Liquid film reaction mass transfer coefficients

In regime 3, the reaction is sufficiently fast to consume the dissolved solid reactant completely in the liquid film. Diffusion and reaction occur simultaneously in a parallel fashion in the liquid film. The mass transfer coefficient... 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

The carbon source affects oxygen demand. In penicillin production, oxygen demand for glucose is 4.9 mol 1 1 h-1. The lactose concentration is 6.7 mol 1 1 h 1, sucrose is 13.4 mol l-1 h. The yield of oxygen per mole of carbon source for CH4 is YQjC = 1.34, T0j/C for Paraffins = 1, and Y(> /c for hydrocarbon (CH20)n = 0.4. The mass transfer coefficient k,a is for gas-liquid reactions, and the film thickness where the mass transfer takes place is 8... 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

Both reactions are slow compared to the film diffusion in the liquid phase13-15. Hence, the reactions can be assumed to take place predominantly in the bulk phase of the liquid. The rate of mass transfer can be calculated using Equation 7.2. The interfacial concentration can be calculated using Henry Law. Mass transfer coefficients, interfacial area and gas hold-up data are required. Gas hold-up is defined as ... 

What is the significance of the parameter fi = (k2C BLDAf5 / kL in the choice and the mechanism of operation of a reactor for carrying out a second-order reaction, rate constant k2, between a gas A and a second reactant B of concentration CBL in a liquid In this expression, DA is the diffusivity of A in the liquid and kL is the liquid-film mass transfer coefficient. What is the reaction factor and how is it related to /l ... 

Reaction between an absorbed solute and a reagent lowers the equilibrium partial pressure of the solute and thus increases the rate of mass transfer. The mass transfer coefficient likewise may be enhanced which contributes further to increased absorption rate. Three modes of contacting gas and liquid phases are possible The gas is dispersed as bubbles in the liquid, the liquid is dispersed as droplets, the two phases are contacted on a thin liquid film deposited over a packing or wall. The choice between these modes is an important practical problem. 

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,... 

Relative Kga valid for all systems controlled by mass transfer coefficient (Kg) and wetted area (a) per unit volume of column. Some variation should be expected when liquid reaction rate is controlling (not liquid diffusion rate). In these cases liquid hold-up becomes more important. In general a packing having high liquid hold-up which is clearly greater than that in the falling film has poor capacity. 

Fig. 9. The molar flux of component A at the vapour-liquid interface (°) and at the boundary between mass transfer film and liquid bulk (S) as function of reaction rate constant in case (a) the mass transfer coefficients are equal and (b) the mass transfer coefficients are different.

Then, to evaluate the intrinsic reaction coefficient, we need the mass transfer coefficient in the liquid film, which can be calculated by means of the correlation of Dharwadkar and Sylvester (fw = 1) (eq. (3.433)) ... 

In a heterogeneous gas-liquid reactor system, that is where gas absorption precedes a liquid-phase reaction, the mass transfer rate has to at least equal the reaction rate. This principle can be used to determine mass transfer coefficients and/or reaction rate constants for certain kinetic regimes (see Section B 3.2.1). To determine the mass transfer coefficient, the kinetic regime must be instantaneous, and the place of the reaction must be in the film (Charpentier, 1981 Beltran and Alvarez, 1996). To determine the reaction rate constant, the kinetic regime must be fast and kLa must be known. 

The design of packed column reactors is very similar to the design of packed columns without reaction (Volume 2, Chapter 12). Usually plug flow is assumed for both gas and liquid phases. Because packed columns are used for fast chemical reactions, often the gas-side mass transfer resistance is significant and needs to be taken into account. The calculation starts on the liquid side of the gas-liquid interface where the chemical reaction rate constant is compounded with the liquid side mass transfer coefficient to give a reaction-enhanced liquid-film mass transfer... 

This equation can be written Nco,s k[CCor where k[ = VA, Deo, and may be regarded as a liquid-film mass transfer coefficient enhanced oy the fast chemical reaction. This is very convenient because it allows us to use the expression in Volume 2, Chapter 12 for combining liquid-film and gas-film coefficients to give an overall gas-film coefficient ... 

From Fig. 4.3 it may be seen that this value, although smaller than that in Example 4.2, is still sufficiently large for all the reaction to occur in the film. Also the concentration of dissolved C02 at the interface in contact with the incoming gas containing C02 at a partial pressure of 0.001 bar will be only 0.001/., i.e. 0.001/25 4 x 10"5 kmoi/m3 which is much less than 0.05 kmol/m3, the concentration of the OH- ion, so that the reaction will still behave as nseudo first-order. The enhanced liquid-side mass transfer coefficient kl will thus be k[ V(9.5 x 103 x 0.05 x 1.8 x 10 9) 0.925 x 10 3 m/s. 

As Fig. 4.15 demonstrates, the two mass transfer steps, gas to liquid and liquid to solid, and then the chemical reaction, take place in series. This means that in the steady state each must proceed at the same rate as the overall process. Continuing then on the basis of unit volume of dispersion, and using the reactant concentrations shown in Fig. 4.15, with the gas-liquid and liquid-solid film mass transfer coefficients kL and ks shown in Fig. 4.20, the overall rate 91, may be written as ... 

As mentioned, from the point of view of practical application, impinging streams is not suitable for the systems given in Table 7.2. On the other hand, the absorption processes for which impinging streams is applicable normally involve fast reaction(s) in liquid and thus are controlled by gas-film diffusion. Therefore the most important should be the gas-film mass transfer coefficient, kti, which is absent in the table. 

As is shown in Figure 2, in the two-phase model the fluid bed reactor is assumed to be divided into two phases with mass transfer across the phase boundary. The mass transfer between the two phases and the subsequent reaction in the suspension phase are described in analogy to gas/liquid reactors, i.e. as an absorption of the reactants from the bubble phase with pseudo-homogeneous reaction in the suspension phase. Mass transfer from the bubble surface into the bulk of the suspension phase is described by the film theory with 6 being the thickness of the film. D is the diffusion coefficient of the gas and a denotes the mass transfer coefficient based on unit of transfer area between the two phases. 6 is given by 6 = D/a. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

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