Graph neural network for multi-physics geothermal simulation with discrete fracture network

Abstract

With the increasing global energy demand, geothermal energy provides a clean and sustainable alternative to traditional fossil fuel energy. Numerical simulation of geothermal energy recovery requires high computational cost, since it considers the coupled physics of fluid flow in porous media, heat transport, and geomechanics. Even though many recent studies focus on developing deep-learning models to accelerate geothermal reservoir simulation, they are relatively limited to geothermal reservoirs with no fractures or relatively simple planar fractures, which typically use Cartesian grids for discretization.

In this study, we develop a novel deep-learning framework to address the computational overburden in fractured geothermal reservoir simulations based on discrete fracture networks, which are discretized with unstructured grids. We develop graph Neural Network (GNN) models to handle fractures with various orientations flexibly and use information associated with graph nodes and edges to characterize the impact of discrete fracture networks on fluid flow, heat transport, and geomechanics. Injection and extraction in fractured geothermal reservoirs can easily induce microseismic events. Therefore, the GNN models take input parameters, including permeability and porosity, and comprehensively predict model output or state variables, including pressure $p$, temperature $T$, effective stress ${\sigma }_{eff}$, shear modulus $G_s$, and magnitude of microseismic events $M_w$. In our numerical experiments, we demonstrate that GNN can accurately predict the spatial and temporal evolution of $T$ ($R^2$=0.997), $p$ ($R^2$=0.984), ${\sigma }_{eff}$ ($R^2$=0.954), $G_s$ ($R^2$=0.962), and $M_w$ ($R^2$=0.973) in fractured geothermal reservoirs. Besides, GNN models perform predictions with a CPU cost of 2.634 $seconds$ per simulation case, which is much cheaper than numerical reservoir simulation with a CPU cost of 75 $seconds$ per simulation of temperature field. Moreover, we also find that GNN can handle complex mesh configurations and initial and boundary conditions flexibly. Therefore, the GNN models exhibit excellent efficiency, scalability, and accuracy and thus provide an efficient approach to improve the reservoir simulation of fractured geothermal reservoirs.