Numerical Analysis of the Influence of Preadsorbed Water on Methane Transport in Crushed Shale

Summary Methane migration in shale is affected by preadsorbed water. To understand this effect, we examined several key parameters, including the effective pore diameter Le, the pore volume distribution of Le, the effective porosity ϕe, the equivalent particle diameter da, and the water film thickness h. Using these parameters, we established an equivalent relationship linking the particle packing da and the Le and the ϕe of the capillary pores within a unit-length cuboid of particles. Based on this relationship, a conceptual model was developed to simulate methane adsorption and transport in partially saturated crushed shale, incorporating parameter estimation for the tangential momentum adjustment factor δ and methane desorption rate coefficient kd, where δ characterizes the slip flow intensity and kd is related to the Langmuir adsorption constant. The finite element method was used to calculate the methane permeability ke, Knudsen diffusion coefficient Dke, surface diffusion coefficient Ds, and adsorption phase transition rate Rm, which are all affected by adsorbed water. The model’s numerical results were validated through comparison with the results from adsorption experiments. These results revealed three distinct regions in the trend of the variation in δ with Le: a rapid increase in Region I (Le < 10 nm), a slowing increase in Region II (10 ≤ Le ≤ 100 nm), and a gradual increase in Region III (Le > 100 nm). In addition, kd is positively correlated with da. kd is also correlated with water saturation S; specifically, kd decreases when S ≤ 12%, increases when S = 12% to 45.8%, and decreases again when S exceeds 45.8%. The results also reveal overall negative correlations between h and ke, Dke, Ds and Rm. Furthermore, the rates of change in ke, Dke, Ds and Rm with increasing ε (ε is the bending coefficient associated with adsorbed water) range from 7.5% to 49.4%. Similarly, ke, Dke, and Ds increase by factors of 0.73–7.19 with increasing χ (χ is the coverage rate of the adsorbed water film). Additionally, as the adsorption time t increases, Ds initially increases rapidly, followed by a gradual increase. Between t = 500 seconds and 1,500 seconds, the rate of change in Ds decreases by 20%. Rm shows a three-stage relationship with t, namely, a rapid decrease from t = 0 seconds to 500 seconds, a steady decrease from 500 seconds to 1,000 seconds, and a stabilization from 1,000 seconds to 1,500 seconds, with Rm ranging from 1.10×10-11 mol/(m3·s) to 9.45×10-11 mol/(m3·s) overall. Ds increases with the adsorption amount ratio Ed (Ed is the ratio of the adsorption amount at t to the equilibrium adsorption amount). As Ed ranges from 0.2 to 0.6, the rate of change in Ds increases by 87% to 100%. Furthermore, Rm is negatively linearly correlated with Ed.