Fenske-Underwood-Gilliland

Figure 8-47. Short-cut solution of Fenske-Underwood-Gilliland theoretical trays for multicomponent distillation. Used by permission, Frank, O., Chem. Eng. Mar. 14 (1977), p. 109.

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

The shortcut model is developed based on the assumption that batch distillation operation can be represented by a series of continuous distillation operation of short duration and employs modified Fenske-Underwood-Gilliland (FUG) shortcut model of continuous distillation (Diwekar and Madhavan, 1991a,b Sundaram and Evans, 1993a,b). Starting with an initial charge (B0, xB0) at time f=fo and for a small interval of time At = t, - t0, the batch distillation column conditions at to and ts is schematically shown in Figure 4.1 (Galindez and Fredenslund, 1988). 

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. 

Design a distillation column to separate benzene, toluene, and xylene, using (1) the McCabe-Thiele xy diagram and (2) the Fenske-Underwood-Gilliland (FUG) method. Compare the results with each other. Assume that the system is ideal. 

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,... 

FIGURE 8.5 Graphical representation of Fenske-Underwood-Gilliland procedure. (From Chemical Engineering, McGraw-Hill, 1977.)... 

Make a rough estimate of the number of theoretical stages required. This step employs the procedures developed in Example 8.1. Use the Fenske-Underwood-Gilliland approach rather than the McCabe-Thiele, because the small boiling-point difference indicates that a large number of stages will be needed. 

For preliminary studies of batch rectification of multicomponent mixtures, shortcut methods that assume constant molal overflow and negligible vapor and liquid holdup are useful. The method of Diwekar and Madnaven [Ind. Eng. Chem. Res., 30, 713 (1991)] can be used for constant reflux or constant overhead rate. The method of Sundaram and Evans [Ind. Eng. Chem. Res., 32, 511 (1993)] applies only to the case of constant remix, but is easy to apply. Both methods employ the Fenske-Underwood-Gilliland (FUG) shortcut procedure at successive time steps. Thus, batch rectification is treated as a sequence of continuous, steady-state rectifications. 

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. 

Whereas Example 17.2 was solved based on the McCabe-Thiele method, the way this example is defined favors the shortcut, Fenske-Underwood-Gilliland approach. This method may be used for multicomponent mixtures, but it is not a method selection criterion in this example, which is a binary system. 

Although rigorous computer methods are available for solving multicomponent separation problems, approximate methods continue to be used in practice for various purposes, including preliminary design, parametric studies to establish optimum design conditions, and process synthesis studies to determine optimal separation sequences (Seader and Henley, 2006). A widely used approximate method is commonly referred to as the Fenske-Underwood-Gilliland (FUG) method. 

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