Downscaling state variables of reactive transport flow simulations using recurrent super-resolution networks

Abstract Accurately forecasting the fate of fluids (e.g., injected CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> ) in geological formations involves employing time-consuming fine-scale (high fidelity) multi-physics simulations. This induces a very large computation cost to thoroughly propagate input uncertainties, e.g., on petrophysical property distributions, and methods are needed to overcome this limitation. This study introduces a neural network that predicts fine-scale simulation results from coarse-scale (low fidelity) simulated outputs, compensating for deviations due to the information loss resulting from upscaling. The proposed work adapts the concept of super-resolution neural networks, used for image resolution enhancement, and develops a recurrent super-resolution convolutional neural network for downscaling. The network takes as inputs the uncertain model parameters (e.g., porosity and permeability fields) and the state vector at the current timestep on the fine scale, the upsampled state vector at the next timestep resulting from the coarse-scale simulation, and provides the approximated state vector at the next timestep on the fine scale. The inputs and outputs are treated as multichannel images and recurrency is embedded, allowing each timestep of each realisation to be treated as a training sample. The proposed approach was tested on a synthetic two-phase, two-component flow with random log-Gaussian permeability realisations, and on a more complex case representing CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> injection in a carbonate aquifer considering reactive transport and random facies distributions. The results demonstrate the proposed architecture’s promise. 80 realisations only are considered for training, and the mean squared prediction error after mapping by the trained network remains smaller than the coarse scale original results despite error accumulation over timesteps.