Rate controlling step, mass transfer

When the temperature is high enough to make mass transfer the controlling step, the conversion can be predicted from the flow rate, the external area, and the mass transfer coefficient. For an incremental length of monolith and a surface concentration equal to zero, the mass balance is... 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

Mass-transfer rates have been determined by measuring the absorption rate of a pure gas or of a component of a gas mixture as a function of the several operating variables involved. The basic requirement of the evaluation method is that the rate step for the physical absorption should be controlling, not the chemical reaction rate. The experimental method that has gained the widest acceptance involves the oxidation of sodium sulfite, although in some of the more recent work, the rate of carbon dioxide absorption in various media has been used to determine mass-transfer rates and interfacial areas. 

Example 11.8 With highly reactive absorbents, the mass transfer resistance in the gas phase can be controlling. Determine the number of trays needed to reduce the CO2 concentration in a methane stream from 5% to 100 ppm (by volume), assuming the liquid mass transfer and reaction steps are fast. A 0.9-m diameter column is to be operated at 8 atm and 50°C with a gas feed rate of 0.2m /s. The trays are bubble caps operated with a 0.1-m liquid level. Literature correlations suggest = 0.002 m/s and A, = 20m per square meter of tray area. 

In general, the overall reaction process may comprise several individual steps, as shown in Figure 3.24. It could be seen that these steps pertain to (i) mass transfers of reactants and the products between the bulk of the fluid and the external surface of the solids (ii) transport of reactants and the products within the pores of the solid and (iii) chemical reaction between the reactants in the fluid and those in the solid. In order to be able to determine the rate-controlling step and to ascertain whether more than a single step should be consid-... 

Special forms of equation 8.5-50 arise depending on the relative importance of mass transfer, pore diffusion, and surface reaction in such cases, one or two of the three may be the rate-controlling step or steps. These cases are explored in problem 8-18. The result given there for problem 8-18(a) is derived in the following example. 

If the surface reaction is the rate-controlling step, any effects of external mass transfer and pore-diffusion are negligible in comparison. The interpretation of this, in terms of the various parameters, is that Ag kA, cAs - cAg, and T) and 17 both approach the value of 1. Thus, the rate law, from equation 8.5-50, is just that for a homogeneous gas-phase... 

Mass transfer steps are essential in any multiphase reactor because reactants must be transferred from one phase to another. When we consider other multiphase reactors in later chapters, we will see that mass transfer rates fiequently control these processes. In this chapter we consider a simpler example in the catalytic reactor. This is the first example of a multiphase reactor because the reactor contains both a fluid phase and a catalyst phase. However, this reactor is a very simple multiphase reactor because the catalyst does not enter or leave the reactor, and reaction occurs only by the fluid reacting at the catalyst surface. 

As the temperature is varied in a reactor, we should expect to see the rate-controlling step vary. At sufficiently low temperature the reaction rate coefficient is small and the overall rate is reaction limited. As the temperature increases, pore diffusion next becomes controlling (Da is nearly independent of temperature), and at sufficiency high temperature external mass transfer might limit the overall process. Thus a plot of log rate versus 1 / T might look as shown in Figure 7-15. 

Because interface reaction and mass/heat transfer are sequential steps, crystal growth rate is controlled hy the slowest step of interface reactions and mass/heat transfer. For a crystal growing from its own melt, the growth rate may be controlled either by interface reaction or heat transfer because mass transfer is not necessary. For a crystal growing from a melt or an aqueous solution of different composition, the growth rate may be controlled either by interface reaction or mass transfer because heat transfer is much more rapid than mass transfer. Different controls lead to different consequences, including the following cases ... 

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

The apparent rates of adsorption into adsorbent particles usually involve the resistances for mass transfer of adsorbate across the fluid film around adsorbent particles and through the pores within particles. Adsorption perse at adsorption sites occurs very rapidly, and is not the rate-controlling step in most cases. 

Steps 3 and 5, the diffusion through the relatively unmixed liquid layers of the bubble and the microorganism, are the slowest among those outlined previously and, as a result, control the overall mass-transfer rate. Agitation and aeration enhance the rate of mass transfer in these steps and increase the mterfacial area of both gas and liquid. 

The various steps in the removal of a gas from air by a porous adsorbent may be confined broadly to the following processes (a) mass transfer or diffusion of the gas to the gross surface (b) diffusion of the gas into or along the surface of the pores of granular adsorbent (c) adsorption on the interior surface of the granules (d) chemical reaction between the adsorbed gas and adsorbent (e) desorption of the product and (/) transfer of the products from the surface to the gas phase. Whether surface reaction or diffusion (mass transfer) to the surface becomes the rate-controlling step will become evident in the analysis of the experimental data with respect to the rate constant. 

Either the rate of diffusion to the surface or the speed of the surface reaction governs the rate of removal of the gas from the air stream, depending on which is the slower process. If k is dependent on flow rate, then diffusion is the rate-governing step. From Table XII it is evident that k is proportional to L. Therefore, one can assume that mass transfer is the rate-controlling step and the surface reaction is much faster than the diffusion process. 

Rate Controlling Step Mass Transfer (pore diffusion)... 

The sphere Xp = 1 — (r/R) Rate Controlling Step—Mass Transfer ... 

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