Vapor-liquid equilibrium enthalpy-composition diagrams

Figure 1.2 Enthalpy-composition diagram for the ethanol-water stem, showing liquid and vapor phases in equilibrium at 1 atm.

The figure-that follows for the ethanol + water sy.s-tem is an unusual one in that it shows both vapor-liquid equilibrium and the enthalpy concentration diagrams on a single plot. This is done as follows. The lower collection of heavy lines give the enthalpy concentration data for the liquid at various temperatures and the upper collection of lines is the enthalpy-concentration data for the vapor, each at two pressures, 0.1013 and 1 013 bar. (There are also enthalpy-concentration lines for several other temperatures.) The middle collection of lines connect the equilibrium compositions of liquid and vapor. For example, at a pressure of 1.013 bar, a saturated-vapor containing 71 wt % ethanol with an enthalpy of 1535 kJ/kg is in equilibrium with a liquid containing 29 wt % ethanol with an enthalpy of 315 kJ/kg at a temperature of 85°C. Note also that the azeotropes that form in the ethanol -f water system are indicated at each pressure. 

The first phase-equilibrium diagrams discussed are for two-component liquid-vapor systems. Next, three-component diagrams used in extraction, absorption, leaching, and ion exchange are developed. Finally, enthalpy-composition diagrams, which include energy effects, are constructed. 

For binary flash distillation, the simultaneous procedure can be conveniently carried out on an enthalpy-composition diagram First calculate the feed enthalpy, hp, from Eq. t2-81 or Eq. (2=9b) then plot the feed point as shown on Figure 2-9 (see Problem 2-All. In the flash drum the feed separates into liquid and vapor in equilibrium Thus the isotherm through the feed point, which must be the T nun isotherm, gives the correct values for x and y. The flow rates, L and V, can be determined from the mass balances, Eqs. f2-51 and 2-61. or from a graphical mass balance. 

The method described here was originally presented by Ponchon (1921) and Savarit (1922). Besides the enthalpy-composition diagram, the method makes use of the lever rule for relating the rates of vapor and liquid products of a binary equilibrium stage to their compositions and enthalpies, as described below. 

FIG. 2-7 Enthalpy-concentration diagram for aqueous ammonia. From Thermodynamic and Physical Properties NH3-H20, Int Inst. Refrigeration, Paris, France, 1994 (88 pp.). Reproduced by permission. In order to determine equilibrium compositions, draw a vertical from any liquid composition on any boiling line (the lowest plots) to intersect the appropriate auxiliary curve (the intermediate curves). A horizontal then drawn from this point to the appropriate dew line (the upper curves) will establish the vapor composition. The Int. Inst. Refrigeration publication also gives extensive P-v-xtah es from —50 to 316°C. Other sources include Park, Y. M. and Sonntag, R. E., ASHRAE Trans., 96,1 (1990) 150-159 x, h, s, tables, 360 to 640 K) Ibrahim, O. M. and S. A. Klein, ASH E Trans., 99, 1 (1993) 1495-1502 (Eqs., 0.2 to 110 bar, 293 to 413 K) Smolen, T. M., D. B. Manley, et al.,/. Chem. Eng. Data, 36 (1991) 202-208 p-x correlation, 0.9 to 450 psia, 293-413 K)i Ruiter, J. P, 7nf. J. R rig., 13 (1990) 223-236 gives ten subroutines for computer calculations. 

FIG. 2-10 Enthalpy -concentration diagram for aqueous ethyl alcohol. Reference states Enthalpies of liquid water and ethyl alcohol at 0 °C are zero. NOTE In order to interpolate equilibrium compositions, a vertical may be erected from any liquid composition on the boiling line and its intersection with the auxiliary line determined. A horizontal from this intersection will establish the equilibrium vapor composition on the dew line. Bosnjakovic, Technische Thermodynamik, T. Steinkopjf, Leipzig, 1935.)... 

Each point on the saturated liquid curve is associated with a point on the saturated vapor curve at equilibrium with it. The equilibrium vapor and liquid compositions may be obtained from Y-X or Y-X diagrams. Saturated vapor and liquid points on the H-X diagram at equilibrium with each other are joined by straight lines called tie lines. The single-stage graphical representation described in Section 5.3.1 is an illustration of a tie line. If, for instance, X is known, L can be determined as a point on the saturated liquid curve with composition coordinate X. Point V must lie on the other end of the tie line on the saturated vapor curve. Point F can then be determined either from information on the relative rates of feed, liquid, and vapor or from its composition or enthalpy. 

The Ponchon-Savarit method is summarized in Fig. 5.3-8, The methud involves an enlhalpy-coucen-traiion diagram, and tha enthalpies of the saturated liquid and vapor are first plotted on the diagram. Next, the equilibrium lie 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 cbosen. and the enthalpy of die reflux is located as the lop difference point. A0. (The reflux ratio is equal numerically to the vertical distance from the difference point to the value of yN, divided by the vertical distance from to xD.)... 

To have a simple example, we consider an alkane(l) + aromatic(2) mixture, modeled by the Redlich-Kwong equation (8.2.1). Certain vapor-liquid phase diagrams for this mixture were displayed and discussed in 9.3. Here our objective is to compute residual enthalpies for vapor and liquid that coexist in equilibrium in particular, we want to construct an isothermal plot of vs. x and y. (We will call this an hxy diagram, even though it is that is actually plotted.) To do so, we set the temperature, pick a liquid composition Xp and then perform a bubble-P calculation to obtain values... 

Examine the enthalpy-composition map for G-H mixtures at 1 atm. The dashed lines in the liquid region and the vapor region show the temperature at a given composition and enthalpy. The dashed lines in the liquid-vapor region are tie lines. Unlike the previous phase diagrams, the tie lines in the liquid-vapor region are not horizontal. Liquid and vapor at equilibrium have the same temperature but not the same enthalpy. 

The diagram refers to the enthalpy relationships of a completely miscible binary system at a constant pressure of 1 atm. The mole fraction of component B is plotted horizontally from left to right and the enthalpy of the mixture, relative to the pure components in chosen reference states, is plotted vertically. Curve CD represents the enthalpy of the liquid phase, at its boiling-point, as a fimction of composition. Curve EF represents the enthalpy of the vapour above the boiling liquid as a function of its own composition. (Thus CE and DF are the enthalpies of vaporization of A and B respectively.) OH and IJ are typical tie-lines, i.e. a boiling liquid of composition ( is in equilibrium with vapour of composition H,... 

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