Underwood’s equations

Underwood s equations were designed for systems with constant relative volatility and with constant molal heats of vaporization. As discussed, these assumptions for most systems prove conservative and therefore indeed merit the application herein of practical process engineering. The Underwood equations for RM determination are ... 

Application of Underwood s equation to systems containing distributed nonkey components is as follows ... 

In this approach, Fenske s equation [Ind. Eng. Chem., 24, 482 (1932)] is used to calculate which is the number of plates required to make a specified separation at total reflux, i.e., the minimum value of N. Underwood s equations [/. Inst. Pet., 31, 111 (1945) 32,598 (1946) ... 

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 ... 

Exact mathematical equations for the case of constant molal overflow rate and constant relative volatilities have been presented by Harbert (Ref. 7) and Underwood (Ref. 16). Underwood s equation for a three-component mixture can be arranged as follows ... 

It may be noted that using Underwood s approximation (equation 9.10), the calculated values for the mean temperature driving forces are 41.9 K and 39.3 K for counter- and co-current flow respectively, which agree exactly with the logarithmic mean values. 

Then the minimum reflux and the distribution of the intermediate component are found from the two equations that result from substitution of the two values of 8 into Underwood s second... 

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... 

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... 

Underwood s Method comprises two equations. The first includes all n components in the feed, where a is the volatility with respect to the least volatile component and x/the mole fraction. Knowing the feed quality q), the value of (j) can be calculated. 

Many methods of estimating the minimum reflux ratio have been proposed, most of which are tedious to use and not necessarily very accurate. Since the only purpose of obtaining is to estimate the product compositions at R j and to ensure that the specified R is reasonable, an exact value is not required. Underwood s method [64], which uses constant average a s and assumes constant L/G, s not exact but provides reasonable values without great effort it is recommended (refer to the original papers for a derivation, which is lengthy). Two equations must be solved ... 

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