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. 

Hatta Number A film-conversion parameter is defined as maximum possible conversion in the film... 

Of the parameters making up the Hatta number, hquid diffusivity data and measurement methods are weh reviewed in the hterature. 

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. 

To fully grasp the main feature of the gas-liquid precipitation phenomena, however, it is not enough just to account for the formation of crystal particles, evaluation of the Hatta number is also essential. 

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 first equation gives the rate of gas consumption as moles of gas (n) versus time. This is the only state variable that is measured. The initial number of moles, nO is known. The intrinsic rate constant, K is the only unknown model parameter and it enters the first model equation through the Hatta number y. The Hatta number is given by the following equation... 

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). 

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. 

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. 

They are adapted to other concentrations as suggested by the Hatta number, and estimating that stirring conditions are equivalent to L = 1000 lb/(hr)(sqft). 

Hassium (Hs), l 492t HASTELLOY alloys, 17 102, 103 Hastelloy B, 13 519 Hastelloy B-2, 23 784-785 Hastelloy-C, 14 14 Hastelloy C series alloys, 13 520 Hatch Act of 1887, 24 353-354 Hatta number, 21 345 Haulage distances, 15 60-61 Hausmannite, 15 540 Hayashi-Williams equation, 22 561 Haylage, 10 863... 

Now we define three dimensionless factors The (dimensionless) Hatta number HaA related to ozone and component A ... 

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. 

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