May,
1920
T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
Total heat above 32’ F. in the fatty acid distilled
-
Heat taken up by condensing water
4
Total heat above 32’ F. of steam entering condenser
+
+
Heat lost by evaporation of condensing water
-
Total
heat above 32’ steam leaving condenser
F. in
Heat t o raise stock in condenser drum from 32’ F t o drum temperature
+
493
+
Heat lost by radiation from condenser shell
-
Heat above 32’ in water carried over with stock into settling tank
1
Heat to raise stock from catch basin from 32’ F. t o condenser temperature
Substituting the proper figures in this heat balance, and dividing by the quantity of fatty acid distilled, we find: Total heat above 32’ F. per lb. of fatty acid distilled = 315.3 B. t. u. for Test A Whence, on the assumptions before stated, we have: Heat of vaporization per lb. of fatty acid at 24.51 in. vacuum = 315.3-0.46 (433.8-32) = 130.5 B. t. u. Similarly we find for Test B the values 308.2 B. t. u. and 118.0 B. t . u., but at 25.14 in. vacuum.
9 per cent. This discrepancy can be accounted for in two ways: Firstly, t h e stock was not t h e same in both cases. Undoubtedly, there was some difference in t h e mixtures being distilled, b u t unfortunately no chemical analyses were made t o determine t h e difference; secondly, t h e two tests were made a t somewhat different pressures and temperatures. The heat of vaporization differs with temperature. If i t did not t h e vapor pressure curve would be a straight line, and this we know is not t h e case. Probably t h e discrepancy is due t o a combination of these two factors. The writer desires t o express his appreciation of t h e assistance rendered in this work b y Messrs. S. B. Murdock, J. W. Bodman, and A. D. Whitby, and t o thank t h e N. K. Fairbanks Company, through whose courtesy these figures are published. NUMEKICAL RELATION BETWEEN CELLS AND TREATMENTS IN EXTRACTION PROCESSES By L. F. Hawley FOREST PRODUCTS LABORATORY, U. S. FOREST SERVICB,MADISON,
WISCONSIN Received November 8, 1919
I n a previous study of extraction processes1 conducted at t h e U. s. Forest Products Laboratory, Madison, Wisconsin, it was found t h a t no definite relation had ever been developed between t h e number of solvent treatments received b y each charge of material and t h e number of cells or extractors required t o furnish this number of treatments. It was also evident t h a t t h e ideas in regard t o such a relation were very much confused, and t h a t t h e usual conception was t h e entirely unfounded one t h a t for a certain number of treatments an equal number of cells was required or t h e same number plus one.2 After i t had been determined how many treatments in series were required for efficient extraction and how much time would ’be required for boiling, pumping, discharging, charging, etc., there was still no method b y which i t could be determined how many cells or extractors would be required b y t h e process. I n t h e development of t h e numerical relation between t h e cells a n d t h e treatments i t will be necessary t o consider a general case covering all conditions; and this will require t h e use of terms a n d t h e assumption of conditions t h a t may seem unusual or impractical t o operators who have had experience with only one kind of extraction process and have used a peculiar 1 2
THIS JOURNAI,,9 (1917), 866. Kressmann, Met. b Chem. Eng., 15 (1916), 78.
set of terms for describing t h e various operations. On this account indulgence is requested from t h e readers who find unusual processes described in unusual terms, and they are asked t o overlook these until t h e general principles become clear. There is, of course, a definite relation between t h e number of cells and t h e number of treatments. I t varies with different methods of manipulation, however, and several conditions of treatment must be known accurately before t h e relation can be developed. I t is necessary t o know t h e amount of time required for t h e operations performed on each charge other t h a n t h e typical extraction operations. and this time must be known in terms of t h e typical extraction operations. These latter operations are: I-The movement of solvent from one charge t o another, from t h e last charge t o storage or from t h e solvent tank t o t h e first charge, which movements will be called “pumping” a n d designated b y p . 2-The period of t h e actual solution action of t h e solvent on t h e charge, whether b y standing, boiling, or agitating, which will be called “boiling” and designated by b. These typical operations are necessary parts of every discontinuous extraction process and may vary only in t h e time required for their fu1fillment.l While there are only these two kinds of extraction operations, each may t a k e place a variable number of times in a complete cycle of extractions. The non-extraction operations may vary widely in number, kind, and time required, and include charging and discharging t h e cells, or any preliminary or after-treatment performed on t h e charge while in t h e cells. S I M U L T A N E O U S PUMPING
The simplest way t o determine t h e relation between t h e number of treatments and t h e number of cells i n terms of t h e time required for t h e various operations seems t o be t o use cut and t r y methods under several different sets of conditions and then t o find t h e complete mathematical relation by inspection. This can be readily done b y representing a series of extractions graphically, The easiest system t o s t a r t with is one in which t h e pumping of all cells in action is done simultaneously, A series of extractions in four cells b y this system can be represented as in Fig. I . I n this method of representation t h e arrows indicate movement of t h e solvent or pumping; for instance, t h e first line of t h e diagram indicates simultaneous move1
As will be seen later, b may equal zero in some cases.
~
494
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
ment of solvent from cell 2 t o cell 3, cell 3 t o cell 4, and cell 4 t o storage, while line 3 indicates simultaneous application of fresh solvent t o cell 3, and movement of solvent from cell 3 t o cell 4, and from cell 4 t o cell I . All cells are assumed t o contain solvent except those with a double circle. Those indicated in line 2 as containing solvent b u t without solvent movement show t h e extraction or boiling period. By following this series of operations we find t h a t a complete cycle has been finished in 16 lines and t h a t line 17 is t h e same as line I . During this cycle each cell receives j treatments and each batch of solvent is used j times. I t will be noted t h a t for a period of 3 boilings and 2 pumpings (indicated b y braces) each cell stands idle so far as solvent action is concerned; this period is t h e time available for charging and discharging and for other preliminary or after-treatment of t h e charge. The relation between this idle period, %, t h e number of cells, G, and the number of treatments, t , in terms of t h e boiling period, b , a n d t h e pumping period, p , will now be worked out.1 I n t h e case just shown 9% = 3 b z p when c = 4 and t = 5.
+
-
- d O
1 0 0
0)
Ob
0
0
0
0
O
O
C
O
0
O
06
O
Q
O
Q
Q
O
O
b
b
’
b
-
Q
0-0---0---r0
O
0
b
0
0
O
0
O
061
0
O
O
b
+
+
IZ
= b(2c-t)
+p(2c--t--1)ort=zc---
* + P b
+ P’
It is suggested t h a t more confidence in t h e table 1 The letters used in designating the different variables are all shown either in this sentence or in the headings of Tables I and 11.
12,
No.
j
and in the formula derived from i t will be produced if t h e reader will verify a few of t h e relations shown in t h e table b y preparing diagrams similar t o these given, but for different values of c or t . This procedure will also make i t possible t o follow the further similar developments more readily.
CELLS c
2 2 3 3 3 3 4
4 4 4 4 5
T A B L EI-ALL CELLS PUMPED AT ONE TIME Time Avai!able For Charging, Time between TREATMENTS Discharging, etc. Discharges t 2 3 2 3 4 5 3 4
5 6 7 3
It should be noted further t h a t in this method of operation, zliz., simultaneous pumping of all cells with a boiling period after every pumping period, t h e time elapsed between any similar operations on successive cells (which is t h e measure of t h e output of t h e system) 2 9 , whatever t h e number of is always t h e same, 2 b cells or treatments. This period is indicated b y a on t h e diagrams and shows t h e time elapsed between t h e beginning discharge of two consecutive cells.
+
CONTINUOUS EXTRACTION
It should be noticed here t h a t these formulas are applicable also t o continuous extraction. Continuous extraction is t h e same as t h e system of simultaneous pumping just described in which b = o and p is t h e period of time required for moving t h e liquid contents of one cell t o t h e next or t o storage. Under these conditions, 1z. = p ( 2 c - t - I ) or t = z c - n + P P ’ and a = 2 p . ~
FIQ.3 FIG 1 FIG.2 S I M U L T A N E PUMPING OUS SIMULTANEOUS PUMPING SIMULTANEOUS PUMPING 4 CELLS5 TREATMENTS 4 CELLS6 TREATMENTS 4 CELLS7 TREATMENTS n=3b+2$ n=2b+p n=b a=2b+2p a = 2 b+29 a=2b+29
I n Fig. 2 is shown t h e same number of cells so used as t o give each cell one more treatment. This arrangement shortens t h e idle period ~tt o 2 b I p and our next relation is t h a t when t = 4 and t = 6, f i = 2 b p . I n the same way when one more treatment is obtained, t h e maximum possible in 4 cells, t h e time available for discharging, charging, etc., is reduced t o a single boiling period. (See Fig. 3.) Similar diagrams for various other numbers of cells and treatments were made and from them was prepared Table I in which t h e general relation between the factors c, t , n, b , and p becomes apparent. From inspection of t h e table it is seen t h a t N is composed of boiling periods e q u d in number t o twice t h e number of cells minus t h e number of treatments, and of pumping periods always one less t h a n t h e number of boiling periods, or
Vol.
SEPARATE PUMPING
It has been shown1 t h a t the method of pumping all, cells simultaneously gives much less efficient extraction t h a n pumping one cell a t a time. It might possibly be thought t h a t t h e pumping of only one cell a t a time would take so much longer t h a t in t h e case of a large number of cells i t would lose more in time t h a n would be gained in efficiency of extraction. Some very interesting comparative figures are obtained b y developing t h e relations between G, t , %, etc., under this method of pumping. The method of representation of t h e extraction process is t h e same as in t h e other case, and t h e diagram, Fig. 4, shows t h a t in an operation of 6 treatments in 4 cells 1z = 2 b 4 p. I n this method there are two other variable time periods which are important and will also be studied; these are the average length of time each charge is boiled with each separate batch of solvent, designated b y e, and t h e time elapsed between successive discharges, designated by a. I n this method of pumping t h e actual length of time each charge is boiled with each batch of solvent is not always t h e boiling period b only, b u t is variable. This is due t o t h e fact t h a t sometimes only one and
+
1
THISJOURNAL, LOC.cil.
May,
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
1920
495
I n t h e diagram showing 6 treatments in 4 cells, 2 p and a = 2 b 7 9. I n t h e next diagram, Fig. 5, showing j treatments in 4 cells t h e time .n has 815 p a n d a = 2 b 6 p, e = b increased t o 3 b e = 6
o i o o w @J Q O O - - - - o Q
+
+
+
+-
+ 6 P.
I n the same way diagrams have been prepared showing a wide variation in number of cells and number of treatments, and the resulting values for n, a, and e are given in Table 11. From this table t h e following formulas were developed' showing t h e various relations between G, t , n, a, and e . EXTRACTIONS IN WHICH EVERYCHARGERECEIVES Two TREATMENTS WITH
o---o 0
0
o
FRESHSOLVENT
Simultaneous Pumping n = ( 3 c - t ) b 4- ( 3 c - t -
d
a
-
-
3b
1)p
+3p
e = b Separate Pumping
n = bc ( 3 c - t - I ) - ( 3 ~ - t ( ~ - ) f i
-
b c (3c-t-
1)
- (3c-t
whentis multiple of 3 -1)'-
3 (3 c
(3c-
- 1)
t
- 1) p
when t is not
multiple of 3
0
-0
e = b
d
e = b +
0
0
0
O
O
O
0
0
d
O
M
W
o @
0
a = 2b e =
b
o----O
0
O e
FIG. 4 SEPARATE PUMPING 4 CELLS 6 TREATMENTS n = 2 b+4 D a=2b+79 e= b f 2 p
FIG.5 SRPARATE PUMPING 4 CELLS 5 TREATMENTS n=3b+6p a=Zb+6$ e= b+s/sp
never more t h a n two cells are in t h e pumping stage a t one time, and as soon as one cell is pumped full it can immediately enter t h e boiling stage while t h e others are being pumped. TABLE11-EACH CELL PUMPED SEPARATELY Average Time Available Time Single for Charging, between Boiling CELLS TREATMENTS Discharging, etc. Discharges Period C f n a e 2 3 l b 2 b i - 4 9 b+2/39 2 b + 3 0 b 2 2 2 b + 2 p 3 5 l b 2 b i - 6 9 b+8/5P 3 4 2 b + 3 P 2 b + 5 9 b + g 3 3 3 b + 4 p 2 b + 4 p b+2/3p 3 2 4 b + 5 p 2bt-315 b + 0 9
- 1 ) a - ( f - 1) 3 12
+c(2c-
p , when t is not multiple of 3
t-5)p
+ + 1)P
+ ( 2 t 4- 4 ) p
(f
+( t - 1 ) Z 9 (when t is odd) Zt
o---ooo
-
(t
n = (26-t)b
6 =b
0
+ (t + 2 ) p + ( t / 3 - 1 ) p when t is multiple of 3
a = 3b
oc---o o----o o
+ 'z2 9 (when 1 is even) 2
These formulas are of particular interest in showing that: I-The extra time available for charging, discharging, etc., n, varies directly with t h e number of cells and inversely with t h e number of treatments obtained. a-The length of time between successive discharges of material, a, which is really t h e reciprocal of t h e capacity of t h e system, is not influenced b y t h e number of cells but is increased t o a slight extent by an increased number of treatments. 3-The average actual time each charge is exposed t o t h e boiling operation is not affected by t h e number of cells but varies t o a slight extent with t h e number of treatments. A P P L I C A T I O N O F FORMULAS
Suppose for example i t had been determined t h a t a certain extraction process would require 6 treatments and t h a t t h e pumping would t a k e I O min., t h e boiling 15 min., and t h e charging, discharging and solvent recovery 1.5 hrs. How many cells would be required for t h e process? 1 The development of similar formulas for extractions in which every charge receives two treatments with fresh solvent (THISJOURNAL, Loc. c i f . ) will not be given in detail but following are the formulas for this method of extraction which have been developed by the same method as the fore-
going.
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
496
+ +
b(2 c-t) 1 5 ( 2 c - 6) - 30 c-go 90 = 50 c 160 1z=
go =
250
+
p(2
c-t-
10(2
20
c-
c
I)
- 6 - I)
= 50 c
c = 5 If, however, m had been 60 min: instead of go min. the value of c would have come t o 4.4; this would mean t h a t either 5 cells would have t o be used with a wait of 30 min. after charging before t h e first batch of solvent is ready t o run on or else t h e time of boiling or of pumping would have t o be lengthened so t h a t 4 cells could do t h e work. If, for instance, 4 cells are t o do t h e work, the boiling period must be lengthened t o 2 5 min. 60 = b ( 8 - 6) 1o(8 - 6 - I ) 60 = 2 b IO b = 25 or the pumping period t o 30 min. 60 = 15(8- 6) p ( 8 - 6- I) 60 = 30 4- p
+
+
+
p
= 30.
These examples show t h e method of using the formula in determining t h e number of cells required under different conditions of treatment. COMPARISON O F SIMULTANEOUS AND SEPARATE P U M P I N G SYSTEMS
The formulas also make it possible t o compare t h e time consumed between discharges when pumping simultaneously with t h a t consumed when pumping separately, other conditions of extraction being t h e same. If we take, for instance, a series of 6 extractions in 4 cells, b = 15 and p = 5. With separate pumping t z will be 15(8- 6) 4(86- 5)s (12 4)s = 30 - 60 S o = 50 a will be 30 (6 1)s = 65, and 6-2 e will be 15 p = 25.
+
+
+
+
+ + +
~
2
For a comparison i t would not be fair t o use b with t h e same value in simultaneous pumping as in separate pumping because in t h e latter case, in t h e example just given, although b is 15, t h e actual total boiling time for each charge, e, is 25 min. ( b 2 p ) ; in order t o have conditions t h e same in t h e two systems, therefore, the value of b in simultaneous pumping (which is always the actual total time of t h e boiling) must be 2 5 min. With c = 4, t = 6, b = 2 5 , and p = 5 in simultaneous pumping .n = 25(8-6) 5(S-6-1) = 50 5 = 55 a = 2 b + z p = 5 0 + 1 0 = 6 0 e = b = 25. T h a t is, a, t h e time required between successive discharges of material is a little less in t h e case of simultaneous pumping.1 But there is a practical consideration which changes this relation slightly; pumping several cells a t t h e same time is likely t o take
+
+
+
1 Although this is only one case it may be shown that the difference between o (sep) and a (sim), with other conditions the same, is always P
when t is even and?t
9 when f is odd.
12,
No. 5
longer t h a n pumping a single cell, and therefore if 16 = 66 min., and p (sim) = 8, then a (sim) = 50 a (sep) = 30 3 5 = 6 5 min., t h a t is, when t h e pumping time is increased a little t o allow for the increased difficulty of pumping several cells instead of one cell, t h e time required for a complete cycle may be the same or even less in t h e case of separate pumping.
+
+
70
Vol.
SUMMARY
I-Formulas have been developed which show t h e relation between the number of cells and number of treatments in terms of various typical extraction operations both for separate and simultaneous pumping of t h e solvent in t h e cells. The formulas for simultaneous pumping are also applicable t o continuous extraction processes. 2-These formulas make i t possible t o determine t h e number of separate cells or extractors required t o furnish a certain number of treatments or extractions for each charge when t h e time required for each of t h e various operations is known. 3-With t h e formulas t h e time relation between simultaneous pumping and separate pumping has been developed, showing no advantage or very slight advantage for t h e former. VAPOR COMPOSITION OF ALCOHOL-WATER MIXTURES By W. I(. Lewis RESEARCHLABORATORY OF APPLIEDCHEMISTRY, MAS3ACHUSSTTS IN-! STITUTE O P TECHNOLOQY, CAMBRIDGE, MASS. Received December 18, 1919
I-n t h e field of distillation there is no more important problem t h a n t h e separation of ethyl alcohol from aqueous solutions. Accuracy in t h e design of apparatus for this separation is absolutely dependent upon exact d a t a as t o the composition of the vapors given off by any specific mixture of t h e two liquids. The d a t a on this point hitherto available in t h e literature have been inadequate and unreliable. The figures usually accepted are those recalculated for Maerckerl by Donitz from t h e original experimental results of Groning. These d a t a check reasonably t h e results obtained a half century ago b y Duclaux.2 The more recent work of Sore1 does not check t h a t of Groning and is apparently less reliable. The work of Evans3 is obviously unreliable in view of t h e fact t h a t he finds t h e composition of vapor and liquid identical a t 92 per cent b y weight, whereas a distillate of higher than 95 per cent alcohol can be obtained in commercial practice. I n 1913 Wrewsky4 published the results of a series of careful determinations of t h e vapor composition of alcohol-water mixtures, which bear t h e earmarks of reliability. On t h e other hand, Wrewsky’s work was done, not a t constant pressure, b u t a t constant temperature. Furthermore, he operated at only three temperatures, approximately 40°, 5 5 O , and 75’ C. His work is, therefore, not directly available for industrial practice because the industrial distillation “Handbuch der Spiritus Fabrikation,” 7th Ed., Berlin (1898), 590. (1878), 3 0 5 . STHIS JOURNAL, 8 (1916), 261. 4 Z . phys. Chem., 81 (1912), 1 . 1
* Ann. chim. Phys., 14
