Uncertainty Analysis of Two-Phase Relative Permeability in Porous Media via Pore-Scale Simulation: The Impact of Initial Fluid Distribution

Accurate prediction of steady-state relative permeability via pore-scale modeling is fundamental to understanding multiphase flow processes in diverse engineering applications. However, the stochastic nature of the initial fluid distribution (IFD) in simulations is frequently overlooked, creating uncertainties that may obscure the physical influence of critical parameters on transport behavior. In this study, a color-gradient lattice Boltzmann method was employed to conduct extensive steady-state simulations across two porous media of varying geometric complexity. The investigation focused on evaluating three representative IFD patterns across different capillary numbers (Ca) and viscosity ratios (M). By introducing the coefficient of variation (CV) and distribution interval overlap analysis, the IFD-induced uncertainty was systematically quantified. The results demonstrate that the IFD is a primary source of statistical variance in relative permeability, exhibiting a strong nonlinear coupling with Ca, M, and structural complexity. CV analysis reveals that uncertainty peaks within specific saturation windows, which shift according to the pore geometry. Specifically, the peak uncertainty window for total relative permeability shifts from Sw∈ [0.5, 0.7] in the simple model to Sw∈ [0.3, 0.5] in the heterogeneous model. Notably, the wetting phase exhibits pronounced instability in the low-saturation regime, with the wetting-phase CV reaching its maximum at Sw = 0.3 in the simple model. At low Ca conditions, IFD-induced errors can entirely mask the physical sensitivity of relative permeability to Ca and M within certain saturation intervals. Furthermore, variations in initial configurations lead to divergent evolutions of the fluid-fluid interfacial area relative to wetting saturation, highlighting the role of microscopic topological memory in governing flow behavior. This research provides a quantitative foundation for IFD sensitivity in pore-scale modeling and proposes the integration of a CV-based uncertainty framework into macro-scale models to enhance the robustness and reliability of multiphase flow predictions.