Prediction of 3D Velocity and Temperature Field of Reticulated Foams using Deep Learning

Data-driven deep learning models are emerging as a new method to predict the flow and transport behavior of porous media and to drastically reduce the required computational power. Previous deep learning models, however, experience difficulty or require an additional computation to predict the full 3D velocity field which is essential in the characterization at the pore-level and subsequent transport analysis of porous media. In this study, we design a deep learning model and incorporate a physics-informed loss function to relate the spatial information of the 3D binary image to the full 3D velocity field of a porous medium. We demonstrate that our model, trained only with synthetic porous media, can predict the full 3D velocity field of real reticulated foams which have different microstructures from typical sandstones that are studied in previous works. We also show that our loss function is able to enforce the mass conservation in incompressible flow. Our study provides the framework for predicting the full 3D velocity field of porous media and conducting subsequent transport analysis for various engineering applications. As an example, we conduct heat transfer analysis using the predicted velocity field and demonstrate the capability and advantage of our deep learning model in consecutive transport analysis.