Starting with the classical method of Kremser (op. cit.), approximate group methods of increasing complexity have been developed to calculate groups of equilibrium stages for a countercurrent cascade, such as is used in simple absorbers and strippers of the type depicted in Fig. 13-7£> and d. However, none of these group methods can adequately account for stage temperatures that are considerably higher or lower than the two entering-stream temperatures for absorption and stripping respectively when appreciable composition changes occur. Therefore, only the simplest form of the Kremser method is presented here. Fortunately, rigorous computer methods described later can be applied when accurate results are required. The Kremser method is most useful for making preliminary estimates of absorbent and stripping-agent flow rates or equilibrium-stage requirements. The method can also be used to extrapolate quickly results of a rigorous solution to a different number of equilibrium stages.
Consider the general adiabatic countercurrent cascade of Fig. 13-42 where v and I are molar component flow rates. Regardless of whether the cascade is an absorber or a stripper, components in the entering vapor will tend to be absorbed and components in the entering liquid will tend to be stripped. If more moles are stripped than absorbed, the cascade is a stripper; otherwise, the cascade is an absorber. The Kremser method is general and applies to either case. Application of component material-balance and phase equilibrium equations successively to stages 1 through N - 1, 1 through N - 2, etc., as shown by Henley and Seader (op. cit.), leads to the following equations originally derived by Kremser. For each component i,
is the fraction of component i in the entering vapor that is not absorbed.
is the fraction of component i in the entering liquid that is not stripped.
is the effective or average absorption factor for component i, and
Entering liquid i
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