Bayesian learning of gas transport in three-dimensional fracture networks

Modeling gas flow through fractures of subsurface rock is a particularly challenging problem because of the heterogeneous nature of the material. High-fidelity simulations using discrete fracture network (DFN) models are one methodology for predicting gas particle breakthrough times at the surface but are computationally demanding. We propose a Bayesian machine learning method that serves as an efficient surrogate model, or emulator, for these three-dimensional DFN simulations. Our model trains on a small quantity of simulation data with given statistical properties and, using a graph/path-based decomposition of the fracture network, rapidly predicts quantiles of the breakthrough time distribution on DFNs with those statistical properties. The approach, based on Gaussian Process Regression (GPR), outputs predictions that are within 20%–30% of high-fidelity DFN simulation results. Unlike previously proposed methods, it also provides uncertainty quantification, outputting confidence intervals that are essential given the uncertainty inherent in subsurface modeling. Our trained model runs within a fraction of a second, considerably faster than reduced-order models yielding comparable accuracy (Hyman et al., 2017; Karra et al., 2018) and multiple orders of magnitude faster than high-fidelity simulations.