Equilibriumstage Concept

Until recently, energy and mass-transfer processes in an actual distillation column were considered too complicated to be readily modeled in any direct way. This difficulty was circumvented by the equilibrium-stage model, developed by Sorel in 1893, in which vapor and liquid streams leaving an equilibrium stage are in complete equilibrium with each other andthermodynamic relations can be used to determine the temperature of and relate the concentrations in the equilibrium streams at a given pressure. A hypothetical column composed of equilibrium stages (instead of actual contact trays) is designed to accomplish the separation specified for the actual column. The number of hypothetical equilibrium stages required is then converted to a number of actual trays by means of tray efficiencies, which describe the extent to which the performance of an actual contact tray duplicates the performance of an equilibrium stage. Alternatively and preferably, tray inefficiencies can be accounted for by using rate-based models that are described below.

Use of the equilibrium-stage concept separates the design of a distillation column into three major steps: (1) Thermodynamic data and methods needed to predict equilibrium-phase compositions are assembled. (2) The number of equilibrium stages required to accomplish a specified separation, or the separation that will be accomplished in a given number of equilibrium stages, is calculated. (3) The number of equilibrium stages is converted to an equivalent number of actual contact trays or height of packing, and the column diameter is determined. Much of the third step is eliminated if a rate-based model is used. This section deals primarily with the second step. Section 14 covers the third step. Sections 3 and 4 cover the first step, but a summary of methods and some useful data are included in this section.

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