Towards a stochastic model of the permeability of rough fractures

This paper presents the construction of a surrogate statistical model for the permeability tensor of a random self-affine fracture. The model is constructed from thousands of flow simulations performed with the Lattice Boltzmann Method on GPUs, using the Generalised Additive Models for Location Scale and Shape (GAMLSS). To achieve good accuracy at acceptable cost, the constructed model uses information from simulations at different fidelities. The results show substantial divergence from the commonly-assumed cubic law and high variability of the permeability for mismatched surfaces