Comput Geosci (2013) 17:83–97 DOI 10.1007/s10596-012-9315-1 ORIGINAL PAPER A parallel ensemble-based framework for reservoir history matching and uncertainty characterization Reza Tavakoli · Gergina Pencheva · Mary F. Wheeler · Benjamin Ganis Received: 27 December 2011 / Accepted: 27 August 2012 / Published online: 5 October 2012 © Springer Science+Business Media B.V. 2012 Abstract We present a parallel framework for his- tory matching and uncertainty characterization based on the Kalman filter update equation for the appli- cation of reservoir simulation. The main advantages of ensemble-based data assimilation methods are that they can handle large-scale numerical models with a high degree of nonlinearity and large amount of data, making them perfectly suited for coupling with a reser- voir simulator. However, the sequential implementa- tion is computationally expensive as the methods re- quire relatively high number of reservoir simulation runs. Therefore, the main focus of this work is to de- velop a parallel data assimilation framework with mini- mum changes into the reservoir simulator source code. In this framework, multiple concurrent realizations are computed on several partitions of a parallel ma- chine. These realizations are further subdivided among different processors, and communication is performed at data assimilation times. Although this parallel frame- work is general and can be used for different ensemble techniques, we discuss the methodology and compare results of two algorithms, the ensemble Kalman filter (EnKF) and the ensemble smoother (ES). Computa- tional results show that the absolute runtime is greatly reduced using a parallel implementation versus a serial one. In particular, a parallel efficiency of about 35 % is obtained for the EnKF, and an efficiency of more than 50 % is obtained for the ES. R. Tavakoli (B ) · G. Pencheva · M. F. Wheeler · B. Ganis Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station, ACES, C0200, Austin, TX 78712, USA e-mail: tavakoli@ices.utexas.edu Keywords Automatic history matching · Ensemble Kalman filter · Ensemble smoother · Parallel efficiency 1 Introduction Data assimilation is now considered as the state-of- the-art approach within the atmospheric and oceano- graphic sciences. This technique consists of integrat- ing observed data into dynamical models to determine the best estimate of poorly known parameters and/or states. The ensemble Kalman filter (EnKF) algorithm was introduced by Evensen [4] as a better alternative to solving the computationally demanding equation used in the extended Kalman filter. In the reservoir engi- neering field, EnKF was first used for history matching and uncertainty characterization by Nævdal et al. [23, 24], and since that time, it has been used extensively for parameter estimation and uncertainty quantification as a reservoir management tool [1, 10–12, 29]. The EnKF method is a Monte Carlo formulation of the Kalman filter, in which an ensemble of reservoir models is used to estimate the correlation between predicted data (such as production rates and bottom- hole pressures) and state variables (consisting of static model parameters such as porosity and permeability, as well as dynamic variables such as pressure and satura- tion for two-phase flow). Every time observation data are present, one applies the Kalman update equation to assimilate these data into prior reservoir model para- meters and primary variables. In addition, the ensemble is used to provide an estimate of uncertainty in future reservoir performance.