Distillation column design tray number determinations

Based on the same equations for the distillation columns design presented in Section 4.3.2, we formulate the problem to determine the number of trays as function of the L/D ratio. We use McCabe-Thiele method to compute the number of theoretical trays, where the equilibrium composition is given by the following equation ... 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

Determining the number of theoretical and actual trays in a distillation column is only part of the design necessary to ensure system performance. The interpretation of distillation, absorption, or stripping requirements into a mechanical vessel with internal components (trays or packing, see Chapter 9) to carry out the function requires use of theoretical and empirical data. The costs of this equipment are markedly influenced by the column diameter and the intricacies of the trays, such as caps, risers, weirs, downcomers, perforations, etc. Calcvdated tray efficiencies for determination of actual trays can be lost by any unbalanced and improperly designed tray. 

This illustrative example is taken from the recent work on interaction of design and control by Luyben and Floudas (1994a) and considers the design of a binary distillation column which separates a saturated liquid feed mixture into distillate and bottoms products of specified purity. The objectives are the determination of the number of trays, reflux ratio, flow rates, and compositions in the distillation column that minimize the total annual cost. Figure (1.1) shows a superstructure for the binary distillation column. 

A distillation column is designed to separate a 70-30 mole percent mixture to produce a distillate product with 97.5% mole component 1 and a bottoms product with 20% mole component 1. The column has a partial condenser and reboiler and operates at 1 atm pressure. Determine the required number of theoretical trays and the optimum feed location at a reflux ratio of 1.5. Calculate the recovery of component 1 in the distillate. Calculate the recovery at the same distillate purity and reflux ratio if the feed is introduced three trays below the optimum feed tray. Use thermodynamic data from Problem 6.1. 

The second stage, including the selection of the best reflux numbers and the quantity of column section trays, will be the important one. The geometric distillation theory makes it possible to determine the feasible compositions that are to be in trays above and below the feed cross-section, then make the design calculations of the trajectory of sections and determine the best ratio of section tray numbers. The new algorithms allow for an increase in the design quality and apart from that, they make it possible to lower the separation costs and to practically exclude the human participation in the process of calculation. 

The geometric approach develops methods of conceptual design calculation of simple and complex distillation columns (i.e., methods of determination of optimal values of the main process parameters, of the numbers of theoretical trays at... 

Design calculation for the set value of a = R/Rmin comes to the determination of tray numbers in the sections of the column Nr and Ns at which section trajectories are joined (i.e., the componentwise material balance in the feed cross-section is valid). The distillation trajectory may be put as follows ... 

Kirkbride equation An equation used for the design of distillation columns to determine the ratio of the number of trays above and below the feed point. It is therefore used to determine the location of the feed tray in the column ... 

For very complex mixtures, the entire distillation design can be done using the Older-shaw column by changing the number of trays and the reflux rate until a combination that does the job is found. Since the commercial column will have an overall efficiency equal to or greater than that of the Oldershaw column, this combination will also work in the commercial column. This approach eliminates the need to determine vapor-liquid equilibrium (VLE) data (which maybe quite costly), and it also eliminates the need for complex calculations. The Oldershaw column also allows one to observe foaming problems TKister. 19901. 

The main object of the distillation theory is the development of new methods of designing the units for separation of mixtures into required products at minimum costs. Two basic interconnected stages of the conceptual design of distillation units are (1) synthesis of optimum flowsheet and (2) determination of the best reflux number, quantity of trays in the column sections, and optimum recycling flows. 

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