Fractionating columns operating lines

The usual operating data to be determined or estimated for isothermal systems are the liquid rate(s) and the terminal concentrations or mole fractions. An operating line that describes operating conditions in the column is obtained by a mass balance around the column (as shown in Figure 72). 

Since the liquid and gas components do not change phases, their flow rates remain constant in the column. It follows that, if the distributed component compositions are expressed as mole ratios to the liquid or gas instead of mole fractions, the column operating line becomes a straight line. 

Fractionation columns in tar-acid refineries are generally operated under vacuum and heated by high pressure steam or circulating hot oil. Calandtia in the reboders, condensers, mndown lines, and receiving tanks are constmcted of stainless steel, or, in the case of the condensers, of tin or nickel. 

FIG. 22-42 Four alternative modes of contimioiis-flow operation with a foam-fractionation column (1) The simple mode is illustrated hy the solid lines. (2) Enriching operation employs the dashed reflux line. (3) In stripping operation, the elevated dashed feed line to the foam replaces the solid feed line to the pool. (4) For combined operation, reflux and elevated feed to the foam are both employed. 

After filling the receiver, reflux runs down the column at the same molar rate as the vapor back up (L = G). The operating line has a slope of 1.0. Then there are n plates/trays between composition Xp and xj (the mol fraction in distillate). As the distillation continues, the operating line moves closer to the 45° line of the diagram, and x and Xp (and Xj) become richer and leaner, respectively, until at the end xj becomes Xq and x becomes x. The required time is 02. 

Otherwise expressed, the number of theoretical plates required for a given separation increases when the reflux ratio is decreased, i.e. when the amount of condensed vapour returned to the column is decreased and the amount distilled off becomes greater. The variation in the reflux ratio is achieved by the use of a suitable take-off head (or still-head), usually of the total condensation variable take-off type. In use, all the vapour is condensed and the bulk of the condensate is returned to the fractionating column, small fractions of the condensate being allowed to collect in a suitable receiver. The design may be appreciated from the line diagram shown in Fig. 2.107 in which the controlled collection of distillate is by the socket-cone screw-operated valve sited just below the condenser drip end. 

For stripping, the entering liquid and gas concentrations are known. The fraction stripped and therefore the exit liquid concentration is also known, but the exit gas concentration is unknown. Therefore point 2 - at the bottom of the column is fixed, but point 1 - at the top of the column - is not fixed. The maximum exit and minimum gas flow rate gas concentration is obtained when the operating line intersects the equilibrium curve, as shown by the dashed line in Figure 6.16. The intersection is given by Equation 6.21.1S, which is also obtained by the simultaneous solution of a component balance and an equilibrium relation. 

Since we used definition (84) based on the vapor mole fractions, we should start our stepping process at the bottom of the column, rather than the top. In other words, we start at (xq, x ) and step upwards until either the vapor or the liquid mole fraction exceeds xj). By stepping from the bottom up, the step from the operating line toward the equilibrium curve involves changes in y, whereas when we step from the top down, the step from the operating line toward the equilibrium curve involves changes in x instead of y. The latter is appropriate when the efficiency is defined in terms of x instead of y. 

At a given point in time, the amount of liquid in the reboiler is and its composition in terms of the mole fraction of the lighter component is The distillate rate and composition at time / are D mol/h and Xg, respectively. The internal liquid and vapor flows at the same instant areL and P mol/h, assumed constant from tray to tray. A material balance at / around an envelope that includes the condenser and a column section from the condenser to any tray gives the following operating line equation if the holdups are neglected ... 

The portion of the column that lies below the feed plate is called the stripping section. The function of this section is to obtain a nearly pure bottoms stream, B, of the less volatile component of the feed. As with the rectifying section, we can analyze in terms of a mass balance to obtain an operating line relating the vapor-phase mole fraction to the liquid-phase mole fraction exiting a stage. Again, it is assumed that the molar flowrates B, L and V are constant and that constant molar overflow applies. The overall mass balance around the bottom of the column, then, becomes ... 

Acetone is to be absorbed from wet air into pure water in a plate column. The laden air enters at 35°C, and the water solvent enters at 25°C. Pressure is atmospheric. The air contains 2.0 mole-% acetone and is 70% saturated with water vapor (4 vol-% water). The concentration of acetone in the air is to be reduced to 0.05 mole-% = 0.975). The solvent rate is chosen such that the operating line has a slope of 3.49 on a mole fraction-plotting basis. How many stages are needed ... 

The effluents from the different quench boilers are first collected together. They undergo supplementary in-line cooling, and are then sent to a so-called primary fractionation column, whose bottom stream, itself previously cooled, serves for the direct qnench operation. This column also separates the gases at the top that are sent to the compression section, and a gasoline sidestream. The diluent steam which is condensed at various levels, is purified and re-used in a dosed circuit, with make-up process water. 

The McCabe-Thiele method hinges upon the fact that, as an approximation, the operating lines on the xy diagram can be considered straight for each section of a fractionator between points of addition or withdrawal of streams. This is true only if the total molar flow rates of liquid and vapor do not vary from stage to stage in each section of the column. This is the case if ... 

In the adaptation of an existing column to a new separation, the point of introducing the feed is limited to the location of existing nozzles in the column wall. The slope of the operating lines and the product compositions to be realized must then be determined by trial and error, in order to obtain numbers of theoretical stages in the two sections of the fractionator consistent with the number of real trays in each section and the expected tray efficiency. 

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