This chapter reviews methods for updating estimates of reservoir properties and states when new data are available for assimilation. These methods are called recursive because the new estimate is a function of the previous estimate. The Kalman filter is the classical approach to data assimilation for linear problems, and the extended Kalman filter is an adaptation for nonlinear problems. Neither method is well suited for the large problems that typify reservoir history matching or characterization. In the final sections of this chapter, the ensemble Kalman filter (EnKF) method is introduced as a viable alternative to classical recursive methods and to traditional history matching.

Basic concepts of data assimilation

In reservoir history-matching problems, the assumption is often made that the initial state of the reservoir is known (pressure, saturations, and concentrations are at equilibrium), and that the joint probability of the reservoir parameters before assimilation of data can be characterized. In many cases, the permeability and porosity are assumed to be realizations of a random process whose characteristics are known. It is often valid to also assume that the conditional probability distribution of future states of the reservoir, given the present state and all past states, depends only upon the current state and not on any past states.