Equilibrium tie line

The bubble-point line is also the locus of compositions of the liquid when two phases are present. The dew-point line is tire locus of compositions of the gas when gas and liquid are in equilibrium. The line which ties the composition of the liquid with the composition of gas in equilibrium is known as an equilibrium tie-line. Tie-lines are always horizontal for two-component mixtures. 

Fig, 2-26. Ternary phase diagram of mixtures of methanejjpropane, and n-pentane at 500 psia and 160°F with equilibrium tie-line, 123. (Data from Dourson et al., Trans. AIME, 151, 206.)... 

For the disordered (A2) phases, rjeq = 0, Eq. 17.19 is satisfied automatically, and equilibrium tie-lines are present if W < 0 and T < Tcrit = W/k, as illustrated in Fig. 17.5. In the nearest-neighbor model, ordered B2 solutions can appear at any uniform composition Xb Nonzero equilibrium structural order parameters appear only if W > 0 at temperatures T satisfying... 

Only one equilibrium tie-line, such as R-E, is required to fix the convex point X, which is then determined by making the dotted fine shown through points B and A to the intersect of the line through points R and E. Any other equilibrium tie-line can then be made simply by drawing a fine from X through the curves as done for the tie-line R-E. 

The equilibrium tie-line intersect on curve segment D,R,P represents a feed-raffinate three-component liquid composition (wt%) in equilibrium with the same tie-line intersect point on curve segment P,E,M. This P,E,M curve point is the three-component composition solvent-extract liquid phase. 

Figure 4.21 Enthalpy concentration chart for n-butane-n-heptane at 100 psia. Curve DFHC is the saturated vapor curve BEGA is the saturated liquid. The dashed lines are equilibrium tie lines connecting y and X at the same temperature.

Hence, we see that the equilibrium tie-line is uniquely fixed by the initial masses charged to the cell, since there is only one tie-line that passes by M (otherwise, more than two phases in equilibrium could coexist, which is not possible in a system of Type I as is the case here). 

Table 3.4 Mutual equilibrium (tie-line) data (wt%) for furfural-ethylene glycol-water. ...

Problems 7.9 to 7.12 refer to the system water (A)-chlorobenzene (B)-pyri-dine (C) at 298 K. Equilibrium tie-line data taken from Treybal (1980) in weight percent are given in Table 7.6. 

Problems 7.17 to 7.19 refer to the system cottonseed oil (A)-liquid propane (B)-oleic acid (C) at 372 K and 42.5 atm, Equilibrium tie-line data taken from Treybal (1980) in weight percent are given in Table 7.7. Oleic acid is a monounsaturated fatty acid found naturally in many plant sources and in animal products. It is an omega-nine fatty acid, and considered one of the healthier sources of fat in the diet. It s commonly used as a replacement for animal... 

Figure 10.11 demonstrates the analogous Ponchon constructions. In Fig. 10.11a where the minimum reflux ratio is determined by feed conditions, the difference points P and P" are located by extending the equilibrium tie line through Zg to its intersections with the two difference points. 

Case 2 in Figs. 11.3c and 11.4 (difference point P2) represents a pinch point on plate n, since an equilibrium tie line and operating line coincide along P2X +,y 3-If less solvent is used, point M3 is lowered, P2 is raised, and the contactor is inoperable. 

Furthermore, assuming operation in vapor-liquid equilibrium, the mole fractions on tray n, x , and lie at the ends of the equilibrium tie lines. 

To determine the number of stages or flow rates and conpositions inside the cascade, stage-by-stage calculations are needed after we use the external mass balances to find concentrations. But first we use the external mass balances to find concentrations y n and y and flow rates Ej and R. Starting at stage 1 tFigure 13-201 we note that streams R and E both leave equilibrium stage 1. Therefore, these two streams are in equilibrium and the concentration of stream E can be found from an equilibrium tie line. 

Consider again the stage-by-stage calculation routine that was outlined previously. We start with the known concentration of raffinate product stream and use an equilibrium tie line (stage 1) to find the... 

The Ponchon-Savarit method is summarized in Fig. 5.3-8. The method involves an enthalpy-concentration diagram, and the enthalpies of the saturated liquid and vapor are first plotted on the diagram. Next, the equilibrium tie lines are added, based on phase equilibria. Compositions of feed, distillate, and bottoms are then located on the diagram (in the example shown the feed is mixed vapor-liquid and the distillate and bottoms are saturated liquids). A reflux ratio is chosen, and the enthalpy of the reflux is located as the top difference point, Ag- (The reflux ratio is equal numerically to the vertical distance from the difference poim to the value of y/v> divided by the vertical distance from y to Xg.)... 

To illustrate the thermodynamic behavior required by the process in Fig. 7.8-5, consider Fig. 7.8-6. If the LLE step is carried out at temperature T, to achieve an extract with composition 1, then cooling this hot extract to temperature 7 2 wiil result in two liquid phases with the compositions at points 2 and 3, which are connected by the equilibrium tie line (points 2 and 3 at T ), that also intersects the hot extract at composition 1. The relative amounts of raffinate to solvent phase at temperature are given by the inverse lever rule (i.e., the length from point 1 to 2 divided by the length from point 1 to 3). 

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,... 

B)-acetone (Q, water (/4)-chloroform (B)-acetone (C), and benzene (/l)-water (B)-acetic acid (C). Referring to Fig. 12.5-2, liquid C dissolves completely in A or in B. Liquid A is only slightly soluble in B and B slightly soluble in A. The two-phase region is included inside below the curved envelope. An original mixture of composition M will separate into two phases a and b which are on the equilibrium tie line through point M. Other tie lines are also shown. The two phases are identical at point P, the Plait point. 

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