Abstract
History-matching of heterogeneous hydrocarbon reservoirs is carried out to construct predictive reservoir models that: i) provide accurate predictions of fluid displacement and future reservoir production behavior; ii) honor all existing measurements; and iii) preserve prior knowledge about geological continuity. Estimating individual gridblock heterogeneous reservoir properties from limited static data and spatially averaged dynamic production measurements inherently leads to an ill-posed inverse problem that can have several non-unique solutions. Many geologic formations consist of a finite number of continuous rock types (facies) with distinct hydraulic properties and spatial distributions that constrain the global fluid displacement patterns. In such cases, a feature-based history-matching technique (instead of gridblock property estimation) is more appropriate. In this paper, we present a novel and geologically motivated feature estimation method for solving history-matching problems more effectively and consistently. Using an ensemble of prior geologic models, we apply a sparse learning algorithm to generate a large number of geologically relevant model elements (similar to "words in a dictionary"). The sparsity of the constructed dictionary implies that only a small set of dictionary elements (i.e., "words") are needed to construct, according to the information in the static and dynamic production measurements (i.e., "intended meaning"), a history-matched model (i.e., "a sentence"). The sparse learning method used to generate the geologic dictionary is a recently developed machine-learning algorithm known as K-SVD. The K-SVD algorithm builds a "sparse dictionary", with flexible dimensionality, from a prior model library. An important property of the geologically learned dictionary is that only a small set of its elements is needed to reconstruct the history-matched model (i.e., solution sparsity). To achieve solution sparsity, we implement an iteratively reweighted (sparsity) regularized least-squares algorithm to selectively combine and weigh a small subset of relevant model elements from the learned dictionary that explains the observed data. We use several examples from fluvial formations with channel features and Tarbert-like formations resembling prograding near shore depositional environments, to illustrate the validity and effectiveness of the proposed history matching approach.
