INDUSTRIAL AND ENGINEERING CHEMISTRY
1042
PRESSURE, LBS./IN'.
Figure 11.
Logarithmic Plot of Curves in Figure 8
binder. This decrease was interpreted as a reduction in tlie size of flow segmrnt of the binder Inolecule in t,ht: presence of large amounts of fillcr. T h e fact t h a t X A does not decrease markcdly with addition of large amounts of filler, \yhile tht. apparent viacosity inrreases, is strong evidence that the presence of tht: filler causes a n increase in the free energy required to make a moving unit change its position. This increaac woyld be a n entropy coiltribution due to the more tortuous path which thc moving unit must follow. CONCLUSION s
With one exception, the high polymer systenis studied exliibited exponrntial type of flow with pressure when extruded. O i ~ r
Vol. 39, No. 8
bindisr containing low viscosity nitrocellulose in Paraples exhibited plastic flow, but this could be changed to exponent in1 by using nitrocellulose of high viscosity. dddition of filler in excess of by bveigkit t o the bindrrs caused a rapid increase in tht: apparent viscosity of the systems and tended to emphasize the exponential shape of the flow curVe. Fine filler gave the greatest increase in viscosity, in thPoretica1 density, and in apparent yield point, and tLs1iihitt:d strongest tendencies towards emphasizing the esp~iiientialcharacteristics of the prcssure-flow curvl's. hnorrialou~ low viscositics obtained viith fillers -SO, and --O-SOs groups in Paragave indication of the presence of a e phenomenon around the filler particles. Tl-ith increascx of filler content the viscous volume of th(, flow scgmcnt tendcd to dccrease i n size, and the amount of decrease was i n the order of increasing molecular weight of the polynier binder. The order of size of the change i n vulunie indicated that resist,ancc to flow when filler ~tlded might be in the fluid phssc,. i C K YOWLEDGMENT
The authors wish to thank I). C. Rose of the Canadiun .irnianit:nt Research and Development Establishment for arr:tngiriy and facilitating publication of this papdr. LlTERATURE CITED
(1) Kuuziiiaiiii and Eyring, .I. A m , C h r m . S o c . , 62, 3113 (1946). (2) Xa,on, J . A p p l i e d P h y a . . 16,388 (1945). ( 3 ) Tobolsky and Eyring, J . Chem. Phys., 1 1 , 125 (1942). (4) Tobolsky, Powell, and Eyring, "The Chemistry of Large Molecules," p. 179, Xew York, Interscience Publishers, Inc., 1943.
Batch Distillation Nomograph for Binary or Multicomponent Mixtures W.4LTEK H . STASTON Morinari t o
Cheniical C o m p u n y , S t . Lo&. a
=
VI*P.
relative volatility of A to B, K A / K B(or if Itaoult's law applies N = PA/PB)
Figure 1 is a nomograph o! k:quation 2. T o illustrate it> tist', sample protilcm ( 2 ) is illustratd. .\ssume a mixturfs 01' propancl, butane, and pent ano, I J t~l i t . foliowing romposirion :
n
\.\eight
%
8 0 65.6
where A , = total molcs (or pouirdd) of coniporit~iitA i n (iriginal chargr A?
=
R,
=
b9
=
t,otal moles (or pounds) of component h rt,nmining in residual charge after batch distillatioil operation total moles (or pounds) of component B in original charge tot,al moles (or pounds) of c:omponrnt I3 remaining in residual charge after batch distillation operation
26.4 100.0
On the basis of 100 pounds of this original mixture, considcv that 32.2 pounds of but,ane are t o be left in the rcsidual liquid after ii batch distillation procc~ss. I t is desired to calculate the amount of propane and pentane in the residual liquor. Average 01 values in the temperature rangcxs under consideration are for C d ( ' 3 . a = 0.22; for C4/C5,cz = 4.3. Connect the point 63.6 o n thc: 1,scale with 32.2 on the A? scale and continue the line to tlic x a l o marked C. Connect the point on the C scale with thc a
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
August 1947
loo
1043 r
IO0
3
30 20
QI
i
- - _- - _- _
0.2 0.3
-OD01
IO
0.4
5
0.5
4
3 2 I.c
-
0.01
0: 03 0.;
I.o
2
0.;
-
0.I
-.. -0.0 I
3 -
0.001
3
0.1
4
.
0.2
.
0.3
-
1.0
-
2
-
3
-
4 5
-
IO
5
1
lo
,,
.,,io - 30 -
-
,
-
40 50
I
100
El00
Figure 1
valuw (4.3 and 0.22j to obtain points on the D scale. Connect these points on the D scale with 26.4 and 8.0 on the B, scale, and scale give the answcrs of 22.5 pounds of interscctions on the in the residual liquid. C5and 0.31 pound o T h e nomograph offers a n accurate and rapid solution t o the type of problem illustrated. I t applies t o binary or multicomponent mixtures, and deals in total pounds or moles which is often advantageous in that a conversion to weight fraction or mole fraction is eliminated. A limitation to the use of the nomograph is the fact t h a t it applies only over a range where 01 remains fairly (*onstant. For mixtures where wide variations in a values are obtained, a stepviise solution is required. The range covered in each step must be small enough so that a constant a value may he used. For batch distillations of binary mixtures over temperature ranges involving wide variations in a, it is advisable to use the rxact form of the Rayleigh equation ( 2 ):
(3) where
L,
=
moles (or pounds) of original charge
x:! = mole fraction (or weight fraction) of more volatile
component in residual charge L.2 y
= mole fraction (or weight fraction) of more volatile
component in vapor in equilibrium with more volatile component in residual liquid at any time, t The equai-ion as written is exact but has the disadvantage of being time consuming since, in general, a graphical determination of the area under the curve l/(iy-.r) is.5 must be made. A trialand-error solution is required when the nomograph is uscd to deal with problems in which the quantity and composition of original charge and the quantity of residual charge art! set, and the composition of the residual charge is to tie determined. For batch distillation problems of this type, Sord’s nomograph ( I ) of the integrated form of Equation 3 may be used so t h a t the problem can be solved without trial and error. This nomograph also is limited to applications where a remains fairly constant. I n general, Figure 1 has the particular advantage of applying to multicomponent as well as binary mixtures and of dealing in t,otal pounds or moles rather than pound fraction or mole fraction. Furthermore, it offersa rapid and accurate means of solving batch distillation problems whcre the variations in Q: are slight over the temperature range in question.
I,? = moles (or pounds) of residual charge after I,, - ill2 have been distilled off = mole fraction (or weight fraction) of more volatile
component in original charge L1
LITERATURE CITED (1) Nord, Melvin, IND. ENG.CHEM., 39, 232 (12147). ( 2 ) Perry, J. H., Chemical Engineer’s Handbook, 2nd ed., pp. 1382-
7 (1941).
