Fractures are commonly observed in subsurface rocks affecting applications ranging from aquifer management to hydrocarbon and geothermal production. Modeling the flow of fluids through fractured porous media depends on estimating its effective permeability ( \(k_e\) ). Conventional approaches that involve running numerical flow simulations are problematic because achieving accurate estimates of \(k_e\) requires highly refined computational grids, which can be computationally expensive both to generate and to employ in flow resolution. Conversely, while flow simulations using coarser meshes are more computationally tractable, they produce less reliable estimates. To address this challenge, we developed a novel \(k_e\) estimation framework by leveraging (1) the high accuracy of a multi-fidelity simulation approach based on the upscaled discrete fracture mixture (UDFM) algorithm and (2) the efficiency of machine learning (ML) algorithms. Specifically, we first utilized the UDFM algorithm to generate multilevel grid meshes in fractured porous media. Second, we employed random forest (RF) models to correlate input features derived from flow, mesh, and graph representations of networks with the single output \(k_e\) at different octree refinement levels ( \(orls\) ). This approach enables quick and reliable estimation of \(k_e\) in fractured porous media across multiple \(orl\) meshes. We tested the developed ML framework on two case studies, one a set of semi-generic fracture networks where fracture sizes and apertures follow a truncated power-law distributions, and another loosely based on the fractured granite in Forsmark, Sweden, which is a potential host for the long-term storage of spent nuclear fuel. Our results show that the developed estimation framework can provide a reliable prediction of \(k_e\) for the two case studies with remarkable speed-up compared to direct simulation. Specifically, our methods yield \(R^2\) values of 0.94 in training and 0.68 in testing of the two case studies, respectively. However, the computational efficiency associated with \(k_e\) estimation improves significantly for both cases. The proposed RF-based framework dramatically reduces the computational cost of \(k_e\) estimation. For example, in one case, the computational speed of the framework exceeds 20,292 times that of the conventional simulation-based approach. It is believed that this workflow can be generalized to address many other similar engineering problems.
