Energy vs. Feed in .NET framework

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Energy vs. Feed
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A certain amount of energy is required to separate a given feed stream into its components. It is reasonable to assume that energy requirements will be roughly in proportion to feed rate. In a distillation tower, energy is introduced as heat Q to the reboiler, which generates a proportional flow of vapor V:
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The term H, represents the latent heat of vaporization. Expressing heat input in terms of vapor flow enables evaluation of separation in terms of dimensionless ratio of vapor to feed rate, V/F.
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At total reflux, distillate flow is zero, therefore feed rate is also zero. The separation at total reflux has already been established by the Fenske equation : Lim S = ayn+l
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A second limit needs t o be established to allow the relationship of S to V/F to be outlined. For a given column, the minimum vapor to feed ratio (V/l;),,;;, can be defined as that condition under which controlled product quality requires that no product be withdrawn. A t (V/F),r,, if y is controlled, D/F = 0 and x = 2. If x is controlled, D/F = 1 and y = x. In other words, at minimum vapor to feed ratio, production is zero, just as it is at total reflux. Separation Smi*, at minimum V/F, is
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s = m,n Y(l
x(1 - y)
z(1 - x)
x(1 - 2)
Equat,ion (11.9) is derived to satisfy the upper limit of S and to pass through the points representing normal and minimum V/F:
The point V/F = 0, S = 0 will not be satisfied, but this is of no concern, because it lies outside the operating region. To gain a better appreciat ion of this relationship, the equation will be restated using the numbers in the example, given a minimum V/F of 2.0:
s= 19+570(1-+$)
The curve generated by this equat ion appears in Fig. 11.4. The shape of the curve undoubtedly varies somewhat with the shape of the JlcCabe-Thiele equilibrium curve, but the general characteristics
FIG 11.4. Separation S varies hyperbolically with vapor to feed ratio.
0 2 4 V/F 6 8
1 Applications
4 V/F
FIG 11.5. To maintain control of distillate composition, D/F must change with V/F, with a subsequent change in bottoms composition.
remain: a sharp increase in separation at the minimum V/J , gradually tapering off to approach 01 +l. Enough information is now available t o completely evaluate the effects of V/F and D/F in the control of distillate composition. Values of A can be found for current values of V/F, which can be used to determine x: for a controlled value of y. Then the D/F ratio required for control can be found from the material balance. Figure 11.5 is a plot of x and D/F VS. V/F for x = 0.5 and y controlled at 0.95. The slope of the bottoms composition curve at the normal operating conditions, that is, V/F = 5, is ___ = -0.007 dW/F) Compare this slope to dz/d(D/F) = -0.9 at the same conditions. Composition is over 100 times more sensitive to changes in distillate flow than to changes in heat input. If both x and y are to be controlled, separation must be constant. This can be done by maintaining a constant V/F, with D/F varying only with feed composition. But if heat input is fixed at maximum, so as to
FIG 11.6. With heat input constant, control of y calls for D/F and x to vary with F.
Distillation
TABLE 11 .l Column Variables vs. Feed Rate for Constant Boilup Composition and Feed
F V/F = 2.5/F
0 10.25
m 589 10
0.5 5 361
0.625 4 304
0.833 3 209
1.0 2.5 133
s = 19 + 570 1 - 2.0 V/F > (
5= 0.95
0.95 + 0.05s
~ 0.95 - z
0.032 0.038
0.050 0.059 0.084 __--0.500 0.250 0.494 0.308 0.480 0.400
D/F =
0.5 - z
0.510 0.507 0 0.127
0.455 0.455
D = (D/F)F
maximize separation at all rates of feed, V/F will change with feed rate. Then D/F must also change with feed rate, in order to control y. Again, returning to the numerical example, let V be fixed at 2.5 times the fullscale feed rate. Then V/F will vary from infinity to 2.5 as feed rate varies from 0 to 100 percent. Distillate flow must then increase less than proportionately to feed rate in order to maintain control with decreasing separation. A plot of distillate flow vs. feed rate for y = 0.95 and z = 0.5 appears in Fig. 11.6. Table 11.1 has been prepared to enable the reader to follow all the numerical manipulation. Included in Fig. 11.6 are two broken lines representing operation under conditions of constant separation at V/F = 2.5. Alt,hough this arrangement maintains control of bottoms composition while saving heat input at low rates of feed, average distillate flow is less, and loss of the light component out the bottom is subsequently greater. If bott oms composition were controlled with a constant vapor rate, the curve of distillate vs. feed rate would bend in the opposite direction. If D/F were maint ained constant under conditions of variable V/F, both x and y would turn toward one another as feed rate increased.
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