Multicomponent Mass Transfer Coefficients

The development for multicomponent mixtures is best carried out by using n — l dimensional matrix notation. We, therefore, define a matrix of finite flux mass transfer coefficients [fc ] by 

The finite flux coefficients are related to the zero-flux or low-flux coefficients by a matrix equation of the form 

In Eqs. 7.1.9 we define n — 1 X n — 1 elements of the mass transfer coefficients with the help of n — 1 linear equations. It follows that the elements k - are not unique that is, another set of these coefficients can also lead to the same value of the fluxes N. Put another way, making mass transfer measurements in a multicomponent system for the fluxes and Ax does not uniquely determine the values of the mass transfer coefficients. A large 

---

Our knowledge of multicomponent mass transfer coefficients is improving, but this is a slow process. I still occasionally have to pray that my estimate of some coefficient will not be off by more than one order of magnitude. 

In many cases, a priori estimates of the film thickness f cannot be made, and we resort to empirical methods of estimating the mass transfer coefficients. Most published experimental works have concentrated on two component systems and there are no correlations for the multicomponent [/ ]. The need to estimate multicomponent mass transfer coefficients is very real, however. The question is How can we estimate multicomponent mass transfer coefficients when all we have to go on are binary correlations In this section we look at the various methods that have been proposed to answer this question. 

To calculate [A ], which is the value needed to compute mass transfer fluxes, we may avoid computing [Sh]. Equations 8.4.23 or 8.4.30 and 8.4.31 may be used directly as written to compute the multicomponent mass transfer coefficients with the eigenvalues of [A ] computed from the appropriate expression in Section 9.2 as described above. 

SOLUTION For the purposes of this calculation we shall assume the drop to be noncirculating. Thus, the matrix of multicomponent mass transfer coefficients [A] may be computed from Eqs. 9.4.18 and 9.4.19 with the help of Sylvester s expansion formula or the modal transformation. At both the long and short contact time limits, however, we may calculate the ratios of mass transfer coefficients ky2/kii and A 21/A 22 without evaluating the series expansions needed in Eq. 9.4.19. 

The matrix of multicomponent mass transfer coefficients defined by... 

The next step is to compute the multicomponent mass transfer coefficients modified for the effect of a nonzero total flux. The total mass flux is needed for the evaluation of the high flux correction factor and is... 

The matrices of multicomponent mass transfer coefficients in all three zones may be estimated using the procedure developed in Section 8.8. The overall mass transfer coefficient matrix for each zone may be obtained from Eq. 8.8.20... 

The multicomponent mass transfer coefficients may be evaluated with the help of Eqs. 8.3.30 and 8.3.31 using the binary mass transfer coefficients determined above and the bulk gas-vapor composition. The result of the calculation is the following matrix ... 

Repeat Example 8.8.1 (ternary distillation in a wetted wall column) using the linearized equations to calculate the molar fluxes but following the suggestion given in the second paragraph of Section 8.8.3 for estimating the multicomponent mass transfer coefficients in terms of the binary mass transfer coefficients. 

Repeat Example 15.1.2 using the Toor-Stewart-Prober method of estimating the multicomponent mass transfer coefficients. 

In the five chapters that make up Part II (Chapters 7-11) we consider the estimation of rates of mass and energy transport in multicomponent systems. Multicomponent mass transfer coefficients are defined in Chapter 1, Chapter 8 develops the multicomponent film model, Chapter 9 describes unsteady-state diffusion models, and Chapter 10 considers models based on turbulent eddy diffusion. Chapter 11 shows how the additional complication of simultaneous mass and energy transfer may be handled. 

B] Multicomponent mass transfer coefficient matrix, kmol/(m2-s)... 

From the Maxwell-Stefan theory for multicomponent diffusion, Taylor and Krishna (1993) developed the following scheme to estimate the matrices of zero-flux multicomponent mass-transfer coefficients from binary-pair mass-transfer coefficients, Fy. These are obtained from correlations of experimental data, with the Chan and Fair (1984) correlations being the most widely used. For an ideal gas solution ... 

The mass transfer outside catalyst particles was modelled with rigorous Maxwell-Ste n equations, along with simultaneous heat transfer [9]. The multicomponent mass transfer coefficient matrix was calculated by assuming a film model for mass transfer and estimating the jo factor for the packed bed [10], The mass transfer coefficient correlations were extended into multicomponent systems by approximate matrix function calculations [11]. 

For the multicomponent mass transfer, the mass transfer rate is closely related to the composition due to the complicated molecular interaction between components and exhibit different characters with two-component system. For instance, for the two-component system, the mass flux is transferred from high to low concentration, yet in multicomponent system, some components can be transferred from low to high concentration. This is what we called bizarre phenomena (see Sect. 4.1.3.7). Thus, the mass transfer coefficient in multi-component system is complicated and can be calculated only under the individual condition based on the coefficients of relevant two-component pairs (see Sect. 3.7.2). For this reason, no general correlation for multicomponent mass transfer coefficient is available. 

---