Stochastic Modeling of Two-Phase Transport in Fractured Porous Media Under Geological Uncertainty Using an Improved Probabilistic Collocation Method

Abstract

Summary Simulation of multiphase transport through fractured porous media is highly affected by the uncertainty in fracture distribution and matrix block size that arises from inherent heterogeneity. To quantify the effect of such uncertainties on displacement performance in porous media, the probabilistic collocation method (PCM) has been applied as a feasible and accurate approach. However, propagation of uncertainty during the simulation of unsteady-state transport through porous media could not be computed by this method or even by the direct-sampling Monte Carlo (MC) approach. Therefore, with this research, we implement a novel numerical modeling workflow that improves PCM on sparse grids and combines it with the Smolyak algorithm for selection of collocation points sets, Karhunen-Loeve (KL) decomposition, and polynomial chaos expansion (PCE) to compute the uncertainty propagation in oil-gas flow through fractured porous media in which gravity drainage force is enabled. The effect of uncertainty in the vertical dimension of matrix blocks, which are frequently an uncertain and history-matching parameter, on simulation results of randomly synthetic 3D fractured media is explored. The developed numerical model is innovatively coupled with solving governing deterministic partial differential equations (PDEs) to compute uncertainty propagation from the first timestep to the last timestep of the simulation. The uncertainty interval and aggregation of uncertainty in ultimate recovery are quantified, and statistical moments for simulation outputs are presented at each timestep. The results reveal that the model properly quantifies uncertainty and extremely reduces central processing unit (or CPU) time in comparison with MC simulation.