# Mitigation of Gravity Segregation by Foam to Enhance Sweep Efficiency
## 3 Character of Gravity Segregation in Homogeneous Porous Media  
### Gas-Water Coinjection and Foam Injection  
A two-dimensional horizontal rectangular grid, with each grid block of 1 \(\times\) 1 \(\times\) 1 m, is constructed to validate the simulations. Numerical results are compared to an analytical model for a uniform horizontal reservoir with a permeability of 56.8 mD. Both foam injection and gas-water coinjection are tested with varying injected water fractions. No-flow boundaries are made at the top and bottom surfaces of the model, while the left boundary is characterized by injection wells that maintain an injection rate of 1.2 m\({}^{3}\)/day under reservoir conditions. The segregation length is estimated to be around 10\({}^{3}\) m for these four sandstones with different permeabilities, assuming a total injection rate of 1.2 m\({}^{3}\)/day with a water fraction (\(f_{w}\)) of 25%, based on Equation (1). However, to better observe the foam behavior within a shorter distance, the injection rate thus is reduced to 0.12 m\({}^{3}\)/day with \(f_{w}\) = 25%, except where noted. The production well is situated along the right boundary, perforated along its length, and has a fixed bottom-hole pressure of 138 bar. To ensure uniformity of \(f_{w}^{1}\) throughout the reservoir, separate injection wells with a constant injection rate and \(f_{w}\) are used for simulations in each grid block. The study neglects capillary pressure, assuming isotropy of the reservoir (equal horizontal and vertical permeability). Previous studies [15; 29] suggest that one pore volume (PV) of gas injection proves adequate in attaining a steady state. However, in this study, two PVs of gas are injected to achieve complete segregation of the injected gas and water. Eight cases are tested with varying injected water fractions of 5.0%, 10.0%, 15.0%, 20.0%, 25.0%, 30.0%, 35.0%, and 40.0%. The water-saturation profile under steady-state conditions is depicted in Figure 4 for the case where gas and water are coinjected uniformly throughout the entire vertical interval with \(f_{w}\) = 25%. The profile consists of a mixed zone exhibiting nearly uniform saturation, a steady-state override region wherein water persists at its residual saturation, and an underride zone characterized by pure water (\(S_{w}\) = 1). However, when foam is injected, notable differences can be observed. Firstly, the water saturation within the mixed zone exhibits a significant decrease when foam injection is implemented compared to the  
Figure 3: Single foam-quality scan of different formations. The symbols in the plots represent the experimental data, while the solid curves depict the results obtained from fitting the data. absence of foam, accommodating the injected fractional flow of water. It can be attributed to the reduced gas mobility induced by foam, leading to an elevation in injection pressure despite a constant injection rate. It is noteworthy that even with a tenfold increase in the total injection rate, the injection pressure difference with foam injection (\(\sim\)70 bar) is approximately 7 times greater than without foam (\(\sim\)10 bar). The augmented apparent viscosity of foam has the potential to amplify the injection pressure, surpassing the fracture pressure of the formation or limits imposed by surface facilities [30; 31; 32]. In addition, the introduction of foam injection at identical rates results in a substantial increase in the segregation length, surpassing a tenfold magnitude extension. According to Equation (1), the effect of gravity segregation is mitigated, because foam injection results in a reduction in the overall mobility of the mixed zone. However, the aforementioned result is accompanied by the consequence of heightened injection pressure. In Figure 5, a comparison is presented between the analytical and numerical solutions for the segregation length with and without foam, for different injected water fractions. Figure 5a shows the disparity in segregation length when considering the presence or absence of the transition zone.