Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation

Multi-physics Markov chain Monte Carlo methods for subsurface flows

“…For transferring the information, we use an upscaling procedure such that effective permeability and porosity fields on the coarse-grid produce a similar average response as that of the fine-grid problem locally. As described in [10,22] we find the effective permeability on the coarse-grid cells. We then solve (1) on the coarse-grid with k replacing k to get the upscaled Darcy's velocity.…”

“…We use partial (in time) data from production wells to characterize permeability and porosity fields. A set of accepted proposals is then sent to the numerical model to run the forward problem and predict the remaining portion of measured production data by aggregating the solutions of the forward problem [22]. We refer to this prediction stage as the Monte-Carlo (MC) step of our Bayesian framework.…”

Uncertainty propagation using infinite mixture of Gaussian processes and variational Bayesian inference

“…A standard quarter-five spot problem with one injection well on the bottom left and one production well on the top right is considered. We consider, immiscible, and incompressible two-phase flow (water and oil) [7,44,45]. The capillary pressure and gravity are not included in the model.…”

“…The fraction of water/oil in the produced fluid as a function of time, F(t), is of great interest [4,7], and it is known as the water-cut curve defined as…”

“…In addition, including both fields practically doubles the dimensionality of the uncertainty propagation problem. To the best of our knowledge, [7] is the first effort to simultaneously treat as random fields both permeability and porosity. In this work, we do the same.…”