Gas- -Liquid Mass Transfer Models

The fundamental gas-liquid mass transfer models lack the ability to obtain and process all necessary information and factors integral to bioreactor operation. Gas-liquid systems are simply too complex. Therefore, a theoretical equation, which is widely applicable, does not exist (Garcia-Ochoa and Gomez, 2004). Empirical correlations have been developed to simplify analysis and design and have become exclusive in the literature and practice (Kawase and Moo-Young, 1988). Model parameters are chosen that are thought to influence the operation, and their powers and constants are fltted to the experimental data. The correlations are used for design and scale-up while theoretical mass transfer models are used to explain the influence of various operational inputs. 

Reynolds number is defined in Eq. (3.11) in Section 3—Gas-Liquid Mass Transfer Models. 

Several reported chemical systems of gas-liquid precipitation are first reviewed from the viewpoints of both experimental study and industrial application. The characteristic feature of gas-liquid mass transfer in terms of its effects on the crystallization process is then discussed theoretically together with a summary of experimental results. The secondary processes of particle agglomeration and disruption are then modelled and discussed in respect of the effect of reactor fluid dynamics. Finally, different types of gas-liquid contacting reactor and their respective design considerations are overviewed for application to controlled precipitate particle formation. 

A non-ideal MSMPR model was developed to account for the gas-liquid mass transfer resistance (Yagi, 1986). The reactor is divided into two regions the level of supersaturation in the gas-liquid interfacial region (region I) is higher than that in the main body of bulk liquid (region II), as shown in Figure 8.12. 

Kolbel et al. (K16) examined the conversion of carbon monoxide and hydrogen to methane catalyzed by a nickel-magnesium oxide catalyst suspended in a paraffinic hydrocarbon, as well as the oxidation of carbon monoxide catalyzed by a manganese-cupric oxide catalyst suspended in a silicone oil. The results are interpreted in terms of the theoretical model referred to in Section IV,B, in which gas-liquid mass transfer and chemical reaction are assumed to be rate-determining process steps. Conversion data for technical and pilot-scale reactors are also presented. 

The volumetric gas-liquid mass transfer coefficient ki a) has been obtained by fitting the concentration profile of dissolved oxygen to the axial dispersion model [8, 18]. The value of... 

Chapter 24. In this chapter, we are concerned with the kinetics of these reactions, and hence with reaction models, which may have to include gas-liquid mass transfer as well as chemical reaction. 

In the treatment to follow, we first review the two-film model for gas-liquid mass transfer, without reaction, in Section 9.2.2, before considering the implications for ki-netics-in Section 9.2.3. 

V. Linek, M. Fujasova, M. Kordae, T. Moucha, Gas-liquid mass transfer coefficient in stirred tank interpreted through models of idealized eddy structure of turbulence in the bubble vicinity, Chem. Eng. Proc. (in press). 

Similar equations can also be written for the gas phase. Thus, the gas-liquid mass transfer is modeled as a combination of the two-film model presentation and Max-well-Stefan diffusion description. In this stage model, the thermodynamic equilibrium is assumed only at the phase interface. 

In this case study we will model, simulate and design an industrial-scale BioDeNOx process. Rigorous rate-based models of the absorption and reaction units will be presented, taking into account the kinetics of chemical and biochemical reactions, as well as the rate of gas-liquid mass transfer. After transformation in dimensionless form, the mathematical model will be solved numerically. Because of the steep profiles around the gas/liquid interface and of the relatively large number of chemical species involved, the numerical solution is computationally expensive. For this reason we will derive a simplified model, which will be used to size the units. Critical design and operating parameters will be identified... 

Parameters k and k2 can be easily related to the hydrodynamic conditions (flow rate, stirring rates) and to the current density by empirical equations. The influence of the current density can also be related to the reagent dose for parameter k and to the bubble generation for parameter k2 (the flow rate of cathodically generated hydrogen is proportional to the current density). Thus, this semiempirical model considers easily and simultaneously the gas-liquid mass transfer, the collections of solid particles in electroflotation processes, and the effect of the current density. 

For this model to be valid the following assumptions have been considered i) very small satellite bubbles formed in the break-up do not significantly contribute to gas hold-up and gas-liquid mass-transfer only relatively large bubbles are considered ii) bubble Sauter... 

Just as with the gas holdup, gas-liquid interfacial area should also be divided into two parts. The literature, however, gives a unified correlation. The same is true for volumetric gas-liquid mass transfer coefficients and mixing parameters for both gas and liquid phases. The fundamental r.echanism for inter-phase mass transfer and mixing for large bubbles is expected to be different from the one for small bubbles. Future work should develop a two phase model for the bubble column analogous to the two phase model for fluidized beds. 

Gas-liquid mass transfer is commonly modeled in terms of a gas film (between the bulk gas and interface) and a liquid film (between the interface and bulk liquid). Hindrance to mass transfer causes soluble gas (e.g., O2) concentrations to decrease across these films. The highest mass transfer resistance usually exists in the liquid film therefore, it controls the overall oxygen transfer rate (OTR). In aerobic fermentation, an effective fermenter design achieves an efficient OTR through intimate gas-liquid contact. OTR is described in terms of oxygen concentration and characteristics of the gas-liquid interface, as follows ... 

However, for a given gas velocity, any change in gas or liquid properties, downcomer and riser geometry, phase separation conditions, liquid volume, reactor height, or gas distribution causes changes in liquid velocity and gas holdup. Therefore, no generalized model or correlation for the volumetric gas-liquid mass transfer coefficient in airlift reactors exists. 

The calculation of k using Eqs. 9.2.11 and 9.2.12 requires a priori estimation of the exposure time or the surface renewal rate s. In some cases this is possible. For bubbles rising in a liquid the exposure time is the time the bubble takes to rise its own diameter. In other words, the jacket of the bubble is renewed every time it moves a diameter. If we consider the flow of a liquid over a packing, when the liquid film is mixed at the junction between the packing elements, then is the time for the liquid to flow over a packing element. For flow of liquid in laminar jets and in thin films, the exposure time is known but in these cases it may be important to take into account the distribution of velocities along the interface. In the penetration model, this velocity profile is assumed to be flat (i.e., plug flow). For gas-liquid mass transfer in stirred vessels, the renewal frequency in the Danckwerts model s may be related to the speed of rotation (see Sherwood et al. 1975). 

It is possible to model the fermentation biological process from a fluid mechanics standpoint, even though the impeller is not related properly geometrically to the gas-liquid mass transfer step. Thus, one scale of pilot plant might be usable for one or two of the fermentation mass transfer steps, and/or chemical reaction steps, but might not be suitable for analysis of other mass transfer steps. The decision, then, is based on how suitable existing data are for any steps which are not modeled properly in the pilot plant. 

A model has been developed for oxidation of calcium sulfite in a three-phase, semibatch reactor, The overall rate of conversion to sulfate depends on the rates of solid dissolution and liquid phase chemical reaction. In this first treatment of the problem, gas-liquid mass transfer resistance did not affect the overall rate of oxidation. 

Very often the rates of chemical transformations are affected by the rates of other processes, such as heat and mass transfer. The process should be treated as a part of kinetics. The gas/liquid mass transfer in multiphase heterogeneous and homogeneous catalytic reactions could be treated in a similar way. The mathematical framework for modelling diffusion inside solid catalyst particles of supported metal catalysts or immolisided enzymes does not differ that much, but proper care should be taken of the reaction kinetics. 

Lekhal et al. [6] proposed a pseudo-homogeneous gas-liquid-liquid model based on the Higbie penetration theory to account for simultaneous absorption of two gases into the liquid phases. Because of the assumption of rapid liquid-liquid mass transfer of reactants leading to the equilibrium between two liquid phases, the model was simplified greatly and the detail of phase dispersion and distribution and multiphase flow was avoided. Reasonable success was achieved and the results of analysis suggested that the only limitation to the conversion of hydroformylation of 1-octene was the gas-liquid mass transfer of CO and H2. 

The remainder of this book is organized as follows. All bioreactors have common modes of operation, which are described in Chapter 2. General gas-liquid mass transfer considerations are then summarized in Chapter 3. Various hydrodynamic and gas-liquid mass transfer measure techniques are then outlined in Chapter 4, followed by a summary of multiphase flow modeling... 

Many mass transfer models exist, but most of them depend on three assumptions and are simplified versions of actual mass transfer mechanisms, many of which occur simultaneously. The first assumption is that the different phases and the phase interface offer resistance to mass transfer in series, in a similar manner to heat transfer resistances. The second assumption maintains that mass transfer is controlled by the phase equilibrium near the interface, which changes more quickly than the bulk phase equilibrium (Azbel, 1981). In other words, mass transfer occurs at the microscale level (van Elk et ak, 2007). Finally, gases are assumed to be single component. Multiple component problems are more complicated because each individual gas component making up the mixture has to be considered for the limiting gas-liquid mass transfer step. The complexity grows further once the relationships between each gas component and, for example, the bacteria in a bioreactor are considered. 

Stenberg, O., and Andersson, B. (1988b), Gas-liquid mass transfer in agitated vessels-II. Modelling of gas-liquid mass transfer, Chemical Engineering Science, 43(3) 725-730. 

Let us consider the gas-liquid mass transfer. In the stagnant film model, it is postulated that mass transfer proceeds via steady-state molecular diffusion in a hypothetical stagnant film at the interface with thickness while the bulk of the... 

A relatively simple model to describe the gas-liquid mass transfer in circular channels with slug flow pattern was proposed by van Eaten and Krishna [47]. For their fundamental model the authors considered an idealized geometry of the Taylor bubbles as shown in Figure 7.12. The bubbles consist of two hemispherical caps and a cylindrical body. The Higbie penetration model was applied to describe the mass transfer process of a compound from the gas phase to the liquid (Equation 7.8). For a rising bubble, the liquid will flow along the bubble surface of the cap. The average distance... 

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