Hatta number, liquid film reaction

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. 

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,... 

As discussed in Sec. 7, the factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption, i.e., Kq is replaced by EKq. The theoretical variation of E with Hatta number for a first- and second-order reaction in a liquid film is shown in Fig. 19-25. The uppermost line on the upper right represents the pseudo first-order reaction, for which E = Ha coth (Ha). Three regions are identified with different requirements of liquid holdup 8 and interfacial area a, and for which particular kinds of contacting equipment may be best ... 

According to the film theory, in reactive-absorption processes the resistance to mass transfer is concentrated in a small region near the gas/liquid interface. The ratio between tbe rate of chemical reaction and liquid-phase mass transfer is given by the Hatta number. For a second-order reaction (12.1), the Hatta number is defined as ... 

Equation 7.146 for the utilization factor corresponds to 7.107 for the case of heterogeneous catalysis with diffusional limitations. The analogy between 7.146 and 7.107 is complete when Shm = 1, i.e. when the reaction occurs simultaneously with diffusion throughout the complete liquid volume. The presence of a Sherwood number, besides the Hatta number, is needed to describe situations where a significant part of the reaction occurs in the bulk of the liquid, i.e. in series with the transport through the film. Such a situation is often encountered. Typical values for the Sherwood number are ... 

Fluid-fluid reactions are reactions that occur between two reactants where each of them is in a different phase. The two phases can be either gas and liquid or two immiscible liquids. In either case, one reactant is transferred to the interface between the phases and absorbed in the other phase, where the chemical reaction takes place. The reaction and the transport of the reactant are usually described by the two-film model, shown schematically in Figure 1.6. Consider reactant A is in phase I, reactant B is in phase II, and the reaction occurs in phase II. The overall rate of the reaction depends on the following factors (i) the rate at which reactant A is transferred to the interface, (ii) the solubihty of reactant A in phase II, (iii) the diffusion rate of the reactant A in phase II, (iv) the reaction rate, and (v) the diffusion rate of reactant B in phase II. Different situations may develop, depending on the relative magnitude of these factors, and on the form of the rate expression of the chemical reaction. To discern the effect of reactant transport and the reaction rate, a reaction modulus is usually used. Commonly, the transport flux of reactant A in phase II is described in two ways (i) by a diffusion equation (Pick s law) and/or (ii) a mass-transfer coefficient (transport through a film resistance) [7,9]. The dimensionless modulus is called the Hatta number (sometimes it is also referred to as the Damkohler number), and it is defined by... 

For GL reactions, whether the reaction is controlled by gas phase mass transfer, rate of mass transfer through the liquid film resistance at the surface or the reaction rate affects the configuration we select for the reactor. Two parameters that show where the reaction occurs are the Hatta number, Ha, and the dimensionless bulk/film volume ratio (ratio of the total liquid volume to the film volume),... 

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 ... 

The Hatta number that is indicative of the relative rates of reaction in the gas-liquid film and the rate of diffusion across the liquid film is defined as... 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

Figure 4.4.5 Influence of the Hinterland ratio (Hi) and the Hatta number (Ha) on the concentration profile in the liquid mass transfer film for a first-order reaction of gaseous reactant A according to Eqs. (4.4.35) and (4.4.28).

Gas-liquid reactions are governed by dimensionless numbers, namely, the Hatta number Ha, which reflects the ratio of the reaction rate to the rate of mass transfer, and the Hinterland ratio Hi, which is the ratio of the volume of the liquid phase to the liquid film volume. 

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