Dynamic bayesian networks as a possible alternative to the ensemble kalman filter for parameter estimation in reservoir engineering

The objective of reservoir engineering is to optimize hydrocarbon recovery. One of the most common and efficient recovery processes is water injection. The water is pumped into the reservoir in injection wells in order to push the oil trapped in the porous media towards the production wells. The movement of the water front depends on the reservoir characteristics. To avoid an early water breakthrough in the oil production wells, a good knowledge of the subsurface is imperative. The properties of the rock, e.g. porosity and permeability, are therefore important for oil extraction since they influence the ability of fluids to flow through the reservoir. They represent unknown parameters that need to be estimated when simulating a reservoir. In this paper the authors are concerned with estimating the permeability field of a reservoir. To characterise the fluid flow into the reservoir we use a two phase (oil-water) 2D °ow model which can be represented as a system of coupled nonlinear partial differential equations which cannot be solved analytically. Consequently, we build a state- space model for the reservoir. There are many ways of representing state-space models, one of the most common being the Kalman Filter (KF) model and its variants, e.g. En(semble)KF. A more general representation is a dynamic Bayesian network. Recently, the performance of the EnKF and that of a non-parametric BN were investigated and compared in a twin experiment for permeability estimation [1]. The NPBN approach proved a promising alternative to the EnKF. Yet a fair number of open questions emerged from the comparison of the two methods. Moreover, in all investigations the assumptions of the EnKF method were used in the NPBN approach for a proper comparison. In this paper we try to answer some of the questions left open, and extend the initial work by making more realistic assumptions. Copyright © (2012) by IAPSAM & ESRA.