Underwood minimum reflux

Table 1.3-8 shows subsequent calculations using the Underwood minimum-reflux equations. The (X andxo values in Table 1.3-8 are those from the Fenske... 

Underwood minimum reflux constant XjF = Mol fraction of component i in the feed XjD = Mol fraction of component i in the distillate q = Thermal condition of the feed Bubble point liquid q =1.0 Dew point vapor q =0 General feed q = (Ls - Lr)/F... 

The Underwood minimum reflux equations of main interest are those that apply when some of the components do not appear in either the distillate or the bottom products at minimum reflux. These equations... 

Table 13-6 shows subsequent calculations using the Underwood minimum reflux equations. The a and Xo values in Table 13-6 are those from the Fenske total reflux calculation. As noted earlier, the % values should be those at minimum reflux. This inconsistency may reduce the accuracy of the Underwood method but to be useful, a shortcut method must be fast, and it has not been shown that a more rigorous estimation of x values results in an overall improvement in accuracy. The calculated firnin is 0.9426. The actual reflux assumed is obtained from the specified maximum top vapor rate of 0.022 kg- mol/s [ 175 lb-(mol/h)] and the calculated D of 49.2 (from the Fenske equation). 

Ultrafiltration, 631 applications, 633 membranes, 637-639 Underwood minimum reflux binaty, 387 multicomponent, 397 Units, conversion of, 671, 672 UMQUAC equation, 475 Upflow fixed beds, 609 Uranium recovery, 515 Utilities, typical characteristics, 15... 

Because of their relative simplicity, the Underwood minimum reflux equations for Class 2 separations are widely used, but too often without examining the possibility of nonkey distribution. In addition, the assumption is frequently made that (/ )min equals the external reflux ratio. When the assumptions of constant relative volatility and constant molal overflow in the regions between the two pinch-point zones are not valid, values of the minimum reflux ratio computed from the Underwood equations for Class 2 separations can be appreciably in error because of the sensitivity of (12-34) to the value of q as will be shown in Example 12.5. When the Underwood assumptions appear to be valid and a negative minimum reflux ratio is computed, this may be interpreted to mean that a rectifying section is not required to obtain the specified separation. The Underwood equations show that the minimum reflux depends mainly on the feed condition and relative volatility and, to a lesser extent, on the degree of separation between the two key components. A finite minimum reflux ratio exists even for a perfect separation. 

The shortcut column performs Fenske-Underwood shortcut calculations for simple refluxed towers. The Fenske minimum number of trays and the Underwood minimum reflux are calculated. A specified reflux ratio can then be used to calculate the vapor and liquid traffic rates in the enriching and stripping sections, the condenser duty and reboiler duty, the number of ideal trays, and the optimal feed location. The shortcut column is only an estimate of the column performance and is restricted to simple refluxed columns. For more realistic results, the rigorous column operation should be used. This operation can provide initial estimates for most simple columns. 

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