Page 27 - Principles of Catalyst Development
P. 27

CATALYTIC  FUNCTIONS                                             13
            reactors where values of N Re  are extremely low.  In such cases it is advisable
           to  use  the expression(21)

                                                                          (LlO)

                Equation (1.10) shows which parameters decrease the rate of diffusion.
            Increasing  the  velocity  and  diffusivity  and  decreasing  particle  diameter,
            density, and viscosity result in  an increase in the external diffusion rate.  In
            practice,  only  adjustments  in  linear  velocity  and  particle  diameter  are
            possible.


            1.4.2.  Internal  Pore  Diffusion
                The second  step in  the  mechanism  is  diffusion  into  the  pores leading
           to the reacting surface sites. Resistance to this diffusion is through collisions
           either with  other molecules  (bulk  diffusion)  or with  the  walls  of the  pore
           (Knudsen diffusion). Satterfield has described methods for calculating bulk
           and  Knudsen  diffusivities,  D[j  and  D K ,  respectively.(21)  It is  important  to
            remember that


                                                                         (1.11)


           with  T  the  temperature,  PT  the total  pressure, and

                                                                         (l.l2)

           where  r"  is  the  radius  of the  pore.
                Usually  DB  and  DK  are  combined


                                                                         (1.13)


           and corrected for  particle  porosity, e,  and  tortuosity of the  pores,  T,
                                               De
                                         Dell =-                         ( 1.14)
                                               T
               Porosity is  measurable, but  T  is  difficult to characterize. As  an approxi-
           mation,
                                         T  =  1/ e                      (1.15)
   22   23   24   25   26   27   28   29   30   31   32