Mass diffusion column

In mass diffusion, separation of isotopes occurs throu diffusion of the li t isotope of a gas mixture into a condensible vapor at higher rate than diffusion of the heavy isotope. Mass diffusion separation has been canied out in a cascade of individual mass diffusion stages and in a mass diffusion column. 

Because the separation obtainable in a mass diffusion stage is even smaller than in a gaseous diffusion stage, a practical degree of separation requires either a multistage cascade, such as the 48-stage cascade used by Hertz [H3] to separate neon isotopes, or a mass diffusion column. 

Sweep diffusion is a form of mass diffusion column in which the screen separating the counterflowing light and heavy streams is not present. Cichelli et al. [C4] developed the theory of such a column and used it to separate hydrogen from natural gas and to enrich air. Table... 

Because it has no screen, the sweep diffusion column is simpler to construct and has a lower transfer-unit height than the mass diffusion column. A disadvantage is the greater difficulty of maintaining undisturbed counterflow over a long column. 

In general, the procedure for designing a bubble column reactor (BCR) (1 ) should start with an exact definition of the requirements, i.e. the required production level, the yields and selectivities. These quantities and the special type of reaction under consideration permits a first choice of the so-called adjustable operational conditions which include phase velocities, temperature, pressure, direction of the flows, i.e. cocurrent or countercurrent operation, etc. In addition, process data are needed. They comprise physical properties of the reaction mixture and its components (densities, viscosities, heat and mass diffusivities, surface tension), phase equilibrium data (above all solubilities) as well as the chemical parameters. The latter are particularly important, as they include all the kinetic and thermodynamic (heat of reaction) information. It is understood that these first level quantities (see Fig. 3) are interrelated in various ways. 

The experimental pairs H and f are the variables of Eq. 1. By introducing them into the data lines of the GWBASIC program, such as given in the Appendix of Ref. [9] together with other easily obtained quantities required by the input lines (such as the geometric details of the diffusion column, mass and porosity of the catalyst bed, solute amount, as well as its diffusion coefficient in the carrier gas, and the carrier gas flow rate), the various physicochemical parameters related to the studied catalyst are calculated. 

For integrating Eq. (4-9), vji= ei Er) should be known as a function of and operating variables. However, the momentum diffusivity is the only term we know, with essentially no systematic data for In the case of free turbulence of a homogeneous fluid, the diffusivity of a scalar quantity like heat and mass is estimated to be about two times that of momentum (S4) and the two diffusivities are not far apart for turbulent pipe flow (S8). However, such a relation is not available yet for gas-liquid bubble flow in bubble columns. Generally the local radial mass diffusivity may be expressed by a, with a being a numerical coefficient of order unity. 

Despite this unfavorable conclusion for uranium isotopes, mass diffusion does appear to have favorable features for small-scale separation of isotopes of heavy elements such as argon, for which the column type of separator can be used. 

Isotopes separated. Table 14.24 gives examples of some of the highest reported concentrations of separated isotopes that have been obtained by thermal diffusion. Most of these separations were on a small laboratory scale. The high purity to which scarce isotopes such as C, N, and 0 have been concentrated is a notable feature of these examples of thermal diffusion. The feasibility of concentrating rare isotopes of intermediate mass, such as Ne and A, by thermal diffusion is also noteworthy. These separations are facilitated by the large number of stages obtainable from a single thermal diffusion column. 

Figure 8.8. Entropy production rate profile for a 15 stage RD column for MTBE synthesis. Legend 5m entropy produced by interfacial mass diffusion S entropy produced by interfacial energy transfer Srx. entropy produced by chemical reaction Remarks stages are numbered from top to bottom reboiler and condenser drum are not depicted MeOH feed stream is fed at 9 tray and iCt stream at 10 tray. The operational and design variables are listed in table 8.4.

Second, the mass balance equation for the pollutant in the region z (diffusion column)... 

Fig. 3.2 The simulated mass diffusivity Di contours on a column tray using different % modeling equations and model constants (II) The conditions of a, b, and c are given in Fig. 3.1 (Reprinted from Ref. [4], Copyright 2007, with permission from Elsevier)...

Fig. 4.34 Average turbulent mass diffusivity along the column height at different F factors (reprinted from Ref [32], Copyright 2009, with permission from Elsevier)...

Over the last decades, the application of computational fluid dynamics (CFD) to study the velocity and temperature profiles in packed column has been frequently reported [1-5]. However, for the prediction of concentration profile, the method commonly employed is by guessing an empirical turbulent Schmidt number Sc, or by using experimentally determined turbulent mass diffusivity D, obtained by using the inert tracer technique under the condition of no mass transfer [6, 7]. Nevertheless, the use of such empirical methods of computation, as pointed out in Chap. 3, is unreliable and not always possible. To overcome these drawbacks, the development of rigorous mathematical model is the best choice. 

Fig. 5.38 Simulated axial fluctuating mass flux, concentration gradient, and axial mass diffusivity of OH in the column for CO2 absorption into aqueous NaOH (Til), x—distance measured from column top (x is measured from column top) [10], a m c c in radial direction, b K c in axial direction, c in radial direction, d in axial direction...

From Eq. (3.37) and Figs. 7.12a and 7.13a, the axial turbulent mass diffusivity Dt,x can be obtained as given in Fig. 7.14. As shown in the figure, Dt,x is in the wavy shape and fluctuated strongly beyond r/R — 0.6. It is mainly due to the high fluctuation of gas-phase velocity in both axial and radial directions as shown in Fig. 7.15. However, the tendency of turbulent effect looks increasing toward the column bottom. 

To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in equation 12.27 or equation 12.28. The easiest way to accomplish this is by adjusting the velocity of the mobile phase. At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. As shown in Figure 12.15 (which is interpreted in terms of equation 12.28), the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of u. 

Kovat s retention index (p. 575) liquid-solid adsorption chromatography (p. 590) longitudinal diffusion (p. 560) loop injector (p. 584) mass spectrum (p. 571) mass transfer (p. 561) micellar electrokinetic capillary chromatography (p. 606) micelle (p. 606) mobile phase (p. 546) normal-phase chromatography (p. 580) on-column injection (p. 568) open tubular column (p. 564) packed column (p. 564) peak capacity (p. 554)... 

Equimolar Counterdiffusion. Just as unidirectional diffusion through stagnant films represents the situation in an ideally simple gas absorption process, equimolar counterdiffusion prevails as another special case in ideal distillation columns. In this case, the total molar flows and are constant, and the mass balance is given by equation 35. As shown eadier, noj/g factors have to be included in the derivation and the height of the packing is... 

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