ABSTRACT
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Michel Quintard and Stephen Whitaker
CONTENTS 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Diffusive Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Volume Averaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.6 Convective and Diffusive Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.7 Nondilute Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.7.1 Constant Total Molar Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.7.2 Volume Average of the Diffusive Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.8 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.8.1 Closed Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
This chapter deals with multicomponent mass transfer and heterogeneous reaction under conditions where temperature effects can be ignored. The process is illustrated in Figure 1.1 where we have identified a flowing fluid as the γ -phase and an impermeable solid as the κ-phase. The chemical reaction takes place at the γ –κ interface, and when convective transport is important this situation is often referred to asmass transferwith reaction at a nonporous catalyst. Such systems are commonly treated in texts on reactor design [1-4] and in many cases one must consider the effect of heat transfer on the reaction rate. When convective transport is negligible, the process illustrated in
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Figure 1.1 represents a case of diffusion and reaction in a porous catalyst, and this is a major problem in the area of reactor design. In texts on reactor design, problems of mass transfer and reaction are
uniformly presented in terms of an uncoupled, linear convective-diffusion equation, or as an uncoupled, linear diffusion equation in the case of porous catalysts. This simplification is applicable when the reacting species is dilute and this requires that the mole fraction of the reacting species be small compared to one. When this is not the case, the diffusive transport becomes nonlinear, and what is often considered to be a routine transport problem becomes quite complex. Direct numerical solution of the nonlinear problem is possible; however, transport processes in porous media necessarily demand spatially smoothed equations [5] and this increases the complexity of the analysis.
