Non-parametric Bayesian networks for parameter estimation in reservoir simulation: a graphical take on the ensemble Kalman filter (part I)

Abstract

Reservoir simulation models are used both in the development of new fields and in developed fields where production forecasts are needed for investment decisions. When simulating a reservoir, one must account for the physical and chemical processes taking place in the subsurface. Rock and fluid properties are crucial when describing the flow in porous media. In this paper, the authors are concerned with estimating the permeability field of a reservoir. The problem of estimating model parameters such as permeability is often referred to as a historymatching problem in reservoir engineering. Currently, one of the most widely used methodologies which address the history-matching problem is the ensemble Kalman filter (EnKF). EnKF is a Monte Carlo implementation of the Bayesian update problem. Nevertheless, the EnKF methodology has certain limitations that encourage the search for an alternative method. For this reason, a new approach based on graphical models is proposed and studied. In particular, the graphical model chosen for this purpose is a dynamic non-parametric Bayesian network (NPBN).