Simulation and Dimensional Analysis of Foam Processes in Porous Media

Foam can improve sweep efficiency in gas-injection improved-oil-recovery processes. The success of continuous-injection foam processes in overcoming gravity override in homogeneous, anisotropic (kx kz) radial or rectangular reservoirs depends on a single dimensionless number first proposed by Stone and Jenkins for gas flooding without foam. Their model fits foam simulation results remarkably well over a wide range in reservoir properties and geometry, flow rates, foam quality and foam strength, density difference between phases, initial reservoir pressure, and model for the mechanisms of foam collapse. This approach leads to optimal design strategies for such processes. It may be impossible, however, for a continuous-injection foam process to suppress gravity override in some cases, due to limitations on injection-well pressure. The possibility of gravity override within the foam bank should be considered in evaluating foam propagation in field trials of foam processes Introduction Gases, such as steam, carbon dioxide, natural gas, and nitrogen, are used as driving fluids in improved-oil-recovery (IOR) processes. However, these gases have high mobilities compared with oil and, thus, tend to finger through oil as well as to channel selectively through zones of high permeability. Also, because they are less dense than oil, these gases tend to migrate to the top of the reservoir, overriding oil-rich zones. Gas channeling and gravity override lead to poor sweep efficiency. Foam can significantly reduce gas mobility and overcome these problems under certain conditions, and therefore, improve sweep efficiency. This paper examines the ability of foam to overcome gravity override in homogeneous reservoirs. By inspectional analysis, Shook et al. obtain five scaling numbers rigorously sufficient to characterize a two-phase immiscible displacement process, given certain assumptions. These assumptions include incompressible, completely immiscible phases; a homogeneous, rectangular, horizontal, possibly anisotropic (kx kz) reservoir; absence of dispersion; and relative permeabilities that fit Corey expressions. (Six groups are required to characterize a process in a tilted reservoir.) For a foam process, the number of groups required would be much larger, due to the complexities of representing foam behavior. However, though a complete characterization is not guaranteed with fewer groups, it is possible that only a portion of these groups effectively govern behavior under many conditions. Shook et al. for instance, found that only three groups are needed to characterize waterfloods under a wide range of conditions, and Craig correlated waterflood sweep efficiency in terms of a gravity number and a reservoir aspect ratio. Suitable definitions for these two parameters for foam processes would be [1] [2] where Ng is gravity number, the ratio of the vertical driving force for segregation to horizontal pressure gradient; RL is reservoir aspect ratio; Pf is the lateral pressure gradient within the foam bank in the absence of gravity segregation; is the difference in densities between gas and liquid; g is gravitational acceleration; L and H are reservoir length and height, respectively; and kx and kz are absolute horizontal and vertical permeabilities. Note that Eq. 2 uses the first power of the ratio of horizontal to vertical permeability rather than the square root of this ratio as proposed by Shook et al. and Rossen et al.; the reason is discussed below. Others have noted the importance of the relative magnitude of viscous and gravity forces in foam processes and other processes. A similar analysis may apply to capillary crossflow with foam.