Calculation of Absorber Performance and Design Improved Methods GEORGE HORTON AND W. B. FRANKLIN Humble Oil & Refining Company, Baytown, Texas where X,
moles of component in li uid from plate m per mole of liquid entering Lsorber Ym = moles of component in vapor from plate m per mole of gas entering absorber Lo = moles of liquid entering absorber Vw = moles of vapor entering absorber
This paper presents the derivation of general absorption and stripping factor equations. No assumptions are involved, and hence the equations are applicable to all cases of absorption and stripping. A simple rule is presented to estimate the knockout or stripping gradient from plate to plate, and two methods of calculating absorber performance are illustrated. These methods of calculating absorber and stripper performance have been compared to plate-to-plate calculations. In spite of discrepancies on intermediate plates, good over-all agreement was obtained between both methods and the plate-to-plate calculations.
=
Assume equilibrium between vapor and liquid can be expressed by where ,y,
T
Lm-1
+ k m - l V,-1
ym+l
T
= Vw(Ym +
I
-
Ym)
(4)
Lm
Now define the absorption factor as Am =
Lm-1 k and A m b l = km V m k,-i V m - i
(5)
substitute in Equation 4, and obtain
For a one-plate absorber (7)
For a two-plate absorber
By substituting the expression for Y 1 from Equation 7 i n Equation 8 and rearranging,
+
+ A+X. AiAa + A2 + 1
( A ~ 1) ya
Y2
=
Similarly for a three-plate absorber,
material balance around plate m of an absorber, By where the plates are numbered from top to bottom, the following relation is obtained:
- X m - I)
Ym-1
I+k,Vm
Derivation of Equations for Absorbers
Lo(Xm
rr
By substituting in Equation 1 for X , and X m- I , Ym =
H E concept of absorption and stripping factors, as developed by Kremser (6) and later by Brown (6),has been favored over plate-to-plate calculation methods by designers and absorbers of strippers because of the ease and rapidity with which the calculations can be made. The assumption of constant molal vapor and overflow rates throughout the tower, which was made in the derivation of the absorption factor equation, leads to appreciable error in the calculation of commercial absorbers in which there is variation in the oil and gas rates from plate to plate. This limitation can be offset to some extent by experienced designers in their choice of effective absorption factors or can be eliminated entirely by using these relations only as first approximations to the more rigorous graphical treatment described by Sherwood (4). The perfectly general absorption factor equation involving only the assumption of equilibrium between gas and liquid on each theoretical plate is derived below. This relation, representing the algebraic solution of a plate-to-plate calculation expressed in stoichiometric units, is then modified with the proper simplifying assumptions to facilitate its use in design and the evaluation of tower performance without appreciable loss of accuracy.
(2)
~ r n= k m x m
xm = mole fractions in vapor and liquid, respectively
(AiAz ys =
(1) 1384
+ AZ + 1) Y4 + AiAz + AzAs + As + 1
AIAzAs
Xo
OCTOBER, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
1385
Derivation of Equations for Strippers
The general equation can now be written for an absorber of n plates: Y"
=
+ + + +
+
The derivation of stripping equations is made in a manner analogous to that for absorbers. I n order to obtain equations similar in form to the absorption equations, the plates are numbered from bottom to top in the stripper, and the stripping factor is defined as
(AiAzAa. . .An-1 + A Z A s . . . A n - l . . . + A n - ] l ) Y n + l + A l A e . . . A n -v lw ~ X , AiAZAa., .An AZAa.. .An . . . An 1
+
For convenience write Equation 11 thus:
sm -- Y?&? 7
hm
Since it is desirable to obtain equations involving no concentrations within the absorber, Y , will be eliminated as follows: The over-all material balance around an absorber of A trays may be written Lo(Xn
-Xo)
= Vto( Yn + I
- YI)
The general stripping equation is xn+l-X1= SISuSa ... Sn+SuSs . . .S n + +sm SlSvSn.. . S n Sa,...Sn . . Sn 1 Xn+1 . .. S n 1 VE Y E SvSa...Sn Sa.. . S n --
+ + + + + + + + + sa3. . + . . . + s, + I . a .
L, + 1 xn+ 1 SlSBS. . . s n
-
.sn
(19)
(13)
As in case of absorbers, the following simplification can be made by using the effective average value of the stripping factor, S, and substituting for Y E its equivalent in term3 of
By substituting Equation 3 in 13,
X E:
or
- Lo x o Y n + 1 ... AnYn - v w X, = y n + l -
Ln Y , k,V,
~1
(14)
YI
Procedures for Predicting Absorber Performance
The above equations may be used to calculate the performance of an absorber of a given number of theoretical L plates when the amount and composition of the wet gas and Yn+1 - Y I Xo the lean absorption oil are known. Two methods of cal(15) Y" = An culation are possible. The first involves the use of separate absorption factors on each plate for each component throughand equating 15 and 12, out the absorber, and substitution of these in the general absorption Equation 16. The second and shorter method involves the use of an effective absorption factor for each component and substitution of these in Equation 17. I n A, An ' An an an either method the total moles of gas absorbed must be L O AlA,. ..An Xo estimated and determined by trial and error. In addition, Lo Anan-1 Yn+l xo = Yn+1 - Y 1 + -i t is necessary to compute, by heat balance, the temperature an VU an of rich oil leaving the absorber for the estimated amount of absorption. Two trials are usually sufficient. The second Substituting the values of a, and a, - 1, defined by Equations method, being the shorter, is recommended for the first trial. 11 and 12, we obtain METHOD I, USEOF PLATE ABSORPTION FACTORS. After an estimate is made of the total moles of AIAzAs ...An+AzAs . . .An+ . . . + A n gas absorbed and the corresponding rich oil temy n + l - y l = y n + l (AzAzAa ...An AzAa ...An An 1 perature is calculated, it is necessary to estimate AiAz. . .An the distribution of knockout and temperature v w x a (l - A , A ~ A.~. A. , + A ~ A. .~A ., + .. . + An + 1) on each plate of the tower. Although no rule AiAnAa.. .An A d a . . . A , . . . An Yn+t - Y1 can be devised to give these distributions ex.. AeAs.. . A n . . . A , 1 Yn+1 = ( A I A ~ A s.An actly, the following simple rules have proved Lo X o A d s . ..An As ...Am ... An 1 -satisfactory for this purpose in all cases V , Yn + 1 (AIAIAI. . .An AxAa. . .An . . An 1 (16) tried: Solving for Y n in Equation 14,
+6
ru
+
+
+
+
+ +
+
+
+ + + + + + + ) + + +
+
Equation 16 is the exact expression for the efficiency of absorDtion of an absorber of n plates. The second term to the right of the equality is the correction term for the presence of solute in the lean absorption oil. A useful approximate form may be obtained by substituting for X,its equivalent in terms of Y o from Equation 3 and by assuming that the series AIA2.. A , A d , . . A n . . A . and AoA2Aa..An . AoAn A , can both be expressed by A B I . .A, an average absorption factor A as (An+' - A ) / ( A - 1). The equation then simplifies to a form analogous to that of Souders and Brown (6): An+' - A Y n + i - Yi (*'I A"+' - 1 Y n + i - Yo
+ +. +
+ + +
+ )
+
and
Vw - Vm+l V w - V1
- Ts Tn
- Tm - T,
These obviously assume constant per cent absorption on each plate throughout the tower and temperature change proportional to the contraction. The predicted material balances and temperatures on each plate may differ considerably from those actually obtained in a given absorber, but use of these predictions gives an over-all absorption efficiency for each component which agrees closely with plate-to-plate calculations. Use of the above empirical rules will enable the calculation of vapor and overflow rates and oil temperatures on each plate, and hence the ratio L/V on each plate can be computed.
INDUSTRIAL AND ENGINEEHIh C; CHEMlSTHk
1386
The values of k( = y/x) can be obtained for each component on each plate, and A (= L / V k ) , the absorption factor for each component, is computed throughout the tower. Substitution of these values for each component in Equation 16 gives the absorption efficiencies from which the residue gas composition and the total moles absorbed can be calculated. Illustration. The starting conditions are those of absorber A ( T a b l e m containing four theoretical plates: moles lean oil per mole wet gas, 1.103; temperature of lean oil, 90" F.; tower pressure, 4.0 atmospheres absolute. Compositions of met gas and lean oil are as follows: Component Methane Ethane Propane n-Butane n-Pentane Lean oil
Moles Wet Gas 0,286
...
0:022 0.055 1.026
Total
1.000
1.103
The total knockout of 0.4451 mole is irn sufficiently close agreement with the assumed value that an additional calculation is unnecessary. METHOD11, USE OF EFFECTIVE ABSORPTION FACTORS.In this method of calculation it is necessary only to calculate the L / V ratio and oil temperature for that point in the tower corresponding to the effective absorption factor for the component in question. Careful consideration of the series expressions in Equation 16 will show that the effective absorption factor for the very light Components will correspond to a position near the bottom of the absorber and for the very heavy components, to a position near the middle of the tower. Table I1 is presented as a guide to the selection of proper effective absorption factors.
Moles Lean Oil
0.157 0.240 0.169 0.148
T ~ B L11 E
--
+
e)"'"
(3) By heat balance the rich oil temperature is found to be 115" F., and i t is assumed that the temperature change is proportional to the contraction,
A material balance may now be written around each plate : Moles oil Moles vapor Temp. oil, F. L/ v
1.103 ,,
90
.
, , ,
1.192 0.551 95 2.16
Plate 3
Plate 4
Moles Wet Gas
1.294 0.640 101 2.02
1.413 0.742 107 1.90
1.552 0.861 115 1.80
1:OOO
v,
... .. .
A Plate3
0.0432 0.170 0,720 2.62 8.64
0.0392 0.151 0.620 2.24 7.34
0,0354 0.0327 0.135 0.120 0.542 0.473 1.95 1.65 6.33 5.14
CI
cr
CS n-Cd
n-a
r
A Plate4
Yn+1- Yl Yn+i
0.0328 0.122 0.501 0.916 0.956
Yn+i
-
0.0094 0,0192
g::;
Y1
=
(y) = O . X I ~ ~=/ 0.861 ~ Lo + V , - Vi 1.103 + (1.0 - 0.551) = 1.552 VI
2.2
O.55lT = 0.721
V2.8
lLZ
L2.8
=
1.103
+ (0.551
- 0.551) = 1.388 1.2
T2.8
AEffective
=
115
- 25
1.0
- 0.551T
0.449 = 1.388/(0.721 X 0.95)
= 106
2.02
The completed solution is given in Table IV.
OF ABSORPTION EFFICIENCIES TABLE I. SOLUTION
A Plate 2
1 0 0 9 0 8 0 7 0.6
+1 La TI = l l 5 ' F . A ~ f f ~=~ 1.552/(0.861 t i ~ ~ X 55.0) = 0.0327 For butane m / n is equal to 0.7 and m is equal to 2.8:
Equilibrium constant k , used in calculating the absorption factors, was taken for the purpose of illustrating the method, as P / T . Values of P were read from the Maxwell vaporpressure chart (3). The calculated absorption factors are substituted in Equation 16 to obtain the absorption efficiencies. The complete solution is given in Table I.
A Component Plate 1
m/n*
0-0 0 1-0 0 4-1 1 0-4
The effective absorption factors are therefore calculated from the L / V ratios and temperatures corresponding to positions in the tower obtained from Table 11. Substitution of these effective values in Equation 17 gives the absorption efficiencies for each component, from which the residue gas composition and the moles of gas absorbed can be calculated. When Equation 17 is used t o correct for the presence of solute in the lean oil, Y o is calculated from the solute composition of the lean oil, X,, using Equation 3 and assuming that T i is equal to VI. This method has not been tested over wide ranges but appears to give a good approximation for commercial absorbers, in which there are usually four or more theoretical plates, and where the components normally encountered in the lean oil (butane and pentane) are characterized by effective absorption factors greater than unity. For special cases i t is recommended that method I be used for those components present in the lean oil. Illustration. Absorber A (Table 111) will again be used to illustrate method 11. From Table 11, m / n for methane is taken as 1.0 and m is equal to 4 :
L, can be calculated from the material balance, L, = Lo vm+l VI or from an equation similar to that used for l',,,,
Plate 2
EFFECTIYE ABSORPTION F~CTORS
.4 (or S )
3771 = plate corresponding to effective factor; n = total nurnbpr uf ttiroretical plates.
Or it has been suggested (I) that per mole of wet gas,
hhks Lean Oil Plate 1
LOC.4TION O F
1 4 0 0 Above 4 . 0
The following assumptions are made: (1) Moles knockout per mole wet gas = 0.449; actually this value was obtained as the result of calculation by another method. (2) The distribution of the contraction from plate to plate may be expressed by
L, = Lo
\ O L . 32. N O . 10
YI
?/I
0.2766 0.1378
0.4986 0.2480
~:~~~~ 0.1415 0.0065 0.0117 0,4451 0.5549 1 .OOOO
Procedure for Design I n the design of absorption towers, the selection of tower size and oil circulation is usually made as the result of economic balances. However, under certain conditions, either tower height or oil circulation rate may be fixed by physical
OCTOBER, 1940
IKDUSTRIAL AND ENGINEERING CHEMISTRY TABLE 111. RESULTSOF
C'oniDosition
PLATE-TO-PL4TE CALCULATIONS
Plate 2 Moles hloles oil in gas out
Plate 1 Moles Moles lean oil residual gas
1387
;\Ioles oil in
Plate 3 Moles gas out
Plate 4 Moles Moles' oil in gas out
Moleb Rich Oil
Moles Wet Gas
Absorber A, Operating Pressure = 4 Atmospheres -4bsblute
.. ..
Mrthane Ethane Propane n-Butane ,,-Pentane Lean oil Total O i l temp.,
0.2497 0.1250 0.1070 0.0125 0.0058
0:02 0.05 0.93 1.00
.... - O
0.0113 0,0223 0.0805 0.0342 0.0520
0.2610 0.1473 0.1875 0,0267 0.0078
1.1303
0.6303 96
90
F.
....
o.9300
0.5000
0.0125
0 0089 0.0195 0.1190 0.1020 0.0780
0 2586 0.1445 0.2260 0.0945 0.0338
0 6911
1.2574
O
0.2594
0.0097 0.0213 0.1140 0.0594 0.0567 0.9300 __ 1.1911
0 1463 0 2210 0 0519
0.9300
.... -
0 0087
0 2584 0 0178 0.1428 0 1101 0.2171 0 1607 0.1532 0 1782 0.1340 0.9300 -~ 1 4055 0.9055
...
....
m
115
105
100
Absorber B, Operating Pressure = 4 Atmospheres Absolute Methane Ethane Propane n-Butane n-Pentane Lean oil Total
0.1750 0.1200 0.1300 0.0725 0,0025
.. ..
.... 0.5000
0125 0.25
F.
Oii t e m p ,
0.0023 0.0061 0.0267 0.0543 0.0059 0.2500 0,3453
0.0021 0.0057 0.0284 0.0823 0.0173
0.5953
0 3858
.... -
b -
90
0.1773 0.1261 0.1567 0.1268 0.0084
0,1771 0.1257 0,1584 0.1548 0,0198
0.0021 0.0055 0.0273 0.0935 0.0369
0.6358
0 4153
o.2500
....
0.2500
110
105
0.1771 0.1255 0.1573 0.1660 0.0394
.... ~. 0 6653 115
120
Stripper A. Operating Pressure = 2 Atmospheres Absolute Plate 1 Moles Mole? lean oil vapor in 0.10
Steam Methane Ethane Propane n-Butane n-Pentane n-Hexane Lean oila Total Oil t e m p , 0
.
.. ..
.... ....
..... .....
..
0.00248 0.00805 0.01270 1.01200 1.03524
.. .. .. 0.16
.. . . .. .
254
Prate 4 Moles Noleg' oil out vapor in .. . . . 0 10000
.....
0.00045 0.00406 0.00847 0.00369 0.03300 0.14667
I
0.00210 0.01010 0,01289 0,01443 1.02150 1.06102
256
Moles Rich Oil
.. .. ..... j o : b i i z s
.....
..... .....
.....
0.00045 0.00506 0.01047 0.01369 1.01700 104667
0.00149 0.00305 0.00270 0.02800 0.13524
_-
..
F.
Plate 3 hloles Moles oil out vapor In .. . 0.10000
..... ..... .....
....
..
0.0010 0.0050 0.0100 0.9840 1.0000 O
Plate 2 Moles Mole?' oil out vapor in .. . . 0.10000
0.00210 0.00910 0.00789 0,00443 0.03750 0.16102
Moles Vapor Out 0.10000 0.01125
~
0,01362 0.02650 0.01870 0.01675 1.03825. 1.12507
0.01362 0.02550 0.01370 0.00675 0.05425 0.22507 265
25s
Denuded lean oil is assumed to have a vapor pressure equivalent t o C B H ~ O . OF ABSORPTION EFFICIENCIES TABLE IV. SOLUTION
Components Methane Ethane Propane n-Butane n-Pentane
m/n 1.0 0.9 0.8 0.7 0.6
-
Effective Values Yn+1 Yl L/V T P/r A Yn+i Yo Yn+i YI 1 . 8 0 115 5 5 . 0 0.0327 0.0327 0.0094 1.84 112 1 4 . 5 0.127 0.127 0.0199 1 . 8 8 110 3.54 0.53 0.509 0.1220 1 . 9 2 106 0.75 2.02 0.968 0.1556 1.97 103 0.275 7.16 ... 0.1419
-
Total
YI 0.2754 0.1371 0.1180 0.0134 0.0061
0.5010 0.2495 0.2140 0,0244 0.0111
0.5513
1.0000
The absorber is to operate at 4 atmospheres absolute. The lean oil is assumed to be a t a temperature of 90" F., and to be solutefree. The effective absorption factor is calculated frorn Equation 17:
Yl
-yn+l
-
Yn+1
-A = 0.568 = AS A6
-
1
A = 0.603
dimensions of existing equipment, and the other is calculated to obtain a specified recovery of the key component. I n the case where the oil circulation rate is to be determined to obtain a specified recovery of the key component, with an absorber of a given number of theoretical trays, the following procedure is recommended : From the specified recovery and the number of plates, the effective absorption factor can be calculated from Equation 17 or read from Brown's absorption factor us. efficiency chart (5). The position in the tower a t which the effective liquid and vapor rates occur may be determined from Table 11. The usual assumptions as to the total knockout and its distribution from plate to plate will allow a direct solution for the lean oil necessary for the required recovery. Illustration. An absorber with four theoretical plates (absorber B, Table 111) is t o be supplied with sufficient lean oil to recover 56.8 per cent of the butane in wet gas of the following amount and composition : Component
Mole
Methane Ethane Propane n-Butane n-Pentane
0.253 0.179 0.223 0.240 0.105
-
I.000
from Table= or
m / n = 0.80
rn = 3.2
Assume : (1) The over-all knockout is 0.285, and the temperature rise is 30" F. (2)
v, =
ll+
VI
1- m
( 7 )
1.8
Va.2
= 0.715
= 0.86
L3.z = 0.603 X 0.86 X 1.05 = 0.545
By a material balance,
++
Lo = L?n VI - v,+1 Lo = 0.545 0.715 - 0.936 = 0.324
Moles of lean oil required per mole of wet gas is 0.324 as compared to the value of 0.356 determined in the plate-toplate calculation (absorber B, Table 111).
INDUSTRIAL AND ENGINEERING CHEMISTRY
1388
VOL. 32, NO. 10
I n the case where the quantity of lean oil is fixed and the variable is absorber height, an additional assumption must be made as to the number of theoretical plates required for a given recovery of the key component. However, this does not greatly complicate the calculation because the effect of adding or subtracting plates may be estimated from any completed solution. Using the effective absorption factors obtained from the first trial, the required number of plates for the second trial can be determined from Equation 17 or Brown’s absorption factor us. efficiency chart (6).
11. However, even in this case good agreement as to the amount of each component absorbed was obtained between methods I and I1 and the plate-to-plate calculation. The maximum deviation in the absorption efficiency occurred in the absorption of propane, and was 5.4 per cent between method I1 and the plate-to-plate method (4.2 per cent between method I and the plate-to-plate method). The relative error in the proportion of pentane in the residue gas was 20 per cent, but the absolute error was only 0.1 per cent and the error in the per cent pentane recovered was less than 1 per cent. I n stripper A the absorption oil is stripped with steam conAccuracy of Calculation Methods taining no hydrocarbon vapor (case analogous to solutefree lean oil in absorption). The assumed distribution of I n order to demonstrate the accuracy of the proposed the stripping on the various plates did not agree with that methods of absorber calculation, three arbitrary cases were obtained by plate-to-plate calculation, but the three methods set u p and calculated by progressing from plate to plate. agreed satisfactorily; the maximum deviation in the fraction The results of these calculations are given in Table 111. of any component stripped from the lean oil was less than As in the previous calculations, Raoult’s and Dalton’s laws 5 per cent. were assumed to obtain the equilibrium relations (y = P / x z), It should be emphasized that although the assumed and Maxwell’s vapor pressure chart (3) was used for the vapor gradients of temperature and oil-to-gas ratios gave reliable pressures of the pure hydrocarbons. over-all solutions, exact results could be obtained if the corAmounts and composition of wet gas and lean oil calrect gradients were used. Experienced designers will be able culated by the plate-to-plate method were used as starting t o improve upon their results by modifying the distribution conditions for methods I and 11, and absorption efficiencies of temperature and knockout by inspection of the composiand residue gas analyses were computed. A comparison of tion of the entering streams and the amount of lean oil (or the three methods is presented in Table V. stripping vapor). All three cases considered involved a n appreciable change in oil rates, vapor rates, and temperature throughout the OF VARIOUS METHODS OF CALCULATION column, and one case involved use of partially stripped lean TABLE V. COMPARISON Method 2 Method 1 Plate-to-Plate oil. However, the equations developed above, together with the simplifying assumptions described in methods I and 11, Residue Residue Residue Fraotion gas. Fraction gas, Fraction gas, provided accurate and rapid solutions. Such an approach absorbed mole ’% absorbed mole % absorbed mole % should facilitate and improve the accuracy of absorption and Absorber A stripping calculations. 49.85 0.0336 49.95 0.0327 50.10
Methane Ethane Propane n-Butane n-Pentane
0.0328 0.122 0.501 0.916 0.956
24.80 21.60 2.58 1.17
-
0.125 0.506 0.9185 0.9568
100.00
25.00 21.40 2.50 1.15
-
0.127 0.509 0.921 0.959
1oe.00
24.95 21.40 2.44 1.11 100.00
Abaorber B Methane Ethane Propane n-Butane n-Pentane
35.3 24.2 26 0 14.1 0.4
0.0122 0.0438 0.174 0.584 0.9716
-
0.0118 0.0422 0.167 0.568 0.976
100.0 Method 1 Fraction etripped Methane Ethane Propane n-Butane n-Pentane n-Hexane Lean oil
1.0
1.0 0.9988 0,9687 0,757 0.417 0.051
’
Lean oil mol:%
...
0:ooz
-
0.0122 0.0438 0.176 0.584 0.9732
100.0
Stripper A Plate-to-Plate Fraction stripped 1.0 1 .o
1.0 0.083 0.9623 0,434 0.733 0.977 0.403 98.484 0.0522 100.000
35.0 24.0 26.0 14.5 0.5
Lean oil, mole 5%
... ... .. .
0.1 0.5 1.0 98.4
100.0
35.3 24.2 26.0 14.1 0.4
100.0
Method 2 Fraction stripped 1.0 1.0
0.9988 0.9706 0.770 0.399 0.0515
Lean oil, mole %
...
0:ooz 0.078 0.430 1.007 98,483 100.000
Absorber A represents operation a t relatively high oil-togas ratio and, in addition, shows the effect of using partially stripped lean oil. The agreement between all three cases was exceptionally good; the maximum deviation lay in the butane and pentane contents of the residue gas, and was less than 4 per cent. Absorber B represents operation with a well-stripped lean oil but with a normal oil-to-gas ratio. I n this case the distribution of the knockout and temperature between the various plates, as found by the plate-to-plate method, was considerably different from that assumed in methods I and
Nomenclature A = absorption factor = L/Vk k = equilibrium constant = y/x L = moles of oil m = a plate at random in absorber or stri per n = number of theoretical plates in absorger or stripper P = vapor pressure of a pure hydrocarbon x = total pressure S = stripping factor = V k / L T = temperature V = moles of vapor X = moles of any component in liquid per mole of liquid entering absorber or stripper x = mole fraction of any component in liquid Y = moles of any component in vapor per mole of vapor entering absorber or stripper y = mole fraction of any component in vapor
Subscripts E = stripping medium entering tower (steam, etc.) F = lean oil leaving stripper o = conditions at top of an absorber (lean oil) w = wet gas entering absorber
Literature Cited (1) Hogan, J. J., Private communication, 1940. (2) Kremser, A., Natl. Petroleum News,22, No. 21 ( M a y 2 1 , 1930). (3) Maxwell, J. B., IND. ENQ.CHEM..24, No. 5, 502 (1932). (4) Sherwood, T. K., “Absorption and Extraction”, p. 114. New York, McGraw-Hill Book Co., 1937. ( 5 ) Souders, Mott, Jr., and Brown, G. G., IND. ENC). CHEM.,24, No.
5, 619 (1932).
PREBENTED before the Division of Petroleum Chemistry a t the 99th Meeting of the American Chemioal Society, Cincinnati, Ohio.
