... to response surfaces generated with polynomial chaos expansion (PCE). PCE allows for non-linear mapping of parameter uncertainty to the predicted results. In the current work, the geological parameter uncertainties affecting WAG modelling in fractured carbonates are evaluated. These include end-member fault...

..., these methods suffer from the computational complexities in reservoir simulation. It is hence of great interest to propose a sparse approximation technique to represent the posterior probability density function and conditional expectations given the data. Polynomial Chaos Expansion (PCE) is a powerful tool...

... Abstract In this work, an approach for estimating non-Gaussian permeability field is developed, through a probabilistic collocation based Kalman filter (PCKF). In this approach, the polynomial chaos expansion is used to parameterize the non-Gaussian permeability field. The state variables...

... Abstract Polynomial Chaos Expansions (PCE) as applied with the Probabilistic Collocation Method (PCM) has been shown to be a promising approach for uncertainty quantification in reservoir simulation. In particular, it has been shown to be more accurate and efficient compared to traditional...

... to the EnKF in the sense that it estimates the correlations between the state variables from the Polynomial Chaos Expansion (PCE). The coefficients in the PCE are determined by the Probabilistic Collocation Method (PCM). In this paper, the PCKF method is applied to a synthetic reservoir model that mimics...

... Smolyak method Artificial Intelligence Upstream Oil & Gas flow in porous media Polynomial chaos expansion PCM expansion equation collocation point probabilistic collocation method stochastic collocation method saturation realization differential equation permeability Introduction...