# Mitigation of Gravity Segregation by Foam to Enhance Sweep Efficiency
## 1 Introduction  
Gas injection has demonstrated its potential in improving oil recovery in low-permeability reservoirs, where water injection is challenging [1, 2]. The injected gas, which includes natural gas and CO2, increases pressure and displaces more oil towards the production wells. However, gas injection often faces unsatisfactory sweep efficiency due to factors such as reservoir heterogeneity, gravity override, and viscous instability. Fortunately, the utilization of foam, which consists of gas bubbles interconnected by delicate liquid films, can effectively surmount these challenges and enhance the sweep efficiency of gas injection enhanced oil recovery (EOR) techniques [3, 4, 5, 6]. Due to this ability, foam is widely used in conventional or unconventional reservoirs to overcome the poor sweep efficiency of gas injection [7, 8, 9]. Furthermore, foam can expand the storage capacity for CO2 sequestration in aquifers [10, 11, 12, 13, 14]. In the context of water-gas conjinjection, the phenomenon of gravity segregation may manifest, whereby the injected gas ascends to the uppermost regions of the reservoir to displace oil, while the injected water descends to the lower sections and facilitates the movement of oil towards the production wells. A steady-state analytical model was presented by [15] to describe gravity segregation during simultaneous and uniform waterand gas coinjection into horizontal, homogeneous reservoirs. This model can also be employed in the context of water-alternating-gas (WAG) injection, under the assumption that the injection cycles are sufficiently short to guarantee thorough amalgamation of all slugs in close proximity to the well. As illustrated in Figure 1, the model posits the existence of three distinct regions characterized by uniform saturation within a reservoir, wherein discernible demarcations separate them: an overriding zone housing solely gas, an underride zone exclusively containing water, and an adjacent mixed zone near the wellbore where simultaneous gas and water flow coexist. This model can be utilized to estimate the maximum sweep efficiency during water-gas coinjection or WAG to enhance oil recovery. This model can also provide valuable insights for real-field applications by predicting the vertical distribution of different fluids within reservoirs, which helps optimize oil recovery strategies. The length over which the mixed zone disappears from the injection well is known as the segregation length (\(L_{g}\)). Two equations for \(R_{g}\) (in a cylindrical reservoir) or \(L_{g}\) (in a rectangular reservoir) are derived as:  
\[L_{g}=\frac{Q_{t}}{k_{z}(\rho_{w}-\rho_{g})gW\lambda_{rt}^{m}}, \tag{1}\]  
\[R_{g}=\sqrt{\frac{Q_{t}}{\pi k_{z}(\rho_{w}-\rho_{g})g\lambda_{rt}^{m}}}, \tag{2}\]  
where \(\lambda_{rt}^{m}\) denotes the total relative mobility in the mixed zone, and the parameters \(Q_{t}\), \(k_{z}\), \(\rho_{w}\), \(\rho_{g}\), \(g\), and \(W\) represent the total volumetric injection rate of gas and water, vertical permeability, densities of water and gas gravitational acceleration, and the thickness of the rectangular reservoir perpendicular to flow, respectively. The extent of volumetric sweep efficiency rises with higher values of \(L_{g}\) or \(R_{g}\), which are influenced by the total injection rate \(Q_{t}\). Several researchers have performed numerical simulations in order to comprehend the underlying mechanisms involved in this process. Ref. [17] suggested that increasing the injection pressure during steady injection into a reservoir is the only way to regulate  
Figure 1: Representations of the three distinct uniform regions within the gravity-segregation model, which is employed to analyze the continuous coinjection of water and gas under steady-state conditions [15; 16]. gravity segregation. Furthermore, the ramifications of this model for foams utilized in practical field applications were deliberated upon. Ref.