Vertical Permeability Distribution of Reservoirs with Impermeable Barriers

The presence of impermeable horizontal barriers (such as shales) in a reservoir is known to have a significant effect on its vertical permeability. Since calculation of an effective vertical permeability of such a reservoir is important, approximation of the distribution of vertical permeability may also be useful for analysis of the two-phase vertical flow of buoyant fluid, such as may occur in the subsurface injection of carbon dioxide into saline formations. In this situation, the maximum likely vertical permeability of a reservoir with impermeable barriers, which could be estimated from the probability distribution of the vertical permeability, is a more useful metric than an overall effective value for the vertical permeability due to its presumed relationship to breakthrough time. In this article, we derive expressions for the mean and variance of the vertical permeability of both two and three-dimensional reservoirs using the statistical streamline method of Begg and King (Paper No. 13529, 1985), and calculate the probability distribution of the vertical permeability of a reservoir with impermeable barriers. In addition, we also provide a simple statistical analysis of the presence of high vertical permeability regions in the reservoir, which may be of importance in coarse-scale simulations of vertical migration.