Anisotropy of two-phase relative permeability in porous media and its implications for underground hydrogen storage

Subsurface rocks with anisotropic pore structures that exhibit anisotropic absolute permeability also tend to display anisotropic behavior in relative permeability. As a key input for reservoir simulation, relative permeability is essential for evaluating and optimizing the performance of subsurface energy systems. However, this anisotropy is often overlooked in simulations due to the complexity involved in its characterization under varying conditions. A major challenge lies in the fact that relative permeability anisotropy is influenced by multiple factors, including fluid saturation, rock wettability, and the capillary number of the displacement process. Unlike absolute permeability, which can be succinctly characterized using an anisotropy ratio, relative permeability lacks a similarly concise representation. This study investigated how these factors affect relative permeability anisotropy in the context of underground hydrogen storage and provides insights for its modeling. Three types of porous media were designed to represent key forms of anisotropic pore structures: stratified sedimentary structure (SSS), directionally varying pore geometry (DVPG), and oriented fracture network (OFN). Direct pore-scale simulations using the lattice Boltzmann method were conducted to examine the anisotropic behavior of relative permeability in each medium. The degree of anisotropy was quantified using a relative permeability anisotropy ratio, $R_{rA}$, and its dependence on water saturation and wettability was analyzed. Results showed that $R_{rA}$ in the SSS medium varied significantly with water saturation and wettability, while $R_{rA}$ in DVPG and OFN media remained largely insensitive to these factors. A geometric average anisotropy ratio, ${\overline{R}}_{rA}$, was proposed to characterize the overall degree of relative permeability anisotropy under specific wetting conditions. This metric showed that ${\overline{R}}_{rA}$, was greater than 1 for all porous media types and was comparable in magnitude to the absolute permeability ratio. These findings suggested that neglecting relative permeability anisotropy in reservoir simulations could introduce significant errors. The results enhanced theoretical understanding of two-phase flow in complex porous media and offered practical guidance for reservoir-scale modeling in anisotropic formations.