Surfactant-Alternating-Gas (SAG) is a popular enhanced oil recovery method that utilizes foam to decrease gas mobility and subsequently improve reservoir sweep efficiency. SAG is known to have many benefits, such as mitigating corrosion effects and increasing gas injectivity. Despite this, liquid injectivity is typically very poor during the SAG process. Currently, there is not a consistent model for liquid injectivity during SAG. However, Gong et al. recently conducted core-flood experiments to gain clarity on how gas and liquid injectivity are affected during SAG in near-wellbore conditions. Gong et al. determined that gas and liquid injectivity are represented by the propagation of multiple banks. For gas injectivity, there are two banks: the collapsed-foam bank and the foam bank. For liquid injectivity, there are three banks: the collapsed-foam bank, the gas dissolution bank and the liquid-fingering bank.
Conventional foam simulators, such as CMG’s STARS, use the Peaceman equation to obtain an estimate for well pressure as well as liquid and gas injectivity. Gong et al. came to the conclusion that conventional foam simulators do not take the propagation of the collapsed-foam bank into account. Thus, Gong et al.’s results indicate that the Peaceman equation greatly underestimates gas and liquid injectivity during SAG in a 100 by 100 meter grid block. Subsequently, this paper aims to determine how refining the 100 by 100 meter grid block will alter well pressure and liquid and gas injectivity, especially in the near-wellbore region.
We used CMG’s STARS, a conventional foam simulator, to test the impact of grid refinement on injectivity and well block pressure. Our grid set-ups include a base grid of 5x5 equal blocks and two refined grid cases, in which the center grid blocks are partitioned into 9 and 25 equal block pieces. Our results indicate that as we refine the grid, the dimensionless pressure drops occur quicker and the magnitude of pressure decreases. When compared to the base grid, the pressure drops of the refined grids were discovered to be approximately 9 and 25 times faster for the 3x3 center grid case and the 5x5 center grid case respectively. Additionally, we observed additional dimensionless pressure peaks in the refined cases, which can be explained by a drop in relative mobility when the foam reaches a new grid block.
Although our foam parameters were based on Gong et al.’s foam scan, our foam parameters are not exactly the same as the parameters listed in Gong et al.’s paper because we did not include foam shear-thinning properties. In order to build on this paper’s research, future research should look into comparing our STAR’s results to the fractional-flow theory. Additionally, future models and research should look into reducing the simulation’s time step in order to increase the number of iterations calculated by the simulator, especially around the region in which the pressure drop occurs. Lastly, it would also be important to look into finding the best method to represent the well block pressure for a refined grid case.

Scope: Surfactant-alternating-gas (SAG) is the preferred method of foam injection to improve sweep efficiency in enhanced-oil-recovery (EOR). Here, for the first time, fractional-flow theory is extended to include the shock for gas injection in the high-quality regime for radial flow in a non-Newtonian SAG process for shear-thinning and shear-thickening foams.
Methodology: To represent non-Newtonian behavior in the high-quality regime, the limiting water saturation for foam stability varies as superficial velocity decreases with radial distance from the well. We look at the interactions between the shock and the characteristics. The mobility control at the shock front and injectivity are examined. The system is compared to a Newtonian foam.
Results and conclusions: For shear-thinning foam, the foam front’s dimensionless velocity decreases with time, while the characteristics accelerate and collide with the shock. As the foam front propagates, the mobility ratio and mobility control becomes more favorable. The injectivity decreases until breakthrough, then improves slightly.
For shear-thickening foam, dimensionless velocity of the foam front increases with time, while the shocks slow down. Mobility control worsens and injectivity improves as the foam propagates, even before breakthrough. For extremely shear-thickening foam, the near-wellbore region exhibited shear-thinning behavior. This has three causes: a shift from the high- to the low- quality regime, the extrapolation of f mdry over a too large range, and the Namdar Zanganeh correction.
Recommendations: Future models should replace the shock with the colliding characteristic, instead of eliminating the characteristic. For shear-thickening foams, new characteristics should split off from the shock. Include the shear-thinning factor for the low-quality regime to check if the foam is still in the high-quality regime.

Non-Newtonian foam flow in a reservoir can be modeled numerically by discretization of the corresponding analytical formulas. The injection of foam is compared to the injection of water by comparing the injection pressures, which is represented as a dimensionless pressure rise at the injection well. The model first applies the forward-difference method to compute the changes in water saturation over space and time as the foam is injected. These changes in water saturation are related, via Darcy’s Law, to changes in dimensionless pressure. The non-Newtonian foam behavior is implemented in the model by making the gas relative permeability a function of position in radial flow, based on the exponent defined for a power law fluid.
The validity of the model is assessed by a comparison with an analytical model using the method of characteristics to simulate Newtonian foam flow. This model was created by A.H. Al Ayesh. From this comparison, it follows that the numerical model converges to a correct solution for sufficient fine discretizations. Finer discretizations do however introduce drawbacks, such as long computation times and high computer-memory requirements. Another drawback of the numerical model is the inevitable error that is introduced by a numerical artifact in the computation of the total relative mobility in each grid block at the front as foam advances. This error can only be reduced by even-finer discretizations.
The validity of the model for non-Newtonian foam flow simulations is not assessed directly in this thesis. But the model is expected to have similar or coarser grid-refinement criteria for shear-thinning foam flow, and finer or similar grid refinement criteria for shear-thickening foam flow.