Page 28 - Principles of Catalyst Development
P. 28

14                                                       CHAPTER  1

            is useful. If e is not known, sufficient accu'racy is achieved by the approxima-
            tion e = 0.5.  Thus

                                       Dell  =  (0.25)0                  (l.16)


            is  good enough!
                For simple  nth-order irreversible  reactions,  models for diffusion-reac-
            tion  lead  to  the  relationship,  shown  in  Fig.  1.6,  between  the  effectiveness
            factor,  1],  and the Thiele  modulus



                                                                         (1.17)


            where  k,  is  the  areal  rate  constant  (per  unit  surface  area)  and  d p  is  the
           pellet density,
               Combining these  factors  gives  a  rate  constant for internal diffusion

                                                                         (1.18)


           For cases  of extreme  pore diffusion  limitations,  1]  is  low and
                                         1]=I/c/>                        0.19)



                 1.0~---=~~~--~~-----'------.----r~r-r
              -  0,8
            a:
            o    0,6
            f-
            ()
            <{
            lJ..
                0.4
            (j)
            (j)
            LJ.J
            Z
            LJ.J
            >   0,2
            f-
            ()
            LJ.J
            lJ..
            lJ..
            LJ.J   0.1   ~ ____ ~ ____ ~~ __ ~ ____ ~ ______ ~ __ ~ __ -L~
                    0.2      0.4  0,6    1.0       2.0      4.0  6,0     10.0
                                     THIELE  MODULUS,  <l>
                        Figure  1.6.  Effectiveness  factor  of an  nth-order reaction,
   23   24   25   26   27   28   29   30   31   32   33