INDUSTRIAL A N D ENGINEERING CHEMISTRY
248
tive in increasing flow. Oblad and Xewton (12) showed glycerol glass t o be very slow in attaining the full heat content, and Bekkedahl and Scott (a) demonstrated nonequilibrium thermal conditions in a synthetic rubber. Anomalous viscosities of mineral oils at low temperatures under nonequilibrium conditions have been observed (9). Thus, the degrees of freedom involved in flow may remain activated by the energy expended, and the lower apparent viscosities a t the higher rates of shear may be due t o flow in which the parts of the molecules involved in the flow are at “effectively higher temperatures”. Interpretations of the anomalous rheological properties of materials such as polystyrene, which exhibit both highly elastic and viscous deformation, are of interest for the light they may throw upon highly elastic behavior in general.
1. Nomographs for calculating viscosity from data on parallelplate compressions and from data on the filling of a capillary have been utilized. 2. The empirical equation giving apparent viscosities of polystyrene for low stresses as a function of absolute temperature is =
40,000 __
RT
- 3o
3. Greatly lowered apparent viscosities a t higher stresses have been observed and various interpretations of this behavior have been considered.
This chart provides a rapid means f o r approximating the number of theoretical plates and corresponding reflux ratios f o r problems in the distillation of birmry mixtures.
F
ACKNOWLEDGMENT
The writer wishes to thank Clifford Eddison, head of the Chemical Engineering Section, RCA Victor Division of Radio Corporation of America, for encouragemenb and advice. LITERATURE CITED
(1) Am. SOC. for Testing Materials, Standards, Part 111, p. 1220, D569-41T (1942). urds. 2
(5) Burns, R., Proc. Am. SOC.Testing M a t e i i a l s , 40, 1283 (1940). (6) Ewell, R . H., J . A p p l i e d P h y s . , 9, 252 (1938). (7) Eyiing, H., J . Chem. P h y s . , 4, 283 (1936).
(8) Houwink, R., “Physikalisohe Eigenschaften und Feinbau von
CONCLUSIONS
lnq
Vol. 36, No. 3
(9) (10) (11) (12)
Natur- und Kunstharzen”, Leipaig, Akad. Verlags., 1934. Louis, Jordachescu, and Thiebault, P h y s i c s , 4, 401 (1933). Merrington, A. C., N a t u r e , 152, 214 (1943). Nutting, P. G . , J . FraniZinInst., 235,513 (1943). Oblad, A. G., and Newton, R. F., J . Am. C h e m . SOC.,59,2495
(1937). (13) Peek, R.L., J . Rheol., 3,345 (1932). (14) Scott, J. R., T T Q ~I nSs .t . Rubber Ind., 7 , 169 (1931). (15) Scott Blair, G. W., “Introduction to Industrial Rheology”, Philadelphia, P. Blakiston’s Son and Co. 1938. (16) Stefan, M. ,J., Sitzber. A k a d . W’iss. Wien, M a t L n a t u r w . K l a s s e , Abt. 11, 69, 713 (1874). (17) Tuckett, R. F., T r a n s . Faraday SOC.,39, 158 (1943). ENQ.CHEM.,ANAL.ED., 15, 424 (1943). (18) Weltmann, R. N., IND.
IXTURES J. W. FAASSEN E. I. du Pont d e Nemours & Company, Inc., Niagara Falls, N. Y.
REQUENTLY a quick approximate answer to a problem is more valuable than a highly accurate result which requires a detailed and time-consuming analysis. Toward this end a chart has been developed to provide such approximations for problems in the distillation of binary mixtures, subject to the limitations described. Underwood ( 3 ) presented a nomograph for solving the Fenske equation for the number of theoretical plates required at total reflux for a given system. Smoker ( 2 ) evolved a similar nomograph and also one for finding the reflux ratio required for an infinite number of plates. These provide a rapid means for fixing the extreme limits on distillation equipment. I n addition, Gilliland (1) developed a n approximate correlation relating a function of the actual and minimum reflux ratios to a function of the actual and minimum number of theoretical plates for distillation problems in general. The present chart (Figure 1) combines a solution for the Fenske equation and the Gilliland correlation, when the minimum reflux is known. For convenience in finding minimum reflux, Smoker’s nomograph is reprinted (Figure 2); an equation for this variable is also included t o cover problems outside the range of the nomograph. Thus, a complete solution for t h e number of theoretical plates and corresponding reflux ratios required for a given two-component separation can be effected in a few minutes.
The chart is applicable to binary mixtures for which the usual simplifying assumptions can be made regarding equal molar heats of vaporization, etc., and where 01, the relative volatility, does not change radically from top column conditions t o bottom column conditions. The latter stipulation is met by systems in the following categories: 1. Mixtures which show reasonable agreement with Raoult’s law, where the vapor pressure curves of the two components do not show abnormal angular convergence. I n the latter case a will be found t o vary considerably with the composition of the mixture and accuracy will be impaired. 2. Iionideal mixtures whose vapor-liquid equilibrium curves are reasonably symmetrical. 3. Mixtures having irregular vapor-liquid equilibrium curves, where the concentration change in the column is small enough to limit a n otherwise abnormal variation in a.
Obviously the chart is not applicable t o mixtures which form azeotropes, except in rare problems which fall in category 3. When applied to continuous distillation, the results pertain to the case of liquid feed at the boiling point. USE OF THE CHART
To apply the chart it is necessary t o have a mean value for a and t o know the minimum reflux ratio, (L/D)nr, in addition t o .
,
March, 1944
INDUSTRIAL AND ENGINEERING CHEMISTRY
249
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
250
Vol. 36, No. 3
17 16
15
I
14
~
~
~
~
_
_
_
_
~
NOMOGRAM FOR MINIMUM REFLUX]
13
12
I! IO
9
0.0
8
0.1
0.2 0.3 0.4 0.5
XD
0.6
0 .’I 0.8 0.9
0
1.0
Figure 2
the boiler, top column, and feed compositions. Knowing these, N , the number of theoretical plates, may be fixed and a corresponding value found for L I D , or vice versa. For mixtures following Raoult’s law, CY is computed as the ratio of the vapor pressures of the two components a t a given temperature. For other mixtures a may be calculated from the equation: .
where
mole fraction in liquid y = equilibrium mole fraction in vapor Subscripts A , B = low and high boiler, respectively 5 =
Since a changes with composition for nearly all mixtures, a mean value should be used for the particular problem involved. Where the change in LY from top column to bottom column conditions is small, an arithmetical average may be taken. Where 01 changes appreciably, however, accuracy may be improved by weighting the mean value in favor of the concentration range in which the greatest number of plates is required. Also, where a varies considerably the value used in calculating (L/D),w should be representJativeof the feed composition. This value may be somewhat
different from the mean figure as applied to the CY curves on t h e chart. ( L / D ) Mmay be found from Smoker’s nomograph (Figure 2), or it may be calculated from the equation:
The nomograph is limited t o systems where CY does not exceed 3.0. The value of ( L I D )M obtained by either means is valid for liquid feed a t the boiling point. To apply Figure 1 to continuous distillation, determine the values for the required variables, enter the chart a t XD, proceed t o xs, then to CY, and horizontally to the N curves. Here a value of N may be selected and L I D found, or L I D may be chosen and corresponding value for N may be found. The former procedure is generally useful for predicting the performance of existing equipment, in which case a vertical line from the selected value for N will intiersect (L/D),w at the proper value for L I D . The latter procedure will generally be more useful in designing new equipment, where a value for L I D may be chosen within the normal optimum range and a corresponding value for N may be found. Optimum values for L I D usually fall in the range from 20 to 100 per cent greater than (L/D).w.
INDUSTRIAL AND ENGINEERING CHEMISTRY
March, 1944
For batch distillation XF and xs become identical, I n such problems, by assuming a constant distillate composition and a trial value for N , the reflux ratios required at various representative boiler compositions can be determined. If the reflux ratios appear unreasonable for the assumed value for N , a second value may be chosen and the process repeated. Having achieved a reasonable balance between N and L / D , a plot of L I D 1 against pounds of product distilled can be made for a complete batch. Integration of this curve will give the total boilup per batch, and from this a n approximate column design can be made. This procedure is strictly accurate only where the holdup in the column is negligible compared with the contents of the boiler a t the end of the batch, but it will serve as a useful approximation for many problems. I n some instances the numerator and denominator of the equation for ( L / D ) Mwill be small fractions of unity. I n these cases care must be exercised to perform the arithmetic accurately, or the figure obtained for ( L / D ) Mmay be in error by several per cent. Smoker's nomograph will be found more convenient than the equation, but the latter i s included to cover values of CY outside the range of the nomograph. I n the hypothetical example represented by the dotted lines, it is assumed that a mixture containing 37 mole per cent trichloroethylene (boiling at 87.0' C.) and the balance perchloroethylene (boiling 121' C.) is to be separated continuously a t atmospheric pressure into distillate containing 99.2 mole per cent trichloroethylene and residue containing 5 mole per cent trichloroethylene. It is assumed that the mixture does not deviate widely from Raoult's law and that the usual simplifying assumptions apply. From the specified compositions, the top column temperature will be essentially 87' C., and the boiler temperature is estimated a t 115' C. Using vapor pressure curves for the two components, a a t the top of the column is then:
+
L
251
TABLEI. COMPARISON OF VALUESFROM
THE
CHARTWITH
GRAPHICAL SOLUTIONS XR
XD
xS
(I
0.50 0.20 0.70 0.80 0.70 0.85 0.70 0.90
0.95 0.95 0.80 0.995 0.99 0.95 0.9995 0.95
0.30 0.05 0.30 0.20 0.20 0.50 0.10 0.8
2 8 1.2 2 4 2 4 2
5
(;)M
1.69 0.61 1.71 1.19 0.43 0.45 0.475 0.06
3.0 0.7 3 1.85 0.52 0.70 0.57 3
N, Nfrom Grmhicsl Chart 9 9 8 8 21 20 17 11 l7 12 7.4 9 18 18 2.5 2.5 (estd.)
ACCURACY
For ideal mixtures of constant CY, the chart is basically as accurate as the Gilliland correlation; as such it is designed to give useful approximations for "high spot" engineering work. For a final analysis, one of the more time-consuming graphical or algebraic methods should be resorted to. By way of illuotration, Table I shows a comparison of figures obtained from the chart with the results of graphical solutions by the McCabe-Thiele method for seperal typical problems. Theoretical vapor liquid equilibrium curves drawn for constant values of CY were used for the McCabe-Thiele solutions. I n practice, the accuracy of the results will depend on the spread in values of CY through the column for the particular system involved, and on the degree to which the usual simplifying assumptions apply. As noted previously, where 01 varies appreciably over the concentration range considered, the mean value should be weighted in favor of the concentration range in which the greatest number of plates is required. CONSTRUCTION OF THE CHART
The first two sets of curves give a solution for the Fenske equation : and
CY
a t the boiler is:
(3) Pz
= -'go
115'
640
= 2-65
The last two sets of curves solve the Gilliland correlation for
Since CY does not change greatly through the column, a n arithmetic mean may be used for 0 1 ~ ~: . The equation for ( L / D ) Mis obtained by combining the equation for minimum reflux, The minimum reflux ratio, ( L / D ) M ,is calculated from the equation:
- l)(zF)l - (a)(ZF) - XF + - 1)(XF)l - 0.992 [I + (2.77- 1)(0.37)]- (2.77)(0.37) (2.77)(0.37)- 0.37 [ l + (2.77- 1)(0.37) $011 f
($)A4
(a!
= (Q)(ZF)
=
(CY
1.497,or say 1.5
"rhe same value may be obtained from Smoker's nomograph. I n this problem it will be assumed t h a t L j D = ( ~ . ~ ) ( L / D= )M 2.54,and the required value for N is desired. Enter the chart (Figure 1) at L I D = 2.54,proceed to ( L / D ) M = 1.5, and then vertically to the N curves. Enter the chart again at XD = 0.992, proceed to xs = 0.05,vertically to LY = 2.77,and horizontally to the intersection with the first line. The point of intersection fixes N at about thirteen theoretical plates. This value represents the total number of steps required. Since the boiler acts as one theoretical plate, the column must contain twelve theoretical plates, assuming a total condenser is used. The result agrees within a fraction of one plate with a solution by the McCabeThiele diagram, using an equilibrium curve based on Raoult's law.
with the equation for the equilibrium curve for ideal mixtures, CYX
= 1
+ (CY -
l)X
(3)
where x and y refer to mole fraction of low boiler in the liquid and vapor, respectively, and subscript C refers to conditions a t the intersection of the operating lines. For the condition of liquid feed entering the column at its boiling point,
INDUSTRIAL AND ‘ENGINEERING CHEMISTRY
252
NOMENCLATURE
PP
of low boiler in distillate = mole fraction of low boiler in feed zp xs = mole fraction of low boiler in residue (boiler composition) cy = relative volatility of the two components L I D = molar or weight ratio of reflux t o distillate (L/D)M= minimum molar or weight ratio of reflux t o distillate for a given separation (reflux ratio a t infinite number of plates) N = number of theoretical plates a t L/D reflux ratio N;cr = number of theoretical plates required for a given separation at total reflux PI = vapor pressure of trichloroethylene
Vol. 36, No. 3
= vapor pressure of perchloroethylene
= mole fraction
XD
ACKNOWLEDGMENT
The author is indebted to E. H. Smoker for permission to reprint his nomograph. LITERATURE CITED (1) Gilliland, E.R.,IND. ENQ.CHDM.,32, 1220-3 (1940). (2) Smoker, E. H.9 Ib& 34,509-10 (1942). (3) Underwood, A. J. V., Trans. Inst. Chem. Engrs. (London), 10, 112-52 (1932).
Louis Klein, Henry Grinsf elder, and S . D . Bailey RESINOUS PRODUCTS AND CHEMICAL COMPANY, PHILADELPHIA, PA.
OVING W
I
N T H E past few years much work has been done to overcome
the deficiencies of wood. The principal studies have been centered around the use of phenol-formaldehyde resins (2, 4, 6, I S , 16), heat ( 1 6 ) , and pressure (3)t o improve wood. By cross graining veneers and adhering them together to form plywood, some of the defects of wood are overcome. By use of resins as impregnants of wood, added improvements are made; and by utilizing higher than normal heat and pressure, either or both alone or combined with the above two, further advances can be made in overcoming the defects of wood. When one character of a material is improved, another is liable t o be injured, And while one of these treatments of wood may overcome one disadvantage, other detrimental features may be encountered, either physical, economic, or chemical. I n recent months the scientific and trade literature has been full of suggestions and proposed methods for improving of wood by particular techniques 01 agents. But no comparative study appears t o have been made under conditions which permit adequate evaluation of each method. The purpose of this paper is t o present three methods for producing improved wood and to compare the properties obtained. METHODS OF PRODUCTION
In studies recently undertaken t o improve wood, only resins of the phenol-formaldehyde type have been used. Urea-formaldehyde and melamine-formaldehyde resins have not proved advantageous for the type of improvement being studied. Other resins are limited in usefulness primarily because it is not easy t o prepare them in water or alcohol solutions. However, the recent development in England of the Hyduligum process for improving wood should be noted. This process is unique in t h a t it uses two-way compression by first compressing veneers coated with a thermoplastic resin t o a density of approximately 1.0 in the usual way. Then edgewise pressure is applied t o raise the density above 1.3. The three processes t o be considered here may be classified ad follows: (1) wood impregnation and compression (12, 16), (2) film bonding and compression (3, 8, 16), and (3) resin glue bonding and compression (14, 16). The details of the k s t process may be quite complicated, particularly in comparison t o the other two methods. I n this first process, veneers are immersed in the phenol-formaldehyde solution in water, alcohol, or a mixture of the two. They are kept immersed for a definite time; t o aid in accelerating the impregnation process, vacuum. pressure, or both in series may be ap-
Interest has been aroused recently in improving the physical properties of wood. Predominant among the methods employed is the use of phenol-formaldehyde resin as impregnant, followed by compression of the wood to attain dimensional stability and improved strength. Other methods include the use of resin film interleaved between veneers, or liquid resin applied to veneers by resin glue spreaders and then the application of heat and pressure. The strength properties resulting from each method are somewhat different, and the purpose of this paper i s to compare the advantages and disadvantages of the three methods for impro-ing wood by densification. These properties include dimensional stability to water and heat, tensile strength, impact strength, ease of compression, shear strength, modulus of elasticity in bending, modulus of rupture, ease of manufacture, surface appearance, and cost. Each process has a superiority when only one or two specific properties are being considered; no process is outstanding in all properties. The process with the greatest number of superior properties appears to be film bonding. Its chief weakness has been dimensional stability, but by the use of higher temperatures and pressures, some improvement can be made.
plied to the container. A diffusion period may be required to ensure proper penetration of the resin into the wood cell structure. The impregnated veneers are dried and then assembled in a press where both heat and pressure are applied. At times an extra resin is applied t o the veneers to ensure proper adhesion, While still under pressure the veneer assembly is cooled. It can then be removed from the press. Products made in this manner, t o which the general term “compreg” is applied, are called b y various trade names, such as Pregwood, HiDen, and Jabroc. The second process is much simpler to adapt t o full scale production. Film glue, such as Tego, is dimensioned and interleaved between the veneers. The assembled pack is then placed in a cold press, and heat and pressure are applied t o compress the wood, cure the resin, and produce the union between adjaceht veneers. Cooling in the press may be necessary t o prevent warping and blistering of the panels. Wood compressed in this manner is known commercially as Tegowood, Jicwood, and Superpressed Wood. The third process consists of applying a resin glue in liquid form by a regular resin glue spreader. After the volatiles are permitted t o evaporate from the resin, the veneers are placed in a
