Gilliland method

ESTIMATION OF REFLUX AND NUMBER OF TRAYS (FENSKE-UNDERWOOD-GILLILAND METHOD)... 

The jmethod of O Connell is popular because of its simplicity and the fact that predicted values are conservative (low). It expresses the efficiency in terms of the product of viscosity and relative volatility, pa, for fractionators and the equivalent term HP In for absorbers and strippers. The data on which it is based are shown in Figure 13.43. For convenience of use with computer programs, for instance, for the Underwood-Fenske-Gilliland method which is all in terms in equations not graphs, the data have been replotted and fitted with equations by Ncgahban (University of Kansas, 1985). For fractionators,... 

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

Produce a shortlist of candidates by ranking the alternatives following the total vapor rate. A minimum reflux calculation design based on Fenske-Underwood-Gilliland method should be sufficiently accurate. 

For each column, the recoveries of the light and heavy key components have been specified. Then, the minimum number of trays Nmill and the minimum reflux ratio Rmin have been calculated using the shortcut distillation model DSTWU with Winn-Underwood-Gilliland method in Aspen Plus. The reflux ratio was set to... 

Compare the results of the McCabe-Thiele and the Fenske-Underwood-Gilliland methods. 

A nomograph for the overall Fenske-Underwood-Gilliland method has been derived that considerably reduces the required calculation effort without undue loss of accuracy. It is based on Fig. 8.5, where the subscripts D and B in the abscissa refer to overhead and bottoms product streams,... 

Constants in Gilliland method Bottoms rate Distillate rate Number of components Liquid mole fraction in feed (0 for dewpoint, 1.0 for bubblepoint)... 

The minimum reflux ratio can be evaluated for this two component distillation by using the Fenske-Underwood-Gilliland method and then determining what ratio factor to use to obtain the desired separation using 94 theoretical trays. This approach uses Eq. (15-1), (15-2), (15-3) and (15-4). If this approach is used, Nmm = 21.2 stages and Raun = 2.62. A trial and error calculation with Eq. (15-4) where R is unknown, establishes that a value of 2.75 for R is required to obtain 94 theoretical trays. Thus R = (1.05X2.62) or 2.75 for this colunm. This is reasonable since the ratio ctor for low tonperatures distillation columns is generally between 1.05 and 1.10. 

The simplest distillation models to set up are the shortcut models. These models use the Fenske-Underwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 11. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. 

The Fenske-Underwood-Gilliland methods are again applied to the distillate composition, X (assumed constant), the current reboiler composition, X y+j and the number of trays, N, to determine r and hence the reflux ratio, R. The procedure is repeated by further incrementing the reference component composition for each time step until a target composition X y is reached. 

Given the initial reboiler and the distillate compositions, calculate the minimum reflux ratio and the minimum number of stages by the Fenske and Underwood methods. With a reflux ratio that is twice the minimum, calculate the number of theoretical stages by the Gilliland method. The outcome is the initial reboiler charge and composition for the next step. 

An algorithm for the empirical method that is commonly referred to as the Fenske-Underwood-Gilliland method, after the authors of the three important steps in the procedure, is shown in Fig. 12.1 for a distillation column of the type shown in Table 1.1. The column can be equipped with a partial or total condenser. From Table 6.2, the degrees of freedom with a total condenser are 2N + C + 9. In this case, the following variables are generally specified with the partial reboiler counted as a stage. 

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