FIG. 14-16 Concentration profiles in the vapor and liquid phases near an interface.

FIG. 14-16 Concentration profiles in the vapor and liquid phases near an interface.

diagrammed in Fig. 14-16 for absorption. Accordingly, there exists a stable interface separating the gas and the liquid. A certain distance from the interface, large fluid motions exist, and these distribute the material rapidly and equally so that no concentration gradients develop. Next to the interface, however, there are regions in which the fluid motion is slow; in these regions, termed films, material is transferred by diffusion alone. At the gas-liquid interface, material is transferred instantaneously, so that the gas and liquid are in physical equilibrium at the interface. The rate of diffusion in adsorption is therefore the rate of diffusion in the gas and liquid films adjacent to the interface. The model framework is completed by including terms for species generation (chemical equilibrium and chemical kinetics) in the gas and liquid film and bulk regions. Taylor, Krishna, and Koo-ijman (Chem. Eng. Progress, July 2003, p. 28) have provided an excellent discussion of rate-based models; these authors emphasize that the diffusion flux for multicomponent systems must be based upon the Maxwell-Stefan approach. The book by Taylor and Krishna (Multi-component Mass Transfer, Wiley, New York, 1993) provides a detailed discussion of the Maxwell-Stefan approach. More details and discussion have been provided by the program vendors listed above.

Parameterization of Mass-Transfer and Kinetic Models The mass-transfer and chemical kinetic rates required in the rigorous model are typically obtained from the literature, but must be carefully evaluated; and fine-tuning through pilot-plant and commercial data is highly recommended.

Mass-transfer coefficient models for the vapor and liquid coefficients are of the general form kfj = apj,f(Dm, pv, a,internal characteristics) (14-75a)

kVj = aPfDmj, |v, pv, a,internal characteristics) (14-75b)

where a = effective interfacial area per unit volume, Dm are the Stefan-Maxwell diffusion coefficients, P = pressure, p = molar density, and | = viscosity. The functions in Eqs. (14-75a) and (14-75b) are correlations that depend on the column internals. Popular correlations in the literature are those by Onda at al. [J. Chem.. Eng. Jap., 1, 56 (1968)] for random packing, Bravo and Fair [Ind. Eng. Chem. Proc. Des. Dev., 21, 162 (1982)] for structured packing, Chan and Fair [Ind. Eng. Chem. Proc. Des. Dev., 23, 814 (1984)] for sieve trays, Scheffe and Weiland [Ind. Eng. Chem. Res., 26, 228 (1987)] for valve trays, and Hughmark [AIChE J., 17, 1295 (1971)] for bubble-cap trays.

It is highly recommended that the mass-transfer correlations be tested and improved by using laboratory, pilot-plant, or commercial data for the specific application. Commercial software generally provides the capability for correction factors to adjust generalized correlations to the particular application.

Kinetic models are usually developed by replacing a subset of the speciation reactions by kinetically reversible reactions. For example, Freguia and Rochelle replaced equilibrium reactions (14-74a) and (14-74b) with kinetically reversible reactions and retained the remaining three reactions as very fast and hence effectively at equilibrium. The kinetic constants were tuned using wetted-wall column data from Dang (M.S. thesis, University of Texas, Austin, 2001) and field data from a commercial plant.

Modern commercial software provides powerful capability to deploy literature correlations and to customize models for specific applications.

Deployment of Rigorous Model for Process Optimization and Equipment Design Techniques similar to those described above may be used to develop models for the stripper as well as other pieces of plant equipment, and thus an integrated model for the entire absorption system may be produced. The value of integrated models is that they can be used to understand the combined effects of many variables that determine process performance and to rationally optimize process performance. Freguia and Rochelle have shown that the reboiler duty (the dominant source of process operating costs) may be reduced by 10 percent if the absorber height is increased by 20 percent and by 4 percent if the absorber is inter-cooled with a duty equal to one-third of the reboiler duty. They also show that the power plant lost work is affected by varying stripper pressure, but not significantly, so any convenient pressure can be chosen to operate the stripper.

In this section, we have used the example of CO2 removal from flue gases using aqueous MEA to demonstrate the development and application of a rigorous model for a chemically reactive system. Modern software enables rigorous description of complex chemically reactive systems, but it is very important to carefully evaluate the models and to tune them using experimental data.

Use of Literature for Specific Systems A large body of experimental data obtained in bench-scale laboratory units and in small-diameter packed towers has been published since the early 1940s. One might wish to consider using such data for a particular chemically reacting system as the basis for scaling up to a commercial design. Extreme caution is recommended in interpreting such data for the purpose of developing commercial designs, as extrapolation of the data can lead to serious errors. Extrapolation to temperatures, pressures, or liquid-phase reagent conversions different from those that were employed by the original investigators definitely should be regarded with caution.

Bibliographies presented in the General References listed at the beginning of this section are an excellent source of information on specific chemically reacting systems. Gas-Liquid Reactions by Dankwerts (McGraw-Hill, New York, 1970) contains a tabulation of references to specific chemically reactive systems. Gas Treating with Chemical Solvents by Astarita et al. (Wiley, New York, 1983) deals with the absorption of acid gases and includes an extensive listing of patents. Gas Purification by Kohl and Nielsen (Gulf Publishing, Houston, 1997) provides a practical description of techniques and processes in widespread use and typically also sufficient design and operating data for specific applications.

In searching for data on a particular system, a computerized search of Chemical Abstracts, Engineering Index, and National Technical Information Service (NTIS) databases is recommended. In addition, modern search engines will rapidly uncover much potentially valuable information.

The experimental data for the system CO2-NaOH-Na2CO3 are unusually comprehensive and well known as the result of the work of many experimenters. A serious study of the data and theory for this system therefore is recommended as the basis for developing a good understanding of the kind and quality of experimental information needed for design purposes.

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