Interphase diffusion

Interphase Diffusion. When interphase transport rates are characterized it can be shown that the diffusion rate between two compartments i and j can be expressed as (3)... 

Diffusion of the reactants through a boundary layer or film adjacent to the external surface of the catalyst (film diffusion or interphase diffusion)... 

Figure 2. Stationary concentration (reactant) and temperature profiles inside and around a porous catalyst pellet during an exo thermic, heterogeneous catalytic fluid-solid reaction (a) without transport influence, (b) limited only by intraparticle diffusion, (0 limited by lntcrphase and intraparticle diffusion, (d) limited only by interphase diffusion (dense pellet)...

The Biot number Bim for mass transport. This can be interpreted as the ratio of internal to external transport resistance (intraparticle diffusion versus interphase diffusion) ... 

From this figure, it can be concluded that the reduction of the effectiveness factor at large values of becomes more pronounced as the Biot number is decreased. This arises from the fact that the reactant concentration at the external pellet surface drops significantly at low Biot numbers. However, a clear effect of interphase diffusion is seen only at Biot numbers below 100. In practice, Bim typically ranges from 100 to 200. Hence, the difference between the overall and pore effectiveness factor is usually small. In other words, the influence of intraparticle diffusion is normally by far more crucial than the influence of interphase diffusion. Thus, in many practical situations the overall catalyst efficiency may be replaced by the pore efficiency, as a good approximation. 

Provided the interphase mass transfer resistance (1 /k() is sufficiently large, the reactant concentration at the external pellet surface will drop almost to zero. Thus, we may neglect the surface concentration cs compared to the bulk concentration q>. With cs — 0 in eq 115, it is obvious that in this case the reaction will effectively follow a first-order rate law. Moreover, it is also clear that the temperature dependence of the effective reaction rate is controlled by the mass transfer coefficient k(. This exhibits basically the same temperature dependence as the bulk diffusivity Dm, since the boundary layer thickness 5 is virtually not affected by temperature (kf = Dm/<5). Thus, we have the rule of thumb that the effective activation energy of an isothermal, simple, nth order, irreversible reaction will be less than 5-lOkJmor1 when the overall reaction rate is controlled by interphase diffusion. 

If we assume that the Biot numbers of the two species are roughly the same, we note from eq 170 that when the ratio Bim/fa is sufficiently large (i.e. compared to AAcl/2 and to unity), indicating that interphase diffusion effects are not likely to influence the effective reaction rate, then, with c2,o = 0, eq 170 essentially transforms to eq 167. However, if this is not the case, the overall selectivity will be further reduced with decreasing value of Bim/fa. 

Figure 24 illustrates the dependence of Type III selectivity on intraparticle and interphase diffusion effects by plotting the apparent overall selectivity from eqs 159, 167 and 168 for Bim/fa = 1, against the conversion of reactant Ai. From this figure, it appears that the influence of intraparticle diffusion may reduce the overall selectivity in Type III reactions by a factor of about two. Wheeler [113] reported that this degree of reduction is independent of the intrinsic selectivity factor AA . It may therefore serve as a general rule of thumb. 

The purpose of the equipment used for mass-transfer operations is to provide intimate contact of the immiscible phases in order to permit interphase diffusion of the constituents. The rate of mass transfer is directly dependent upon the interfacial area exposed between the phases, and the nature and degree of dispersion of one phase into the other are therefore of prime importance. 

Interface a surface that forms the boundary between two materials (sharp transition). Interphase diffuse transition zone between two phases (e.g., solid/Uquid). 

Increase of temperature will obviously improve mobility of kinetic units, which stipulate viscous properties in eaeh of eoexisting phases and assiuning other conditions being the same, total system viseosity in a whole reduces, that is shown experimentally the drop of viseosities of single - phase systems is subject to the Arrenius law (see Figme 3.39). The effeet of temperature in two-phase systems is more complex. Temperature - stimulated increase of mobility leads not only to reduetion of viscosity. At the same time, it promotes the rate of interphase diffusion and to inevitable increase of the rate of mutual dissolution of components. Firstly, this process results in increase of oligoimide concentration in dispersion... 

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