Binary distillation equilibrium relationships

The digital simulation of a distillation column is fairly straightforward. The main complication is the large number of ODEs and algebraic equations that must be solved. We will illustrate the procedure first with the simplified binary distillation column for which we developed the equations in Chap. 3 (Sec. 3.11). Equimolal overflow, constant relative volatility, and theoretical plates have been assumed. There are two ODEs per tray (a total continuity equation and a light component continuity equation) and two algebraic equations per tray (a vapor-liquid phase equilibrium relationship and a liquid-hydraulic relationship). 

The above applies to both binary and multicomponent distillation. In multicomponent distillation, once the above are specified, other components will distribute according to the equilibrium relationship. Frequently, a product spec sets the maximum concentration of impurities that can be tolerated in the product. Product specs are less than" specifications. The one impurity which is dependent on the column separation and is most difficult to achieve sets the composition specification in the column. This is illustrated in Table 3.1 for a propylene-propane separation (Ca splitter). Since the light nonkeys (hydrogen, methane, ethylene, ethane, and oxygen) end up in the distillate, their concentration in the distillate is independent of the column. Of the others, the most difficult purity to achieve sets the composition specification, Similarly, the heavy nonkeys (MAPD, C4 and... 

Equation 12.9 relates the bottoms composition, X to the distillate composition, E, at total reflux. The derivation of this equation on the basis of material balances and equilibrium relationships is equivalent to the graphical solution for binary mixtures described in Chapter 5. However, in the binary graphical solution, the material balance is represented by the operating curves, not necessarily at total reflux, while in the present derivation the material balance equation is obtained on the basis of total reflux. 

To calculate the vapor composition, it is necessary to develop an equilibrium relationship. For the distillation of an ideal binary system of components A and C, the equilibrium relationship is given by ... 

In this simple distillation process, it is assumed that the vapor formed within a short period is in thermodynamic equilibrium with the liquid. Hence, the vapor composition xp is related to the hquid composition xb by an equiUbrium relation of the form xp = fixs)- The exact relationship for a particular mixture may be obtained from a thermodynamic analysis depending on temperature and pressure. For a system following the ideal behavior given by Raoult s law, the equilibrium relationship between the vapor composition y (or xp) and liquid composition x (or xb) of the more volatile component in a binary mixture can be approximated using the concept of constant relative volatility a), and is given by ... 

Since the boiling point properties of the components in the mixture being separated are so critical to the distillation process, the vapor-liquid equilibrium (VLE) relationship is of importance. Specifically, it is the VLE data for a mixture which establishes the required height of a column for a desired degree of separation. Constant pressure VLE data is derived from boiling point diagrams, from which a VLE curve can be constructed like the one illustrated in Figure 9 for a binary mixture. The VLE plot shown expresses the bubble-point and the dew-point of a binary mixture at constant pressure. The curve is called the equilibrium line, and it describes the compositions of the liquid and vapor in equilibrium at a constant pressure condition. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

The equilibrium distillation behavior of the model fuels is adequately covered in the fuel oil discussion. However, the case for the rapid droplet vaporization, which was not clearly seen for fuel oils, is more amenable to analysis for a binary system. The surface gradients are given by the following relationship,... 

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