Towards Quantifying the Uncertainty of Relative Permeability Estimates for Rough Fractures

Abstract: In many industrial applications, such as coal seam gas production, understanding the impact of fracture geometry on its hydraulic properties during multiphase flow is crucial for estimating production rates. In contrast to the simplified approximation of a fracture as being a pair of parallel plates, or a special case of a porous medium, fracture geometry can exhibit varying degree of heterogeneity. This influences the phase interactions and results in a wide range of flow behaviours, which can be quantified by the relative permeability of different phases. Additionally, fractures are random surfaces, with each fracture geometry description corresponding to multiple actual realisations of the same geometry. In spite of this, there exists limited studies on the effect of such randomness in fracture realisations on the variance of the permeability, with most relying on ensemble mean. This makes reliability of results and upscaling of the behaviour to the level of fracture networks problematic., In this work, high-fidelity numerical simulations on representative fracture profiles were utilised to investigate the mean and variance of relative permeability. The phase-field lattice Boltzmann method [12] was employed to simulate multiphase flow through a large number of random fracture realisations. The simulation results were analysed to obtain mean and variance of relative permeability estimates at various fluid saturations. The results show a non-trivial relationship between the variance of the permeability and different liquid saturations. Keywords: lattice Boltzmann method, relative permeability, fracture flow, porous media