# Mitigation of Gravity Segregation by Foam to Enhance Sweep Efficiency
## 4 Gravity Segregation in Layered Model
### Variations of Injection Pressure with Fixed Injection Rate  
Ref. [20] pointed out that for homogeneous reservoirs, the gravity segregation length at steady state is dominated by the injection pressure (B). As mentioned above, the overall injection rate is segregated into two distinct streams based on the injectivity characteristics of each layer; therefore, the injection pressure is uniform along the left boundary, theoretically. Three permeability contrasts (extreme ratios, either large, small value, or moderate value) are chosen to examine the influence of injection pressure on gravity segregation.  
Figure 10 shows the injection pressure in different scenarios with various permeability contrasts and thickness ratios. The injection pressure varies significantly among the cases despite a fixed injection rate, owing to differences in injectivity (i.e., total mobility in the two layers). For the cases where the permeability contrast is greater than 1, the injection pressure decreases with increasing thickness of the top layer. Similarly, \(\Omega\) also decreases, indicating that the injection pressure dominates the segregation process. If the thickness ratio is fixed, the injection pressure is greater in a case with a moderate permeability contrast, compared to that in an extreme permeability contrast. Permeability distribution is a key factor that affects the ultimate segregation length. The case with permeabilities \(K_{1}\) and \(K_{4}\) shows that the high-permeability top layer completely dominates the segregation with a thickness ratio above 1.0. Conversely, the low-permeability layer starts to influence the segregation though the injection pressure of both cases is close (Figures 8 and 10).  
To further understand the underlying physics behind the segregation process in layered reservoirs, the water saturation during a transient displacement into two layers of equal thickness is shown in Figures 11 and 12. Gas and water move faster in the high-permeability layer. The progression of a moving front in a high-permeability layer is observed to be advanced in comparison to its progression in a low-permeability layer, if the low-permeability layer is positioned at the top. The gas from the underlying high-permeability layer is transported into the overlying layer characterized by low-permeability, ultimately commingling with the progressing fluids. After gas breakthrough on the upper layer, gas is able to migrate upward with ease while water descends, and a steady state is  
Figure 10: Variations of injection pressure in each case with different permeability contrast and thickness ratio. \(K_{1}/K_{4}\) represents the low-permeability layer on the top. The thickness ratio is defined as \(H_{top}/H_{bottom}\).  
gradually established. In this process, the overall moving front is discontinuous. However, a high-permeability layer on top mitigates the velocity difference along the interface between two layers, leading to a smooth-moving front (Figure 12). The thickness of the overlying zone featuring a high-permeability layer positioned atop exhibits a thinner magnitude compared to the configuration wherein a low-permeability layer occupies the topmost position. It indicates that in practice with foam injection following a large surfactant preflush, the displacement efficiency between the override and underride zones is also greater if a low-permeability layer is present at the top except for the extension of segregation length.