External resistance to transfer

The membrane is usually dense but sometimes micro-porous. If the external resistances to mass transfer are neglected in Figure 10.10, then pFj = p F l and pi, = p P i and Equation 10.20 can be written in terms of the volumetric flux as ... 

Consider an nth-order surface reaction, represented by A(g) — product(s), occurring in a catalyst particle, with negligible external resistance to mass transfer so that cAs cAg- Then the observed rate of reaction is... 

External Resistance to Mass Transfer 699 11.3.1 Mass Transfer Coefficient 699... 

A mathematical analysis of a crossflow magnetically stabilized fluidized bed chromatograph has been presented (14). The geometry of this system is similar to the rotating annular chromatograph and therefore the modeling approach is quite similar to that reported here. A parametric sensitivity study was conducted and the results indicated that the extent of band broadening was most sensitive to two factors. These factors were the external resistance to mass transfer and the width of the feed band. 

For the moment let s assume the transport of A from the bulk fluid to the external surface of the catalyst is the slowest step in the sequence. We lump all the resistance to transfer from the bulk fluid to the surface in the boundary layer surrounding the pellet. In this step the reactant A at a bulk concentration C most travel through the boundary layer of thickness 8 to the external surface of the pellet where the concentration is Cm as shown in Figure 10-8. The rate of transfer (and hence rate of reaction, -r ) for this slowest step is... 

Overview In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants between the bulk fluid and the catalytic surface. By mas,s transfer, we mean any proces.s in which diffusion plays a role. In the rate laws and catalytic reaction steps described in Chapter 10 (diffusion, adsorption, surface reaction, desorption, and diffusion), we neglected the diffusion steps by saying we were operating under conditions where these steps are fast when compared to the other steps and thus could be neglected. We now examine the assumption that diffusion can be neglected. In this chapter we consider the external resistance to diffusion, and in the next chapter we consider internal resistance to diffusion. 

Modeling Diffusion with Chemical Reaction External Resistance to Mass Transfer 771... 

The simple boundary condition for temperature is 7/ = T waii(z), where T waii(z) is the external temperature, but see Appendix 8.2 for the case where there is external resistance to heat transfer. The simple boundary condition for adiabatic reactors is... 

This appendix considers the appropriate wall boundary condition for temperature when the external resistances to heat transfer are significant. We suppose the tube is jacketed with a fluid at temperature Text that transfers heat to the outer wall of the... 

Equation 8.56 is the appropriate wall boundary condition associated with Equation 8.24 when there is external resistance to heat transfer. To implement it as part of the method of lines, an estimate for dTjdr at the wall is needed. A first-order approximation is just... 

Estimate the external resistance to mass transfer by invoking continuity of the normal component of intrapellet fluxes at the gas/porous-solid interface. Then use interphase mass transfer coefficients within the gas-phase boundary layer surrounding the pellets to evaluate interfacial molar fluxes. 

The external resistance to heat transfer is incorporated in reactor design simulations by expressing the normal component of interfacial flux in terms of a transfer coefficient and a driving force, the latter of which is sensitive to the direction of the unit normal vector n and the fact that Fourier s law and Pick s law require a negative sign to calculate the flux in a particular coordinate direction. These considerations produce the following expressions for the conductive energy flux ... 

Important results from earlier sections are summarized here to develop reactor design strategies when external resistances to heat and mass transfer cannot be neglected. Intrapellet resistances require information about... 

Ideal Isothermal Packed Catalytic Tubular Reactors with First-Order Irreversible Chemical Kinetics When the External Resistance to Mass Transfer Cannot Be Neglected... 

Separation of variables provides the analytical solution to this first-order ODE given by (30-60). When the external resistance to mass transfer is significant, the following result allows one to predict reactant conversion in the exit stream as a function of important design parameters based on isolated pellets as well as the entire packed catalytic tubular reactor ... 

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