Effect of Capillary Crossflow on Foam Improved Oil Recovery
Authors: Rossen W.R. , Lu Q. 
Published: December 2007

Abstract
Capillary crossflow can affect foam improved-oil-recovery (IOR) processes. Theory predicts that, for a pair of layers in capillary isolation, foam blocks the high-permeability layer; for layers in capillary equilibrium, however, foam blocks the low-permeability layer. This prediction assumes that the capillary pressure at which foam breaks, pc*, increases with decreasing permeability. This paper addresses two issues:whether pc* does indeed increase with decreasing permeability, andthe conditions under which the extent of crossflow is significant enough to affect foam diversion.
Direct laboratory data on pc* are few, but one can infer indirectly the relation between pc* and permeability from foam-mobility data for cores differing in permeability. A range of published foam-mobility data imply that pc* indeed increases as permeability decreases, supporting the predictions cited above.
Computer simulations over a range of flow rates, foam strengths, foam sensitivities to permeability, and reservoir geometries suggest that capillary crossflow can significantly affect foam diversion over remarkably short distances, even in thick layers, unless there are shale or other flow barriers between the layers. Results presented here, based on one foam model, can all be correlated with a single product of two dimensionless groups: a geometric aspect ratio and the ratio of capillary driving force for crossflow to the lateral pressure gradient with foam.

Introduction
Foam plays two roles in foam-drive processes (Schramm, 1994; Rossen, 1995): it can help in overcoming gravity override, and it can divert flow from higher-permeability to lower-permeability layers. Capillary pressure pc is thought to control foam properties (Khatib et al., 1988; Aronson et al., 1994; Rossen and Zhou, 1995), at least at higher foam qualities (gas fractional flows) (cf. Osterloh and Jante, 1992; Rossen and Wang, 1997). Foam-generation mechanisms depend on capillary pressure, and foam-destruction mechanisms are dominated by capillary pressure, which thins and destroys the individual liquid films, or lamellae, between bubbles. For many foams there is a "limiting capillary pressure" pc* above which foam suffers a marked weakening. The particular value of pc* depends on foam formulation, rock type, and, in many cases, on the gas and liquid flow rates in the foam.
In some cases the value of pc* is fixed for a given foam formulation and rock sample, independent of gas and liquid flow rates (Rossen and Zhou, 1995). In this case, analysis and prediction of foam properties is enormously simplified. Even in cases where it is not quantitatively accurate, the "fixed-pc*" can provide important insights into foam mechanisms.
In particular, the fixed-pc* model, combined with fractional-flow methods, predicts diametrically opposite results for foam diversion in layered rock depending on whether the layers are in capillary isolation or capillary equilibrium (Zhou and Rossen, 1992; Rossen and Zhou, 1995). Simulation results confirm this effect (Rossen et al., 1994). Differences between the capillary pressures in the two layers draws water into the layer at lower capillary pressure. Each layer can be expected to be at or near its pc*. Therefore, since pc* depends on permeability, the layer with the higher value of pc* draws water from the other layer, weakening foam there.
If the layers are in capillary isolation, then the higher capillary pressure in the lower-permeability layer causes foam to weaken or collapse there, and flow is diverted into that layer. If the layers are in capillary equilibrium, however, capillary pressure draws liquid from the higher-permeability layer, weakening foam there. As a results, flow is diverted into the higher-permeability layer, defeating the purpose of the foam. Whether this happens in practice depends on how pc* varies with permeability and on the extent of crossflow between the layers.
Khatib et al. (1988) show that pc* increases with decreasing permeability in very-high-permeability sand- and beadpacks. Rossen and Zhou (1995) extrapolate this trend down to about 1 darcy, based on limited data and some conjectures. Kovscek et al. (1994) assume that pc* does not depend on k. P. 579^