Component balance line

When a computer simulation is available, the component balance lines (Sec, 2.2,3) can be constructed from compositions printed out by the simulation. The simulation energy balances adjust the component balance lines for heat effects. These heat effects convert each component balance line thus constructed into a curve (Sec. 2.4.1). 

Using an H-x diagram to adjust Eqs, (2,9) and (2,10) for latent heat effects. This approach also converts each component balance line into a curve, but the curve is constructed using an H-x diagram instead of a computer simulation. Further details are described by Fisher (10),... 

Component balance (operating) lines (Fig. 2.9b). The component balance equations, Eqs. (2.9) and (2.10), can be represented a6 straight lines on an x-y diagram. The rectifying section component balance line is the locus of points that obey the rectifying section component balance, Eq. 

Unfortunately, component balance lines are referred to as "operating lines." The author believes that operating lines is a poor choice of words, since it states little about the physical nature of these lines. The term component balance lines is feu more descriptive and appropriate, and will be used in this book. 

Therefore, the rectifying section component balance line intersects the 45° diagonal line at the point = xD and x = yD for a total and partial condenser, respectively, The intersection point can be expressed as... 

Equation (2.27) represents the locus of the points at which the rectifying section component balance line intersects the stripping section component balance line, This equation is called the q-line equation. The q-line is illustrated later in Fig, 2,96,... 

In each case the point defined is the intersection of the line with the 45° diagonal line. The slopes and intersection points of each of these lines are summarized in Table 2.3, In addition, it has been shown that the rectifying section component balance line and the stripping section component balance line meet on the q-line,... 

Figure 2,6 The g-Iine and its implications, (a) The 5-line as a (unction of the thermal state of the feed (6) effect of q on stripping section component balance line at censtant reflux ratio.

These lines are shown in Pig. 2.96. Note that the 9-line passes through the intersection of the two component balance lines. 

In Sec. 2.2.4, it was assumed that the feed enters the column at the optimum feed stage, which is located at the intersection of the component balance lines. At that point, the construction was switched from the rectifying section component balance line to the stripping section component balance line,... 

The reason for the greater number of stages is that steps become smaller as the component balance line moves closer to the equilibrium curve, and therefore more steps are required, The optimum feed point is therefore achieved when the active component balance line is as far as possible from the equilibrium curve. 

Pinching. As the component balance line approaches the equilibrium curve, the steps become smaller, An infinite number of stages is required to reach the intersection of the component balance line and the equilibrium curve. This intersection is termed the pinch point. The bottom pinch point is (0,22, 0.4) in Fig. 2.106, and the top pinch point... 

A column is said to be pinching when the component balance line is too close to the equilibrium curve, Physically, this represents a situation where several stages are doing very little separation and are practically wasted. 

In an existing column, mechanical reasons often make it difficult to change feed location. A pinch can then be remedied by increasing reflux and reboil. This draws the component balance line and the equilibrium curve further apart, enlarging the steps, and thereby per-... 

If 17% benzene is unacceptable in the bottom product, reflux and reboil can be raised to achieve the required esparation in 10 stages. The slope of the rectifying section component balance line is increased, and that of the stripping section component balance line is lowered, ThiB is a trial-and-error calculation, which ende when 10 theoretical stages are accommodated betwean the componant balance line and the equilibrium curve, the top and bottom products are at their desired specifications, and the feed enters between stages 4 and 5. The slopes of the component balance lines will determine the new required reflux and boilup rate. The final result is shown in Fig. 2.10c. From this diagram,... 

Check that L fV is the same as that determined from the slope of the component balance line,... 

As the reflux ratio decreases, so does the slope of the upper component balance line, The effect of reflux ratio on the component balance lines is illustrated in Fig, 2,11, using the benzene-toluene system in Exampla 2.1. 

Any practical separation requires that the component balance lines intersect below the equilibrium curve, as for a reflux ratio of 3.0 in Fig. 2,11c. The McCabe-Thiele construction corresponding to this ratio is shown in Fig. 2.9c, If insufficient reflux is provided, the component balance lines intersect above the equilibrium curve, as for a reflux ratio of 1,0 in Fig. 2.11c, The McCabe-Thiele construction (Fig. 2,116) for these conditions shows that even with an infinite number of stages, the separation cannot be achieved. 

At minimum reflux, the pinch occurs at the intersection of the component balance line and the g-line when the equilibrium curve has no inflection points (Fig. 2,11c), This would be expected because the component balance lines intersect on the q-line. When the equilibrium curve has a point of inflection (Fig. 2.12), the pinch between the equilibrium curve and the component balance line may occur at the point of tangency instead of the intersection of the g-line and the component balance line. This condition is termed tangent pinch. 

Figure 2.11 Effect of reflux ratio on component balance lines, (a) Overall (b) R < Amin, impossible operation (c) R = minimum reflux

Using Eqs. (2.12) and (2.17), the stripping section component balance line [Eq- (2.10)] can be expressed in terms of the stripping ratio... 

The condition where the reflux and stripping ratios approach infinity is termed total reflux. No feed enters the column and no product leaves. Both component balance lines coincide with the 45° diagonal line and are therefore furthest away from the equilibrium curve. Total reflux sets the minimum number of stages required for the separation. For Example 2,1, Fig. 3,lid shows that the minimum number of stages required for the separation is 6. 

On an x-y diagram, the denominator equals the spacing between the equilibrium curve and the component balance line (Fig, 2,13), yn is given by... 

E Tbetween equilibrium curve ] y - wvLand component balance line J + %-i... 

The procedure for finding minimum raflux in each section of a complex fractionator is similar. First, the point of intersection of the component balance line with the 45° diagonal is found by using Eq. (2.38). Second, the point of intersection of the q-line for the feed or side product with the equilibrium curve is graphically determined. A straight line is then drawn between the two points. This line is the minimum reflux component balance line. The minimum reflux is found from the intercept of this line on they axis, using Eq. (2.40). 

In case of heat removal or addition, there is no q-line. In such a case, the second point thet is used to construct the minimum-reflux component balance line is the point on the equilibrium curve representing the compositions of the liquid and vapor stream leaving the heat-addition or heat-removal stage. 

The intercept of each component balance line on the y axis can now be calculated from Eq. (2.40), using the actual reflux ratio, Each com-... 

This procedure can be simplified if there are no points of heat eddi-tion or removal, and 9-lines exist between all adjacent sections. In this case, the only intercept on they axis that is actually required is that of the first section. Once the component balance line for this section is drawn, its points of intersection with the first 9-line are used, instead of the intercept on the y axis, to construct the second component balance line, etc. 

---