Improved parameter estimation procedures and uncertainty quantification of foam in porous media

Abstract

Characterization of foam flow in subsurface formations requires protocols capable of managing experimental uncertainties. Existing approaches for mathematical model calibration treat foam properties and multiphase flow functions as independent systems, introducing potential errors in simulations. When considering enhanced oil recovery (EOR), this limitation is compounded by the absence of systematic calibration protocols for water-oil-gas-foam systems, resulting in models with reduced predictive capability. This thesis presents an uncertainty quantification (UQ) protocol for parameter estimation in foam flow models. The protocol integrates Bayesian inference, surrogate modeling, parametric identifiability assessment, uncertainty propagation, and sensitivity analysis, applied to two-phase and three-phase flow scenarios relevant to foam applications in subsurface modeling. Three computational contributions constitute the core of the thesis. First, joint estimation of foam and relative permeability parameters in water-gas systems reveals interdependencies masked by sequential calibration procedures. Polynomial chaos-based emulators enable efficient uncertainty propagation, quantifying predictive reliability bounds. Second, extension of the protocol to three-phase systems is performed considering oil-foam destabilization mechanisms. Numerical experiments establish data sufficiency criteria for parameter identifiability and demonstrate that conventional experimental protocols often yield ill-conditioned inverse problems, potentially leading to erroneous predictions. Third, a reformulated mobility reduction factor expression eliminates the need for relative permeability assumptions, connecting mathematical and experimental interpretations of foam resistance and reducing epistemic uncertainties in calibration. Foam quality scan data for different surfactant concentrations validate the approach and delineate requirements for parameter identifiability. Systematic application of UQ techniques establishes quantitative criteria for parameter estimation reliability and experimental design in foam-enhanced recovery. Inverse UQ defines experimental requirements and model limitations to prevent incorrect characterizations, while forward UQ propagates parametric uncertainties to simulations, connecting laboratory measurements to field-scale predictions. This probabilistic approach incorporates uncertainties in industrial application planning, identifying risks overlooked by traditional deterministic methods and enabling risk-aware decision-making.