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Concentration Dependence of the Diffusion Coefficient During Adsorption of Methane into Partially Water-Saturated Crushed Shale

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Abstract

A numerical model that simulates methane transport and adsorption in crushed shale was developed. This model uses the finite element method to solve the diffusion coefficient (D) and adsorption rate of methane in a spherical particle region, and it was calibrated by fitting experimental data on the adsorption process of methane in unsaturated crushed shale. The results show that the methane free concentration in shale reflected the strength of methane’s diffusion ability. The D increased by 2.2–4.9 times for each 900 mol/m3 increment in the free concentration. The D was 1.43 × 10−11–1.23 × 10−9 m2/s as the boundary concentration ranged from 461 to 2766 mol/m3. Furthermore, the diffusion behavior can be divided into three stages during the adsorption–diffusion process. The increasing trend of the D was slow in the early and late stages of the adsorption–diffusion process, while the D obviously increased in the middle stage. The middle period accounted for 16.2–71.7% of the entire process. Moreover, the variation in the D along the radial axis that started at the center of the model and pointed to the model surface can be divided into two regions. The change in the D tended to be horizontal in a region close to the center, whereas in the other region, the D was positively correlated with the distance to the center. The horizontal area decreased as adsorption–diffusion proceeded, and the rate of shrinkage of this area can be described with an exponential equation.

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Notes

  1. * 1 mD = 1 millidarcy = 9.869233×10−16 m2

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Acknowledgments

This study was funded by the National Natural Sciences Foundation of China (Grant Nos. 41877196, U1612441 and 41272387).

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  1. Beijing Key Laboratory of Water Resources and Environmental Engineering, China University of Geosciences (Beijing), Beijing, 100083, China

    Wentao Ban & Qingchun Yu

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Ban, W., Yu, Q. Concentration Dependence of the Diffusion Coefficient During Adsorption of Methane into Partially Water-Saturated Crushed Shale. Nat Resour Res 33, 299–319 (2024). https://doi.org/10.1007/s11053-023-10281-6

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