The Phase Rule in Distillation

This is perhaps an idea you remember from high school, but never quite understood. The phase rule corresponds to determining how many independent variables we can fix in a process before all the other variables become depmdent variables. In a reflux drum, we can fix the temperature and composition of the liquid in the drum. The temperature and composition are called independent variables. The pressure in the drum could now be calculated from the chart in Fig. 6.4. The pressure is a dependent variable. The phase rule for the reflux drum system states that we can select any two variables arbitrarily (temperature, pressure, or composition), but then the remaining variable is fixed. 

A simple distillation tower, like that shown in Fig. 6.2, 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 variables that must be specified. The operator can choose from a large number of variables, but must select no more than three from the following list  

The prior discussion assumes that the feed rate, feed composition, and heat content of the feed (enthalpy) are fixed. My purpose in presenting this review of the phase rule is to encourage the routine manipulation of tower-operating pressures in the same sense, and with the same objectives, as adjusting reflux rates. Operators who arbitrarily run a column at a fixed tower pressure are discarding one-third of the flexibility available to them to operate the column in the most efficient fashion. And this is true regardless of whether the objective is to save energy or improve the product split. 

The prior discussion assumes that the feed rate, feed composition, and heat content (enthalpy) are fixed. My purpose in presenting this review of the phase rule is to encourage the routine manipulation of 

API Data Book, Vapor Pressure Section, 1986 edition. 

An internal-combustion engine drives a car. Pumps are driven by turbines or motors. Jet planes are pushed by the thrust of an axial compressor. 

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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 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. 

First, the criteria for phase equilibria are discussed in terms of single-component systems. Then, when the ground rules are in place, multi-component systems are discussed in terms of partition, distillation and mixing. 

Besides fluid mechanics, thermal processes also include mass transfer processes (e.g. absorption or desorption of a gas in a liquid, extraction between two liquid phases, dissolution of solids in liquids) and/or heat transfer processes (energy uptake, cooling, heating, drying). In the case of thermal separation processes, such as distillation, rectification, extraction, and so on, mass transfer between the respective phases is subject to thermodynamic laws (phase equilibria) which are obviously not scale dependent. Therefore, one should not be surprised if there are no scale-up rules for the pure rectification process, unless the hydrodynamics of the mass transfer in plate and packed columns are under consideration. If a separation operation (e.g. drying of hygroscopic materials, electrophoresis, etc.) involves simultaneous mass and heat transfer, both of which are scale-dependent, the scale-up is particularly difficult because these two processes obey different laws. 

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. 

The simple rule for the prediction of the possibility of GC analysis of organic compounds is based on the reference data of their boiling points. If any compound can be distilled without decomposition at the pressures from atmospheric to 0.01-0.1 torr, it can be subjected to GC analysis, at least on standard nonpolar polydi-methylsiloxane stationary phases. In accordance with this rule, most of the monofunctional —OH compounds (alcohols, phenols) and their S analogs (thiols, thiophenols, etc.) may be analyzed directly. The confirmation of chromatographic properties of any analytes must be not only verbal (at the binary level yes/no ) but also based on their GC Kovats retention indices as the most objective criteria for example ... 

Equimolar counter diffusion appears in the distillation of binary mixtures. In a distillation column the liquid falls downwards, and the vapour flows upwards, Fig. 1.43. As the liquid flowing down the column is colder than the vapour flowing upwards, chiefly the component with the higher boiling point, the so called least volatile component condenses, whilst the vapour from the boiling liquid mainly consists of the components with the lower boiling points, the more volatile components. The molar enthalpy of vaporization is, according to Trouton s rule, approximately constant for all components. If a certain amount of the least volatile component condenses out from the vapour, then the same number of moles of the more volatile substance will be evaporated out of the liquid. At the phase boundary between liquid and vapour we have cAwA = —cBwB. The reference velocity u is zero because cu = cAwA + cBwB. The molar flux transported to the phase boundary from (1.158) and (1.160) is... 

Thus, in order to define the column operation uniquely, two specifications are required, as already concluded using the description rule (Section 17.1.3). These could be the reflux rate and distillate rate, Lg and D. Note that a subcooled condenser is assumed so that no phase equilibrium equation is written for stage 0 and no Foi variables exist. The column pressure profile is assumed fixed or determined independently from hydraulics calculations and is not included in the column variables. Also, the enthalpies and phase equilibrium coefficients are, in general, functions of the temperature, pressure, and composition (Chapter 1) and are therefore not considered as additional unknown variables. 

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. 

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