Permeability of Argillaceous Sandstone Modeled with Tortuous Capillary Tubes Using Fractal Geometry
Jiacun Liu, Ying Xu, Junjie Xiao, Xing Li, Kaiwen Xia
Abstract
Quantitative characterization of rock permeability is important for enhancing the extraction efficiency of oil and gas resources and maintaining the long-term stability of deep underground engineering. Fractal theory can quantitatively describe the pore size distribution and tortuosity of the seepage channel. Therefore, a permeability model was proposed based on fractal theory and the capillary tube model. This permeability model considered the tortuosity of the seepage channel and the damage evolution within the rock. Permeability data for argillaceous sandstone at different temperatures, pore pressures, and confining pressures were used to validate the permeability model. The permeability model simultaneously captured the permeability decrease owing to the compaction effect of stress and permeability recovery owing to the damage effect of stress, verifying the accuracy and rationality of the permeability model. Permeability influence factors K f (damage effect) and K c (compaction effect) under different temperatures, pore pressures, and confining pressure conditions were examined. The confining pressure and temperature increased K c and decreased K f, respectively, suggesting that the permeability of the rock decreases and recovers more significantly at low confining pressures and temperatures. The effect of pore pressure on the permeability influence factor may depend on the failure pattern of the rock, which changes with the confining pressure. The permeability and permeability influence factors exhibited crossover, which is attributed to macro-fracture formation within the rock. The compaction and damage effects of stress changed with the temperature, pore pressure, and confining pressure, consequently resulting in changes in the evolution process of permeability. This study provides a theoretical reference for exploiting tight sandstone reservoirs.