Upscaling of realistic discrete fracture simulations using machine learning

Upscaling of discrete fracture networks to continuum models such as the dual porosity/dual permeability (DPDP) model is an industry-standard approach in modelling of fractured reservoirs. While flow-based upscaling provides more accurate results than analytical methods, the application of flow-based upscaling is limited due to its high computational cost. In this work, we parametrize the fine-scale fracture geometries and assess the accuracy of several convolutional neural networks (CNNs) to learn the mapping between this parametrization and the DPDP model closures such as the upscaled fracture permeabilities and the matrix-fracture shape factors. We exploit certain similarities between this task and the problem of image classification and adopt several best practices from the state-of-the-art CNNs used for image classification. By running a sensitivity study, we identify several key features in the CNN structure which are crucial for achieving high accuracy of predictions for the DPDP model closures, and put forward the corresponding CNN architectures. Obtaining a suitable training dataset is challenging because i) it requires a dedicated effort to map the fracture geometries; ii) creating a conforming mesh for fine-scale simulations in presence of intersecting fractures typically leads to bad quality mesh elements; iii) fine-scale simulations are time-consuming. We alleviate some of these difficulties by pre-training a suitable CNN on a synthetic random linear fractures’ dataset and demonstrate that the upscaled parameters can be accurately predicted for a realistic fracture configuration from an outcrop data. The accuracy of the DPDP results with the predicted model closures is assessed by a comparison with the corresponding fine-scale discrete fracture-matrix (DFM) simulation of a two-phase flow in a realistic fracture geometry. The DPDP results match well the DFM reference solution, while being significantly faster than the latter.