Stagnation point flow of chemically reactive nanofluid due to the curved stretching surface with modified Fourier and Fick theories

Kolsi, Lioua; Abbasi, Adeel; Al‐Khaled, Kamel; Farooq, W.; Ghachem, Kaouther; Gul, M.; Khan, Sami Ullah

doi:10.1080/17455030.2022.2121443

Cited by 3 publications

(1 citation statement)

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“…Fick's second law of diffusion is a generalization of Fick's first law of diffusion, which states that the flux of a substance across a plane is proportional to the concentration gradient in that plane [33][34][35][36][37].…”

Section: Mathematical Modelmentioning

confidence: 99%

Numerical Simulation of Hydrogen Diffusion in Cement Sheath of Wells Used for Underground Hydrogen Storage

2023

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The negative environmental impact of carbon emissions from fossil fuels has promoted hydrogen utilization and storage in underground structures. Hydrogen leakage from storage structures through wells is a major concern due to the small hydrogen molecules that diffuse fast in the porous well cement sheath. The second-order parabolic partial differential equation describing the hydrogen diffusion in well cement was solved numerically using the finite difference method (FDM). The numerical model was verified with an analytical solution for an ideal case where the matrix and fluid have invariant properties. Sensitivity analyses with the model revealed several possibilities. Based on simulation studies and underlying assumptions such as non-dissolvable hydrogen gas in water present in the cement pore spaces, constant hydrogen diffusion coefficient, cement properties such as porosity and saturation, etc., hydrogen should take about 7.5 days to fully penetrate a 35 cm cement sheath under expected well conditions. The relatively short duration for hydrogen breakthrough in the cement sheath is mainly due to the small molecule size and high hydrogen diffusivity. If the hydrogen reaches a vertical channel behind the casing, a hydrogen leak from the well is soon expected. Also, the simulation result reveals that hydrogen migration along the axial direction of the cement column from a storage reservoir to the top of a 50 m caprock is likely to occur in 500 years. Hydrogen diffusion into cement sheaths increases with increased cement porosity and diffusion coefficient and decreases with water saturation (and increases with hydrogen saturation). Hence, cement with a low water-to-cement ratio to reduce water content and low cement porosity is desirable for completing hydrogen storage wells.

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