Boundary conditions spherical catalyst pellets

The first boundary condition is equivalent to a finite value of I a at the symmetry point in spherical coordinates. This condition was invoked in Section 17.2 along the symmetry axis of long cylindrical catalysts to eliminate the modified zeroth-order Bessel function of the second kind, = 0), from the general solution given by equation (17-22). When the symmetry condition at the center of a spherical pellet is used to evaluate the integration constants, one finds that B = 0 in equation (17-28) because ... 

Equation (64) is the fundamental equation for nth order reaction accompanied by diffusion within a spherical catalyst particle, to be solved with boundary conditions Ca = Co for r = R (i.e., at the surface of the pellet) and dCAldx = 0 when r = 0. The general method of solution is given in the Appendix, Section 2, and Thiele s paper (7) may be consulted for further mathematical details. The essential result is that for first order reaction (n = 1) the fraction of surface available works out to be ... 

For multicomponent systems the diffusive flux terms may be written in accordance with the approximate Wilke bulk flux equation (2.450), the approximate Wilke-Bosanquet combined bulk and Knudsen flux for porous media (2.454), the rigorous Maxwell-Stefan bulk flux equations (2.421), and the consistent dusty gas combined bulk and Knudsen diffusion flux for porous media (2.504). The different mass based diffusion flux models are listed in Table 2.3. The corresponding molar based diffusion flux models are listed in Table 2.4. In most simulations, the catalyst pellet is approximated by a porous sphericai pellet with center point symmetry. For such spherical pellets a representative system of pellet model equations, constitutive laws and boundary conditions are listed in Tables 2.5,2.6 and 2.7, respectively. 

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