Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

Abstract

The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ($$>512^3$$ > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.

Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

“…Further research is required to extend our refined methodology to geological samples on the REV scale. Recent publications suggest hierarchical multiscale neural networks [51] to alleviate the memory requirements of the training and inference procedure. Merging both approaches holds the potential of leveraging our current results to larger scale geological samples.…”

Machine learning-assisted design of flow fields for redox flow batteries

“…With the exponential growth of computing resources and improvements in simulation tools and machine learning techniques, this powerful approach has led to the discovery of novel materials and molecules across diverse applications [45][46][47][48][49] and has promoted advances in fluid mechanics. [69][70][71][72] Compared with traditional high-throughput screening, it benefits from acceleration in data collection and is thus particularly cost-effective for solving complex problems. However, using machine learning-assisted screening to design flow fields faces two challenges.…”

From Computational Fluid Dynamics to Structure Interpretation via Neural Networks: An Application to Flow and Transport in Porous Media

“…In the latter case, the training of the model is performed by providing the CNN with an image of the entire geometry of the porous medium, , in this way, the network autonomously extracts the most effective features for the prediction of the output, and it is not necessary to hand-select the integral parameters. In recent years, CNN for the prediction of the flow field were proposed, and the permeability can be extracted from the predicted fields. − At the moment, little was done to use these modeling techniques to deal with more complex problems, such as reaction and transport in porous media, which is fundamental for chemical engineering applications. Albeit of central importance, the geometry is far from being the only defining factor, and neural networks should be able to deal with both geometrical description and operating conditions information together.…”