Hatta regimes

It must be emphasized that the above considerations were made in the absence of reaction. Interfacial mass transfer followed by reaction requires further consideration. The Hatta regimes classify transfer-reaction situations into infinitely slow transport compared to reaction (Hatta category A) to infinitely fast transport compared to reaction (Hatta category H) [42]. In the first case all reaction occurs at the interface and in the second all reaction occurs in the bulk fluid. Homogenous catalytic hydrogenations, carbonylations etc. require consideration of this issue. An extreme example of the severity of mass transport effects on reactivity and selectivity in hydroformylation has been provided by Chaudari [43]. Further general discussions for homogeneous catalysis can be found elsewhere [39[. 

Longer Reaction Times For homogeneous catalytic systems without reactants in a second phase (P or Pl), the fluid elements in the CSTR, recycle loop, and cells are quite similar at times greater than ca. 100 s. Furthermore, for homogeneous catalytic systems with reactants in a second phase (Pq or Pj ), the fluid elements in the CSTR, recycle loop, and cells are quite similar at times greater than ca. 100 s if transport is fast compared to reaction i. e. Hatta regimes F-H. 

In general, the intrinsic kinetics, the diffusion, mass transfer and Henry coefficients are either known or can be estimated, while the Hatta number can be determined. This is the first step in assessing the working regime of the reactor. 

On the basis of the Hatta number, the transformations carried out in biphasic systems can be described as slow (Ha < 0.3), intermediate (with a kinetic-diffusion regime 0.3 < Ha < 3.0), and fast (Ha > 3). These are diffusion limited and take place near the interface (within the diffusion layer). Slow transformations are under kinetic control and occur mostly in a bulk phase, so that the amount of substrate transformed in the boundary layer in negligible. When diffusion and reaction rate are of similar magnitude, the reaction takes place mostly in the diffusion layer, although extracted substrate is also present in the continuous phase, where it is transformed at a rate depending on its concentration [38, 50, 54]. 

In the following discussion the four most important regimes are briefly explained in order to outline which step is rate controlling for the removal of the pollutants and which practical situation it represents. An in-depth mathematical description of these situations is beyond the scope of this book, and the reader is referred to further literature. The fundamentals of fast gas-liquid reactions were first described by Hatta (1931). Detailed... 

The Hatta-number represents the ratio of maximal possible reaction and mass transfer rates and helps to specify different absorption regimes. Depending on the Hatta-number value, it is possible to discriminate between very fast, fast, average and slow chemical reactions, in respect to physical mass transport [19, 20]. 

This expression is based on Hatta s film concept. Similar expressions result from penetration theory. Figure 3 illustrates the concentration profiles for A and B in and around the fluid film for Regime II. 

For analysis of such coupled fluid-fluid systems it is useful to distinguish between three regimes of the reaction rate (see Figure 1) which are characterized by different values of the Hatta number Ha (eqs. (2) and (3)) and the enhancement factor E (see below) ... 

Solving the diffusion-reaction equation in the liquid, the enhancement factor can be related to the Hatta number Ha, which is similar to the Thiele modulus defined for heterogeneous gas-solid catalysts. Thus, the Hatta number and its relation to the controlling regime are... 

Compute Hatta number M, identify regime, determine enhancement factor rj and corresponding rate equation... 

The aforementioned criterion based on diffusion and reaction times is qualitative. To establish the regime more precisely, the Hatta number is popularly used. For the aforementioned general (p, g)th-order reaction, the Hatta number is given by... 

However, in contrast to regime A, the homogeneous reaction is significantly rapid as compared to the diffusion process in the film (Cg Bg k a). This ensures almost complete consumption of the amount of A supplied to the bulk liquid phase. Effectively, this implies Ag 0. In terms of Hatta number ... 

Regime C Fast Reaction Occurring in the Diffusion Film There are situations where both and are low and comparable. Under these conditions, both reaction and diffusion occur simultaneously in the diffusion film. This regime is characterized by Hatta number >3. Concentration profiles for this regime are shown in Figure 2.3c. 

Experimental data on the absorption of CO2 in blends of Diethanolamine (DEA) and Piperazine (PZ) reported in the literatureare very little. The finding of additional kinetics is very much valuable. In this work, the CO2 absorption rate into aqueous solutions of mixture DEA and PZ was measured and the experimental results are presented in Fig. 1-4. The absorption flux, Rco2> was analysed using the Eq.2 and Eq.3. The pseudo-first order reaction regime assumption was verified by ealeulating Hatta... 

Use Hatta number to determine the controlling regime in a fluid-fluid reaction system. 

Another condition for regime 2 is that the amount of A that reacts in the film before reaching the bulk be negligible. For the very slow and slow reactions, the kinetic term resides along with the differential equation describing the transport of the species in the film, such that the definition of Hatta modulus is necessary as was derived in Chapter 6 for a pseudo-first-order reaction. In Chapter 6, we defined the Hatta modulus as... 

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