We examine the impact of viscous and capillary forces on immiscible, two-phase flow parallel and perpendicular to continuous layers of contrasting material properties. We consider layers of contrasting porosity and relative permeability, in addition to the contrasts in absolute permeability investigated previously. We define a set of dimensionless numbers which characterize flow. Some of these are common to flow both parallel and perpendicular to layering, such as the longitudinal permeability ratio σ and the ratio Rs of the moveable pore volumes (MPV) in each layer. Others are specific to a given flow direction, such as the dimensionless capillary to viscous ratio Ncv, and the effective aspect ratio RL that quantifies crossflow for layer-parallel flow. We examine how variations in the dimensionless numbers affect the trapping/recovery efficiency, defined as the fraction of the model MPV occupied by the injected phase after 1 MPV injected, and which is numerically equivalent to the fraction of the displaced phase recovered from the model after 1 MPV injected. The results are directly applicable to geological carbon storage and hydrocarbon production. We find that the trapping efficiency is clearly controlled by the dimensionless numbers. When flow is perpendicular to layering, heterogeneity only influences flow when capillary forces are significant (Ncv>0). As Ncv is increased, a larger fraction of the non-wetting phase is trapped if the layers have contrasting capillary pressure curves. When flow is parallel to layering, both viscous and capillary forces are important. In the viscous limit (Ncv=0), heterogeneity reduces trapping efficiency if σ≠Rs. As capillary forces become more significant (Ncv increases) and if crossflow between layers can occur (RL>0), the trapping efficiency also increases in response to capillary crossflow and reaches a maximum at a given Ncv. At higher Ncv, the benefit of crossflow is outweighed by along layer diffusion of the injected phase.


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