Fast marching method assisted permeability upscaling using a hybrid deep learning method coupled with particle swarm optimization

Geo-cellar models contain millions of gridblocks and are very time-consuming to simulate. This challenge necessitates upscaling geo-cellular models to obtain fit-for-purpose models for simulation. Simulation-based upscaling methods are computationally demanding, especially if there is a large number of geological realizations. On the other hand, static methods do not take into account the dynamics of the flow. In this paper, a novel hybrid deep learning-based upscaling method is proposed that can handle highly channelized and layered reservoir models. The proposed method combines the ConvLSTM network with the fast marching method (FMM), which is a computationally efficient method to get the dynamic response of the reservoir without the need for full-physics flow simulation. Since reservoir models have deposited during different geological periods, they have a temporal distribution along the third dimension. ConvLSTM layers can simultaneously extract spatiotemporal dependencies that other networks in the literature were not able to do so. The proposed method follows a twostep training process. In the first step, a variational autoencoder with ConvLSTM blocks (ConvLSTM-VAE) is trained and validated unsupervised using 10,000 permeability realizations. This network learns the datagenerating distribution of the realizations and improves the overall upscaling process. Then, the acquired weights are used to initialize the ConvLSTM-FMM network, which is fine-tuned by the particle swarm optimization to accomplish the upscaling task by minimizing the difference between the pressure drop of the fine-scale and upscaled realizations calculated by the FMM. Validity of the FMM to estimate the BHP drop of the wells was verified on the utilized reservoir model. The advantage of the proposed data-driven method is that it can be trained once and used to upscale new realizations, contrary to conventional simulation-based methods that require running the entire process whenever the fine realizations change. The proposed network was applied to upscaling permeability realizations since absolute permeability is one of the most challenging properties to upscale because of its directional nature. Results showed the outstanding performance of the proposed method with a mean absolute percentage error, mean squared error, and coefficient of determination of 15.22, 0.18, and 0.82 on the test realizations, and outperformed the geometric mean and the simulation-based upscaling methods.