Multi-level Parallelization of Ensemble Kalman Filter for Reservoir History Matching

Abstract The ensemble Kalman filter (EnKF) has been successfully implemented to assimilate data in reservoir history matching problems. In the EnKF method, a suite of reservoir models (set of ensemble members) runs independently forward in time (forecast step), and is continuously updated as new data becomes available (analysis step). In this paper, an efficient implementation of the EnKF is presented in which three-level parallelization is employed. The first level of parallelization is during the forecast step, where each ensemble member runs on a separate processor. This is very efficient for a large number of ensemble members, but without additional parallelization, the memory of a single processor constrains the size of the reservoir simulation. Therefore, a second level of parallelization which uses a parallel reservoir simulator for each realization is implemented. The analysis step requires collecting a state vector from each ensemble member. If this data is collected on a single processor, this poses an additional limitation on the size of the EnKF problem in terms of both memory and computation time. Therefore, we propose an algorithm in which a third level of parallelization is achieved for the analysis step. The main computational gain of parallelization of the analysis step comes from the fact that the matrix-vector multiplications can be parallelized efficiently. The parallel EnKF algorithm is applied to a set of reservoir history matching problems. The effect of ensemble sizes on the history matching results is investigated. We present computational results that show the efficiency is greatly enhanced by moving from a serial to a parallel implementation of the EnKF. The initial testing of parallel EnKF has been done on the massively parallel machines Ranger and Lonestar, at the Texas Advanced Computing Center (TACC), and the cluster Bevo2, at the Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin.