The objective of this work is to overcome the computational barriers that arise during large-scale ensemble-based history matching using massively parallel computers. This parallel ensemble-based method is employed to characterize the uncertainty of large-scale Middle East oil fields.
In this work, generating geologically sound ensembles conditioned on prior knowledge is decomposed into the unconditional simulation and a vectorized kriging process. The unconditional simulation utilizes the computationally efficient circulant embedding algorithm based on the Fast Fourier Transform. For each realization, the simulation is done in parallel. Parallelism of the time-consuming kriging process is achieved through decomposition of the reservoir into multiple sub-grids. The resulting prior ensemble is then applied to an improved iterative ensemble Kalman smoother, where hundreds of simulations are required for each iteration. Here each iteration exploits a large parallel cluster, both to run each reservoir simulation within the ensemble independently, and then to run each reservoir simulation in parallel. To minimize spurious long-distance correlations, localization is performed by element-wise multiplication of the localization matrix and the covariance matrix during the ensemble updating step. Due to memory consideration of the large matrices involved in the history matching procedure, the HDF5 file format is utilized for efficient out-of-core memory reading/writing of the large matrices and facilitating the matrix operations.
The iterative smoother has been applied to a 3.5 million cell dual porosity, dual permeability full field model on a 3,000-node cluster with 24 cores on each node. Each prediction run takes about 2 to 3 hours on 500 cores. For an ensemble size of 100, the parallel algorithm manages to finish the history matching process within about 10 hours. The results of the models are then combined together to reconstruct the original reservoir. The results have shown a better match to the observed data than that achieved by traditional methods. Moreover, compared to history matching results from months of effort of the engineers, the ensemble smoother (ES) takes much less manpower to achieve a better match to the data.
This parallel iterative ES has demonstrated the feasibility and performance of history matching large-scale complex real field reservoirs. By exploiting the supercomputers, the systematic history matching workflow can also be applied to large Middle East reservoirs, which generally cannot be achieved using other methods.