Using input-adaptive dictionaries trained by the method of optimal directions to estimate the permeability model of a reservoir

Abstract

The thirst for perfect characterization of petroleum reservoirs is yet to be quenched. Sparse transform is an image compression method the full potential of which is still not employed by the geoscientists in the reservoir characterization workflow. Sparse transform is the state of representing an image model based on a weighted linear combination of a sparse set of columns from a matrix, called dictionary. The required dictionary in the sparse transform scheme is obtained by learning over a training set of model images using dictionary learning algorithms. Meanwhile, the sparse coding algorithms are used to select the sparse proper subset of columns from the trained dictionary and specify appropriate weight to each column in the linear combination. To enhance the results, the property of internal structure and generality for the implicit dictionaries are integrated with the property of adaptability for the explicit dictionaries to regularize and enhance the effectiveness of the input-adaptive dictionary in reconstructing the approximate model.This phenomenon can be employed in the geosciences to estimate the reservoir model if the dictionary is trained over a set of geologic models of a delighted property. The geologic models should be diverse enough to represent the possible variety of the desired property and the limited number of columns from the dictionary should be properly selected such that it adequately captures the variety inherent within the geologic models. In this study, the variety of the geologic models are provided by manipulating two training images by FilterSim multiple-point geostatistical method and generating a large set of realizations. The training images are extracted from a spectral decomposition profile to represent a stationary fracture system and a nonstationary delta system model in an Iranian petroleum reservoir. The dictionary learning algorithm is an alternation of dictionary updating and sparse coding steps. In this paper, the method of optimal directions is used as dictionary learning algorithm and the least angle regression with shrinkage algorithm is used as the sparse coding method.The resultant approximate model achieved by the sparse transform compression scheme is comparable to the reference models both in terms of physical structures and fluid flow characteristics. For the current study, the approximate fracture system model is shown to be superior to 86.16% of the model images in the corresponding population space in terms of fluid flow characteristics. In the case of the delta system, the approximate model is superior to 99.17% of the model images in the population space. Further experiments indicate similar deductions using other methods for dictionary learning, sparse coding, and multiple-point geostatistical modeling.