Phase rule in distillation

The problem presented to the designer of a gas-absorption unit usually specifies the following quantities (1) gas flow rate (2) gas composition, at least with respect to the component or components to be sorbed (3) operating pressure and allowable pressure drop across the absorber (4) minimum degree of recoverv of one or more solutes and, possibly, (5) the solvent to be employed. Items 3, 4, and 5 may be subject to economic considerations and therefore are sometimes left up to the designer. For determining the number of variables that must be specified in order to fix a unique solution for the design of an absorber one can use the same phase-rule approach described in Sec. 13 for distillation systems. 

Mols of component, i, at start of distillation Total mols of liquid in bottoms of still at time, Tj Total mols liquid (not including any steam) in bottom of still at start time Tq (batch charge) y intercept of operating line or constant at fixed pressure for Winn s relative volatility Mols of component, i, in bottoms No. components present, phase rule or no. components, or constant... 

A simple distillation tower, like that shown in Fig. 3.2, also must obey its own phase rule. Here, because the distillation tower is a more complex system than the reflux drum, there are three independent... 

The first three are intensive variables. The fourth is an extensive variable that is not considered in the usual phase rule analysis. The fifth is neither an intensive nor an extensive variable but is a siugle degree of freedom that the designer uses in specifying how often a particular element is repeated in a unit. For example, a distillation column section is composed of a series of equilibrium stages, and when the designer specifies the number of stages that the section contains. 

Surfactant Mixing Rules. The petroleum soaps produced in alkaline flooding have an extremely low optimal salinity. For instance, most acidic crude oils will have optimal phase behavior at a sodium hydroxide concentration of approximately 0.05 wt% in distilled water. At that concentration (about pH 12) essentially all of the acidic components in the oil have reacted, and type HI phase behavior occurs. An increase in sodium hydroxide concentration increases the ionic strength and is equivalent to an increase in salinity because more petroleum soap is not produced. As salinity increases, the petroleum soaps become much less soluble in the aqueous phase than in the oil phase, and a shift to over-optimum or type H(+) behavior occurs. The water in most oil reservoirs contains significant quantities of dissolved solids, resulting in increased IFT. Interfacial tension is also increased because high concentrations of alkali are required to counter the effect of losses due to alkali-rock interactions. 

According to Gibbs phase rule a completely soluble binary mixture is enriched in both phases, whilst an immiscible binary mixture, with its three phases, cannot be enriched (see Fig. 29, a—d). It wiU be recognized, on the other hand, that three-component systems having a miscibility gap, f.e. showing two liquid phases and one vapour phase, are separable by countercurrent distillation [1]. A typical example is the preparation of absolute alcohol by azeotropic distillation with benzene. 

The following discussion of the phase rule, and its application to systems of polymorphic interest, has primarily been distilled from the several classic accounts published in the first half of this century [2-8]. It may be noted in passing that one of the most serious disagreements in the history of physical chemistry was between the proponents of computational thermodynamics and those interested in the more qualitative phase rule. Ultimately the school of exact calculations prevailed... 

In the table the second, third, and fourth problems each result from a permutation of the known and unknown quantities that occur in the bubble-T calculation. We refer to these as P-problems, because each problem is well-posed when values are specified for P independent intensive properties, where the value of T is given by the phase rule (9.1.14). However, the flash problem in Table 11.1 differs from the others in that it is an P -problem it is well-posed when values are specified for T independent intensive properties, with the value of T given by (9.1.12). Flash calculations pertain to separations by flash distillation in which a known amount N of one-phase fluid, having known composition z, is fed to a flash chamber. When T and P of the chamber are properly set, the feed partially flashes, producing a vapor phase of composition xP in equilibrium with a liquid of composition x ). The problem is to determine these compositions, as well as the fraction of feed that flashes NP/N. Unlike the other problems in Table 11.1, the flash problem involves the relative amounts in the phases and therefore a solution procedure must invoke not only the equilibrium conditions (11.1.1) but also material balances. 

In general, it has been divided into five parts. The first part deals with fractional distillation from the qualitative standpoint of the phase rule. The second part discusses some of the quantitative aspects from the standpoint of the chemical engineer. Part three discusses the factors involved in the design of distilling equipment. Part four gives a few examples of modem apparatus, while the last portion includes a number of useful reference tables which have been compiled from sources mostly out of print and unavailable except in large libraries. 

The similarity of such diagrams to the enthalpy-concentration diagramR of Chap. 9 is clear. In extraction, the two phases are produced by addition of solvent, in distillation by addition of heat, and solvent becomes the analog of heat. This is emphasized by the ordinate of the upper part of Fig. 10.10. Tie lines such as QS can be projected to X, Y coordinates, as shown in the lower figure, to produce a solvent-free distribution graph similar to those of distillation. The mixture rule on these coordinates (see Ae upper part of Fig. 10.10) is... 

Distillation is based on the principle that the composition of a component in either the liquid or gaseous phase can be made to increase or decrease by varying the temperature. This phenomenon is used to effect a separation of the components. A distillation column is a device that allows two phases to exist in equilibrium with one another. Since the less dense components move upward while the more dense components move downward, the distillation column is colder at the top than at the bottom. The Gibbs phase rule states that a separation will occur when a temperature gradient is placed across the distillation column. 

Referring again to the Gibbs phase rule, separation occurs because a temperature gradient is maintained from the top to the bottom of the distillation column, with the liquid on each plate colder than the liquid on the plate below it and the condenser colder than the reboiler. Heat is added to the bottom of the column to provide the required vapor flow in the column and heat is removed from the top of the column to provide the necessary flow of condensed liquid down the column. 

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