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-1.415 + ^(-1.415)2 - 4(361864) [-0.868(0.465) - (0.387)(0.26)] « _

These values were not recalculated for a new assumed value of 0/D since both are reasonably close to the first value assumed.

Constancy of Molal Flow Rates. The design calculations presented have been based on the use of constant molal overflow and vapor rates. Enthalpy balances similar to Eqs. (7-13) and (7-27) can be written for each of the components of a multicomponent mixture and, if the data are available, they can be applied plate by plate in the Stepwise calculations. This procedure usually requires trial and error because, in calculating up or down the tower, the temperature on the next plate is needed to complete the enthalpy balance, and it must be assumed and checked in a later calculation. The most serious difficulty is the lack of the necessary enthalpy data, but in most cases these can be approximated by the methods on pages 139 to 142.

The same general considerations relative to the constancy of flow rates apply to multicomponent and binary mixtures. Thus the latent heat of vaporization at various positions in the column should serve as the principal criterion, although in multicomponent systems there is more possibility of large sensible heat effects changing the overflow and vapor rates.

The modified latent heat method (M.L.H.V.) given on page 158 is applicable to multicomponent mixtures, and it probably is the most satisfactory procedure for handling such calculations. It should give good results for the examples considered in this chapter, because the heats of mixing for the mixtures involved would be small, even though the latent heats of vaporization of individual components for the gasoline stabilization problem differ several fold. In this latter example, there is undoubtedly considerable variation in the molal flow rates, and the M.L.H.V. method will give more satisfactory results than the method employed. The calculations were repeated by the M.L.H.V, method using arithmetic average values of latent heats of vaporization at the still and the condenser to calculate the values of p for each component. Table 9-6 gives the latent heat values and the P terms based on the latent heat of n-butane. The values of p are used to calculate pzF, Py0.h., Pzw, and z'F — pzF/2(pzF), Vo.n. = Pyo.K./2(PyoM.), and x'w = pxw/2(pxw). The values of the terminal flow quantities are given below:

W' = 68.4(1.467) = 100 £' = 31.6(0.650) = 20.5 Ff = 100(1.205) - 120.5

Table 9-7 presents the plate-to-plate calculations; the values of yrO Wt are taken from Table 9-6, and the values of t/o.h and 2xR are taken from Table 9-2. The calculations will be made for O/D = 2.0 and for Vm — Vn = 42 which are the same as the values used in Tables 9-2 and 9-3. For F = 100, D = 31.6, 0R = 63.2, and the fourth column of Table 9-7 gives pxR = 0.751 making 0'R = 0.751(63.2) = 47.5, and O'JD' = 47.5/20.5 = 2.32. The remaining columns of Table 9-7 are based on D' » 1.0, 0' = 2.32, V' = 3.32. The values of the

8xp fifth column are 2.82^ - 2.32 ^ - the values of 3.32^ are equal to 2.32x'r + yf0tHt. In order to go to yT, the values of 3.32y'T are divided by the corresponding p terms and yT = (y'T/p)/h(y'T/P). The yT values are used to calculate xT, using the relative volatilities of Table 9-2, and these are converted to x'T.

The general flow quantities are shown in Fig. 9-15 which gives both the normal and modified values. For F = 100, the value of V'n is 68 throughout the top section, but the value of Vn will vary from plate to 3late. Thus VT = 94.8, but VT-i = V^Xiyr-i/P) = 91, and this /alue decreases further for the next plate. This decrease in vapor 'ate is due to the fact that the average latent heat of vaporization is ncreasing from plate to plate down the column, resulting in lower fapor and liquid rates and making the separation more difficult.

The calculations are carried in the same manner down to yT~z- The calculations were given in detail to show the values of y and x as veil as those for y? and x', but this is not necessary because it is possi-)le to go from y' to x' directly by x' = (y'/a)/2(y'/a) in which the lormal a values are employed.

The calculations for the lower section of the tower are given in Table 9-8 on the basis W' « 1.0, 0'm = 2.186, and Vfm - 1.186. The ralue of Vw for F = 100 is calculated from V'm/2{pyw) « 101. This represents a large decrease in vapor from the top of the tower where Vt — 94.8. With Vm — Vn = 42, the vapor from the still would have been 136.8 on the usual basis. The decrease of 136.8 — 101 = 35.8 is due to variation in the latent heats of vaporization. The calculations up to x[ are given in Table 9-8. The calculations up to xrz were made in detail, but from x'z to xi the values of 1.186y' were calculated from

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