Underwood Equations for Minimum Reflux Ratio

The Underwood equations can be used to calculate the minimum reflux ratio in a multicomponent system if the relative volatilities of the components are constant. There are two equations. 

The feed composition Zj (mole fractions j= 1, NC), the desired distillate composition Xpj (/ = 1, NC), and the feed thermal condition q are specified. The relative volatilities ot, (/ = 1, NC) of the multicomponent mixture are known. 

The first equation contains one unknown parameter 6. However, expanding the summation of NC terms and multiplying through all the denominator terms (aj 0) give a polynomial in 6 whose order is NC. Therefore, there are NC roots of this polynomial. One of these roots lies between the two relative volatility values otoc and q hk- This is found using some iterative solution method. It is substituted into the second equation, which can then be solved explicitly for the minimum reflux ratio. 

An example of the use of the Underwood equations is given in Chapter 4. The results of this approximate method will be compared with the results found from rigorous simulation. 

Several methods for analyzing distillation columns have been presented in this chapter. Graphical methods provide valuable insight into how various parameters affect separations in distillation. 

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