Distillation 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.

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... 

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. 

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. 

Shortcut methods for handling multicomponent batch distillation have been developed for the two cases of constant reflux and constant distillate composition (Diwekar and Mandhaven, 1991 Sundaram and Evans, 1993). Both methods avoid tedious stage-by-stage calculations of vapor and liquid compositions by employing the Fenske-Underwood-Gilliland (FUG) shortcut procedure for continuous distillation, described in Section 6.8, at succesive time steps. In essence, they treat batch distillation as a sequence of continuous, steady-state rectifications. As in the FUG method, no estimations of compositions or temperatures are made for intermediate stages. 

The two important design elements of a distillation column are the number of theoretical stages N, and the reflux R ratio. If the mixture is zeotropic, they are related, as illustrated in Fig. 9.35-a. There is a minimum number of theoretical stages as well as a minimum reflux both depending on the sharpness of separation. For zeotropic mixtures with n-components, the shortcut design procedure known as Fenske-Underwood-Gilliland (FUG) method is well-established (Perry s handbook, 1997). 

There is no short-cut method for stabiliser, but this can be easily simulated as a distillation column with vapour distillate. The feed should be sent close to the top. For the separation benzene/toluene and toluene/di-phenyl a short-cut method as Fenske-Underwood-Gilliland can be used. R/Rmin=1.2 or N/Nmin=2 may be taken in a preliminary design. Note that the use of design models in preliminary simulation makes converge easier the recycles by guarantying the specifications. Obviously, the short-cut design must be reliable in order to fulfil later the specifications in rating mode. 

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. 

Use the Fenske-Underwood-Gilliland shortcut method to determine the reflux ratio required to conduct the distillation operation indicated below if NIN , = 2.0, the average relative volatility = 1.11, and the feed is at the bubble-point temperature at column feed-stage pressure. Assume external reflux equals internal reflux at the upper pinch zone. Assume a total condenser and a partial reboiler. 

FTCDC Fully thermally coupled distillation column FUGK Fenske-Underwood-Gilliland-Kirkbride... 

Fenske-Underwood-Gilliland (FUG) Shortcut Method for Ordinary Distillation 445... 

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. 

The simplified method similar to method Fenske-Underwood-Gilliland was developed for calculation of distillation complexes. The comparison of different sequences was made at the example of the mixture obtained at the unit of alkylation. The most interesting result was obtained from sequence (1 2,3,4,5) -> (2,3 4,5) (4 5) (2 3) while uniting the second and third columns into the... 

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

Shortcut calculations provided by the Fenske-Underwood-Gilliland are most effective for a preliminary design before the use of distillation simulation software that utilizes much more rigorous calculation methods. 

In the years from 1940 through the 1960s, several notable shortcut fractionation methods were published. Of these, one method that included several of these earlier methods has stood out and is today more accepted. Fenske, Underwood, and Gilliland [9-12] are the core of this proposed method. Yet one more entry is added, the Hengstebeck [13] proposed method to apply multicomponent distillation. As these earlier methods pointed out only two component separations (called binary systems), the Hengstebeck added contribution is most important for multicomponent applications. 

Truly multicomponent solutions based on continuous distillation shortcut methods have been proposed for batch distillation. The Fenske, Underwood, and Gilliland equations or correlations are commonly used in conjunction with each other to solve continuous distillation problems as described in Section 12.3. Diwekar and Madhavan (1991) describe how these techniques may be modified for the design of batch distillation columns for variable and constant reflux cases. 

Owing to the availability of high-speed computers, short cut methods for designing distillation processes (e.g. McCabe-Thiele and Ponchon-Savarit for binary systems or the equations of Fenske, Underwood and Gilliland for multicomponent mixtures, see Gmehling and Brehm, 1996 and Satder, 2001 for details) are no longer required. 

Gilliland correlation and Fenske-Underwood-GiUiland method for the number of st es GiUiland (1940) developed an empirical shortcut method to determine the number of stages N needed in a distillation... 

For control purposes, somewhat simplified mathematical models usually are adequate. In distillation, for instance, the Underwood-Fenske-Gilliland model with constant relative volatilities and a simplified enthalpy balance may be preferred to a full-fledged tray-by-tray calculation every time there is a perturbation. In control situations, the demand for speed of response may not be realizable with an overly elaborate mathematical system. Moreover, in practice not all disturbances are measurable, and the process characteristics are not known exactly. Accordingly feedforward control is supplemented in most instances with feedback. In a well-designed system (Shinskey, 1984, p. 186) typically 90%... 

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