Pressure Gradient Fractionation of Gases JOSEPH W. CREELY, 51 Manor Avenue, Oaklyn, N. J. GEORGE C. LE COMPTE, 601 Park Road, Washington, D. C.
Equations are developed to show the distribution of a multicomponent gas between a Rolvent and a gaseous phase, the pressure gradient fractionation of a multicomponent gas mixture dissolved i n a solvent, a perfect countercurrent continuous pressure gradient fractionation of a multicomponent gas mixture, and a theoretical pressure gradient fractionation plate for a gas of two components.
N 1870 Mallet (4) patented a scheme for separating air into oxygen-rich and nitrogen-rich fractions. According to his method, water is brought into contact with air a t high pressure, and the dissolved gases are separated by reducing the pressure. The gases are again brought into contact with water in a second vessel. After the process has been repeated a sufficient number of times, the oxygen-rich fraction is collected for use. Morgan (1) improved on the above scheme and demonstrated by experiment the phenomenon of pressure gradient fractionation. He also developed a logarithmic formula describing pressure gradient fractionation. Finlayson (2) made a detailed study of a number of solvents in relation to the pressure gradient fractionation of air. Such questions as rate of solution of gases, absolute solubility, and the effect of temperature and the presence of dissolved substances on the absolute solubilities of oxygen and nitrogen in different solvents were considered. Data on the pressure gradient fractionation of oxygen-nitrogen mixtures are given and agree fairly well with the results calculated from the equation developed b y Morgan. Finlayson found paraffin lamp oil to be the most suitable solvent. He found that the rate of solution of oxygen and nitrogen in water was only one thirteenth of the rate of solution in paraffin lamp oil. I n 1937 Peffer, Shepard, and Sherman (6) patented a similar process for producing oxygen-rich mixtures. They found mineral seal oil and sugar solutions in water to be the most S U i t d J k solvents for separating the components of air. Their device did not take advantage of the principle of pressure gradient fractionation. Nernst (6) mentioned the possibility of separating mixtures of gases by “isothermal reversible fractional solution” but failed to give any formulas governing the process. Recently Schuftan (7) was granted a patent on “separating gases such as methane and acetylene by use of a selective solvent such as water”. I n his process the mixture of gases is washed countercurrently a t a given elevated pressure with a solvent to form a solution, A , with a greater proportion of the more soluble components. The gas not dissolved during the washing is richer in the less soluble components than was the feed gas. Solution A is then passed countercurrently, still a t the given pressure, through a “cycle gas mixture” to form solution B. Solution B contains a greater proportion of the more soluble components than did solution A. Solution B is pumped further on when the pressure upon it is allowed to decrease to a predetermined intermediate pressure, releasing some gases and forming solution C. The gases released in this step form the cycle gas mixture and are com-
I
pressed to the given elevated pressure and pumped countercurrent to solution B. Solution C, which contains a greater proportion of the more soluble components than did solution B, is now brought to the lowest pressure in the process, the dissolved gases being removed to form a gas phase with a high proportion of the more soluble components. This process utilizes the principle of pressure gradient fractionation.
Isothermal Pressure Gradient Fractionation
It is assumed that Henry’s law holds for all the systems considered in the discussion. Henry’s law may be expressed in the following approximate form if the solvent is in equilibrium with a comparatively great volume of gas.
where Di = volume of gas i dissolved in unit volume of solvent at pressure p and, as is true of all volumes in this discussion, measured at 1 atm. of partial pressure and the temperature of the experiment Ti = total volume of gas i dissolved and undissolved per unit volume of solvent at pressure p Si = volume of gas a which will dissolve in unit volume of solvent at 1 atm. partial pressure and the temperature of the experiment (Table I) P = total pressure on the system, atm.
If the solvent is in equilibrium with a limited volume of gas, we may express Henry’s law as Di =
(2)
(i
=
A , B,
. . . ., N )
i = A where Ui = volume of gas i remaining undissolved per unit volume of solvent
Dividing Equations 2, one by another,
Solving,
MARCH, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
From Equation 2, DB=
T B - DB
i = N
(
-
C T i
i = A
NCDi) i = A
psi =
A , B,
.. . ., N ) (4)
Given values of TA, T B ,. . ., T,, SA, SBl. . ., AS’,, and p , we can calculate the values of D,, D B , . ., D N by trial and error. Assuming values for D B , we can calculate corresponding values for DA, De, D D , . ., D , from Equation 3, and then substitute these values in Equation 4 and calculate DE. When the assumed and calculated values of D B agree, the calculated values of D A , D E , , .,D , are to be taken as the solution.
.
431
taining oxygen, nitrogen, and water was constructed as follows: Imagine the system to contain some arbitrary amounts of dissolved oxygen and nitrogen-say, 0.0600 volume of each per unit volume of solvent a t the start of the pressure gradient fractionation. We can plot the point D o ~ F / D N= ~ P 1, D O ~ F= 0.060 on log-log paper. According to Equation 6 when D O ~ = F 0.020,
.
.
Pressure Gradient Fractionation Assume that the pressure p on unit volume of solvent containing D, volumes of gas A , D, volumes of gas B, etc., is allowed to diminish gradually and that the gases liberated are removed as fast as they appear as bubbles. If the pressure drops to ( p - d p ) , D, drops to ( D , - dD.), and Db drops to ( D , - d D J , etc. By Henry’s law,
since the composition of the gas generated during this pressure drop is dD, 4-dDb 4- . . 4- dD,. Dividing Equations 5,
.
This may be rearranged and integrated between the proper ., T , be the volumes of the initially limits. Let Tal T,, dissolved gases and let DAp, DE,, . ., DNF be the final volumes of the dissolved gases A , B, . ., N in the system per unit volume of solvent. Then
.
I
.
.
0.0336
(0.060)b.ole2(o.020) 0.060
0.0162
-
0.0336 0.0162 =
We can now plot the point D o ~ F / D N=~ 3.25, D O ~ F= 0.020 and draw a straight line through the two plotted points. PROBLESZ. Given a system containing water and dissolved gases containing 40 per cent oxygen and 60 per cent nitrogen under a pressure of 5 atmospheres a t 20’ C. (a) Plot a curve showing the composition of the dissolved gases and the pressure on the system if the gases are allowed to escape as rapidly as they are liberated from the solution while the pressure diminishes. ( b ) What will the amount of the dissolved gases be when their composition is 75 per cent oxygen and 25 per cent nitrogen? What will the pressure on the system be under these conditions? ( c ) What will the composition of the dissolved gases be when the amount of dissolved oxygen is reduced to half of the original amount through pressure gradient fractionation? SOLUTION.( a ) Let 2’ be the volume of dissolved gases per unit volume of solvent a t 5 atmospheres pressure. Then = DO,F 0.60~’= DN,F 0.402’
DO,F = 0.40 X 0.10216 = 0.0409 DN,F = 0.60 X 0.10216 = 0.0613 from which we can obtain
..
If P A .P , , ., PN are the partial pressures of A , B, etc., then the total pressure is
. .., N ,
Equation G was used in constructing the graphs of Figure 1. Inspection of Equation G shows that any DAp/D,F us. DAF plot on log-log paper mill be a straight line of constant slope, 1 - S A / S B ,if the temperature is held constant in a system containing the gases A , B, . . ., N and a given solvent. The following numerical solution will illustrate the construction and use of Figure 1. The graph of the system con-
3.25
FIGURE 1. GRAPE@ O F DAF/DBFIS. DAF
INDUSTRIAL AND ENGINEERING CHEMISTRY
432
VOL. 32, NO. 3
TABLEI. VALUESOF S, TERMS -02-7 So,
Liquid Acetic acid Acetone Amyl acetate Amyl alcohol Aniline Benzene Carbon tetrachloride Ethanol E t h y l acetate E t h y l ether Gas oil Isopropanol Methanol Paraffin oil Toluene Water4 Xylene
CitaC. tion
io . . . . . . ...... .... 0.174 ii oIiii3
0.31 0.236 0.175 0 4215 0.154
25 20 20 10 25
O:Zk7 0.202 0.179 0.0336 0,179
i0 25 18 20 16
Acetic acid Acetone Amyl acetate Amyl alcohol -4niline Benzene Carbon tetrachloride Ethanol E t h y l acetate E t h s 1 ether Gas oil Isopropanol Methanol Paraffin oil Toluene Waters Xylene a For SO? t h e S values
id)
(8)
0.129 0.168
26 20
0.095 0.125 0.1348 0.117 0.119
ii Q
..
(3) (8) (8) (3)
is')
(2) (8)
(8) (8)
0.0162 0.119
25 20
25
20 20 20
(8)
(8) (3)
(8) (8)
(8) (8) (8)
io .. . . . .
20
(8)
"
(81 "
(8)
2 : h
...
0 : i3i
...
0.0617 0.0703 0.0743 0.0353 0.0303 0.0707
20 20 20 20 20 20
0:0662 0.0788 0.1195 0.065 0.075 0.0902
2Q 20 10 25 25 20
0.'6838 0.0200 0.0783
20 20
.. .. ..
Cita" C . tion
S,, 0.1689 0.2128 0.2108 0.1706 0.0506 0.1645
(8) (8)
(8) (8) (8) (8)
id!
20 20 20 20 20 20
(8) (8) 18)
(8) (8) (8)
o : i i o i zo (8)
0.2419 0.3842
(8) (8) (3) (3)
..
20 10
(8) (8)
... .
(8)
io id)
o:i+42 0,0259 0.1744
(8)
(8)
io is') 20 20
(8) (8)
-CH4--CitaC. tion
SCaH,
...
.. .. ..
..
,.
-CO-
CitaC. tion
SH,
I
..
....
-----H2-----
-CaHsCita-
SCZR4 C. tion 20
?: . . . . . . .
is
....
(8) (8) (8)
.. ..
6:044
2:426 1.070
....
(8) (8)
(8)
--C2H4Cita-
C. tion 20 20 20 20 20 20 20 20
4:205
Cita-
C. tion 20 20 20 20 20 20
5.129 6.921 4.411 1.941 1.434 2.540 2,502 2,923
...
SN1 0.1172 0.1383 0.151 0.1208 0.0299 0.111
(s,
. .
----COz---Sco,
-lis---
.
.
... ,..
12-13
...
.. .. ..
..
..
.. ..
0: 4496
20
0.430 0.16 0.495
22 20 22
0.459 0.45
22 20
....
... . 19 .. .. .
CitaC. tion
SCa
....
I
..
.. .. . . . . 22 ,.
.. 20 .. ..
... ...
21
0,'237
...
..
42.3 a t 20' C . ( 8 ) .
0.462 0.4564 0.44 0,485 0.03.55 0.515
.. ..
..
20
..
20 20
25 20
21
100 - = _ = Plot the point D o ~ F / D K ,= F 0.667, DO,F = 0.0409 and Nz in dissolved gases = loo 41.5% 1 D o , F / D s ~ F 2.41 draw a straight line parallel to the 02, Nz, HzO graph. From this new line, suited to this particular system, values of O2 in dissolved gases = 100 - 41.5 = 58.5% DOtp can be obtained by assuming values for D o ~ F / D N ~ F . Talues of D N ~ are F calculated from Do,F/Ds,F and Do,F. Perfect Countercurrent Pressure Gradient Po, and Pn2are calculated from the relations PO,= Do~F/SO,, Fractionation of Gaseous Mixtures P K 2= D N ~ F / S Fand ? , PTFis equal to the sum of PO, and Ps,. These quantities, as well as the per ceiit oxygen in the The ideal system which would accomplish the maximum dissolved gases, are given for this system in Table 11. These separation of a gaseous mixture in working between any given data are used in the construction of the curve of Figure 2 . pressure limits would function in the following manner: An ideal system such as drawn in Figure 3 could be imagined. Here the solvent is circulated from the top of the column toward the bottom. A central shaft supports an indefinitely large number of movable separators as projected in top view beside the front view of the column. Each movable separator is tightly fitted against a fixed separator. The separators are so adjusted that, as the shaft driving the movable ones revolves, the ports of the odd numbered pairs of separators counting u p from the bottom (marked A ) are all open a t the w same time or all closed a t the same time. The same will be E ~-t true of the even numbered pairs of separators counting u p from the bottom (marked B). The A separator ports will be --._ open \Then the B separator ports are closed, and vice versa. 40 50 60 70 80 90 100 The feed gas is pumped into the column a t some point be% OXYGEN IN DISSOLVED GASES
+
FIGCRE 2.
PRESSURE GRADIEZTT FRAC-
OF 40 PER CEST OXYGEN60 PERCENTNITROGEN DISSOLVED IZT WATERAT 5 ATMOSPHERESPRESSURE TIONATION
(b) When the composition of the dissolved gases is 75 per cent oxygen and 25 per cent nitrogen, Do,/DN, = 3. Then from Figure 1, Dop = 0.0096 and DK,F = 0.0032. From Figure 2 the pressure will be 0.50 atmosphere. F be 0.0204 and D o ~ ~ / D Nwill , F be 1.41 from (c) D O ~ will Figure 1:
TABLE 11. %0
70
80 90
DISSOLVED GASES
AT VARIOUS
PRESSURES DOSF
2
(Assumed) 40 50 60
OXYGEX I N
D o~' a F / D~. N>F 0.667 1,000 1.500
2,333 4.000 9.000
(from Graph) 0,041 0,028 0,019 0,012 0,0075 0.0036
Po Atd.
P x , ~ PTF~ Arm. Atm.
1.22 0,834 0,565
3.79 1.73 0.78 0.33 0.12 0.024
1
Dx,F 0.061 0,028 0,013 0,0053 0.0019 0,00039
0.366
0,224 0.104
5.01 2.56 1.35 0.69 0.34 0.13
INDUSTRIAL AND ENGINEERING CHEMISTRY
MARCH, 1940
tween the top and bottom of the column. Here it is broken up into bubbles so fine that equilibrium is established with the dissolved gases in a negligibly short time. The bubbles rise through regions of higher and higher pressure countercurrent to the liquid flow. The bubbles finally emerge a t the top of the column, and the gas is collected as one of the products. The liquid containing dissolved gases flows downward through regions of lower and lower pressure and is continually giving u p some of its dissolved gas which rises as bubbles countercurrent to the liquid flow. Liquid from the low-pressure end would be run into a vacuum chamber and the dissolved gases pumped out of it. This would be theotherproduct.
433
Let b,, c,, . . ., n, be defined in the same manner as ai and let b,, c,, ,, n, be defined in the same manner as a,. We can now write the following equation descriptive of the process : i AT = P , - P/ (i = A , B , . . ., N ) (9)
..
i = A
From the definition of a,, b,,
. . ., nu,
Substituting in Equation 9, au(P, - P f ) - + - +b, . . . . +n"
= a,,
SA
SB
SN
By material balance, DA MOVABLE SEPARATOR
also
EA - U A
E A = SAa,P,
So from Equation 10,
FIXED SEPARATOR
LIQUID PUMP I d &
FIGURE 3. IDEAL SYSTEMFOR MAXIMUMSEPARATIOK O F A GA~EOTJS MIXTURE
Suppose a gas containing the n component pure gases A , B,
. . ., N is to be fractionated in an apparatus of this type. be the volumes of A , B, . . . ,, N disLet D,, D,, . . ., D,,,
solved in unit volume of solvent a t the final (low) pressure of the expansion, measured at one atmosphere of partial pressure and the temperature of the experiment. Po P, P,
initial pressure during expansion (point o ) , atm. pressure of liquid where feed is introduced (point e ) , atm. = final pressure during expansion (point f), atm. I , (i = A , B , . . . ., N ) = volumes of i = A, B, . . . ., N dissolved per unit volume of solvent at region where pressure is Po,measured at 1 atm. partial pressure and the temperature of the exDeriment Ei (i = 2,B, . . . ., N ) = the same as above, but at region where pressure is P , Ui (i = A , B, . . . ., N ) = volumes of i = A , B , . . . ., N rising through the liquid from the region below e in the form of bubbles per unit volume of solvent a t the region of pressure P,, measured at 1atm. partial pressure and the temperature of the experiment =
=
a;
=
a,,
=
+ +
IB .... + I N = mole fraction of gas A in the dissolved gases in the region of point o UA = mole fraction of gas A in the
IA
UA+UEf
.... f U N
bubbles rising through the region of point e, also the mole fraction of A in the feed
Similar equations apply t o D,, Dc, . . ., D,, but any one will be sufficient since i t may be used successively on each component of the gas mixture. Assuming a given composition of feed, a given solvent, and an assumed final pressure, P,, Equation 11 reduces to a linear one involving DA and P,. The portion of the column (Figure 3) above region e at which the feed enters might be considered as a large number of theoretical pressure gradient fractionating plates each with a small pressure difference as shown in Figure 4. The theory of such a plate i s presented for gas mixtures of two components. Let
, "
LIQUID
s i:-' FIGURE 4. THEORETICAL PRESSURE GRADIENTPLBTEE) WITH SMALL PRESSUR^ D~FFERENCEs
P , = initial pressure of expansion, atm. P/ = final pressure of expansion, atm. I A ,I B = volume of gas A , B, dissolved per unit volume of solvent at region of pressure Po D.4, D B = volume of gas A , B, dissolved per unit volume of solvent a t region of pressure Pf a,,, bo = mole fraction of gas A , B, in dissolved gases a t region of pressure Po a/, by = mole fraction of gas A , B, in dissolved gases at region of pressure P,
+
x = I A I B = volume of dissolved gas per unit volume of solvent at region of pressure Po
Henry's law is expressed in the following equations:
+ + g )b = p o IA
=
xu,; I B = xbo
(13)
Let R A , R B = volume of gas A , B bubbled into solvent per unit volume of solvent at region of pressure P,; GA, GB = volume
INDUSTRIAL AND ENGINEERING CHEMlSTRY
434
of gas A , B removed from solvent as bubbles per unit volume of solvent at region of pressure Po
+ R A - D A ; GB = I B + RE - DE
(14)
Assuming Henry's law equilibrium with the average dissolved gases,
-
-
S A ) [PoSASB - ( R A - D A ) S A- (RE D B ) S B ] P o S A S B [ S A ( 2 - a/) sB(1 a / ) 1 f SA(R.4 - D A ) [SB(2 a / ) - S A ( 3 - a / ) ] S B ( R B - D B ) [ S A ( 1 a/) s B ( l j ] CS = ( R A - D A ) S A 2 ( 2 - a/) S A S B ( l j ( P d B f RE - D E ) (18) c1
= (88
c?,=
By material balances, G A = IA
where
VOL. 32, NO. 3
-
-
-
-
+
Use of Equations 17 and 18 yields values of a, which can be checked and more accurately determined by trial and error. These equations might also be useful in determining efficiencies of pressure gradient fractionation apparatus of the type shown in Figure 4.
Literature Cited Finlayson, Trans. Inst. Chen. Engrs. (London), 1, 29
(1923).
Ibid., 1, 45 (1923). Frolich, Tauch, Hogan, and Peer, IND.ENQ.CHEM.,23, 548-50 (1931).
Mallet, British Patent 2137 (1869). Nernst, "Theoretical Chemistry", 5th Eng. ed., New York, Mae millan Co., 1923. Peffer,Shepard, and Sherman, U. 5. Patent 2,086,778 (July 13, Eliminating G A / G B from Equations 15 and 16 and reducing, a quadratic equation can be derived in the form, Claoz
+ Cza, + cs = 0
(17)
1939).
Schuftan (to Linde Air Products Co.), Ibid., 2,144,692 (Jan. 24, 1939),
Seidell, "Solubilities of Organic and Inorganio Compounds", New York, D. Van Nostrand Co., Vol. I (1919), Vol. 11, 1928.
THE SYSTEM BENZENE-NITROGEN Liquid-Vapor Phase Equilibria at Elevated Pressures N A PREVIOUS paper a method and ap-
PHILIP MILLER' AND BARNETT F. DODGE
Yale University, paratus for the study of liquid-vapor phase equilibria in binary systems was described, and results were presented for the system benzene-carbon dioxide. As the second of a proposed series of such investigations, the liquid-vapor equilibrium compositions have been determined for the system benzenenitrogen. This system was selected for study because the data of Lewis and Luke (8) were available to provide a check on the experimental method, and because it seemed worth while to extend their data to higher pressures Lewis and Luke (8) measured the equilibrium vapor-phase compositions for the system benzene-nitrogen a t pressures of 75 and 98 atmospheres and temperatures ranging from 100' to 200" C. They used a dynamic method, bubbling nitrogen through benzene in a series of saturators. They also determined the liquid-phase composition at 100" C. for the two pressures independently with a bubble-point apparatus. The only other data for this system are those of Frolich, Tauch, Hogan, and Peer (S), who measured the solubility of nitrogen in benzene at 25" C. and pressures u p to 160 atmospheres. Their method consisted of shaking a steel bottle containing the two components in a thermostat to establish equilibrium, then withdrawing and analyzing a liquid sample. The experimental method used here was essentially similar to that employed by Wan and Dodge (It?) in studying the system benzene-carbon dioxide. Compressed nitrogen, after passing through a purification train, was bubbled through liquid benzene contained in a series of three pressure cylinders, two being presaturators, and the third an equilibrium bomb in which agitation was maintained. Bubbling was carried on for about 24 hours to 1 Present
address, Tennessee Valley Authority, Wilson Dam, Ala.
attain equilibrium, then samples of the liquid and gas phases New Haven, Conn. were taken and analyzed. The apparatus and method were similar in many respects to those used by Saddington and Krase (10) in their study of the water-nitrogen system a t 100-300 atmos heres and 50-250" C. The benzene used was Merck, c. P. ancfthiophene-free. It was further purified by freezing, distilling the solid portion over phosphorus pentoxide, and collecting the fraction boiling between 79.9" and 80 1" C. for use. Compressed commercial nitrogen in cylinders was used.
Establishment of Equilibrium The equilibrium apparatus has already been described (12). Figure 1 is a diagram of the apparatus after some changes were made to adapt i t for use a t higher temperatures. The constant-temperature oil baths, R and S,were reconstructed and lagged with magnesia. All pressure tubing not immersed in the baths, from cylinder E onward, was heated to approximately 300" C. with resistance wire wrapped around it. Entrainment trap L , packed with copper gauze, was inserted, and a resistance coil was installed to heat expansion valve 10. At the beginning of a series of determinations a t a given temperature, about 100 cc. of benzene were introduced into each of the saturators through the liquid sampling line at the bottom. This amount half-filled the bomb, and was usually about half-depleted at the end of the series, when it was renewed. I n general, equilibrium was approached from the direction of supersaturation in both phases-in the liquid phase by making successive runs at decreasing pressure (hence at decreasing solubility), and in the gas phase by maintaining the first presaturator 5" to 10" C. above the equilibrium temperature.
