Fenske-Underwood-Gilliland Method

Your objectives in studying this section are to be able to  

Derive the Fenske equation and use it to determine the number of stages required at total reflux and the splits of nonkey components. 

Use the Underwood equations to determine the minimum reflux ratio for multicomponent distillation. 

Use the Gilliland correlation to estimate the actual number of stages in a multicomponent column and the optimum feed stage location. 

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. 

---

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

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. 

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,... 

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 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. 

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. 

D21. A distillation column is separating 100 kmol/h of a saturated vapor feed that is 30 mol% ethanol, 25 mol% i-propanol, 35 mol% n-propanol, and 10 mol% n-butanol at a pressure of 1.0 atm We want a 98.6% recovery of i-propanol in the distillate and 99.2% recovery of n-propanol in the bottoms. The column has a total condenser and a partial reboiler. For parts b, c, and d, use the Fenske-Underwood-Gilliland method. If we choose n-propanol as the reference, the relative volatilities are ethanol = 2.17, i-propanol = 1.86, n-propanol = 1.0, and n-butanol = 0.412. These relative volatilities can be assumed to be constant. 

There are many so-called shortcut calculation methods for designing industrial distillation columns. The most commonly used one is the Fenske-Underwood-Gilliland method. 

---