Reaction Hatta number

For weU-defined reaction zones and irreversible, first-order reactions, the relative reaction and transport rates are expressed as the Hatta number, Ha (16). Ha equals (k- / l ) where k- = reaction rate constant, = molecular diffusivity of reactant, and k- = mass-transfer coefficient. Reaction... 

The Hatta number Nna usually is employed as the criterion for determining whether or not a reaction can be considered extremely slow. For extremely slow reactions a reasonable criterion is... 

First-order and pseudo-first-order reactions are represented by the upper curve in Fig. 14-14. We note that for first-order reactions when the Hatta number is larger than about 3, the rate coefficient k can be computed by the formula... 

The numerical solution of these equations is shown in Fig. 23-28. This is a plot of the enhancement fac tor E against the Hatta number, with several other parameters. The factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption with zero concentration of A in the liquid. The uppermost line on the upper right represents the pseudo-first-order reaction, for which E = P coth p. 

The process has a large Hatta number that is, the rate of reaction is much greater than the rate of diffusion, so a large interfacial area is desirable for carrying out the reaction in the film. 

RT) and ks - 3.11.10 exp(-13639/RT) m. kmof. s. The value of ki, obtained in this research are almost the same as that obtained by Venugopal. Venugopal neglected the side reactions. The value of E and Hatta Number -/m were greater than 3, so that the reaction system can be considered as pseudo-first order reaction with respect to oxygen and the process was controlled by mass transfer aspect. 

GL 26] [R 3] [P 28] A simple reactor model was developed assuming isothermal behavior, confining mass transport to only from the gas to the liquid phase, and a sufficiently fast reaction (producing negligible reactant concentrations in the liquid phase) [10]. For this purpose, the Hatta number has to be within given limits. 

The reaction (Eqn. 5.4-65) takes place in the liquid phase. The molecules are transferred away from the interface to the bulk of the liquid, while reaction takes place simultaneously. Two limiting cases can be envisaged (1) reaction is very fast compared to mass transfer, which means that reaction only takes place in the film, and (2) reaction is very slow compared to mass transfer, and reaction only takes place in the liquid bulk. A convenient dimensionless group, the Hatta number, has been defined, which characterizes the situation compared to the limiting cases. For a reaction that is first order in the gaseous reactant and zero order in the liquid reactant (cm = 1, as = 0), Hatta is ... 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

Hatta number = (k DAlkuA) for first order reaction in the gaseous reactant and zero order in the liquid reactant... 

The Hatta number Ha, as a dimensionless group, is a measure of the maximum rate of reaction in the liquid film to the maximum rate of transport of A through the liquid... 

Note that the enhancement factor E is relevant only for reaction occurring in the liquid film. For an instantaneous reaction, the expressions may or may not involve E, except that for liquid-film control, it is convenient, and for gas-film control, its use is not practicable (see problem 9-12(a)). The Hatta number Ha, on the other hand, is not relevant for the extremes of slow reaction (occurring in bulk liquid only) and instantaneous reaction. The two quantities are both involved in rate expressions for fast reactions (occurring in the liquid film only). 

Situation 2 slow chemical reaction, Ho<0.3, = 1. The Hatta number is small, and thus the chemical reaction does not modify the mass transfer process and consequently, E 1. However, the chemical reaction is not so slow compared to the mass transfer rate. The hydrogen concentration in the bulk is smaller than the equilibrium concentration. The substrate concentration A is constant in the film and is almost that in the bulk. The consumption of H2 and A is negligible in the film and takes place in the bulk of the liquid. The reactor performances are obtained straightforwardly (see below). The mass transfer rate is obtained by /H LfCfJ.i-CH.L)-... 

A reagent in solution can enhance a mass transfer coefficient in comparison with that of purely physical absorption. The data of Tables 8.1 and 8.2 have been cited. One of the simpler cases that can be analyzed mathematically is that of a pseudo-first order reaction that goes to completion in a liquid film, problem P8.02.01. It appears that the enhancement depends on the specific rate of reaction, the diffusivity, the concentration of the reagent and physical mass transfer coefficient (MTC). These quantities occur in a group called the Hatta number,... 

The numerical solution of these equations is shown on the plot which is due to van Krevelen Hoftijzer (Trans Instn Chem Engrs 32 S360, 1954). The plot is of the enhancement factor E against the Hatta number (3 which is defined in P8.02.01. The parameters along the curves are of a ratio, a = CbLDb/CaLD0. The uppermost curve is for a first order reaction. 

In general the concentration of component A (the toxic pollutant) is low compared to the concentration of ozone. That means that the value of A is smaller than or in the order of 1. The enhancement factor for mass transfer can then be neglected. There is also no influence of the Hatta number HaA. In a similar way we can calculate the transport and diffusion of component B under the assumption that no reaction of ozone with component A takes place. The enhancement factor for mass transfer of ozone, EB, can then be given by the equation... 

In general the concentration of component B (the non-toxic pollutant) is higher than the concentration of ozone. That means that b is much higher than 1. There is also a strong influence of the Hatta number, in this case, HaB. It can therefore be concluded that at high values of HaB, the enhancement of ozone mass transfer due to the reaction of ozone with component B may be substantial. 

From the above it can be concluded that only the reaction with component B may enhance mass transfer of ozone substantially. And only if the Hatta number HaB is much higher than 1. Therefore it can be expected that whenever we have to deal with an enhancement of mass transfer due to chemical reactions, this influences the selectivity of the oxidation process in a negative way. The factor which has to be considered in this respect is the Hatta number for the reaction of ozone with component B (equation 29). HaB increases with increasing value of kB and CBb and with decreasing value of the mass transfer coefficient for ozone, kHq,... 

Additional experiments in a loop reactor where a significant mass transport limitation was observed allowed us to investigate the interplay between hydrodynamics and mass transport rates as a function of mixer geometry, the ratio of the volume hold-up of the phases and the flow rate of the catalyst phase. From further kinetic studies on the influence of substrate and catalyst concentrations on the overall reaction rate, the Hatta number was estimated to be 0.3-3, based on film theory. 

Important hints on the reaction site can be gained by the Hatta numbers (Ha) of mass transport at the G/L- and L/L-phase boundaries. These numbers are also essential in order to estimate mass transport rates and concentration profiles within the boundary layer. Since the main resistance of mass transport is in the aqueous phase, mass transport coefficients and Ha numbers mentioned in the text are related to the aqueous phase. 

The expression for the enhancement factor E, eq. (35), has first been derived by van Krevelen and Hof-tijzer in 1948. These authors used Pick s law for the description of the mass transfer process and approximated the concentration profile of component B by a constant Xb, over the entire reaction zone. It seems worthwhile to investigate whether the same equation can be applied in case the Maxwell-Stefan theory is used to describe the mass transfer process. To evaluate the Hatta number, again an effective mass transfer coefficient given by eq. (34), is required. The... 

Figures 7(a)-(c) show a comparison between the numerically computed absorption flux and the absorption flux obtained from expression (31), using eqs (24), (30) and (34)-(37). From these figures it can be concluded that for both equal and different binary mass transfer coefficients absorption without reaction can be described well with eq. (24), whereas absorption with instantaneous reaction can be described well with eq. (30). If the Maxwell-Stefan theory is used to describe the mass transfer process, the enhancement factor obeys the same expression as the one obtained on the basis of Fick s law [eq. (35)]. Finally, from Figs 7(b) and 7(c) it appears that the use of an effective mass transfer coefficient m the Hatta number again produces satisfactory results.

The use of the Hatta number has been suggested to assess whether the reaction occurs in the bulk phase or in the interface. This parameter relates the transfer rate due to catalysis to the transfer rate due to diffusion. For a given substrate, the Hatta number can be given by... 

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]. 

When Cg (i.e., concentration of B which reacts with A) is much larger than C, Cg can be considered approximately constant, and k Cg) can be regarded as the pseudo first-order reaction rate constant (T ). The dimensionless group y, as defined by Equation 6.23, is often designated as the Hatta number (Ha). According to Equation 6.22, if y > 5, it becomes practically equal to E, which is sometimes also called the Hatta number. For this range. 

The Hatta number is a dimensionless group used to characterize the importance of the speed of reaction relative to the diffusion rate. 

As the Hatta number increases, the effective liquid-phase mass-transfer coefficient increases. Figure 14-13, which was first developed by Van Krevelen and Hoftyzer [Rec. Trav. Chim., 67, 563 (1948)] and later refined by Perry and Pigford and by Brian et al. [AlChE J., 7,226 (1961)], shows how the enhancement (defined as the ratio of the effective liquid-phase mass-transfer coefficient to its physical equivalent q = ki/kl) increases with NHa for a second-order, irreversible reaction of the kind defined by Eqs. (14-60) and (14-61). The various curves in Fig. 14-13 were developed based upon penetration theory and... 

In this respect, much depends on the relation between the mass transfer and reaction rates in a particular RSP. The definition of the Hatta number representing the reaction rate in reference to that of the mass transfer helps to discriminate between very fast, fast, average, and slow chemical reactions (68,77). 

Fm Fraction of absorbed energy in water that it is absorbed for any compound M, defined in Eq. (47), dimensionless Ha Hatta number for gas-liquid reactions, defined in Eq. (9), dimensionless He Henry s law constant for ozone in a water containing substances, Pa M 1... 

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]. 

The enhancement factors are either obtained by fitting experimental results or are derived theoretically on the grounds of simplified model assumptions. They depend on reaction character (reversible or irreversible) and order, as well as on the assumptions of the particular mass transfer model chosen [19, 26]. For very simple cases, analytical solutions are obtained, for example, for a reaction of the first or pseudo-first order or for an instantaneous reaction of the first and second order. Frequently, the enhancement factors are expressed via Hatta-numbers [26, 28]. They can be used in combination with the HTU/NTU-method or with a more advanced mass transfer description method. However, it is generally not possible to derive the enhancement factors properly from binary experiments, and a theoretical description of reversible, parallel or consecutive reactions is based on rough simplifications. Thus, for many reactive absorption processes, this approach appears questionable. 

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