Mass transfer calculation

The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

The particle diameter to be employed in the mass transfer calculations is that of a sphere with the same area as that of the pellets. From equation 12.4.8 with rc = 1/16 and Lc = 1/8,... 

If the bubble size and shape are required, for example for mass transfer calculations, the work of Kumar and Kuloor (1970) and that of Grace, Wairegi and Nguyen (1976) may be consulted. 

The upper curve, which is the result of a curve fitting procedure to the points shown, is the HETP curve. The column was 25 cm long, 9 mm in diameter and packed with 8.5 micron (nominal 10 micron) Partisil silica gel. The mobile phase was a solution of 4.8 Sw/v ethyl acetate in n-decane. The minimum of the curve is clearly indicated and it is seen that the fit of the points to the curve is fairly good. As a result of the curve fitting procedure the values of the Van Deemter constants could be determined and the separate contributions to the curve from the multipath dispersion, longitudinal dispersion and the resistance to mass transfer calculated. 

Mass transfer coefficients In the mass transfer calculations, we need the Henry constant of oxygen in water at 30 °C, which can be evaluated using the relevant correlations presented in Section 1.3.2, Appendix I, and is equal to 34.03. The next parameter we need is the diffusion coefficient of oxygen in water at 30 °C, which can be also found in Table 1.10, Appendix I. The correction for the temperature has been also presented in eq. (1.28) Appendix I. The evaluated diffusion coefficient is 2.5 X 10-9 m2/s. 

This expression is used in discussing the diffusion through films in mass transfer calculations. Note that in very dilute solutions of A the quantity (1 — xa) =1 and Eq. (49) then simplifies to Fick s first law. 

The gassed condition is important in mass transfer calculations. In general, the ungassed- and gassed-power are related by the equation PG = P. The value of P is calculated from the power correlation for Rushton turbines [16]. The correction factor, y, is calculated from the following equations ... 

Another important modeling aspect is the simulation of catalytic process parameters and reactor configurations. Such models are typically associated with process engineering, and involve computational fluid dynamics and heat- and mass-transfer calculations. They are essential in the process planning and scale-up. However, as this book deals primarily with the chemical aspects of catalysis, the reader is referred to the literature on industrial catalysis and process simulations for further information [49,56]. 

In the following, the principles of mass-transfer separation processes will be outlined first. Details of mass-transfer calculations will be introduced next and examples will be given of both equilibrium-stage processes and diffusional rate processes. The chapter will then conclude with a detailed discussion of the two single most applied mass-transfer processes in the chemical industries, namely distillation and absorption. 

Mass-transfer calculations, such as the analysis or design of separation units, can be solved by two distinctly different methods, based on either the concept of (1) Equilibrium stage processes or (2) Diffusional rate processes. 

Net mass transfer between two phases can occur only when there is a driving force, such as a concentration difference, between the phases. When equilibrium conditions are attained, the driving force and, consequently, the net rate of mass transfer becomes zero. A state of equilibrium, therefore, represents a theoretical limit for mass-transfer operations. This theoretical limit is used extensively in mass-transfer calculations. 

Here the c-multiplied diffusion coefficients are used because their dependence on pressure and temperature is simpler, and they are frequently used in mass transfer calculations. 

Fast and satisfactory mass transfer calculations are necessary since we may have to repeat such calculations many times for a rate-based distillation column model or two-phase flow with mass transfer between the phases in the design and simulation process. The generalized matrix method may be used for multicomponent mass transfer calculations. The generalized matrix method utilizes the Maxwell-Stefan model with the linearized film model for diffusion flux, assuming a constant diffusion coefficient matrix and total concentration in the diffusion region. In an isotropic medium, Fick s law may describe the multicomponent molecular mass transfer at a specified temperature and pressure, assuming independent diffusion of the species in a fluid mixture. Such independent diffusion, however, is only an approximation in the following cases (i) diffusion of a dilute component in a solvent, (ii) diffusion of various components with identical diffusion properties, and (iii) diffusion in a binary mixture. 

Reaction-path calculation. A sequence of mass transfer calculations that follows defined phase (or reaction) boundaries during incremental steps of reaction progress. 

Equations 9.3.15 and 9.3.16 represent an exact analytical solution of the multicomponent penetration model. For two component systems, these results reduce to Eqs. 92.1. Unfortunately, the above results are of little practical use for computing the diffusion fluxes because they require an a priori knowledge of the composition profiles (cf. Section 8.3.5). Thus, a degree of trial and error over and above that normally encountered in multicomponent mass transfer calculations enters into their use. Indeed, Olivera-Fuentes and Pasquel-Guerra did not perform any numerical computations with this method and resorted to a numerical integration technique. 

These values are within 5% of the values calculated with the penetration theory correction factor matrix and support our earlier suggestion that it is sufficient to use the simpler film model correction factor matrix in multicomponent mass transfer calculations at high mass transfer rates. ... 

A fundamental shortcoming of the Chilton-Colburn approach for multicomponent mass transfer calculations is that the assumed dependence of [/ ] on [Sc] takes no account of the variations in the level of turbulence, embodied by r turb/, with variations in the flow conditions. The reduced distance y is a function of the Reynolds number y = (y/R )(//8) / Re consequently. Re affects the reduced mixing length defined by Eq. 10.2.21. An increase in the turbulence intensity should be reflected in a relative decrease in the influence of the molecular transport processes. So, for a given multicomponent mixture the increase in the Reynolds number should have the direct effect of reducing the effect of the phenomena of molecular diffusional coupling. That is, the ratios of mass transfer coefficients 21/ 22 should decrease as Re increases. 

The contribution to the total mass transfer of the splash zone is generally negligibly small and is neglected in the working model for mass transfer calculations pictured in Figure 12.4. 

The model of the spray regime for mass transfer calculations is pictured in Figure 12.5. 

The electrode length, 2L, is much smaller than the computational domain used in the fluid simulations. A separate mesh was therefore used for the mass-transfer calculations. Velocity components in the mass-transfer calculations were approximated hy their first terms in a Taylor series expansion in distance y from the wall ... 

J mechanism parameter 0 solution capacity parameter, based on mass-transfer calculation y a variable, in Eqs. (110) and (162)... 

This leads to the concept of mass transfer calculation techniques in scaleup. Figure 36 shows the concept of mass transfer from the gas-liquid step as well as the mass transfer step to liquid-solid and/or a chemical reaction. Inherent in all these mass transfer calculations is the concept of dissolved oxygen level and the driving force between the phases. In aerobic fermentation, it is normally the case that the gas-liquid mass transfer step from gas to liquid is the most important. Usually the gas-liquid mass transfer rate is measured, a driving force between the gas and the liquid calculated, and the mass transfer coefficient, KqO or t a obtained. Correlation techniques use the data shown in Fig. 37 as typical in which KqO is correlated versus power level and gas rate for the particular system studied. 

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