Predicting Rock Fluid Transport and Mechanical Properties Using Graph Neural Networks
Authors: Chung J. , Ahmad R. , Liu M. , Sun W. C. , Cai W. , Mukerji T. 
Published: August 2024

ABSTRACT:
A Graph Neural Network (GNN) approach is introduced for predicting the effective properties of rocks. The Mapper algorithm was employed to convert rock microstructures into graph datasets, effectively capturing the topological features of geomaterials. Two separate GNNs were trained using this dataset to predict permeability and elastic moduli. The results confirm that GNNs are adept at accurately predicting both transport and mechanical properties. Furthermore, GNNs can handle various sizes of digital rock images, an ability not paralleled by Convolutional Neural Networks (CNNs). In a comparative analysis with CNNs, GNNs not only demonstrated comparable high prediction accuracy but also required only 0.4% of the number of trainable parameters. This represents a substantial computational cost saving and offers greater flexibility in hyperparameter tuning. The study underscores the potential of GNNs in predicting a range of rock properties based on geometric details.

1. INTRODUCTION
Predicting rock properties such as elastic moduli and permeability is crucial in various geoengineering and geoscience fields, including CO2 geosequestration (Juanes et al., 2006), energy resource engineering (Sone and Zoback, 2013), and geotechnical engineering (Zhang et al., 2021). These macroscopic material properties are fundamentally determined by the aggregation of microscopic features. Specifically, flow transport properties are largely influenced by the quantity of pore space and their overall geometries and connectivity. In addition, the elastic properties of rocks involve a third element: the mechanical properties of mineral constituents including the previous two aspects (Mavko et al., 2020). Although quantifying pore composition and material properties is relatively straightforward, current metrics for characterizing geometric details, such as porosity and tortuosity, provide limited insight into the microscale geometry of porous media to predict their effective properties. Traditional methods like the Kozeny-Carman equation and differential effective medium (DEM) are commonly used to predict transport and mechanical properties using the materials' geometrical features (Safari et al., 2021; Srisutthiyakorn and Mavko, 2017; Sun et al., 2007; Mukerji et al., 1995). While useful, these methods often require idealized assumptions about the microstructure, leading to significant discrepancies between predictions and actual values.
Recent advancements in imaging techniques, such as micro-CT, reveal rock microstructures without specimen destruction up to the resolution of imaging techniques (Andrä et al., 2013a). Following image segmentation, effective properties can be directly computed using numerical solvers within these microstructures (Andrä et al., 2013b). Although geometrical simplifications to estimate the effective properties is not required in this case, simulations directly applied to various microstructures continue to be demanding in terms of computation cost (Ahmad et al, 2023a).