Page 316 - Modelling in Transport Phenomena A Conceptual Approach
P. 316

296   CHAPTER 8.  STEADY MICROSCOPIC BALANCES  WITHOUT GEN.


           at the pore mouth, i.e., z = 0, is CA,.  As the species A diffuses into the catalyst
           pore, it undergoes a first-order irreversible reaction

                                            A-+B

           on the interior surface of  the catalyst.












                     I TI




                      Gas A


                     Figure 8.31  Diffusion and reaction in a cylindrical pore.


            The problem will be analyzed with the following assumptions:
             1.  Steady-state conditions prevail.

             2.  The system is isothermal.
             3.  The diffusion coefficient is constant.

              For a cylindrical differential volume element of  thickness AT and length Az, as
           shown in Figure 8.31, Eq.  (8.41) is expressed as

             ( NA, lr  27rrAz + NA, 1% ~~FTAT)
                            - [ NA,    2n(r + AT)Az + NA, [%+Ax ~TTAT] = 0  (8.442)

           Dividing Eq.  (8.442) by 2nArAz and taking the limit as AT + 0 and Az  -+ 0
           gives

               1      (‘NArIIr  - (TNAr)Ir+Ar   + lim  NAz  1%  - NA,  [%+A=
               - lim                                                =O      (8.443)
               T Ar+O          AT             Az-4        A2

                                                 dNAZ
                                    Id
                                    - - (TNA,) + -                          (8.444)
                                                         0
                                                       =
                                    T  ar         dz
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