Parameter estimation in a reservoir engineering application

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 history matching problem in reservoir engineering. Currently one of the most widely used methodologies which address the history matching problem is the Ensemble Kalman Filter (EnKF) (Evensen et al. 2007, Aanonsen et al. 2009). EnKF is a Monte-Carlo implementation of the Bayesian update problem. Nevertheless, the EnKF methodology has certain limitations. 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) (Hanea 2009, Gheorghe 2010). The NPBN based approach is compared with the EnKF method. A two phase, 2D flow model was implemented for a synthetic reservoir simulation exercise and the results of both methods for the history matching process of estimating the permeability field are illustrated and compared.