Calculation of Mass Transfer Rate

In solving the mass transfer Eq. (3.1), the evaluation of the source term 5n, which is the mass rate (mass flux) transferred from adjacent phase (outside of the system concerned) or generated by chemical reaction (inside of the system), is very important as it is highly affect the final result. For the gas-liquid two-phase mass transfer process under steady condition and assuming the driving force of mass transfer is the linear concentration difference, we can write the conventional formula for calculating the mass transfer rate of species i [dimension kg s ], denoted by 5n or Nj, as follows  

Note that, in this section, the subscript i and j denotes species i and j, not the directions i, j ki and ko are, respectively, the film mass transfer coefficient of liquid and gas [m s- ] Co. and C,G are, respectively, the bulk concentration of component i [kg m ] in liquid phase and gas phase C l and C q are, respectively, the concentration of component i at the interface in thermodynamic equilibrium with the C,L and C,g (kg m ). The importance of evaluation of mass transfer coefficient kj or g is clearly seen from the foregoing equation. Nevertheless, the prediction of the coefficient is difficult, and so far only relies on experimental measurement. There are two different cases  

---

Gal-Or and Resnick (Gl) have developed a simplified theoretical model for the calculation of mass-transfer rates for a sparingly soluble gas in an agtitated gas-liquid contactor. The model is based on the average gas residencetime, and its use requires, among other things, knowledge of bubble diameter. In a related study (G2) a photographic technique for the determination of bubble flow patterns and of the relative velocity between bubbles and liquid is described. 

Although the absorption of a gas in a gas-liquid disperser is governed by basic mass-transfer phenomena, our knowledge of bubble dynamics and of the fluid dynamic conditions in the vessel are insufficient to permit the calculation of mass-transfer rates from first principles. One approach that is sometimes fruitful under conditions where our knowledge is insufficient to completely define the system is that of dimensional analysis. 

Transfer units are also used extensively in the calculation of mass transfer rates in countercurrent columns and reference should be made to Chapter 10. 

The. /-factors for heat and mass transfer, jh and jd, are found to be equal, and therefore equation 4.44 can also be used for the calculation of mass transfer rates. 

Algorithm 8.1 Algorithm for Calculation of Mass Transfer Rates from an Exact Solution of the Maxwell-Stefan Equations... 

For this problem, you should assume that the mass transfer process occurs within the region surrounding the bubble where the Stokes approximation to the velocity field can be used. Thus the solution will be valid provided that Re Pe. Explain the reason for this condition. Your calculation of mass transfer rate should be carried out to include the first correction because of convention. 

The foregoing example is interesting because it shows population balance models can account for the occurrence of physicochemical processes in dispersed phase systems simultaneously with the dispersion process itself. Shah and Ramkrishna (1973) also show how the predicted mass transfer rates vary significantly from those obtained by neglecting the dynamics of drop breakage. The model s deficiencies (such as equal binary breakage) are deliberate simplifications because its purpose had been to demonstrate the importance of the dynamics of dispersion processes in the calculation of mass transfer rates rather than to be precise about the details of drop breakup. 

EXAMPLE 2.1. Calculation of Mass Transfer Rates in a Parallel Plate Reactor... 

Calculation of Mass Transfer Rate 73 Table 3.2 Some published empirical ctHrelations for binary system with Sh-Re-Sc form ... 

The calculation of mass transfer rate of multicomponent system will be briefly described in the section below and Sect. 4.1.3 of Chap. 4. 

Calculation of Mass Transfer Rate Similarly, we have... 

---