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method of calculation breaks down completely as shown by the fact that the discontinuity of the vapor-liquid diagram is incompatible with the ideal solution laws. The effect of the physical properties of the mixture on the equilibrium constants of one of the constituents is shown by FIGURE 7. COMPARISON the difference in the equilibrium curves for butane dissolved OF EQUILIBRIEM CONin ethane and in heptane (Figure 6) and that for heptane disSTANT CERVES FOR nsolved in ethane and in butane (Figure 7). The difference HEPTANPIN n-BUTANE between the two sets of curves is associated with the difference AND HEPTANE IN ETHANE in the critical temperatures and pressures of the mixtures. The critical temperature of mixtures of ethane and butane, ethane and heptane, and butane and heptane is nearly proportional to the sum of the products of the weight fraction and I I I i J the critical temperature of the pure constituents. However, .I .2 .4 .6 .8 I EQUILIBRIUM CONSTANT no such simple relation exists for the critical pressure. In all three systems of mixtures the critical pressure-composition curve has a maximum pressure point, the magnitude of which is a function of the absolute molecular weight as well as the difference in molecular weight of the constituents. Thus, the From the curves in Figure 4 data were obtained for calcumaximum critical pressure is greater for ethane-heptane than lating the vapor-liquid equilibrium constants for butane disfor ethane-butane mixtures but is smaller for butane-heptane solved in heptane and heptane dissolved in butane. The rethan for ethane-butane mixtures, though the difference in lation of these constants t o the pressure is shown graphically molecular weight is greater. I n other words, the first memby a series of isothermal curves in Figure 5 . At temperabers of the paraffin series exert a much greater effect than do tures between 306” and 513” F., the critical temperatures of the higher members. butane and heptane, respectively, the two branches of these isothermal curves meet in the critical point of the mixture (where K = 1) a t a pressure equal to the critical pressure. Literature Cited When these curves are compared with those calculated from (I) Kay, W. B., IND.ENQ.CHEST., 30,459 (1938). the fugacity of the hydrocarbons (represented by the dotted (2) Ibid., 32, 353 (1940). curves constructed from tables given by Sherwood, S), the 13) Shermood. “AbsorDtion a n d Extraction”.. D. _ 105. New York. agreement is moderately good in the low temperature-presMcGraw-Hill Book Co.. 1937. sure region; but as the temperature and pressure increase, the properties of the mixture deviate farther and farther from PREBENTBD before the Division of Petroleum Chemistry a t the IOlst Meeting those of an ideal solution, and finally a t the critical point the of the American Chemical Society, St Louis, M o , ~I
BATCH FRACTIONATION Calculation of Theoretical Plates Required for Separation of Two Normal Liquids ARTHUR ROSE The Pennsylvania State College, State College, Penna.
N EARLIER paper of this series (6) gave a method
A
for calculating the minimum plates required for any specified separation of two components by batch fractionation. The method was very general (S), but required the use of the vapor pressure ratio, a,and has been useful in cases where reflux ratio was high enough t o be equivalent t o total reflux. This paper introduces the concept of a “standard separation”, and gives and discusses the limitations of simple methods for estimating approximately the plates and reflux ratio required for such a standard separation of a pair of s i m h liquids with normal vapor equilibrium relations, when the usual simplifying assumptions of distillation are justified and holdup is negligible.
Choice of Standard Separation I n batch fractionation it is confusing to use the difference between still and product composition as a measure of the effectiveness of the process, This is because the compositions are changing continually throughout the distillation. The best procedure is to use the shape of the actual curve of product composition versus per cent distilled as the measure of effectiveness and thus relate the conditions (a,n, R, etc.) of the distillation directly t o the eventual results. This may be done in the following way. Each of the curves of Figure 1represents a different separation of two components. Each may be satisfactory for some particular purpose, and each separation requires different
May, 1941
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
For mixtures of similar normal liquids with normal vapor-liquid equilibrium relations, and in cases where the usual simplifying assumptions of distillation and negligible holdup are justified, the equations,
are suggested for estimating approximately the equivalent number of theoretical plates, n, and reflux ratio, R, required for a standard separation in which the first 40 per cent distilled has an average purity of 95 mole per cent. The derivation of the equations is described, the limitations of such approximation formulas are emphasized, and they are compared with a correlation of more complicated Rayleigh equation calculations which ahow that the number of plates required may be chosen from any value within a limited range, provided the accompanying reflux is properly fixed. The limits of the range of n and the methods of choosing the proper reflux are indicated.
conditions. Thus, for an ideal two-component mixture with CY = 1.25 (boiling point difference about €4’ a t 100’ C.) it can be calculated that ten plates are necessary to obtain curve A, twenty plates for curve B, and thirty plates for curve C, provided proper reflux is used in each case and holdup is negligible. Before attempting to devise any means for calculating the number of plates required for a separation of two components, it is essential to choose one particular batch fractiona-
P€R C€NT D/ST/LL€D OV€R f/oa-L)
tion curve (product composition os, per cent distilled) as a standard of satisfactory separation of the two components. To make such a choice it has been assumed that for most practical purposes a curve such as B of Figure 1 will be considered a satisfactory separation. The first 40 per cent distilled over will have an average purity greater than 95 per cent. This is therefore designated the
