On the mobility reduction factor for the quantification of foam strength in porous media

Foam effects in multiphase flow are commonly modeled as a mobility reduction factor that scales gas mobility. Conventional parameter estimation relies on prior relative permeability functions, introducing epistemic uncertainties that propagate to foam characterization. In this work, an alternative mobility reduction factor formulation expressed solely in terms of pressure drop measurements is derived, eliminating the need for relative permeability assumptions and directly aligning with the modeling hypothesis of gas-only mobility reduction. The approach is evaluated using synthetic foam-quality scan datasets at multiple surfactant concentrations. Profile likelihood analysis shows that the proposed formulation preserves parameter identifiability relative to conventional methods based on apparent viscosity. Robustness is assessed under both correct and misspecified relative permeability models, with the Lomeland-Ebeltoft-Thomas formulation used for data generation and Brooks-Corey curves for parameter estimation. Systematic sampling of relative permeability parameters further demonstrates that, even when the model structure is correct, the proposed mobility reduction factor reduces estimation errors by confining uncertainties to the foam component only. These results establish the new mobility reduction factor definition as a reliable and practical metric for quantifying foam strength in laboratory experiments and for improving parameter estimation in implicit-texture models.