Overall Prediction of Breakthrough Curves in Fracture Networks Using Graph‐Based Simulation and Machine Learning

Abstract

Discrete fracture network (DFN) models are widely used to simulate fluid and solute transport through fracture networks that serve as their preferential pathways. In DFN models, fractures are generated stochastically based on fracture properties. This necessitates an ensemble of DFN simulations, which makes the simulation computationally expensive. In recent studies, researchers have combined graph representations with machine learning (ML) to reduce DFN simulation costs; however, accurately predicting overall breakthrough curves (BTCs), particularly late‐time tail behaviors, remains challenging. We propose an emulation method to predict overall BTCs by combining graph‐based transport simulations with multi‐output ML regression. The core concept involves using the BTCs computed from the graph‐based transport simulations as the main input to the ML models. We evaluate the predictive accuracy and robustness of the proposed method in an in‐distribution setting, where we perform training and testing within DFNs generated from the same generation parameters, and an out‐of‐distribution setting, where we apply the trained ML models to DFNs generated with different parameters without retraining. Across DFNs with different fracture radius distributions, fracture densities, and hydraulic properties, the proposed method accurately predicts the average BTCs across realizations in the in‐distribution setting. In the out‐of‐distribution setting, the method can also predict average BTCs when the differences in DFN‐generation parameters induce relatively minor changes in BTC shapes, thereby reducing the need for computationally expensive DFN simulations to generate training data. These results demonstrate that the robustness of average‐BTC prediction is primarily governed by the similarity between training BTCs and those of target DFNs.