Underwood’s Method

An alternate improved solution for Underwood s method is given by Erbtir, Joyner, and Maddox [113] with an example, which is not repeated here. 

Calberg NA and Westerberg AW (1989) Temperature-Heat Diagrams for Complex Columns 2, Underwood s Method for Side-Strippers and Enrichers, Ind Eng Chem Res, 28(9) 1379. 

Minimum reflux ratio, using Underwood s method... 

The minimum reflux ratio, Rm is calculated using Underwood s method (Example 11.16) as 0.83 and, using Fenske s method, Example 11.17, the number of plates at total reflux is nm = 8. The following data have been taken from Figure 11.42, attributable to Gilliland(30) ... 

Minimum Reflux. Underwood s method employs two relations. First an auxiliary parameter 8 is found in the range 1 < 8 < a by solving ... 

Carlberg NA, Westerberg AW. Temperature-heat diagrams for complex columns. 2. Underwood s method for side strippers and enrichers. Ind Eng Chem Res 1989 28 1379. 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

Example 3.2 Calculate the minimum reflux for the depropanizer in Example 2.4 using Underwood s method. 

Example 3J Calculate the minimum reflux for > depropanizer similar to that of Example 2.4 using Underwood s method, hi this case, butane is acceptable both in the top and bottom product, but it is required that 98 percent of the propane in the feed is recovered in the top product, and 9B percent of the pantane is to be recovered in the bottom product. 

Use of Underwood s Method. Table III presents an example that illustrates a computation we might do to compute the minimum reflux flows for a column. In this example, species C distributes between the top and bottom product in the column. Underwood s method permits us to compute how it distributes. The approach for using Underwood s equations to compute minimum reflux is as follows ... 

How can we estimate a marginal vapor flow for a column One approach is to estimate the minimum reflux required using any method that is appropriate. If the separation is among species that are acting nearly ideally, we can use Underwood s method. 

Applying Underwood s method gives us a minimum vapor flow of 72.5 kmol/h for a column accomplishing the separation of AB/CDE. Without species A, D, and E present, the minimum vapor flow is computed to be 44.5 kmol/h. The marginal vapor rate is therefore 38.0 kmol/h. 

Because errors in these numbers can occur, we might want to look at anything within 20% of the best with a more accurate analysis. If none exists, we are done with a relatively cheap analysis. If some exist, we could use Underwood s method (i.e., find the roots) to estimate the minimum reflux ratios as we did above for one of the columns. 

Carlberg, N. A. and Westerberg. A. W. Temperature-Heat Diagrams for Complex Columns. 3. Underwood s Method for the Petlyuk Configuration." hul. Eng. Chem. Res. 28, 1386 (1989b). 

This method makes similar assumptions to the psuedo-binary method except that aU components are considered, not just the two key components. In particular, the assumptions made by Underwood s method are ... 

Once < ) is determined, we can calculate Rfnin froiu (103). This is called Underwood s method. 

Solution Recall the feed and product compositions (see sketch at right). Using Underwood s method, we first determine the root of (102). 

Underwood s method can be extended to calculate the number of plates analytically when the equal molal overflow assumption and constant relativity are appropriate. But even then, the calculations are sufficiently involved that a... 

The feed to a depropanizer is 66% vaporized at the column inlet. The feed composition and average relative volatilities are given in the table below. It is requited that 98% of the propane in the feed is recovered in the distillate, and 99% of the pentane is to be recovered in the bottoms product. Calculate the minimum reflux ratio for this case using Underwood s method. 

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