Thermal Experiments for Fractured Rock Characterization: Theoretical Analysis and Inverse Modeling

Abstract

Field-scale properties of fractured rocks play a crucial role in many subsurface applications, yet methodologies for identification of the statistical parameters of a discrete fracture network (DFN) are scarce. We present an inversion technique to infer two such parameters, fracture density and fractal dimension, from cross-borehole thermal experiments data. It is based on a particle-based heat-transfer model, whose evaluation is accelerated with a deep neural network (DNN) surrogate that is integrated into a grid search. The DNN is trained on a small number of the heat-transfer model runs and predicts the cumulative density function of the thermal field. The latter is used to compute fine posterior distributions of the (to be estimated) parameters. Our synthetic experiments reveal that fracture density is well constrained by data, while fractal dimension is harder to determine. Adding nonuniform prior information related to the DFN connectivity improves the inference of this parameter.