Liquid-phase chemical reaction rates, mass transfer effects

Mass Transfer Effects on Liquid-Phase Chemical Reaction Rates... 

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... 

The solubility of terephthalic acid in the above-mentioned solvents is very low, which means that the acid must diffuse continuously from the solid particules to the solution where the reaction takes place. In such a case, the first question which arises is does the diffusion control the kinetics of the overall process In all cases, the authors claimed that the reaction rate is never affected by the amount of undissolved terephthalic acid and that the reaction proceeds through a chemical kinetic control. Under the experimental conditions used by Bhatia et al. the diffusion rate of terephthalic acid from the solid particles to the solution is 9.5x 10 mol cm" s at 100 °C and that of ethylene oxide from the gas phase to the liquid is 19.4 x 10" mol cm" s" . These values are far above the rate of formation of the diester(bishydroxy-ethylterephthalate), as this is only 5.84 x 10" mol cm" s" . Moreover, the independence of the reaction rate on the mass transfer effects was shown by varying the values of some parameters (e.g., ethylene oxide flow-rate, stirrer-speed, particule size, terephthalic acid charge) in a large range. 

This reaction provides a wide variety of hydrocarbons (Ci to 50-200) from synthesis gas, becoming a very attractive route for the production of clean fuels (LPG, gasoline, kerosene, and diesel) and a source of chemicals (namely, linear olefins) [42]. However, it is important to ensure an appropriate size and type of reactor due to its exothermicity (Af/R = -165kJ/mol). Mass transfer effects are also significant since catalyst pores are filled with liquid products (waxes and water) limiting the diffusion rate. Despite the gas phase of reactants, selectivity to C5+ seems to decrease notably for diffusion lengths exceeding 0.1-0.3mm. Therefore, MSRs have been proposed as a suitable alternative. 

As already has been mentioned mass transfer of ozone from the gas phase to the liquid phase may be enhanced by the chemical reactions of ozone with components A and B and by the decay of ozone. The effect of this enhancement in mass transfer on the selectivity will be discussed now semi-quantitatively13. To that aim we consider a gas phase in contact with a liquid phase. The liquid phase consists of a thin stagnant film at the interface with the gas phase, and a liquid bulk phase. We assume that the ozone is completely converted in the stagnant liquid film. This is for example the case if we have to deal with a high reaction rate constant and a relatively high concentration of one of the pollutants in the liquid film. Figure 5 gives a schematically presentation of this situation. 

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. 

The best possible mode of gas-liquid contact for a given process depends upon a combination of effects, including hydrodynamics, mass transfer, and chemical kinetics. In treating this combination, a dimensionless parameter P has been defined as the ratio of total volume of the liquid phase to volume of the liquid diffusion layer. Krishna and Sie reported general values of jS to be 10 0 for thin liquid films and liquid sprays, and 10 -10" for gas bubbles within a continuous liquid. The relative rates of mass transfer and chemical reaction show whether high values or low values of jS best utilize available reactor volume. 

The following development applies to almost all chemical absorptions. Solute molecules in the gas diffuse to and across the interface, then diffuse in the liquid until meeting a reactant. If the reaction is very fast, the nonreactive mass transfer relations, previously discussed, apply—but very conservatively the effective rate is higher. The flux equation for liquid phase transfer of component i is modified as follows ... 

A signihcant number of commercial absorption processes involve a chemical reaction in the liquid phase. The effect of the reaction is to speed up the rate of mass transfer and, to some extent, make the determination of transfer units or stages simpler. 

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