Distillation enriching equations

Enriching-column distillation. Enriching towers are also sometimes used, where the feed enters the bottom of the tower as a vapor. The overhead distillate is produced in the same manner as in a complete fractionating tower and is usually quite rich in the more volatile component A. The liquid bottoms is usually comparable to the feed in composition, being slightly leaner in component A. If the feed is saturated vapor, the vapor in the tower V = F. Enriching-line equation (11.4-7) holds, as does the ij-line equation (11.4-19). 

The equihbrium shown in equation 3 normally ties far to the left. Usually the water formed is removed by azeotropic distillation with excess alcohol or a suitable azeotroping solvent such as benzene, toluene, or various petroleum distillate fractions. The procedure used depends on the specific ester desired. Preparation of methyl borate and ethyl borate is compHcated by the formation of low boiling azeotropes (Table 1) which are the lowest boiling constituents in these systems. Consequently, the ester—alcohol azeotrope must be prepared and then separated in another step. Some of the methods that have been used to separate methyl borate from the azeotrope are extraction with sulfuric acid and distillation of the enriched phase (18), treatment with calcium chloride or lithium chloride (19,20), washing with a hydrocarbon and distillation (21), fractional distillation at 709 kPa (7 atmospheres) (22), and addition of a third component that will form a low boiling methanol azeotrope (23). 

Example This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required. If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation. 

The component balance equations for reflux drum, column enriching section, feed plate, column stripping section and the column base and reboiler are very similar to those derived previously for the binary distillation example CONSTILL, but are now expressed in multicomponent terms as described in Section 3.3.3.4. 

This relation enables the composition of the vapour to be calculated for any desired value of x, if a is known. For separation to be achieved, a must not equal 1 and, considering the more volatile component, as a increases above unity, y increases and the separation becomes much easier. Equation 11.14 is useful in the calculation of plate enrichment and finds wide application in multicomponent distillation. 

Of special interest in stable isotope geochemistry are evaporation-condensation processes, because differences in the vapour pressures of isotopic compounds lead to significant isotope fractionations. For example, from the vapour pressure data for water given in Table 1.2, it is evident that the lighter molecnlar species are preferentially enriched in the vaponr phase, the extent depending upon the temperature. Such an isotopic separation process can be treated theoretically in terms of fractional distillation or condensation under equilibrium conditions as is expressed by the Rayleigh (1896) equation. For a condensation process, this equation is... 

If one starts with an equimolar mixture of A and B and wishes to obtain about 95 per cent pure A in die distillate, the initial distillate would have to contain about 98 mole per cent A, since the enrichment decreases as the distillation progresses. The value of a would be given by the Fenske equation... 

Equation (14.181) may be compared with the corresponding differential equation for the enriching section of a two-stream, close-separation, countercurrent column like a distillation column ... 

The combination of an absorption cascade topped by a condenser is referred to as an enricher. A partial reboiler topped by a stripping cascade is referred to as an exhauster. As shown in Fig. 12.25 stages for an enricher are numbered from the top down and the overhead product is distillate, while for an exhauster stages are numbered from the bottom up. Feed to an enricher is vapor, while feed to an exhauster is liquid. The recovery equations for an enricher are obtained from (12-64) by making the following substitutions, which are obtained from material balance and equilibrium considerations. 

The methods of steam distillation have been summarized by Bernhauer [13] and Thormann [14]. A detailed discussion of practical and theoretical aspects of steam distillation as illustrated by the distillation of essential oils is given by von Weber [15], Rigamonti [16] developed a nomogram which can be used to calculate the steam requirements for various enrichments. Prenosil [16a] compared theoretical and experimental steam distillation data for multicomponent mixtures. He modified the calculating method by introducing a value for evaporation efficiency. Steam distillation can also be carried out in thin-film apparatus. Berkes etal. [16 b] give a description of the material transfer conditions of a steam distillation performed in such apparatus in terms of the balance equations. 

This equation represents a general plate in the enriching section of a binary distillation column. In the usual case, a total condenser is used, so F = L + D, and L/D = R is the recycle ratio, D being the distillate product removed. In the present case, it is the liquid composition that is monitored, so we proceed to eliminate y using the equilibrium relation, Eq. 5.92... 

Equations (1) and (2) refer to measurements on separated Isotopes. It is also Important to develop a relation between the reduced partition function ratio (RPFR) and measured separation factors, a, referring to single stage Isotopic enrichments (on distillation) for dilute nonideal solutions. In the case of infinite dilution the molar volumes of the two Isomers are Identical (they are determined by environment) and one obtains (19)... 

Equations for enriching section. In Fig. 11.4-3 a continuous distillation column is shown with feed being introduced to the column at an intermediate point and an overhead distillate product and a bottoms product being withdrawn. The upper part of. the tower above the feed entrance is called the enriching section, since the entering feed of binary components A and B is enriched in. this section, so that the distillate is richer in A than the feed. The tower is at steady state. 

We start by noting, as we have done on other occasions, that any of the variables appearing in Equation 7.5g may be regarded as an xmknown. Thus, for a given boiler content W, the equation will yield the corresponding composition Xy, and conversely we can calculate die fraction to be distilled 1 - W/W°, by prescribing a desired enrichment Xy - Xy/)/Xyf. What is often overlooked is that the equilibrium relation/(x, ) can also be established from experimental vs. W data. A particularly simple case arises when the/(Xw)... 

The Underwood equations (Underwood, 1948) provide a shortcut method for determining the minimum reflux ratio, ilmin, in multicomponent distillation under the following assumptions constant relative volatilities and constant molal overflows in the stripping section as well as in the enriching section. The minimum reflux ratio, i min> is obtained from a solution of the following two equations for n components ... 

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