Interfacial gradient

Finally, the question rises whether an accurate simulation of the reformer tubes does not have to include consideration of radial gradients. The two dimensional model developed for this purpose in this work neglects interfacial gradients, for reasons explained already above, but maintains the mass transfer limitations inside the catalyst, of course. 

In this case, the interfacial gradients of surfactant occur because of interfacial gradients in the bulk concentration driven by bulk convection rather than interfacial convection. Although generally requiring numerical analysis, an analytic approximation can be obtained in the limit k

interface concentration is small. Again, we shall consider this case shortly. 

Example 3.3-1 Interfacial Gradients in Ethanol Dehydrogenation Experiments... 

Figure 11.8.a-1 One-dimensional heterogeneous model with interfacial gradients. 

Figure I I.8.a-2 One-dimensional heterogeneous model with interfacial gradients. Nonmique steady-state case Pq = 0.15 atm. To = 393°C. Initial T, A 393°C, B = 560f°C (after Liu and Amundson 91], from Froment [9]).

Figure II.8.b-I One-dimensional heterogeneous model with interfacial gradients. Start up of reactor, transient temperature profiles. AT = temperature increase of gas phase above feed value AT = increase of solid temperature above initial value.

The reactor model chosen is one dimensional and heterogeneous with interfacial gradients. Intraparticie gradients are accounted for implicitly throi the fit of the experimental data by means of Eq. 1. The operation is adiabatia Furthermore, as mentioned already, the operation is of a non-steady-state nature, since the oxidation takes place in a zone that gradually moves through the reactor. 

The simplest heterogeneous model considers only the interfacial gradients between sohd and fluid phases, imposing mass and energy balances for all phases involved and introdueing mass and heat transport from the gas bulk to catalyst surface and vice versa. Typical mass and energy balances equations are ... 

Taylor flows generated by the differences in the flow rates of the different phases provide excellent mixing characteristics. Taylor flow domains shown schematically in Figure 11.5 (of Interlude II) eliminates the interfacial gradients and enhances the rates of mass transfer that was inhibited by the interfacial gradients. Indeed, several orders of magnitnde greater rates of mass transfer were measured in microfluidic devices (Sobieszuk et al., 2012). 

We may now define an external effectiveness factor >jex as the ratio of the rate with external chffusion resistance to the rate without interfacial gradients ... 

Gonzo and Gottifredi [1983] applied (3.9-17) and extensions accounting also for interfacial gradients to experimental data of Wu and Nobe [1977] on the reduction of NO with ammonia and of Kehoe and Butt [1970] on benzene hydrogenation. 

One-Dimensional Model Accounting for Interfacial Gradients 1L8.1 Model Equations... 

In this set of equations and in those to follow in this chapter, C stands for the concentration of a reactant A. Figure 3.2.1-1 and 3.2.2-1 of Chapter 3 show many of the correlations available to date for l and hf [Froment, 1972]. Except perhaps for the most stringent conditions, these parameters are now defined with sufficient precision. The most likely interfacial gradient to occur is the temperature gradient. 

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