Ensemble-based analyses are useful to compare equiprobable scenarios of the reservoir models. However, they require a large suite of reservoir models to cover high uncertainty in heterogeneous and complex reservoir models. For stable convergence in ensemble Kalman filter (EnKF), increasing ensemble size can be one of the solutions, but it causes high computational cost in large-scale reservoir systems. In this paper, we propose a preprocessing of good initial model selection to reduce the ensemble size, and then, EnKF is utilized to predict production performances stochastically. In the model selection scheme, representative models are chosen by using principal component analysis (PCA) and clustering analysis. The dimension of initial models is reduced using PCA, and the reduced models are grouped by clustering. Then, we choose and simulate representative models from the cluster groups to compare errors of production predictions with historical observation data. One representative model with the minimum error is considered as the best model, and we use the ensemble members near the best model in the cluster plane for applying EnKF. We demonstrate the proposed scheme for two 3D models that EnKF provides reliable assimilation results with much reduced computation time.

This paper presents a review of 71 research papers related to a distance-based clustering (DBC) technique for efficiently assessing reservoir uncertainty. The key to DBC is to select a few models that can represent hundreds of possible reservoir models. DBC is defined as a combination of four technical processes: distance definition, distance matrix construction, dimensional reduction, and clustering. In this paper, we review the algorithms employed in each step. For distance calculation, Minkowski distance is recommended with even order due to sign problem. In the case of clustering, K-means algorithm has been commonly used. DBC has been applied to various reservoir types from channel to unconventional reservoirs. DBC is effective for unconventional resources and enhanced oil recovery projects that have a significant advantage of reducing the number of reservoir simulations. Recently, DBC studies have been performed with deep learning algorithms for feature extraction to define a distance and for effective clustering.

Training image (TI) has a great influence on reservoir modeling as a spatial correlation in the multipoint geostatistics. Unlike the variogram of the two-point geostatistics that is mathematically defined, there is a high degree of geological uncertainty to determine a proper TI. The goal of this study is to develop a classification model for determining the proper geological scenario among plausible TIs by using machine learning methods: (a) support vector machine (SVM), (b) artificial neural network (ANN), and (c) convolutional neural network (CNN). After simulated production data are used to train the classification model, the most possible TI can be selected when the observed production responses are put into the trained model. This study, as far as we know, is the first application of CNN in which production history data are composed as a matrix form for use as an input image. The training data are set to cover various production trends to make the machine learning models more reliable. Therefore, a total of 800 channelized reservoirs were generated from four TIs, which have different channel directions to consider geological uncertainty. We divided them into training, validation, and test sets of 576, 144, and 80, respectively. The input layer comprised 800 production data, i.e., oil production rates and water cuts for eight production wells over 50 time steps, and the output layer consisted of a probability vector for each TI. The SVM and CNN models reasonably reduced the uncertainty in modeling the facies distribution based on the reliable probability for each TI. Even though the ANN and CNN had roughly the same number of parameters, the CNN outperformed the ANN in terms of both validation and test sets. The CNN successfully classified the reference model’s TI with about 95% probability. This is because the CNN can grasp the overall trend of production history. The probabilities of TI from the SVM and CNN were applied to regenerate more reliable reservoir models using the concept of TI rejection and reduced the uncertainty in the geological scenario successfully.