Underwood system of equations

The Underwood system of equations can be obtained from the conditions of componentwise material balance and of phase equilibrium in the cross-section of constant concentration zones of each section. For example, the following expression can be obtained from the equation of componentwise material balance at the contour, embracing the part of top section from the cross-section in the zone 

Designating cp = LjVKn and summing up by all the components, we obtain one of the main equations of Underwood  

The main achievement of Underwood consists in the proof of equality of parameters (j) and ir in Eqs. (5.1) and (5.2) in the mode of minimum reflux. Sum up these equations is following main equation  

For the set composition of the top product and for the set reflux number, the number of roots of Eq. (5.1) equals that of the components in top product k)  

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