Inference of Transmissivity in Crystalline Rock Using Flow Logs Under Steady-State Pumping: Impact of Multiscale Heterogeneity

The significance of fracture roughness for hydraulic characterization of sparsely fractured (crystalline) rock using flow logs under steady-state pumping conditions is investigated by numerical simulations in three-dimensional fracture networks. A new solver for simulating flow in three-dimensional discrete fracture networks is implemented using a hybrid finite volume and finite element method. The analysis is focused on different scales of heterogeneity in three-dimensions: the network scale heterogeneity, the fracture-to-fracture scale heterogeneity, and the individual fracture scale heterogeneity (fracture roughness). The results show that the individual fracture scale heterogeneity due to fracture roughness is potentially an additional source of uncertainty for hydraulic tests in fractured rocks using flow logs. Specifically, it enhances the variation in measured flowrates and inferred transmissivity in addition to the network scale heterogeneity and the fracture-to-fracture scale heterogeneity. However, the individual fracture scale heterogeneity has relatively small impact on the inferred transmissivity distributions compared to the fracture-to-fracture scale heterogeneity. Moreover, fracture roughness and fracture-to-fracture heterogeneity have limited influence on the median values of the inferred transmissivity such that the median transmissivity is mostly reliable when inferred from flow logs. Comparison between the inferred and underlying input transmissivity distributions shows that interpreting hydraulic tests in crystalline rock using flow logs and the Thiem equation may underestimate the variation range of the underlying transmissivity. The results are helpful for understanding the uncertainty in hydraulic characterization of sparsely fractured rocks using flow logs that are relevant for various geo-engineering and water resources applications. Plain Language Summary We study the impact of fracture roughness on inferred transmissivity from flow log information, in three-dimensional discrete fracture networks of crystalline rocks. For simulation of water flow, a new solver for three-dimensional discrete fracture networks using a hybrid finite volume and finite element method is implemented in this work to include borehole hydraulics. We consider three scales of heterogeneity in discrete fracture networks: the network scale heterogeneity, the fracture-to-fracture heterogeneity, and the individual fracture roughness. We find that the fracture roughness slightly increases the variability of measured flowrates and inferred transmissivity. The median values of the inferred transmissivity are close to that of the actual underlying input transmissivity, indicating that the fracture roughness has limited impact on the median values. In other words, median values of transmissivity inferred from flow logs under steady-state pumping are generally representative for the median values of the underlying transmissivity distributions. The method presented in this study is useful for modeling flow in sparsely fractured crystalline rock with conducting boreholes and rough fractures, while the presented results are helpful for understanding and quantifying uncertainty in transmissivity distributions inferred from flow log measurements.