Intraphase transport effects

To this point we have dealt only with transport effects within the porous catalyst matrix (intraphase), and the mathematics have been worked out for boundary conditions that specify concentration and temperature at the catalyst surface. In actual fact, external boundaries often exist that offer resistance to heat and mass transport, as shown in Figure 7.1, and the surface conditions of temperature and concentration may differ substantially from those measured in the bulk fluid. Indeed, if internal gradients of temperature exist, interphase gradients in the boundary layer must also exist because of the relative values of the pertinent thermal conductivities [J.J. Carberry, Ind. Eng. Chem., 55(10), 40 (1966)]. 

If necessary, an overall effectiveness factor incorporating both interphase and intraphase transport limitations can be determined [12] however, it is very likely that either the kinetic control regime or one of the two transport control regimes will dominate, and this is discussed later. 

The effectiveness factor was defined as the ratio of global rate to intrinsic rate. If both rates are expressed in terms of pellet surface conditions such that the effectiveness factor represents the effects of internal (intraphase) transport resistances, it is termed the internal effectiveness factor as opposed to the external effectiveness factor, which represents the effects of transport resistances external to the pellet surface. The internal effectiveness factor for various pellet shapes will now be derived. 

The overall effectiveness factor is actually comprised of the individual effectiveness factors for intraphase and interphase transport ... 

The definition of equation (7-1) does not envision differences between bulk and external surface concentrations, a point that will be discussed later. We will first treat the problem of transport limitations within the porous matrix (intraphase), then the combination of boundary-layer (interphase) transport with the intraphase effects. ... 

Optimal reactor design is critical for the effectiveness and economic viability of AOPs. The WAO process poses significant challenges to chemical reactor engineering and design, due to the (i) multiphase nature of WAO reactions (ii) temperatures and pressures of the reaction and (iii) radical reaction mechanism. In multiphase reactors, complex relationships are present between parameters such as chemical kinetics, thermodynamics, interphase/intraphase intraparticle mass transport, flow patterns, and hydrodynamics influencing reactant mass transfer. Complex models of WAO are necessary to take into account the influence of catalyst wetting, the interface mass-transfer coefficients, the intraparticle effective diffusion coefficient, and the axial dispersion coefficient. " ... 

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