JUNE 1947
431
The procedure presented here oficrs grvater simplicity, rapidity, and reproduction than previous methods employing dyes such as bromophenol blue. dccuracy and sensitivity are satisfactory for routine control determinations of quaternarv ammonium compounds.
LITERATURE CITED
(1) (2) (3) (4)
-iuerba&, M . E., ISD. ESG. CHEII., SAL. ED.. 15, 492 (194.7). ~ t ~ i d16, . , 739 (1944). DuBois, A. S.,Am. Dyeslii,fl R c p t r . 34, '245 (1945). DuBois, A . S.,IXD.Esc;. CHEM.,- ~ s . \ L . ED.,17, 744 11945).
Nomograph for Flash Vaporization AIELVIK SORU', .Yord & Co., Znc.,Keyport, X. J . flash vaporizatiori problemr;, \y]iei,e multicomponent teriis involv,2c{,tedious trial-and-eryor solutionq irc,(l, If one desires t o evaluate the entire flash vaporization c u r ~ cof per cent distilled us. liquid temperature, the time required for thc' calculations is out of proportion to their value. Several attempt> have been made to reduce the burden of the calculations in these problems, notably b y Gilbert (a). This paper presents a nomographic method which further simplifies the calculations.
where Z F ~ xi, , and Y, represent the mole fractions of component i in the feed, h u i d , and rapor, respectively. If t'he equilibrium between liquid and vapor is represented as y, = Iiix; and the fraction vaporized as T' r = -F
FXFi = I
XF L
?Jt
LZt f T'yt
(2)
Present addresp, T a y n e 1-nirersity. Detroit, 3lich.
loo
LL
f
d 250'-
-
K a Q053, h 5
Figure 1. h-ornograph
0.0700
a
0.09,
y,'Ki = TZi
(5) 6,
(7)
Equation 7 states the fact that the mole fractions must always add up to 1. These cquntions arc essentially the same as those presented by Dodge ( 1 ) . The solution o € the flash vaporization equatiom rcquires trial and error. If the feed composition and the flash vaporization temperature and pressure are known (thus fixing the values of the equilibrium constants), it is necessary to assume a value for the frnction vaporized, T , in order t o detrrmine the vapor composition from Equation 5 . Thcn, the sum of nll the vapor mole fractions, Zy, must be compared with unity, in accordance with Equation 7'. If a check is not thus obtained, new values of r must be assumed and recalculations made until the required check is obtained. The tion may then be determined from
0%
XF
+ (1 - r) /Xt
xy, = 1
,080
EKhMPLE:
T
ZI =
(1)
and
(4)
the equations for a flash vaporization may be written as
Consider a multicomponent mixture which is to be flash-vaporized. Let the number of moles of feed be called F , and the number of moles of liquid residue and of vapor be called L and T', respectively. Then, by material balances, we have
F = L + T '
(3)
The nature of the flash vaporization equations makes the elimination of trial snd error impractical when there :ire many components. When the number of components is small, a nomographic solution without trial and error is feasible, but as the number of components increases, such a solution becomes too univieldly. However, it is poqsible, by means of a nomograph, to rably the numerical computations e trial-and-error process, and thereby he problem considerably. Such a represented by Figure 1, wGch is a plot of Equation 5 . Inorder to solve a flash vaporization problem with this chart, the following procedure is used: Assume a value of the fraction vaporized, r, and find the curve corresponding t o that value. At the appropriate value of K for a given component, follow a vertical line to this r curve, and then go horizontally over to the center pivot line. This locates a pivot roint, which when connected by means of a straightedge t o the value of the feed concentration, ZF, determines a line intersecting the vapor composition axis at the appropriate value of the vapor concentration. This procedure is indicated in the figure. Thus, a value of y for each component is obtained, and a check made t o determine whether they all add up to unity. The
V O L U M E 19, NO. 6
432
Table I.
Flash Vaporization of Hydrocarbon Mixture (50 atmospheres, 200’ F.) T=,
Cornponent
CHI CaHa CaHa
i-C4Hl@ n-CdHlo i-CsH1z n-CoHn
COH14
=F
0,125 0.150 0,200 0,100 0,150 0,100 0,100 0,075
6.30 2.35 0,850 0,670 0,610 0,400 0,345 0,215
p =
0.5Q Y 0,216 0.210 0.184
0.40 Y
0.252 0.229 0.181 0,077 0.080 0,114 0,109 0.057 0.053 0.051 0,045 0.026 0,023 0.938 0,969
p =
0.30 Y 0,304 0.251 0,178 0.074 0,104 0,049 0.043 0.021, 1,024
r =
0.34 Y 0.281 0,241 0.181 0,075 0,106 0,050 0,044 0.022
0,045 0.103 0,213 0,112 0,173 0,124 0,129 0.102
1,000
1,000
2
values of x are determined by means of Equation 6,. after a check has been obtained. What the nomograph accomplishes, then, is the solution of Equation 5 by graphical means, instead of a series of two sliderule settings and one addition and one subtraction, which would be required normally for each component, for each trial. That this actually represents a considerable saving in time can be shown by comparing the two methods of calculation for a typical problem. Such B problem is represented by the case of a hydrocarbon mixture containing 12.5 mole yo methane, 15% ethane, 20% propane, 10% isobutane, 15’% n-butane, 10% isopentane, 10% n-pentane, and 7.5% hexane. Assume that such a mixture is Bash-vaporized a t 50 atmospheres and 200’ F. A normal set of calculations would probably go somewhat as indicated in Table I. Values of K were taken from Robinson and Gilliland (9). Comparison of the normal method of calculations with the nomographic method indicates the saving in time and effort effected by the latter method.
The use of the nomograph rather than the analytical method of calculation introduces no inaccuracies other than those associated with graphical methods in general. The larger the nomograph is made, the more accurate it can be, but the more unwieldly it becomes and hence the less useful. With the size shown, a relative error of about 270 can generally be obtained. If greater precision is desired, the nomographical solution may be regarded as a hrst approximation, and the calculations may then be completed analytically. However, since the values of K are not absolutely accurate (depending, for example, upon the assumption that the solutions are ideal), it would seem that the nomographical result, though less precise, is about as accurate ae the analytical method. For most practical cases, therefore, the use of the nomograph is justified. NOMENCLATURE
F Kr L r V
= number of moles of feed = equilibrium constant of component i
= number of moles of liquid residue = fraction vaporized = number of moles of vapor
Z F ~=
mole fraction of component i in feed
z i = mole fraction of component i in liquid residue yj = mole fraction of component i in vapor LITERATURE CITED
(1) Dodge, B. F., “Chemical Engineering Thermodynamics,” 1st ed., p. 599,New York, McGraw-Hill Book Co., 1944. (2) Gilbert, M.,C h m . M e t . Eng., 47,No. 4,234 (1940). (3) Robinson, C. S., and Gilliland, E. R., “Elements of Fractional Distillation,” 3rd ed., p. 45,New York, McGraw-Hill Book Co., 1939.
Melting Point Bath liquids Useful up to 440” C. LAWRENCE RI. WHITE, Western Regional Research Laboratory, U.S . Department of Agriculture, Albany, Calif.
ACK of a clear, mobile, heat-stable fluid suitable for use in L high-temperature melting point baths has caused many workers to devise more or less complicated melting point blocks, hot stages, and air baths for use in determining the melting points of high-melting organic compounds. Melting point blocks and hot stages require extensive calibration with compounds of known melting point, and Markley (5)has shown that the use of air baths may lead to erroneous results even a t relatively low temperatures. Materials available as melting point baths above 300” C. have been limibed to sulfuric acid containing potassium bisulfate (8) or potassium sulfate (6), mixtures of ortho- and metaphosphoric acids ( I ) , and “hard” hydrogenated vegetable oil ( 7 ) . Temperatures in excess of approximately 350” C. cannot be reached with these baths and there are numerous disadvantages in their use. Two groups of organosilicon compounds having remarkable heat stability have been developed in recent years. The tetraaryl ofthosilicates (4)boil a t approximately 400’ C. and are said to be stable at their boiling points, particularly in an atmosphere of nitrogen. ?;one of these materials was available for study at the time of this investigation. Silicone fluids are members of a group of orgariosilicon oxide polymers. Some of these fluids have properties that render them suitable for use in melting point baths up to 425‘ t o 440” C. This paper reports the behavior of three silicone fluids xhen heated and cooled repeatedly in two types of melting point equipment. APPARATUS AND MATERIALS
The melting point apparatus described by Conte ( 2 ) was made by sealing a jet and delivery tube into a Pyres No. 0640 Thiele tube and winding a 20-ohm heating coil on the curved portion. The coil was insulated with asbestos. Figure 1 shows how the melting point apparatus described by
Hershberg (3) has been modified to allow the bath liquid to be kept under an inert atmosphere. The ball bearings used to guide the stirrer shaft in the original equipment have been replaced by short glass tubes sealed to each end of aT29/42 inner joint which replaces the loose cap used by Hershberg. The glass tubes that serve as bearings and the stirrer rod were selected to give a good fit, so that the gas entering through the side tube is forced through the by-pass tube and out around the thermometer cap. Since the bath fluid undergoes an expansion of approximately 35y0 on being heated to 425“ to 440’ C. the arms of the apparatus must be sufficiently long to accommodate the increased volume. A 20-ohm heating coil was wound on the curved portion of the tube and insulated with asbestos. A second Hershberg apparatus, without provision for using an inert gas, was used for heating the fluids in contact with air. Silicone fluids type 550-84 centistoke grade, type 550-142 centistoke grade, and type 703-64 centistoke grade were used in this study. (Type numbers are the descriptions used by the manufacturer.) Compressed air, water-pumped nitrogen, hydrogen, and carbon dioxide were bubbled through concentrated sulfuric acid before being introduced into the melting point apparatus. PROCEDURE
The fluid was introduced into the clean, dry apparatus and heated to the desired temperature in about 25 minutes. The temperature was maintained about, 5 minutes, then the liquid was permitted to cool to room temperature. The gas used to stir the bath or to maintain an inert atmosphere flowed during the entire test. after the heating and cooling cycle had been repeated the desired numbcr of times, a portion of the liquid was placed in a 25-mm. cuvette and the per cent light transmittance over the range 400 to 700 millimicrons n-as recorded by a reoording spectrophotometer. .kfter the per cent light trasmittance had been recorded the fluid \vas returned t o the apparatus for additional heating at the same or a higher temperature. The per cent transmittance at 550 millimicrons was selected w a measure of the darkening of the fluid, since each of the unheated silicone fluids transmitted virtually all of the incident light of
