# Mitigation of Gravity Segregation by Foam to Enhance Sweep Efficiency
## 4 Gravity Segregation in Layered Model
### Sweep Efficiency with Two Injection Strategies  
In this part, we compare the sweep efficiency between two injection strategies in the layered reservoir: fixed injection pressure and fixed injection rate with foam quality of 75% in all cases. The ratio of the volume occupied by CO\({}_{2}\) foam to the total pore volume is commonly used to quantify the sweep efficiency. The relative-permeability model utilized in this study is inadequate in characterizing the behavior of trapped gas in the transition zone located below the override zone. The gas saturation should be much higher there because the presence of foam in that zone can increase the trapped gas saturation. Therefore, we assume that 70% of gas is trapped in the transition zone [34].  
Figure 13 shows that the sweep efficiency with different injection strategies is obviously distinct. With a thin low-permeability top layer, the sweep efficiency increases if the injection rate is fixed (Figure 13a), consistent with the conclusion in Stone [15]. As the thickness of the low-permeability upper layer increases, the associated sweep efficiency rises, nearing the magnitude of homogeneous porous media with low permeability. A significant contrast in permeability has the potential to result in a substantial increase in sweep efficiency as the necessary thickness ratio for the dominance of the low-permeability layer is amplified. Conversely, an increase in the thickness of the high-permeability top layer results in a decrease in sweep efficiency, indicating that the presence of a high-permeability top layer has an adverse effect on sweep efficiency. However, once the top  
Figure 11: Temporal evolution of water saturation in transient flow conditions, with a specific focus on the scenario where the low-permeability layer is positioned at the top. The permeability contrasts between the layers are quantified by the ratio of \(K_{1}\) to \(K_{4}\), while both layers possess equal thicknesses. (**a–d**) is 0.172 PVI, 0.344 PVI, 0.688 PVI, and 4.0 PVI gas injection, respectively.  
Figure 12: Temporal evolution of water saturation in transient flow conditions, with a specific focus on the scenario where the high-permeability layer is positioned at the top. The permeability contrasts between the layers are quantified by the ratio of \(K_{1}\) to \(K_{4}\), while both layers possess equal thicknesses. (**a–d**) is 0.172 PVI, 0.344 PVI, 0.688 PVI, and 4.0 PVI gas injection, respectively.  
high-permeability layer starts to dominate the segregation, the sweep efficiency rebounds and gets close to the value of uniform porous media with high permeability.  
If the injection pressure is fixed in the layered model, a thin low-permeability layer on the top to extend the sweep efficiency occurs only when the permeability contrast is not huge (Figure 12(b)). Given a significant contrast in permeability, the impact of a thin top layer exhibiting low permeability may be disregarded as the quantity of gas present in the low-permeability layer is insufficient to influence the segregation within the underlying layer with high permeability. The sweep efficiency diminishes as the top low-permeability layer thickness increases, owing to the decreased injectivity of the entire layer, while the sweep efficiency increases significantly with a thicker high-permeability top layer.