{"id":64,"date":"2021-10-02T23:21:36","date_gmt":"2021-10-02T23:21:36","guid":{"rendered":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/chapter\/exercise-1\/"},"modified":"2022-01-09T17:58:01","modified_gmt":"2022-01-09T17:58:01","slug":"exercise-1","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/flux-equations-for-gas-diffusion-in-porous-media\/chapter\/exercise-1\/","title":{"raw":"Exercise\u00a01","rendered":"Exercise\u00a01"},"content":{"raw":"
\r\n

Argon and helium diffuse through dry fine sand with a porosity n\u00a0<\/em>=\u00a00.3 in the diffusion chamber of Figure\u00a0Exercise\u00a01-1. The molecular weights are 39.9\u00a0g\/mole for argon (species A<\/em>) and 4 g\/mole for helium (species B<\/em>). The pressure in both headers is maintained at 1\u00a0\u00d7\u00a0105<\/sup>\u00a0Pa and the temperature is 25 \u00b0C. The effective molecular diffusion coefficient is 2.37\u00a0\u00d7\u00a010\u2212<\/sup>5<\/sup>\u00a0m2<\/sup>\/s under these conditions. To a close approximation, the mole fraction of argon is x<\/em>A<\/em><\/sub>\u00a0=\u00a01 in the left header and x<\/em>A<\/em><\/sub>\u00a0=\u00a00 in the right header. The diffusion chamber is 0.05\u00a0m long. For the steady-state condition:<\/p>\r\n\r\n

    \r\n \t
  1. Compute the magnitude and direction of the total diffusive mole flux for both species. Compare with the values of flux computed from Equation\u00a011<\/a>.<\/li>\r\n \t
  2. Compute the magnitude and direction of the non-equimolar flux.<\/li>\r\n \t
  3. Derive an equation for x<\/em>A<\/em><\/sub>(l<\/em>) that shows how x<\/em>A<\/em><\/sub> varies along the diffusion path.<\/li>\r\n \t
  4. Compute the values for J<\/em>A<\/em><\/sub> and J<\/em>B<\/em><\/sub> at the midpoint of the diffusion chamber.<\/li>\r\n<\/ol>\r\n

    \"Figure<\/p>\r\n

    Figure\u00a0<\/strong>E<\/strong>xercise\u00a01<\/strong>-<\/strong>1\u00a0<\/strong>-<\/strong>\u00a0<\/strong>Isobaric diffusion of argon (species A) and helium in a sand-filled chamber.<\/p>\r\n

    Click here for solution to E<\/span>xercise\u00a0<\/span>1<\/span><\/a><\/p>\r\n

    Click here to return to where the text links E<\/span>xercise\u00a0<\/span>1<\/span><\/a><\/p>\r\n

    <\/p>\r\n\r\n<\/div>","rendered":"

    \n

    Argon and helium diffuse through dry fine sand with a porosity n\u00a0<\/em>=\u00a00.3 in the diffusion chamber of Figure\u00a0Exercise\u00a01-1. The molecular weights are 39.9\u00a0g\/mole for argon (species A<\/em>) and 4 g\/mole for helium (species B<\/em>). The pressure in both headers is maintained at 1\u00a0\u00d7\u00a0105<\/sup>\u00a0Pa and the temperature is 25 \u00b0C. The effective molecular diffusion coefficient is 2.37\u00a0\u00d7\u00a010\u2212<\/sup>5<\/sup>\u00a0m2<\/sup>\/s under these conditions. To a close approximation, the mole fraction of argon is x<\/em>A<\/em><\/sub>\u00a0=\u00a01 in the left header and x<\/em>A<\/em><\/sub>\u00a0=\u00a00 in the right header. The diffusion chamber is 0.05\u00a0m long. For the steady-state condition:<\/p>\n

      \n
    1. Compute the magnitude and direction of the total diffusive mole flux for both species. Compare with the values of flux computed from Equation\u00a011<\/a>.<\/li>\n
    2. Compute the magnitude and direction of the non-equimolar flux.<\/li>\n
    3. Derive an equation for x<\/em>A<\/em><\/sub>(l<\/em>) that shows how x<\/em>A<\/em><\/sub> varies along the diffusion path.<\/li>\n
    4. Compute the values for J<\/em>A<\/em><\/sub> and J<\/em>B<\/em><\/sub> at the midpoint of the diffusion chamber.<\/li>\n<\/ol>\n

      \"Figure<\/p>\n

      Figure\u00a0<\/strong>E<\/strong>xercise\u00a01<\/strong>–<\/strong>1\u00a0<\/strong>–<\/strong>\u00a0<\/strong>Isobaric diffusion of argon (species A) and helium in a sand-filled chamber.<\/p>\n

      Click here for solution to E<\/span>xercise\u00a0<\/span>1<\/span><\/a><\/p>\n

      Click here to return to where the text links E<\/span>xercise\u00a0<\/span>1<\/span><\/a><\/p>\n

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