Examples minimum reflux ratio, Underwood equation

Example 8-23 Minimum Reflux Ratio Using Underwood Equation Calculate the Minimiun Reflux Ratio... 

Underwood Algebraic Method, 71 Example 8-23 Minimum Reflux Ratio Using Underwood Equation, 73 Minimum Reflux Colburn Method, 74 Example 8-24 Using the Colburn Equation to Calculate Minimum Reflux Ratio,... 

Example 11.2 Using the Underwood Equations, determine the best distillation sequence, in terms of overall vapor load, to separate the mixture of alkanes in Table 11.2 into relatively pure products. The recoveries are to be assumed to be 100%. Assume the ratio of actual to minimum reflux ratio to be 1.1 and all columns are fed with a saturated liquid. Neglect pressure drop across each column. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters assumed to be zero (see Chapter 4). Determine the rank order of the distillation sequences on the basis of total vapor load for ... 

The errors associated with the Underwood Equations were discussed in Chapter 9, which tend to underpredict the minimum reflux ratio. This introduces uncertainty in the way that the calculations were carried out in Examples 11.2 and 11.3. The differences in the total vapor load between different sequences are small and these differences are smaller than the errors associated with the prediction of minimum reflux ratio and minimum vapor load using the Underwood Equations. However, as long as the errors are consistently low for all of the distillation calculations, the vapor load from the Underwood Equations can still be used to screen between options. Nevertheless, the predictions should be used with caution and options not ruled out because of some small difference in the total vapor load. 

The relative volatilities 0 are defined by Eq. (13-33), is the minimum-reflux ratio L +i/D) ia, and q describes the thermal condition of the feed (e.g., 1.0 for a bubble-point feed and 0.0 for a saturated-vapor feed). The values are available from the given feed composition. The 0 is the common root for the top-section equations and the bottom-section equations developed by Underwood for a column at minimum reflux with separate zones of constant composition in each section. The common root value must fall between ahk and aik, where hk and Ik stand for heavy key and light key respectively. The key components are the ones that the designer wants to separate. In the butane-pentane splitter problem used in Example 1, the light key is n-C4 and the heavy key is i-Cs. 

Underwood [39] derived Equations 6.27.3 and 6.27.4 for estimating the minimum reflux ratio for a specified separation of two key conponents. These equations assume constant molar overflow and relative volatility. Underwood showed that at minimum reflux the value of 0 in Equations 6.27.3 and 6.27.4 must lie between the relative volatility of the heavy and light key components. If the key components are not adjacent, there will be more than one value of 0. This case is illustrated in an example by Walas [6]. Here, we will assume that the key con5)onents are adjacent. As has been pointed out by Walas [6], the minimum reflux ratio calculated by the Underwood equations could turn out to be negative, which means that the equations do not apply for the given separation. 

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. 

For multicomponent mixtures, all components distribute to some extent between distillate and bottoms at total reflux conditions. However, at minimum reflux conditions none or only a few of the nonkey components distribute. Distribution ratios for these two limiting conditions are shown in Fig. 12.14 for the debutanizer example. For total reflux conditions, results from the Fenske equation in Example 12.3 plot as a straight line for the log-log coordinates. For minimum reflux, results from the Underwood equation in Example 12.5 are shown as a dashed line. 

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