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Continuous Differential Mass Transfer

In general, the performance of a packed column can be represented by an equilibrium curve, y =jYX, and an operating line. The latter relates crossing vapor and liquid compositions at any point in the column, and is based on material balance for the transferred component. For constant vapor and liquid flows, L and V, if at some reference point the concentrations of that component in the liquid and vapor are X-j-and Yf, and at another point in the column they are X and T, then by material balance, L X - Xj-) = KTj. - T), or, Y = Tj- -H (L/y)(Xj- - X). [Pg.530]

If instead of the discrete stages a packed column is used, an equivalent number of [Pg.530]

FIGURE 15.1 Simple absorber straight, parallel, operating line and equilibrium curve. [Pg.531]

In the special case where the operating line and the equilibrium curve are straight and parallel, the difference K-fis constant and the integration gives [Pg.531]


Referring to one fiber alone, the scheme of the reacting system is similar to those examined so far. However, the reaction does not occur in either regions 1, 2 or 3. The set of differential mass transfer and continuity equations defining substrate and product concentration in these regions are equal to those previously examined. The description of mass transport in the shell-side region is somewhat more complicated. Differences in the environment surrounding each fiber, the position of fibers in the bundle, and the ultrafiltration fluxes make both the analytical and the numerical approach quite difficult. [Pg.451]

Mass transfer processes involving two fluid streams are frequently carried out in a column countercurrent flow is usually employed although co-current flow may be advantageous in some circumstances. There are two principal ways in which the two streams may be brought into contact in a continuous process so as to permit mass transfer to take place between them, and these are termed stagewise processes and continuous differential contact processes. [Pg.621]

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. [Pg.129]

Mass transfer in packed columns is a continuous, differential, process, so the transfer unit method should be used to determine the column height, as used in absorption see Section 11.14.2. However, it often convenient to treat them as staged processes and use the HETS for the packing employed. For random packings the HETS will, typically, range from 0.5 to 1.5 m, depending on the type and size of packing used. [Pg.623]

For some biological systems, the species that eventually crosses the cell membrane has travelled through different media, each one with its own mass transfer characteristics. As an example, we deal with the case where the two media are the bulk solution and the cell wall (with the separation surface parallel to the cell membrane) with diffusion as the only relevant mass transfer phenomenon in each medium. Apart from having different parameters in the differential equations in each medium (due to the unequal diffusion coefficients), we need to impose two new boundary conditions at the separating plane which we denote as a. The first boundary condition follows from the continuity of the material flux ... [Pg.127]

The term on the right side of the equations quantitatively defines mass transfer from the dispersed to the continuous liquid, which is explained more fully in section 9.6. The coupled differential equation system can be analytically or numerically integrated for the appropriate practical boundary conditions. [Pg.400]

Specifically this paper describes an expression for the entropy production due to the mass fluxes in binary mass transfer systems with application to continuous differential contactors. [Pg.289]

Continuously operated, fixed bed reactors are frequently used for kinetic measurements. Here the reactor is usually a cylindrical tube filled with catalyst particles. Feed of a known composition passes though the catalyst bed at a measured, constant flow rate. The temperature of the reactor wall is usually kept constant to facilitate an isothermal reactor operation. The main advantage of this reactor type is the wealth of experience with their operation and description. If heat and mass transfer resistances cannot be eliminated, they can usually be evaluated more accurately for packed bed reactors than for other reactor types. The reactor may be operated either at very low conversions as a differential reactor or at higher conversions as an integral reactor. [Pg.91]

As we do for all mass transfer problems, we must satisfy the differential equation of continuity for each species as well as the differential momentum balance. Since we are dealing with a porous medium having a complex and normally unknown geometry, we choose to work in terms of the local volume averaged forms of these relations. Reviews of local volume averaging are available elsewhere (23-25). [Pg.39]

To derive the overall kinetics of a gas/liquid-phase reaction it is required to consider a volume element at the gas/liquid interface and to set up mass balances including the mass transport processes and the catalytic reaction. These balances are either differential in time (batch reactor) or in location (continuous operation). By making suitable assumptions on the hydrodynamics and, hence, the interfacial mass transfer rates, in both phases the concentration of the reactants and products can be calculated by integration of the respective differential equations either as a function of reaction time (batch reactor) or of location (continuously operated reactor). In continuous operation, certain simplifications in setting up the balances are possible if one or all of the phases are well mixed, as in continuously stirred tank reactor, hereby the mathematical treatment is significantly simplified. [Pg.751]

Liquid-liquid extraction columns may be designed in three different ways (1) as a collection of equilibrium stages, (2) as a continuous differential contactor with mass transfer, or (3) using purely kinetic models. The first two methods are more commonly used (particularly the first) and, when correctly and carefully performed, they give essentially the same results. The latter method, design... [Pg.720]


See other pages where Continuous Differential Mass Transfer is mentioned: [Pg.530]    [Pg.10]    [Pg.394]    [Pg.530]    [Pg.10]    [Pg.394]    [Pg.542]    [Pg.728]    [Pg.403]    [Pg.542]    [Pg.167]    [Pg.170]    [Pg.248]    [Pg.65]    [Pg.247]    [Pg.58]    [Pg.454]    [Pg.1199]    [Pg.143]    [Pg.281]    [Pg.157]    [Pg.65]    [Pg.106]    [Pg.650]    [Pg.650]    [Pg.149]    [Pg.650]    [Pg.650]    [Pg.264]    [Pg.1780]    [Pg.380]    [Pg.837]    [Pg.53]    [Pg.268]    [Pg.536]    [Pg.94]   


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