Ensemble-based-History-Matching-with-a-Machine-Learning-Surrogate-Reservoir-Simulator
We have used a novel supervised learning, Cluster Classify Regress algorithm (CCR) for approximating 2 phase flow in a synthetic toy reservoir with very high accuracy. We compared the performance of CCR with a single DNN architecture in recovering the evolving pressure and saturation fields. The method consists of creating different surrogate machines equivalent to the number of time-steps (dynamic pressure and saturation snapshots). The inputs to the machine are the x,y,z spatial pixel (grid) location, the absolute permeability at each grid, effective porosity at each grid and the pressure and saturation field for each grid, for the previous time step. The outputs are the pressure and saturation field for the current time step Prediction is computationally cheap as each pressure and saturation map (for each time step) is recovered from each of the machines. The initial pressure and saturation field (Time 0) is fixed and set in the ECLIPSE data file. Learning of the function is first initiated by running eclipse once for the โ1st time stepโ alone to get the preceding pressure and saturation field, CCR and DNN was then used to construct the different machines for each of the snap shots. CCR attained R2 accuracies of greater than 96% for both the recovery of the pressure and saturation field and Structural similarity index metric (SSIM) value of greater than 90% to the true pressure and saturation fields. We also use this newly constructed surrogate model in an ensemble based history matching frame-work. We show the overall frame work gives an acceptable history match (avoiding an inverse crime) to the synthetic true reservoir model. Finally we show the wall cock performance time of CCR in prediction (9.25 seconds on a standard personal laptop computer) compared to the full fidelity ECLIPSE reservoir solver to be 19.34 seconds. This is crucial in an ensemble based uncertainty quantification (UQ) task where the size of the ensemble ranges from 100 to 500 for full field reservoir history matching problems.
