Abstract This chapter describes the ensemble Kalman filter for the purpose of reservoir characterization and uncertainty assessment through the assimilation of dynamic data. The key advantages of the ensemble Kalman filter approach are its ability to handle diverse measurements efficiently and in real time, thereby exploiting the continuous stream of data from operational well sensors and field monitoring systems. Two examples, including a field-level study, are presented to illustrate these advantages. Finally, we detail some of the difficulties associated with the ensemble Kalman filter formulation and describe some recent developments that address these challenges. The economic impact of inaccurate predictions of future petroleum reservoir performance is substantial, making proper characterization of the reservoir and uncertainty analyses in production forecasts a crucial aspect of any reservoir development strategy. In the petroleum industry, management decisions and business projections are guided by findings from reservoir simulation studies, with the ultimate goal being production optimization to improve reservoir performance and productivity. The validity of the simulation study and thus the reliability of reservoir management decisions depend on the accuracy with which the geology of the reservoir, the structural and stratigraphic compartmentalization, and the associated complexities are understood, characterized, and modeled. In building the geologic model, however, the available data are commonly restricted to a sparse set of static information, such as measurements derived from a limited number of wells, the interpretation of the depositional environment and subsequent geologic events, outcrop studies, geologic controls on reservoir quality, and the processing of any available seismic surveys ( Deutsch and Journel, 1992 ). The geostatistical modeling of the relevant reservoir properties anchored on these observations enables the construction of the subsurface geologic model ( Chiles and Delfiner, 1999 ; Caers and Zhang, 2004 ; Ma et al., 2009 ). Reservoir simulation models are typically scaled-up derivatives of the corresponding geologic models and are commonly referred to as static models that are expected to be geologically consistent and physically meaningful.

Abstract History matching is to integrate dynamic data in the reservoir model–building process. These data, acquired during the production life of a reservoir, can be production data, such as well pressures, oil production rates or water production rates, or four-dimensional seismic–related data. The ensemble Kalman filter (EnKF) is a sequential history-matching method that integrates the production data to the reservoir model as soon as they are acquired. Its ease of implementation and efficiency has resulted in various applications, such as history matching of production and seismic data. We focus on the use of the EnKF for history match of a synthetic reservoir model. First, the method of ensemble Kalman filtering is reviewed. Then the geologic and reservoir characteristics of a case study are described. Several experiments are performed to investigate the benefits and limitations of the EnKF approach in building reservoir models that reproduce the production data. Last, special attention is paid to the sensitivity of the method to a set of parameters, including ensemble size, assimilation time interval, data uncertainty, and choice of initial ensemble. A reservoir model relies on two sources of data: static data and dynamic data. Although static data (e.g., geologic observations, measurements on cores, logs, etc.) are constant through time, dynamic data change with time. They include production data measured at wells, such as pressures and oil production rates. As static data are too sparse to deterministically describe the spatial variation in transport properties (porosity and permeability) within the reservoir, they serve to characterize the parameters of a geostatistical model. Therefore, we refer to a stochastic framework in which reservoir models are viewed as realizations of a random function.