Operating line, equilibrium diagram

Xnt 0.10, Xsi = 0, Xbi 0.557 wt. fraction acetone. On the triangular diagram, Fig. 6.33, the operating point 0 is located as before. Random lines from 0 cut the equilibrium solubility curve at concentrations Xr on the water-rich side, Xr on the solvent-rich side, to provide data for the operating line. Equilibrium tie lines provide data for the equilibrium curve. The operating diagram prepared from these data is shown in Fig. 8.4. From this figure,... 

FIGURE 6.1 7 Operating line-equilibrium curve diagrams () absorption, and (c) stripping. 

Figure 1-6. Operating line-equilibrium curve diagram fbr absorption column.

FIG. 13-34 Illustration of how equdihrium stages can he located on the x-q diagram through the alternating use of the equilibrium curve and the operating line. 

Using the vapor-liquid equihbrium data, plot a y-x diagram. Draw a number of operating lines at a slope of 0.75. Note the composition at the 45° intersection, and step off seven plates on each to find the equilibrium value of the bottoms. Some of the results are tabulated in the following table ... 

For certain simplified cases it is possible to calculate directly the number of stages required to attain a desired product composition for a given set of feed conditions. For example, if equilibrium is attained in all stages and if the underflow mass rate is constant, both the equilibrium and operating lines on a modified McCabe-Thiele diagram are straight, and it is possible to calculate direc tly the number of ideal stages required to accommodate arw rational set of terminal flows and compositions (McCabe, Smith, and Harriott, op. cit.) ... 

In addition to the previously mentioned shortcut equations, plotting a McCabe-Thiele diagram is also a very useful tool. The equation for the equilibrium X-Y diagram and plotting of the operating lines are described next. 

Lj and are the pure liquid and inert gas loading rates, respectively, in units of Ib-moles/hr-ft. The second expression is the operating line on an equilibrium diagram. In all scrubbing application, where the transfer of solute is from the gas to the liquid, the operating line will lie above the equilibrium curve. When the mass transfer is from the liquid to the gas phase, the operating line will lie below the equilibrium curve. The latter case is known as stripping . 

On a y-x (McCabe-Thiele) diagram, this equation represents the operating line which extends between the points (y , x" ) and (yf , x") and has a slope of Lj/Gi, as shown in Fig. 2.5. Furthermore, each theoretical stage can be represented by a step between the operating line and the equilibrium line. Hence, NTP can be determined by stepping off stages between the two ends of the exchanger, as illustrated by Fig. 2.5. 

On a y-x (MeCabe-Thiele) diagram, this equation represents the operating line that extends between the points (y/", xj") and (y , x ) and has a slope of Ly/G,. Equation (2.10) has thitee unknowns, yf , Lj and xj . Let us first fix the outlet composition of the waste stream, yf". As depicted by Fig. 2.9, the maximum themetically attainable outlet composition of the MSA, xj", is in equilibrium with y ". An infinitely laige mass exchanger, however, will be needed to undertake... 

Both liquid and vapor products are withdrawn, with liquid reflux composition being equal to liquid product composition. Note that on an equilibrium diagram the partitd condenser liquid and vapor stream s respective compositions are in equilibrium, but only when combined do they represent the intersection of the operating line with the 45° slope (Figure 8-14). 

The area under the curve between Xgo and is the value of the integrtil. Plot the equilibrium curve for the more volatile component on x - y diagram as shown in Figure 8-33. Then, select values of xd from the operating line hav ing the constant slope, L/V, from equation... 

Note that if the problem of accurate graphical representation occurs in the rectification end of the diagram, the corresponding relation to use to calculate the balance of the trays, assuming straight line operating and equilibrium lines in the region is [59] ... 

Note that the 10% (wt) aqua product operating line is shown on the diagram, but such a concentration cannot be reached when operating at 150 psig. A greater pressure is required in order to lower the equilibrium curve. 

Figure 8.24. Left schematic diagram of an adiabatical three-bed, indirectly cooled reactor with two heat exchangers. Right a diagram showing the equilibrium curve to the upper right, the optimal operating line and the operation line for the reactor are to the left. [Adapted from C.J.H. Jacobsen, S. Dahl, A. Boisen, B.S. Clausen,...

Data could be obtained from such a graph to construct a McCabe-Thiele type diagram. Tie line points on the binodal curve would provide data for an equilibrium curve, and data could be obtained to construct an operating line (from lines drawn from 0 through the binodal curve). 

The three sets of vapor-liquid equilibrium data appearing on the x-y diagram show some disagreement, so that great accuracy cannot be expected from determination of tray requirements, particularly at the low water concentrations. The upper operating line in the first column is determined by the overall material balance so it passes through point (0.995, 0.995), but the initial point on the operating line is at x = 0.53, which is the composition of the reflux. The construction is shown for 50% vaporized feed. That result and those for other feed conditions are summarized ... 

Figure 13.9. Combined McCabe-Thiele and Merkel enthalpy-concentration diagrams for binary distillation with heat balances, (a) Showing key lines and location of representative points on the operating lines, (b) Completed construction showing determination of the number of trays by stepping off between the equilibrium and operating lines.

A typical diagram for the complete absorption of pentane and heavier components is shown in Fig. 14-11. The oil used as solvent is assumed to be solute-free (i.e., X2 = 0), and the key component, butane, was identified as that component absorbed in appreciable amounts whose equilibrium line is most nearly parallel to the operating lines (i.e., the K value for butane is approximately equal to... 

Four theoretical trays have been stepped off for the key component (butane) on Fig. 14-11, and are seen to give a recovery of 75 percent of the butane. The operating lines for the other components have been drawn with the same slope and placed so as to give approximately the same number of theoretical trays. Figure 14-11 shows that equilibrium is easily achieved in fewer than four theoretical trays and that for the heavier components nearly complete recovery is obtained in four theoretical trays. The diagram also shows that absorption of the light components takes place in the upper part of the tower, and the final recovery of the heavier components takes place in the lower section of the tower. 

Example 7.1 The next part of the McCabe-Thiele diagram is the operating line. To generate the operating line, the problem for Fig. 7.2 must be stated. The following conditions are given. Find the required solvent rate and number of theoretical equilibrium stages to meet the treated water specification of 1.0% acid remainder. Benzene will be the solvent. Also determine what solvent inlet purity is required to meet this water specification. A step-by-... 

Figure 2. Equilibrium curves for the carburization of tungste and molybdenum. The tungsten diagram shows experiment points for W2C (open circles) and WC (solid circle) (39). Tl molybdenum diagram shows the operating line for synthesis wii 20% CH4 in H2 [11] (reproduced with permission from Ref. 3).

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