Page 23 - Applied Process Design For Chemical And Petrochemical Plants Volume II

12 Applied Process Design for Chemical and Petrochemical Plants

(text continuedj-om page 5) Renon’s techniques valuable for the complexities of mul-
ticomponent systems and in particular the solution by dig-
p. =- fi (8 - 10) ital computer.
’ Yip Renon’s [ 581 technique for predicting vapor-liquid rela-

The Vinal Equation of State for gases is generally: tionships is applicable to partially miscible systems as well
as those with complete miscibility. This is described in the
Pv B C D reference above and in Reference 54.
z=---lc-+-+-+ ... (8 - 11)
RT v v2 v3 There are many other specific techniques applicable to
particular situations, and these should often be investigat-
where B, C, D, etc. = vinal coefficients, independent of pres- ed to select the method for developing the vapor-liquid
sure or density, and for pure components
are functions of temperature only relationships most reliable for the system. These are often
v = molar volume expressed in calculation terms as the effective “K” for the
Z = compressibility factor components, i, of a system. Frequently used methods are:
Chao-Seader, Peng-Robinson, Renon, Redlich-Kwong,
Fugacities and activities can be determined using this Soave Redlich-Kwong, Wilson.
concept.
Other important equations of state which can be related Azeotropes
to fugacity and activity have been developed by Redlich-
Kwong [56] with Chueh [lo], which is an improvement Azeotrope mixtures consist of two or more components,
over the original Redlich-Kwong, and Palmer’s summary of and are surprisingly common in distillation systems. There
activity coefficient methods [jl] . fore it is essential to determine if the possibility of an
Activity coefficients are equal to 1.0 for an ideal solution azeotrope exists. Fortunately, if experimental data are not
when the mole fraction is equal to the activity. The activi- available, there is an excellent reference that lists known
ty (a) of a component, i, at a specific temperature, pres- azeotropic systems, with vapor pressure information [20,
sure and composition is defined as the ratio of the fugaci- 28,431. Typical forms of representation of azeotropic data
ty of i at these conditions to the fugacity of i at the are shown in Figures 85 and 8-6. These are homogeneous,
standard state [54]. being of one liquid phase at the azeotrope point. Figure 87
illustrates a heterogeneous azeotrope where two liquid
a (T, P, x) = fi (T’ py ,liquid phase phases are in equilibrium with one vapor phase. The sys-
fi (T,Po,xo) tem butanol-water is an example of the latter, while chlo-
roform-methanol and acetone-chloroform are examples of
(Zero superscript indicates a specific pressure and
composition) homogeneous azeotropes with “minimal boiling point”
and “maximum boiling point” respectively.
The activity coefficient yi is A “minimum” boiling azeotrope exhibits a constant
composition as shown by its crossing of the x = y, 45” line
y i = 5 = 1 .O for ideal solution in Figure 8-8, which boils at a lower temperature than
Xi
either of its pure components. This class of azeotrope
The ideal solution law, Henry’s Law, also enters into results from positive deviations from Raoult’s Law. Like-
the establishment of performance of ideal and non-ideal wise, the “maximum” (Figure 8-9) boiling azeotrope rep-
solutions. resents negative deviations from Raoult’s Law and exhibits
The Redlich-Kister [35, 571 equations provide a good a constant boiling point greater than either pure compo-
technique for representing liquid phase activity and classi- nent. At the point where the equilibrium curve crosses x =
fying solutions. y, 45” line, the composition is constant and cannot be fur-
The Gibbs-Duhem equation allows the determination of ther purified by normal distillation. Both the minimum
activity coefficients for one component from data for and maximum azeotropes can be modified by changing
those of other components. the system pressure and/or addition of a third compo-
Wilson’s [77] equation has been found to be quite accu- nent, which should form a minimum boiling azeotrope
rate in predicting the vapor-liquid relationships and activ- with one of the original pair. To be effective the new
ity coefficients for miscible liquid systems. The results can azeotrope should boil well below or above the original
be expanded to as many components in a multicompo- azeotrope. By this technique one of the original compo-
nent system as may be needed without any additional data nents can often be recovered as a pure product, while still
other- than for a binary system. This makes Wilson’s and obtaining the second azeotrope for separate purification.