Impacts of permeability heterogeneities on foam flow in porous media: Uncertainty quantification and sensitivity analysis

Foam injection in porous media has been extensively studied for its ability to improve sweep efficiency by mitigating nonlinear phenomena such as gravitational segregation and viscous fingering. However, modeling foam flow remains a significant challenge, mainly due to the complex interactions between foam and heterogeneous geological formations, which are often difficult to characterize. In particular, the spatial distribution of absolute permeability is difficult to obtain, due to scarce data and strong heterogeneity. These challenges introduce uncertainties into predictive models. In particular, the relationship between foam flow and uncertainties related to absolute permeability fields remains underexplored in the literature. This work performs uncertainty propagation studies to investigate the influence of permeability heterogeneity on foam flow in porous media. This is achieved by coupling the Karhunen-Loève expansion (KLE), which generates Gaussian random permeability fields, with Polynomial Chaos Expansion (PCE), a method for propagating uncertainties in a computationally efficient manner. This approach allows for the evaluation of permeability variations impact on key quantities of interest (QoIs) related to flow performance. The results, derived from uncertainty quantification (UQ) and sensitivity analysis (SA), reveal that foam behavior is highly sensitive to the spatial correlation structures of permeability, with important implications for optimizing foam flow processes. The integration of KLE and PCE provides the first systematic framework for uncertainty propagation in foam flow analysis, unveiling previously unexplored correlations and behaviors. These findings highlight the importance of incorporating permeability uncertainties into modeling to improve the reliability and efficiency of both subsurface flow applications, including resource recovery and carbon sequestration efforts. The proposed methodology can be particularly beneficial in practical scenarios such as enhanced oil recovery or CO${}_2$ sequestration, where foam is used to improve mobility control in complex formations.