The PoreFlow-Net provides fast and accurate fluid flow predictions for 3D digital rock images. We trained our network to extract spatial relationships between the porous medium morphology and the fluid velocity field. Our workflow computes simple geometrical information from 3D binary images to train a deep neural network (the PoreFlow-Net) optimized to generalize the problem of flow through porous materials. Our results show that the extracted information is sufficient to obtain accurate flow field predictions in less than a second, without performing expensive numerical simulations providing a speed-up of several orders of magnitude. We also demonstrate that our model, trained with simple synthetic geometries, is able to provide accurate results in real samples spanning granular rocks, carbonates, and slightly consolidated media from a variety of subsurface formations, which highlights the ability of the model to generalize the porous media flow problem. The workflow presented here shows the successful application of a disruptive technology (physics-based training of machine learning models) to the digital rock physics community.