ENTHALPY-CONCENTRATION DATA

TABLE 1.1 Enthalpy-concentration Data for the Single-phase Liquid Region and Also the Saturated Vapor of the Acetic Acid-water System at 1 Atmosphere 

Reference state Liquid water at 32°F and 1 atm solid acid at 32 F and 1 atm. 

Liquid or Vapor Enthalpy— Btu/lb Liquid Solution Enthalpy Saturated 

TABLE 1.2 Vapor-liquid Equilibrium Data for the Acetic Acid-water System Pressure = 1 Atmosphere 

X Mole Fraction Water in the Liquid y Mole Fraction Water in the Vapor 

---

The lower part of the column is covered by stepping off stages in a fashion similar to that in the upper part of the column, and the final conni of theoretical stages is then determined. The Ponchon-Savarit method may be used for many situations more complex lhan the simple one just described mixed vapor-liquid distillate product, side draw streams, multiple feeds, and so on. Standard unit operations textbooks should be consulted for more dentils on this methnd. As mentioned, it suffers from a need for enthalpy-concentration data, but even a crude approximation based on linear variation of enthalpy with concentration can be better than the McCabe-Thiele approach if there is a very large difference in the latent heats of vaporization of the iwo components being distillnd. 

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 advantage of the enthalpy-concentration diagram method is that both heat and mass effects are taken into account simultaneously. This method has only limited use, however, because of the difficulty in obtaining enthalpy-concentration data that have been published for only a few systems. In using either method, however, it is necessary to make a corresponding mass balance since the heat effects in a crystallization process are related to the quantities of solids produced through the heat of crystallization. 

The McCabe-Thiele constructions described in Chapter 8 embody rather restrictive tenets. The assumptions of constant molal overflow in distillation and of interphase transfer of solute only in extraction seriously curtail the general utility of the method. Continued use of McCabe-Thiele procedures can be ascribed to the fact that (a) they often represent a fairly good engineering approximation and (b) sufficient thermodynamic data to justify a more accurate approach is often lacking. In the case of distillation, enthalpy-concentration data needed for making stage-to-stage enthalpy balances are often unavailable, while, in the Case of absorption or extraction, complete phase equilibrium data may not be at hand. 

Example 10.1. One hundred kilogram-moles per hour of saturated n-hexane-n-octane vapor containing 69 moIe% hexane is separated by distillation at atmospheric pressure into product containing 90 mole% hexane and bottoms containing 5 mole% hexane. The total condenser returns 42.5 mole% of the condensate to the column as saturated liquid. Using the graphical Ponchon method and the enthalpy-concentration data of Fig. 10.8 calculate ... 

Introduction. In Section 11.4B the McCabe-Thiele method was used to calculate the number of theoretical steps or trays needed for a given separation of a binary mixture of A and B by rectification or fractional distillation. The main assumptions in the method are that the latent heats are equal, sensible heat differences are negligible, and constant molal overflow occurs in each section of the distillation tower. In this section we shall consider fractional distillation using enthalpy-concentration data where the molal overflow rates are not necessarily constant. The analysis will be made using enthalpy as well as material balances. 

Enthalpy-concentration data. An enthalpy-concentration diagram for a binary vapor-liquid mixture of A and B takes into account latent heats, heats of solution or mixing, and sensible heats of the components of the mixture. The following data are needed to construct such a diagram at a constant pressure (1) heat capacity of the liquid as a function of temperature, composition, and pressure (2) heat of solution as a function of temperature and composition (3) latent heats of vaporization as a function of composition and pressure or temperature and (4) boiling point as a function of pressure, composition, and temperature. 

Table 11.6-2. Enthalpy-Concentration Data for Benzene-Toluene Mixtures at 101325 kPa (I atm) Total Pressure... 

To analyze the enriching section of a fractionating tower using enthalpy-concentration data, we make an overall and a component balance in Fig. 11.6-2,... 

The enthalpy-concentration data presented in Table 6.3 are used to construct an enthalpy-concentration diagram as shown in Fig. 6.21. To determine the minimum reflux ratio, the equilibrium tie line with the lowest slope is plotted on this diagram. An extension of this tie line to the intersection with the vertical Xp, and Xq lines represents the principal operating line for the condition of minimum reflux. The intercept of 12,970 kJ/kg mol on the x line permits evaluation of (2c/ )min from... 

Rework Problem 6.19 using the Ponchon-Savarit approach and utilizing the enthalpy-concentration data at 0.101 MPa for nitrogen-oxygen mixtures as presented in Table 6.3. 

---