Distillation equilibrium line

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. 

A graphical stepwise procedure offered by Sherwood [62] also summarized by Reference 18. Y and X are plotted and handled stepwise as in distillation. The equilibrium line equation is for any single component ... 

Equation 11.66 is not of much practical use in distillation, as the slopes of the operating and equilibrium lines will vary throughout the column. It can be used by dividing the column into sections and calculating the slopes over each section. For most practical purposes, providing the plate efficiency does not vary too much, a simple average of the plate efficiency calculated at the column top, bottom and feed points will be sufficiently accurate. 

Several hundred plants have been installed for the dehydration of ethanol by pervaporation. This is a particularly favorable application for pervaporation because ethanol forms an azeotrope with water at 95 % and a 99.5 % pure product is needed. Because the azeotrope forms at 95 % ethanol, simple distillation does not work. A comparison of the separation of ethanol and water obtained by various pervaporation membranes and the vapor-liquid equilibrium line that controls separation obtained by distillation is shown in Figure 9.9 [40], The membranes... 

An analytical solution is also available for theoretical stages as opposed to transfer units, and the height equivalent to a theoretical plate (HETP). The number of theoretical stages or plates Np can be determined by counting the steps between the operating line and the equilibrium line as is done with distillation problems (see Example 8.1 in Section 8, Distillation), but a more convenient analytical solution is as follows ... 

It was realized that in the water/acetic acid system, in the range of low acid concentrations, the vapor/liquid equilibrium line very nearly coincides with the diagonal, so that obtaining pure water by simple distillation would require a monstrous number of stages (in the order of 150) as well as a huge reflux ratio (in the order of 9). In view of this situation, various considerations have led the BASF to choose azeotropic distillation using butyl acetate as entrainer. 

Higher relative volatilities correspond to easier separation by distillation. The greater the slope of the vapor vs liquid (y>A vs Xa ) equilibrium line, or the larger the difference between yA and Xa, the easier the separation. The relative volatility must exceed one but, realistically, must be greater than 1.3 for distillation processes [2]. It is important to note that oab is dependent on pressure and that it is not necessarily constant over a composition range. 

The graphical solution to absorption is identical to that for the rectifying section of a distillation column, except that the operating line is now above the equilibrium line. This is because the solute is now being transferred from the gas to the liquid instead of from the liquid to the gas. The stepping off stages procedure is as follows. 

Analogous to the minimum reflux ratio in distillation, there exists a minimum L/G ratio in absorption. Figure 6.3 compares the operating line to the equilibrium line for absorption. Because the slope of the operating line is L/G, reducing the liquid mass-separating agent flowrate decreases the slope of the line. Compare lines aA and ab for a separation in which the gas enters with concentration of solute which must be removed to Ya and the liquid... 

For distillations, the vapor resistance dominates, whereas for the stripping or absorption of slightly soluble materials, the liquid resistance dominates. In Equation (12.75), m is related to the VLE ratio [Equation (12.19)], and for the binary distillation of an i-j mixture is defined as the slope of the equilibrium line on a y-x diagram ... 

The additional subscript M has been added to emphasize the fact that the number of overall transfer units computed by Eq. (13-35) may differ slightly from the number computed by use of Eq. (13-34). The difference results from the fact that over any one stage of a distillation column, the slope of the equilibrium line generally changes, which gives rise to more than one possible choice for m as demonstrated in the last section of Sec. 13-2. 

As in absorption and distillation, the quantitative performance of a counter-current system can be analyzed by utilizing an equilibrium line and an operating... 

Calculate the effect of the change in slope of the equilibrium line on the local efficiency in a sieve-tray distillation column. Use the benzene-toluene system as an example, and predict / for plates where the mixture is mostly toluene and for those where it is mostly benzene, starting with an estimated value of for the middle of the column. 

Also note that in the x-y diagrams of figures a and c, the equilibrium line relating the composition of the liquid to the composition of the vapor is the curved line. The straight, v = y lines in these figures, that is, the 45° lines, are usually added to x-y diagrams to indicate the difference between the vapor and liquid compositions. The difference between the equilibrium and. r = v lines is an indication of how easy or difficult it will be to separate the components by distillation. This will be discussed briefly later in this section. 

An absorption column for laboratory use has been carefully constructed so that it has exactly 4 equilibrium stages, and is being used to measure equilibrium data. Water is used as the solvent to absorb ammonia from air. The system operates isothermally at 300 K and 1 atm. The inlet water is pure distilled water. The ratio LtV - 1.2, the inlet gas concentration is 0.01 mole fraction ammonia, and the measured outlet gas concentration is 0.0027 mole fraction ammonia. Assuming that Henry s law applies, calculate the slope of the equilibrium line. 

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