water front becomes unstable and a (gravity) water tongue develops along the bottom of the dipping structure, causing early water breakthrough and oil bypassing.
This study assumes homogeneity and qualifies the role of rock anisotropy on water invasion and oil bypassing in edge water systems. Numerical reservoir simulation, inspectional analysis and statistical techniques are used to understand the mechanism oil bypassing and quantify the effects of reservoir parameters. Inspectional analysis is used to build a general regression model of oil recovery. Inspectional analysis is an extension of dimensional analysis where a final dimensionless formulation is tested against the variables from which it has been developed. The dimensional analysis gives only dimensionless groups without the governing equations. Inspectional analysis is based on existing differential equations and boundary conditions and, as such, has become the preferred method in reservoir engineering(3).
The regression model is developed by considering gravity and viscous forces, as well as rock anisotropy.
