Shortcut methods determining reflux

Now that the minimum number of theoretical stages is determined, the minimum reflux is required at infinite theoretical stages. I will reference this reflux as RM, which is the molar ratio of the tower returned liquid L divided by the outgoing overhead product D. There have been several shortcut methods to derive this minimum RM. Probably the most popular algebraic method is that of Underwood [11,12], which has been proven over many years and which I personally applied while working in a major EPC company on my first process design job, in 1959. 

Minimum reflux can be determined by graphical (Secs. 2.3.5, 2.4.1), shortcut (Secs. 3.2.2 to 3.2.4), or rigorous techniques. Most graphical and shortcut methods give good results either when constant molar overflow (Sec. 2.2.2) applies, or when the method is corrected for energy balance. Unfortunately, shortcut methods in most commercial simulations apply no energy balance correction, and wBd minimum reflux predictions are not uncommon. 

The shortcut methods can also be used for approximate analysis of the performance of an existing column. Here, the number of trays, N, is fixed, and the objective is to determine the reflux ratio required to meet a specifled separation. The Fenske and Underwood methods (Equations 12.17, 12.29, and 12.30) are used to calculate the minimum trays and minimum reflux ratio, and R. The operating reflux ratio corresponding to the given number of trays is then read from the Gilliland chart (Figure 12.4). The internal vapor and liquid rates are calculated from the reflux ratio and product rates. A check must be made to determine if the existing column can handle the calculated vapor and liquid traffic. 

The first step is to assume a set of temperatures Tj and vapor flows Vj. The temperatures can be obtained by linear interpolation between the condenser and reboiler temperatures, determined by dew point and bubble point calculations of products estimated by shortcut methods or on the basis of past experience with similar columns. The vapor rates are estimated from the specified distillate and reflux rates. Constant vapor rates are assumed above and below the feed. The... 

If the distillation were to be started at twice the minimum reflux ratio, determine the required number of stages. If the initial charge is 100 kmol and the distillate rate is 10 kmol/h, calculate the reflux rate, the amounts of distillate and residue, and the residue composition as a function of time. Irrespective of tray hydraulics and reboiler and condenser capacity constraints, when should the distillation be stopped Assume negligible tray holdups and use shortcut methods. 

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. 

The number of theoretical stages is first determined by well-known shortcut methods and then by a multicomponent simulation of the separation process. Both parts can and will be used for analyzing the separation process with respect to the effect of separation factor, reflux ratio (the amount of top product reintroduced to the separation), degree of separation etc. on the number of theoretical stages. There, computational methods provide insight into the separation process without actually carrying out the separation. 

Underwood s shortcut method to calculate R (Ul, U2) uses constant average a values and also assumes constant flows in both sections of the tower. This method provides a reasonably accurate value. The two equations to be solved to determine the minimum reflux ratio are... 

The Underwood equations (Underwood, 1948) provide a shortcut method for determining the minimum reflux ratio, ilmin, in multicomponent distillation under the following assumptions constant relative volatilities and constant molal overflows in the stripping section as well as in the enriching section. The minimum reflux ratio, i min> is obtained from a solution of the following two equations for n components ... 

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. 

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