Nomographs for Minimum Reflux Ratio and Theoretical Plates for Separation of Binary Mixtures E. H. SMOKER The United Gas Improvement Company, Philadelphia, Penna. FTEN distillation problems can be simplified so that the separation to specified purities of only two components, having constant relative volatility and obeying Raoult’s law, is necessary. Usually the first step in such problems is the fixing of boundary conditions-namely, (1) the estimation of the minimum number of plates at infinite reflux, and (2) the estimation of the minimum reflux ratio a t intinite plates. These can be computed by the following algebraic expressions:
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The terms XF and 20, which normally refer to the feed and overhead compositions, can in Equation 1 represent any two liquid compositions in the column as long as 20 is greater than XF. Since these two equations are used frequently, nomographs have been constructed for them by well known mathematical methods‘. Figure 1 is a common type of IAllcook, H. J., and Jones, J. R., “The Nomogram-the Prsatical Construction of Computation Charts”, 1932.
Theory and
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INDUSTRIAL AND ENGINEERING CHEMISTRY
VOl. 34, No. 4
13
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FIGURE 2
nomograph having the four variables expressed along each of four individual straight lines. There are two pairs on either side of the tie line, xo and XF on the right, and NMIN and a on the left. From the point where a straight line through the values of the two known variables of either pair cuts the tie line, another straight line is drawn through the known value of the third variable to obtain the required value of the fourth. Figure 2 is a grid-type nomograph in which the values of bwo of the variables, ZF and a,are expressed along two intersecting families of curves. A single point within the intersection area represents fixed values for these two. Therefore three points, one within the grid area and the other two on the zo and RMINlines, fix the values for all four of the vari-
ables. Since the positions of two of the points are always known, the third point, and therefore the fourth variable, can be determined by drawing a straight line through the two known points.
Nomenclature NMIN= minimum theoretical plates required at infinite reflux ratio RMIN = minimum reflux ratio required at infinite theoretical plates XF = mole fraction of lower boiling component in feed 20 = mole fraction of lower boiling component in overhead product a = relative volatility of the two components
