- ConvLSTM-VAE was proposed for parametrization of 3D permeability realizations.
- The proposed method improved the parametrization of the realizations.
- Three-dimensional CNN was not able to provide satisfactory parametrization.
- ES-MDA-ConvLSTM could properly reduce the range of uncertainty.
- A good match was obtained in the prediction phase using the proposed method.
Abstract
Most of the geological parametrization techniques used in history matching of sub-surface formations including the deep learning-based methods could not capture the non-linear and non-Gaussian dependencies and were limited to facies realizations. This paper proposes a novel method for parametrization of permeability realizations using ConvLSTM layers to build a Variational Autoencoder, named ConvLSTM-VAE, for the first time in this study. Since geological layers of the reservoir models are deposited during different periods, reservoir properties have a spatial distribution along the third dimension that can be regarded as a temporal distribution. To evaluate the proposed method, its parametrization results were compared with those of 3D convolutional VAE (3DCNN-VAE), which was recently used in the literature. Quantitative and visual results showed that the proposed method was far better than the 3DCNN-VAE, where the train, validation, and test losses obtained by the ConvLSTM-VAE was 0.3663, 0.3695, and 0.3710, and by the 3DCNN-VAE was 0.3980, 0.4086, 0.4095, respectively. In addition, history matching with parametrized realizations by the ConvLSTM-VAE could preserve the geologic realism in the conditioned realizations with significantly low data mismatch errors in the historical and prediction phases; however, history matching with 3DCNN-VAE parametrization and without any parametrization could not preserve the geologic realism. Finally, this paper can guide reservoir engineers to select a proper parametrization method for highly channelized, 3D, complex reservoirs with non-linear and non-Gaussian distribution of the uncertain parameters.