Mass transfer coefficient groups

Example 9 Calculation of Mass-Transfer Coefficient Group. 12-15... 

Table 16.4 Alternatfve mass transfer coefficient groupings for gas absorption... 

Note that the group on the left side of Eq. (14-182) is dimensionless. When turbulence promoters are used at the inlet-gas seclion, an improvement in gas mass-transfer coefficient for absorption of water vapor by sulfuric acid was obsei ved by Greenewalt [Ind. Eng. Chem., 18, 1291 (1926)]. A falhug off of the rate of mass transfer below that indicated in Eq. (14-182) was obsei ved by Cogan and Cogan (thesis, Massachusetts Institute of Technology, 1932) when a cauTiiug zone preceded the gas inlet in ammonia absorption (Fig. 14-76). 

Not only is the type of flow related to the impeller Reynolds number, but also such process performance characteristics as mixing time, impeller pumping rate, impeller power consumption, and heat- and mass-transfer coefficients can be correlated with this dimensionless group. 

Pavlushenko et al. (P4) in their dimensional analysis considered Ks, the volumetric mass transfer coefficient, to be a function of pc, pc, L, Dr, N, Vs, and g. They determined the following relationship for the dimensionless groupings ... 

In their analysis, however, they neglected the surface tension and the diffusivity. As has already been pointed out, the volumetric mass-transfer coefficient is a function of the interfacial area, which will be strongly affected by the surface tension. The mass-transfer coefficient per unit area will be a function of the diffusivity. The omission of these two important factors, surface tension and diffusivity, even though they were held constant in Pavlu-shenko s work, can result in changes in the values of the exponents in Eq. (48). For example, the omission of the surface tension would eliminate the Weber number, and the omission of the diffusivity eliminates the Schmidt number. Since these numbers include variables that already appear in Eq. (48), the groups in this equation that also contain these same variables could end up with different values for the exponents. 

For the mass-transfer coefficient of a bubble in a group of bubbles, Ruckenstein (R9) assumes that... 

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,... 

We will now describe the application of the two principal methods for considering mass transport, namely mass-transfer models and diffusion models, to PET polycondensation. Mass-transfer models group the mass-transfer resistances into one mass-transfer coefficient ktj, with a linear concentration term being added to the material balance of the volatile species. Diffusion models employ Fick s concept for molecular diffusion, i.e. J = — D,v ()c,/rdx, with J being the molar flux and D, j being the mutual diffusion coefficient. In this case, the second derivative of the concentration to x, DiFETd2Ci/dx2, is added to the material balance of the volatile species. 

Consider the mass transfer across a flat plate. In this case, the important variables are (dimensions in parentheses) the mass transfer coefficient k (L/T), the bulk fluid velocity u (L/T), the kinematic viscosity of the fluid v (L2/T), the solute diffusion coefficient I) (L2/T), and the plate length / (L). The number of independent variables n = 5 and the number of the involved dimensions m = 2. Hence, die number of dimensionless groups Pi = n — m = 3. 

The methods to determine mass transfer coefficients can be grouped according to whether the concentration of the transferred compound changes over time ... 

The influence of pressure on the mass transfer in a countercurrent packed column has been scarcely investigated to date. The only systematic experimental work has been made by the Research Group of the INSA Lyon (F) with Professor M. Otterbein el al. These authors [8, 9] studied the influence of the total pressure (up to 15 bar) on the gas-liquid interfacial area, a, and on the volumetric mass-transfer coefficient in the liquid phase, kia, in a countercurrent packed column. The method of gas-liquid absorption with chemical reaction was applied with different chemical systems. The results showed the increase of the interfacial area with increasing pressure, at constant gas-and liquid velocities. The same trend was observed for the variation of the volumetric liquid mass-transfer coefficient. The effect of pressure on kia was probably due to the influence of pressure on the interfacial area, a. In fact, by observing the ratio, kia/a, it can be seen that the liquid-side mass-transfer coefficient, kL, is independent of pressure. 

Figure 4.19 illustrates the effect of liquid phase mass transfer, represented by the dimensionless group Kuq (see Eqs. (55) and (57)). If the evaporation velocity is in the same order of magnitude as the liquid phase mass transfer coefficient, then the selectivity of the evaporation process vanishes though the relative volatility as well as the gas phase mass transfer coefficients remain unchanged. 

The extension of ideal phase analysis of the Maxwell-Stefan equations to nonideal liquid mixtures requires the sufficiently accurate estimation of composition-dependent mutual diffusion coefficients and the matrix of thermodynamic factors. However, experimental data on mutual diffusion coefficients are rare, and prediction methods are satisfactory only for certain types of liquid mixtures. The thermodynamic factor may be calculated from activity coefficient models such as NRTL or UNIQUAC, which have adjustable parameters estimated from experimental phase equilibrium data. The group contribution method of UNIFAC may also be helpful, as it has a readily available parameter table consisting of mam7 species. If, however, reliable data are not available, then the averaged values of the generalized Maxwell-Stefan diffusion coefficients and the matrix of thermodynamic factors are calculated at some mean composition between x0i and xzi. Hence, the matrix of zero flux mass transfer coefficients [k ] is estimated by... 

Thus, a relation of the type (9-58) may be valid because of the fact that the specific power group leads to nearly equal particle Reynolds number based on the relative velocity. Kuboi et al.67 also showed that, as long as an approximate relative velocity is used, the steady-state theories predict almost as good a mass-transfer coefficient as the more complex unsteady-state theories, a view not supported by some other workers.75,125 They claimed that the velocity of a particle relative to the surrounding liquid may correspond closely to the effective relative velocity for particle-to-liquid mass transfer. 

Variables, such as the heat or mass transfer coefficients from or to the interface or the flow friction coefficient for a given geometry, represent variables that can be included in this group. They have a dynamic effect on the process state and generally represent the dependent variables of the process. 

Transfer properties, the heat and mass transfer coefficient and friction factor, depend not only on transport and thermodynamic properties but also on the hydro-dynamic behavior of a fluid. The geometry of the system will influence the hydro-dynamic behavior. By reducing the parameters by arranging them into dimensionless groups, we can reduce the number of parameters that have to be varied to correlate any of the transfer properties. For example, the ffiction factor equation. 

Ind. Eng. Chem. Res. 41,4911 (2002)] developed two correlations for reconciling the gas-liquid mass-transfer coefficient and interfacial area in randomly packed towers. The correlation for the interfacial area was a function of five dimensionless groups, and yielded a relative error of 22.5 percent for 325 data points. That equation, when combined with a correlation for Nsh as a function of four dimensionless groups, achieved a relative error of 24.4 percent, for 3455 data points for the product k cfl. 

---