Page 26 - Principles of Catalyst Development
P. 26

12                                                       CHAPTER  1

                         A~
                                           I.  E~ternal  diffusion
                           ~
                           ~                    k       =  k
                                                 ext.  dill   g   Sext
                            ¥              2  Internal  diffusion  Int "I
                           A


                                "
                                                k
                                                        =  k  S
                                                           •
                                                 tnt.  dlf f.
                             A
                              '"  A        3  Adsorption

                              ,  )   )   I   //)}  /  I   k
                                                 odo


                              A     8      4  Surfoce  reaction
                              1-    7
                              ://////'            0
                            )                    k
                                    +     5  Desorption  of  B
                                          6  Interna I  diffusion  of  B
                                          7.  External  diffusion  of  B






                              Figure  1.5.  Steps in the  catalytic reactions,


            where  kg  is  the  mass  transfer  coefficient  (cm s -I),  P  is  the  fluid  density
            (g cm- ),  and  DB  is  the bulk diffusivity of A  in the fluid  (cm 2  S-I).
                  3
                This  correlation gives  kg  with  a  fair  degree  of accuracy.  Diffusion  to
            the surface is  a  first-order  rate function  with a  rate  constant

                                                                          ( 1.9)


            where Sex, is the geometrical external surface of the particle per unit particle
            volume.  Equation (1.9)  is  strictly only valid if the reaction at the surface is
            very  rapid,  but it  is  close enough  for most estimates.
                Equation  (1.7)  is  good only for  particle  Reynolds  numbers above 50.
           This  suffices  for  most  industrial  reactors.  Problems  arise  with  laboratory
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