Sensitivity analysis and uncertainty quantification based on the analytical solution for nanoparticle-stabilized foam flow in porous media

A model describing nanoparticle-stabilized foam displacement is proposed in this study. Based on literature experimental data, we include nanoparticle dependence in a simplified version of the Stochastic Bubble Population balance model in local equilibrium. To describe the gas-water fractional flow, we utilize quadratic Corey permeabilities. Our model consists of non-strictly hyperbolic conservation laws, and we investigate the existence of a global solution as a sequence of waves. This simpler model maintains the solution structure of classical Corey's relative permeability model and allows us to obtain algebraic expressions to analyze the solution type and construct the water saturation profiles. We perform uncertainty quantification and sensitivity analysis of the model describing the foam injection assisted by nanoparticles, considering three relevant quantities of interest: breakthrough time, cumulative water production, and pressure drop. The analytical framework developed allows us to obtain these quantities. Our results show that the effect of nanoparticles is greater than the model's uncertainty (for all quantities), suggesting that measuring it experimentally is statistically feasible. The presence of nanoparticles also significantly reduces the uncertainty propagation due to foam stabilization. From the sensitivity study, the endpoints of water and gas relative permeability are the most significant parameters for the breakthrough time. For the maximum pressure drop, the gas endpoint relative permeability and the concentration of nanoparticles stand out. Otherwise, water production is more sensitive to a foam-related parameter most of the time. We achieve convergence even using the classical Monte Carlo method, showing how analytical solutions drastically reduce computational costs.