Surrogate models of heat transfer in fractured rock and their use in parameter estimation

Fracture distribution plays a significant role in the behavior of subsurface environments, affecting such activities as geothermal production, exploitation and management of groundwater resources, and long-term storage of nuclear waste and carbon dioxide. A key challenge in these and other applications is to estimate the fracture network properties from sparse and noisy observations. We evaluate the utility of cross-borehole thermal experiments for this task, using both physics-based particle-tracking (PBPT) heat-transfer approach and deep neural network (DNN) surrogates. Synthetic data are provided by the PBPT models and used to train and test the DNN surrogates over a full range of the fracture network properties. We propose regionalized and step-by-step training techniques to reduce the computational cost of expensive PBPT forward solves over large ranges of the (to-be-estimated) parameters. Our numerical experiments suggest the feasibility of training a regionalized DNN surrogate over parameter ranges for which the PBPT solves are fast and extrapolating its predictions to parameter ranges with few additional data. We analyze the balance between computational cost and model accuracy, and provide both PBPT and DNN models for applications to others kinds of data.