## Rapid Quantification of Uncertainty in Permeability and Porosity of Oil Reservoirs for Enabling Predictive Simulation

**Abstract.**
One of the most difficult tasks in subsurface flow simulations is the reliable
characterization of properties of the subsurface. A typical situation employs
dynamic data integration such as sparse (in space and time) measurements to be
matched with simulated responses associated with a set of permeability and porosity
fields. Among the challenges found in practice are proper mathematical modeling of
the flow, persisting heterogeneity in the porosity and permeability, and the
uncertainties inherent in them. In this paper we propose a Bayesian framework Monte
Carlo Markov Chain simulation (MCMC) to sample a set of characteristics of the
subsurface from the posterior distribution that are conditioned to the production
data. This process requires obtaining the simulated responses over many
realizations. In reality, this can be a prohibitively expensive endeavor with
possibly many proposals rejection, and thus wasting the computational resources. To
alleviate it, we employ a two-stage MCMC that includes a screening step of a
proposal whose simulated response is obtained via an inexpensive coarse-scale model.
A set of numerical examples using a two-phase flow problem in an oil reservoir as a
benchmark application is given to illustrate the procedure and its use in predictive
simulation.