Pattern-Based History Matching for Reservoirs with Complex Geologic Facies

Abstract History matching is performed to obtain reservoir models that reproduce the historical production data while adhering to available prior geologic knowledge and observed static data. In automated history matching workflows, prior models of reservoir properties are continuously updated to match the incoming production history. A challenging problem is to ensure that after applying updates to prior models, the resulting history matched models remain geologically consistent. This is particularly challenging in formations with complex connectivity patterns, e.g., fluvial meandering and curvilinear channels, where preserving the distinct shape and continuity of the underlying geologic features is non-trivial. In this work, we introduce a novel machine learning approach with the aim of preserving the main connectivity patterns of the prior reservoir models during history matching of complex geologic formations. We formulate the history matching problem by defining a feasible set of connectivity patterns that are described by a large number of model realizations. The feasible set encompasses the range of connectivity patterns of the expected geologic objects in the prescribed conceptual model by geologists. A supervised machine learning algorithm is then introduced to learn a mapping operator between any given model and its closest model in the feasible set. For this purpose, a learning dataset, i.e., a set of feature/label pairs, is constructed from the representative samples of the feasible set. The k-Nearest Neighbor (k-NN) classification algorithm is then applied to relate the local connectivity patterns in the feasible set that are closest to the patterns in a proposed model outside the feasible set. The learned mapping operator is invoked during history matching, where the misfit between model-predicted and observed historical production data is minimized while honoring the connectivity in the prior feasible set. The history matching is performed using a two-step alternating directions optimization algorithm, in which the first step implements a gradient-based continuous minimization procedure to decrease the data mismatch objective function while the second step maps the obtained solution from the first step onto the prior feasible set. History matching case studies in channelized reservoirs demonstrate that the proposed supervised learning approach can learn the complex geologic patterns in the feasible set and use them during history matching to preserve the feasible connectivity patterns. The results suggest that the proposed classification and clustering approach can facilitate patter-based history matching problems by learning geologic features from prior models and using them to impose geologic feasibility.

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