Mass transfer coefficient, liquid-side model

Yadav,G.D. and M.M.Sharma. "feffect of diffusivity on true gas-side mass transfer coefficient in a model stirred contactor with a plane liquid interface". Chem.Engng.Sci. 34 (1979) 1423. 

The first term on the right-hand side of Eq. (257) is provided by the quasisteady model, whereas the second represents the contribution of the transient process. Measurements of the mass transfer coefficients from the dissolution of the wall of a tube into a turbulent liquid having Schmidt numbers as large as 10s could be correlated with the expression [56]... 

Abstract—Gas-liquid interfacial areas a and volumetric liquid-side mass-transfer coefficients kLa are experimentally determined in a high pressure trickle-bed reactor up to 3.2 MPa. Fast and slow absorption of carbon dioxide in aqueous and organic diethanolamine solutions are employed as model reactions for the evaluation of a and kLa at high pressure, and various liquid viscosities and packing characteristics. A simple model to estimate a and kLa for the low interaction regime in high pressure trickle-bed reactors is proposed. 

Gas-liquid interfacial areas, a, and volumetric liquid-side mass transfer coefficients, kLa, are measured in a high pressure trickle-bed reactor. Increase of a and kLa with pressure is explained by the formation of tiny bubbles in the trickling liquid film. By applying Taylor s theory, a model relating the increase in a with the increase in gas hold-up, is developed. The model accounts satisfactorily for the available experimental data. To estimate kLa, contribution due to bubbles in the liquid film has to be added to the corresponding value measured at atmospheric pressure. The mass transfer coefficient from the bubbles to the liquid is calculated as if the bubbles were in a stagnant medium. 

The penetration model (Eq. 9.2.11) is used to predict the liquid-phase mass transfer coefficients with the exposure time assumed to be the time required for the liquid to flow between corrugations (a distance equal to the channel side)... 

The bottom product rates were specified in molar units. For column 1 the side stream flow rate also was specified in molar units. Specification of the molar flow rates makes the simulations converge more easily. Nonstandard specifications can be harder for a nonequilibrium model to converge than for a corresponding equilibrium model because nonstandard specifications are more likely to lead to large variations in vapor and liquid flows from iteration to iteration. Since mass transfer coefficient and pressure drop calculations may... 

In the previous sections, stagnant films were assumed to exist on each side of the interface, and the normal mass transfer coefficients were assumed proportional to the first power of the molecular diffusivity. In many mass transfer operations, the rate of transfer varies with only a fractional power of the diffusivity because of flow in the boundary layer or because of the short lifetime of surface elements. The penetration theory is a model for short contact times that has often been applied to mass transfer from bubbles, drops, or moving liquid films. The equations for unsteady-state diffusion show that the concentration profile near a newly created interface becomes less steep with time, and the average coefficient varies with the square root of (D/t) [4] ... 

This rather simple equation contains three cracial quantities that depend on design and operation of the packed colunm These quantities are the effective interfadal area, the gas side mass transfer coefficient /5q, and the liquid side mass transfer coefficient. According to the present state of the art, no models based on first principles are available for the prediction of these rather cracial quantities. Only some empirical correlations have been published so far (e.g., in Kister 1992). 

Film and penetration models are most commonly used defining the liquid-side mass transfer coefficients (k ) as follows ... 

Various models are available to calculate liquid side mass transfer coefficients kj. The value of this hydrodynamic parameter and the equations that apply to its calculation largely depend on bubble size and the constitution of the bubble surface. Fig. 6 presents some recent measurements on mass transfer from single bubbles (19) which demonstrate the above influences. The evaluated kL values are plotted as Sherwood numbers vs. Peclet numbers. Large circulating bubbles with mobile surface yield kj, values which approach the... 

Hallensleben (19) has shown recently that liquid-side mass transfer coefficients obtained from measurements with single bubbles apply with good accuracy to bubble swarms provided the bubbles do not interfere. This is the case if the gas-in-liquid dispersion is operated in the bubbly flow regime, i.e. at gas velocities less than about 5 cm/s. Therefore the models and correlations for single bubbles can be utilized to... 

In fact the piston flow model, as well as the diffusion model, gives too ideal picture of the structure of the flows. They take into account neither the diffusion boundary layer nor the real movement of the phases. These models are especially far from the real situation in flie apparatus in respect to the liquid phase which moves not like a piston flow but in the form of film, drops and jets which are not only separate in space but have also different and continuously changing velocities. Nevertheless, not only the diffusion model but in some cases also its simpler variant, the piston flow model, gives oflxm very good description of the mass transfer processes in industrial apparatuses. This can be explained with the comparatively weak influence of the real structure of the flows on the mass transfer. On the other side using in the model such experimentally obtained values as mass transfer coefficient, effective surface, and Peclet number, it is possible to take into account the important for the mass transfer rate characteristics of the flows structures. In Chaptra 8 the cases when it is possible to use the simpler piston flow model, and when it is necessary to use the diffusion model are considered and specified. 

Another type of a model system, used for determinatirm of the gas-side controlled mass transfer coefficient, is evaporation of liquids (usually ter) in a gas stream [82]. The disadvantage of this meftiod is the strong d malence of the equilibrium partial pressure of the evaporated liquid on the temperature, and the fact that because of the hi value of the evaporation heat, it is practically impossible to cany out the process isothermally and therefore to determine precisely the equilibrium partial pressure of the liquid. This leads to a significant error of this method, especially in comparison with that of nonequilibriuffl absorption companied by instantaneous chemical reaction. 

The investigations of Murrieta [268] tiiow that for calculation of the liquid-side controlled mass transfer coefficient in case of corrugated packii the Higbie penetration model (Chapter 1) can be used, when the erqmsure time 0g in it is calculated the equaticm... 

The axial mixing in foe liquid phase is very important. The ratio of foe liquid-side controlled mass transfer coefficient for the dispersion and the piston flow model is up to 6 [53]. 

The fllm theory is the simplest model for interfacial mass transfer. In this case it is assumed that a stagnant fllm exists near the interface and that all resistance to the mass transfer resides in this fllm. The concentration differences occur in this film region only, whereas the rest of the bulk phase is perfectly mixed. The concentration at the depth I from the interface is equal to the bulk concentration. The mass transfer flux is thus assumed to be caused by molecular diffusion through a stagnant fllm essentially in the direction normal to the interface. It is further assumed that the interface has reached a state of thermodynamic equilibrium. The mass transfer flux across the stagnant film can thus be described as a steady diffusion flux. It can be shown that within this steady-state process the mass flux will be constant as the concentration profile is linear and independent of the diffusion coefficient. Consider a gas-liquid interface, as sketched in Fig. 5.16. The mathematical problem is to formulate and solve the diffusion flux equations determining the fluxes on both sides of the interface within the two films. The resulting concentration profiles and flux equations can be expressed as ... 

The model of mass transfer jn nted in Chapter 1, Eqs. (16S) to (168), can be us also for calculation of processes with chemu reaction by correcting the liquid-side partial transfer coefficient with the influence of the chemical reaction on it Practically, the theory on the area of mass transfer with chemical reaction is dealing with that correction. In this chapter onl the main part of the theory is presented. For mote information the cited books [1-3] can be used. 

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