An Improved Probabilistic Collocation Method for Uncertainty Quantification of Oil–Water Transport through Fractured Porous Media: Effect of Uncertain Gravity Imbibition

Simulation of subsurface flow through fractured media is significantly influenced by uncertainty in matrix block size, fracture aperture and fracture distribution due to inherent heterogeneity. In recent years, probabilistic collocation method (PCM) has emerged as a precise approach for quantifying uncertainty. However, computing uncertainty propagation during simulation of unsteady multiphase transport in porous media could not be performed through previous PCM-based studies or even Monte Carlo simulation. Therefore, this study introduces an innovative numerical modeling framework that improves PCM on sparse grids and integrates it with Smolyak procedure to generate collocation points sets, Karhunen–Loeve and polynomial chaos expansions to assess the uncertainty associated with oil–water flow through fractured media with consideration of gravity imbibition force. By coupling developed numerical framework and solving deterministic equations, uncertainty propagation from initial time-step to final time-step of simulation is computed and the effect of uncertainty in vertical dimension of matrix blocks, a parameter with significant role in gravity imbibition and commonly subject to uncertainty and history matching, on simulation outputs of randomly synthesized 3D porous media is quantified. The confidence interval and aggregated uncertainty in ultimate production are computed, and at each time-step, statistical moments of simulation outputs are obtained. The findings demonstrate that proposed model effectively quantifies uncertainty while significantly reducing CPU time compared to Monte Carlo simulation.