Reaction-diffusion problem cylindrical pellet

Wheeler s treatment of the intraparticle diffusion problem invokes reaction in single pores and may be applied to relatively simple porous structures (such as a straight non-intersecting cylindrical pore model) with moderate success. An alternative approach is to assume that the porous structure is characterised by means of the effective diffusivity. (referred to in Sect. 2.1) which can be measured for a given gaseous component. In order to develop the principles relating to the effects of diffusion on reaction selectivity, selectivity in isothermal catalyst pellets will be discussed. 

Next, the classical problem of diffusion with reaction in a cylindrical catalyst pellet is considered [8] [4]... 

Consider diffusion with a second-order reaction in a cylindrical catalyst pellet (exercise problem 2 chapter 3). Solve this problem using recursion technique described in section 10.1.2. 

Consider diffusion with reaction in a non-isothermal cylindrical pellet (Finlayson, 1980, exercise problem 7, chapter 6). The governing equations and boundary conditions are ... 

Solid catalyzed fluid-phase reactions This is a very common class of reactions involving mass transfer and chemical reactions. The reaction system involves film mass transfer, diffusion through the pores, and surface reactions. We will solve the problem for a spherical pellet and give the results for a cylindrical pellet and for a slab. 

The catalyst packing of the reactor consists of an iron oxide Fe20s, promoted with potassium carbonate K COo, and chromium oxide Cr O-s,. The catalyst pellets are extrudates of a cylindrical shape. Since at steady state the problem of simultaneous diffusion and reaction are independent of the particle shape, an equivalent slab geometry is used for the catalyst pellet, with a characteristic length making the surface to volume ratio of the slab equal to that of the original shape of the pellet. 

The problem of pore diffusion is only limited to immobilized enzyme catalysts, and not enzyme catalyzed reactions in which the enzyme is used in the native or soluble form. Immobilized enzymes are supported catalysts in which the enzyme is supported or immobilized on a suitable inert support such as alumina, kiesulguhr, silica, or microencapsulated in a suitable polymer matrix. The shape of the immobilized enzyme pellet may be spherical, cylindrical, or rectangular (as in a slab). If the reaction follows Michaelis-Menten kinetics discussed previously, then a shell balance around a spherical enzyme pellet results in the following second order differential equation ... 

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