Abstract
In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.
Highlights
Deterministic Ensemble KalmanThe ensemble Kalman filter (EnKF) is a data assimilation method to estimate poorly known model solutions and/or parameters by integrating the given observation data
A parallel framework was given by Tavakoli et al [15] using the EnkF and ensemble smoother (ES) methods based on the simulator IPARS, in which a forecast step was parallelized while an analysis step was computed by one central processor
A parallel technique is used to implement the deterministic ensemble Kalman filter (DEnKF) for reservoir history matching
Summary
The ensemble Kalman filter (EnKF) is a data assimilation method to estimate poorly known model solutions and/or parameters by integrating the given observation data. A parallel framework was given by Tavakoli et al [15] using the EnkF and ensemble smoother (ES) methods based on the simulator IPARS, in which a forecast step was parallelized while an analysis step was computed by one central processor. The DEnKF is implemented for reservoir history matching with a parallel technique and our in-house parallel black oil simulator Both forecast and analysis steps are parallelized according to a relationship between an ensemble size and a processor number. The EnKF and DEnKF are given, followed by a parallel technique used in our computations Based on this technique, numerical experiments on the estimation of relative permeability curves with known endpoints and unknown endpoints are presented.
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