December, 1934
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.00011 - 60)0.310.62 where D = diffusion constant, sq. ft./hr, t = temp., ” F. 7 = abs. viscosity of original oil, in centipoises, at temp. at which diffusion is taking place
D =
[v/(t
This relation is shown graphically in Figure 6. It is a t best only a close empirical approximation, but it covers a wide variety of petroleum oils and can be used to predict the value of D from the viscosity and the temperature. The location of the point for Smackover crude above the loner end of the line is probably not due to experimental error but rather to the fact that there is an additional variable not taken into account by the viscosity-temperature relation I n order to check the correctness of the solubility results, B. H. Sage made a determination with the same methane and pentane at 86 O F. and 300 pounds per square inch in the variable-volume cell described by Sage, Schaafsma, and Lacey ( 3 ) . His solubility value was 2 per cent higher than that obtained for the solubility of methane in pentane in the rateof-solution apparatus. The check is considered to be good because the methods are quite different, and it is within the experimental error. This agreement shows that the method of obtaining the gas volume over the initial oil a t the pressure of the determination, by extrapolating the curves for the square root of the time us. the volume of gas admitted to the cell back to zero time, is reliable. The diffusion constant for solution of methane in isopentane reported by Pomeroy and eo-workers (1) is 5 per cent higher than that rchported here. This value lies within the probable total error of the determination. The variation
1327
between check determinations with the same oil was less than 3 per cent. However, owing to impurities in the methane, the degree of reproducibility of many of the oil samples, and probable errors in the experimental measurements, the accuracy of the results is probably not better than 5 per cent. The determinations made a t 86” F. are considerably more reliable than those made a t 113” or 140” F. owing to improvements made in the apparatus and the reduction of the amount of impurities in the methane. ACKNOWLEDGMENT This investigation lvas carried out with funds provided by the American Petroleum Institute as part of its Research Project 37. The following agencies kindly furnished the authors with samples of oil used: Union Oil Company, Ohio Oil Company, Bartlesville Experiment Station of the U. S. Bureau of Mines, Humble Oil and Refining Company, Shell Oil Company, Standard Oil Company of Louisiana, and Forest Oil Company. The assistance of B. H. Sage in the preparation of the methane and in measuring the solubility of methane in isopentane is deeply appreciated. LITERATURE CITED (1) Pomeroy, R. D., Lacey, W. K., Scudder, N. F., and Stapp, F. P., IND. EHG.CHEY.,25, 1014 (1933). (2) Sage, B. H., and Lacey, W. S . ,Ibid., 26, 103 (1934). (3) Sage, B. H., Schaafsma, J. G., and Lacey, W. N., Ibid., 26, 1218 (1934).
RECEIVED August 28. 1934
Rate of Solution of Propane in Quiescent Liquid Hydrocarbons E. S. HILLAND W. N. LACEY,California Institute of Technology, Pasadena, Calif.
I
S F O R b I l T I O S on the rate of solution of natural gases in petroleum oil> has become important in recent years in connection \T ith the procesb of “represuring” by returning hydrocarbon gases t o partly depleted oil formations. Aside from furiiiahing energy underground, thi> proceqs offers the possibility of favorably affecting the properties of the oil by solution of gas therein. Since these latter advantages are obtained only to the extent to nhich solution takes place, the rate of qolution in a quiescent body of oil with a limited surface eupoyed to the gas is of interest in the evaluation of possible re-ults from such a process. h knonledge of the behavior of natural gases of all composition> likely to be found can probably be obtained b e d by determining first the behavior of the individual constituents. Such information for methane has already been presented by the authors ( I ) , The present experiments relate t o propane, which, although present in smaller amounts in natural gases, has a much greater solubility in petroleum oils than methane under the same conditions. The mechanism of the solution of methane in hydrocarbon oils was inveqtigated by Pomeroy and eo-workers ( 2 ) . The use of Fick’s proposition for diffuqion was found to be satisfactory and was integrated for the case of a cylinder of liquid of infinite length, and for that of a cylinder of finite length. The experimental results demonstrated that the diffusion constant could be calculated for methane from the experi-
mental data obtained with the apparatus described ( 2 ) , by use of the integrated equation for the case of a cylinder of infinite length. However, in obtaining thiq ~olutionof the Fick propoaition, certain acqumptionq were made (u) In the case of a gas diffusing into a liquid, the layer irninediately under the wrface is a h a y s saturated; ( b ) the diffudon constant does not change with the concentration; ic) the gas mows through the liquid only by diffusion. Assumption n is still concidered t o be true for propane for the same reaFons as those advanced by Ponieroy ( J ) , which hare been further verified by the data obtained with propane.
~IATERIALS ANI APPARATIX The propane used for thew measurementi \vas prepared by distillation of commercial propane in a gla- .till with a column 10 feet long. The column was filled with glasb rings. Solid carbon dioxide was used as the cooling medium to keep the pressures low enough t o be used in the glass apparatus. The final condenser was a steel bomb which was warmed after each filling, and the propane transferred to a storage tank. A fractionation analysis of the product showed 99.2 per cent propane and 0.8 per cent isobutane. The properties of the refined oils, in which the measurements of the rate of solution of propane were made, are given in Table I. The same two oil samples are included in the liquids used for the measurements with methane ( I ) .
INDUSTRIAL AND ENGINEERING
1328
TABLEI. PROPERTIES OF REFINED OILS SP. G ~ . ( 1 ' / 3 9 . 1 ~ F . ) 86'F. 1130F. 140'F. Kerosene 0 . 7 9 4 4 0 . 7 8 3 7 0 . 7 7 3 0 Spray oil 0.8617 0 . 8 5 1 9 0 . 8 4 1 8
OIL
Av. A. P. I. MOL. VISCOSITY (60°/600F.) WT. (CentiDoises) . . 86.F. 113'F. 140'F. 44.2 167 1 . 4 1 7 1.245 0 . 8 9 7 . 30.7 287 1 3 . 4 5 7 . 8 5 5 . 0 9
The same apparatus was used for these measurements as for those on the rate of solution of methane, with some necessary changes. The reservoir gage tube, with a pressure range of 1000 pounds per square inch, n-as replaced by another stainless-steel gage tube having a range of 300 pounds per square inch, in order to give a larger deflection without approaching too near the vapor pressure of liquid propane. ATMOSPHERES
I
2
4
I
0
8
IO
I2
I
14
CHEMISTRY
Vol. 26, No. 12
namely, 86.0" F. (30" C.), 113.0" F. (45" C.), and 140.0' F. (60" C.). These measurements required, in addition, the determination of the increase in the volume of the liquid, and the final amount of gas dissolved in the oil a t equilibrium. The expansion of the liquid volume due to the solution of propane is illustrated in Figures 1 and 2 for kerosene and spray oil as a function of the partial pressure of the propane in the gas phase. These curves show a marked increase in the volumes of the solutions per pound increase in propane partial pressure, being much larger than for the solution of methane a t similar pressures and temperatures ( I ) . Since these determinations were made a t temperatures below the critical temperature of propane, the percentage increase in volume of the liquid would be infinite a t the vapor pressure of liquid propane, where propane would condense in the cell whether any other substance was present or not. From these data and the solubility values, the values of the increase in volume of the liquid per unit volume of gas dissolved were calculated and are shown in Table 11. Again these are larger than those found for methane. Similarly, the apparent specific gravity of the dissolved propane as shown in the tables is greater than for methane, as would be expected. The apparent specific gravity of the dissolved propane is defined as the weight of dissolved gas per unit of volume increase of the resulting solution, divided by the weight of the same volume of water a t its maximum density. The apparent specific gravity of the dissolved propane is higher than the saturated liquid propane specific gravity,which it approaches as the pressure of the propane approaches the vapor pressure of liquid propane. 2
1
I
ATHOSPHCRES 4
e
10
I2
14
I
I
Y
I J
so
Q
FIGURE 1. REL.4TIVE VOLUMES OF SATURATED SOLUTIONS O F PROPANE IN KEROSENE
5
40
P
- 30 Y
In making these measurements, it was found necessary to remove the air from the gas space over the oil and from the oil itself before beginning a determination, after a sample was placed in the absorption cell. At the higher pressures near the vapor pressure of liquid propane for the temperature of the determination, the rate of solution was very rapid. This involved the measurement of gas a t a more rapid rate than could be accurately measured with the reservoir. Consequently, a cylindrical metal slug was placed in the absorption cell extending from the bottom up into the gas space in order to reduce the area of the exposed liquid surface. The area of cell B a t 86" F. was 1.540 square inches (9.935 sq. cm.), the area with B, slug was 1.533 square inches (9.891 sq. cm.), and the area with Ri slug was 0.764 square inch (4.927 sq. cm.). The increase in volume of the liquid phase due to the solution of propane was measured in the same glass apparatus as was used for methane. The air was removed from the gas space and from the oil in these measurements also. The average molecular weights of the oils were determined by the method depending on the freezing point lowering of benzene. The viscosities of the oils were measured with an Ostwald type of viscometer with an accuracy of 0.5 per cent. EXPERIMENTAL RESULTS
Measurements were made on the rate of solution of propane in the kerosene and the spray oil described above at pressures up to nearly 67 per cent of the vapor pressure of liquid propane a t the temperature of the determinations;
2
:20 I
+
6 IO Y
25
LO
71
P A ~ T I A LPRESSURE OF
40 125 I50 175 ZW PROPANE I N WUHOS PCR SQUARE INCH
VOLUMESOF SATURATED FIGURE 2. RELATIVE
.
SOLUTIONS OF P R O P A N E IN SPRAY OIL
The volume of propane dissolved in the oils a t equilibrium has been shown in Table I1 as S,the volume of gas per unit volume of original oil; as C,, the volume of gas per unit volume of saturated solution; and as mole fraction of propane in the liquid. A satisfactory correlation is shown in Figure 3 where all the data for the solubility values of propane that were measured have been plotted for the mole fraction of propane in the liquid a t equilibrium as a function of the percentage of the vapor pressure of saturated liquid propane. Values for the vapor pressure of pure propane and for the compressibility of propane gas can be obtained from data by Sage and eo-workers (4). The values for both of the oils studied at the three temperatures lie on a nearly straight line. This line must, of course, pass through zero and the point corresponding to vapor pressure = 100 per cent and mole fraction of propane = 1. From this curve the equilibrium concentration, or solubility value, of propane in a fair range of oils can be predicted safely a t temperatures not too close to the critical temperature of propane. At the same temperature and partial pressure, propane is many times more soluble than methane in the same oil.
I N D U ST R I h L A N D E N G I N E E R I K G C H E M I ST R Y
December. 1934
When propane dissolves in an oil, there is, in addition to a large increase in volume of the liquid, a considerable decrease in the specific gravity and a large decrease in the viscosity of the solution as compared to the original oil. This is shown in Figure 4 for saturated solutions of propane in spray oil a t 86" F. The viscosity measurements were made in the apparatus described by Sage (3). The relative decrease in the viscosity is considerably greater than for H solution of dry natural gas in Santa Fe Springs crude oil (3) up to 2500 pounds per square inch. The plots of the experimental data for the determinations of the rate of solution have not been reproduced here, except representative examples for one of the "split runs," because they would not give any more information than is given by the column of slope5, m, in Table 11. These values of the slopes of the experimental curves for the volume of gas admitted to the cell 11s. the square root of the time in minutes have been corrected to 30 inches of mercury and 60' F., in the same units as the measurement of the area of the exposed oil surface. The values of m have been corrected for the increase in volume of the liquid as described by Pomeroy (a),but no correction has been made for any effect on the mechanism of the solution process due to the increase in volume. After considering the large effects which propane has on the properties of the original oil, it is well to reconiider assumptions b and c made in the integration of the Fick proposition. Assumption b was that the diffwion constant was independent of the concentration. In Figure 5 the data for a "split run," made in three parts a t 86" F. dissolving propane gas in kerosene, are given. This curve shows an experimental plot of the volume of gas admitted to the cell as a function of the square root of the time. The lowest line, curve 1, was obtained with a partial preisure of propane of 31.4 pounds per square inch. The oil was next saturated a t this partial pressure, and then the partial pressure was raised 30.3 pounds to a total of 61.7 pounds per square inch where
1329
the rate line, curve 2, was obtained. After saturating a t 61.7 pounds, the partial pressure was again raised 29.2 pounds to a total of 90.9 pounds per square inch, and curve 3 was determined. If the rate of solution were independent of the initial concentration of propane, these lines would all have nearly the same slope because the pressure increments are nearly the same in each case. Instead, the slope of the last
FIGURE 3.
SOLUBILITY OF PROPAIVE GASI N THE Two OILS
is 2.5 times that of the first. The solubility per pound increment in partial pressure also increases with the concentration of the propane. All of these determinations have been made below the critical temperature of propane so that, if the partial pressure were high enough, the gas would condense in the cell without any other liquid being present. Hence, if the partial pressure of propane became equal to the vapor pressure of pure propane a t the temperature of the determination, the process would change from one of simple diffusion into
TABLE11. SUMMARY OF EXPERIMENTAL RESULTS AppAnnNr
% OF PRESSURE
VAPOR PRESSCRE
Lb./sq. in. Atm.
S P . GR. O F DIS-
INCREASE 1 s
TEMP. C E L L O
MOLE
VOL.
FR.ACTION
SOLVED
GAS
m
sq. ft./
%
F.
k X 104 hr.
DIFFUBIOK CONSTANT D X 105 Sq. cm./ see.
sq. R./
hr.
PROPASE I S KEROSENE
30.5 31.4 45.2 61.0 31.4 61.7 AP = 30.3 61.7 104.5 31.4 61.7 AP 30.3 90.9 A P = 29.2 26.1 76.2 149.3 30.8 60.8 121.3 121.3 200.9
-
2.08 2.14 3.08 4.15 2.14 4.20 2.06 4.20 7.11 2.14 4.20 2.06 6.19 1.98 1.78 5.19 10.16 2.10 4.14 8.25 8.25 13.67
19.4 19.9 28.7 38.7 19.9 39.2 39:2 66.4 19.94 39.2
...
57.7 11.7 34.1 66.9 10.1 19.8 39.6 39.6 65.6
86 86 86 86 86 86 86 86 86 86 86 86 86 86 113 113 113 140 140 140 140 140
B
n
B3
B
B B B B8
B1
n. B8
B.
BS
n
Bs
Bs BI B,3
Bs BI
Bs B1
8.80 9.15 15.50 24.9 9.15 25.3 16.17 25.3 78.0 9.15 25.6 15.07 55.0 23.4 5.82 22.8 93.2 5.30 11.68 29.8 29.8 90.9
0.00308 0.00300 0.00314 0.00331 0,00299
27.49 29.25 47.49 72.32 29.40
0.'00325 0.00337 0.00296 0.00346
74.94 222.24 29.78
59.14 123.43 26.99
41.82
36.94
63.85 17.25 63.89 243.56 14.36 31.95 84.66 82.64 225.86
40.73 15.94 50.85 123.25 13.17 27.63 62.98 61.55 114.27
....
0.'00352
....
0.00328 0.00347 0.00372 0,00363 0.00359 0.00346 0.00354 0.00396
....
....
....
....
24.98 36.51 40.66 57.27 26.63
....
....
....
....
0.1967 0.2068 0.2973 0.3919 0.2076
....
.,..
0.4004 0.6645 0.2098
.... ....
0.583 0.598 0.566 0.543 0.600
...
0:552 0.532 0,605 0.519
.... ....
0.509
0.1335 0.3632 0.6850 0.1072 0,2223 0.4309 0.4251 0.6690
0.548 0.518 0.482 0.491 0.500 0.519 0.506 0.453
,..
8.94 9.90 16.86 26.00 10.08
Ij:56 26.50 35.18 10.05 15:71 25:01 6.62 25.07 40.06 6.16 14.05 37.21 86.09 41.48
6.59 7.17 8.91 10.58 7.36 12.25
1.68 1.81 2.25 2.64 1.88 3.10
6.52 7.03 8.73 10.24 7.27 12.00
l0,'42 16.97 7.21 9.96
3.95 1.84 2.52
2 :io
1o:i9 15.32 7.12 9.76
19:53
4 :s9
..
18:95
8.95 10.59 22.05 11.32 13.37 18.06 17.79 27.47
2.29 3.16 5.03 2.90 3.40 4.49 4.42 6.29
8.88 12.23 19.50 11.25 13.17 17.38 17.12 24.37
2.09 3.76 3.68 6.12 3.14 3.10 5.54 7.13 4.07 4.19 6.20 10.S5
0,53 0.95 0.93 1.48 0.81 0.79 1.42 1.75 1.05 1.08 1.56 2.61
2.07 3.68 3.60 5.75 3.12 3.08 5.49 6.78 4.05 4.17 6.05 10.12
...
...
P R O P A N E I N SPRAY O I L
19.9 86 B 31.3 2.13 6.68 0.00308 4.21 39.2 61.8 86 B 17.03 39.2 86 B 17.06 61.9 4.21 0:00341 104.7 1.12 66.5 86 Bs 47.8 0.00334 0.00333 26.5 1.80 11.9 113 BB 4.12 0.00336 26.4 1.80 11.8 11:s n 4.10 43.0 95.9 6.52 113 B 21.6 0,00858 58.9 113 131.9 8.95 B 38.8 0.00351 10.6 140 0.00355 82.6 2.22 B 3.90 33.5 2.28 10.9 140 ns 4.00 0.00775 37 7 115.6 7.87 140 Ba 18.6 0.00353 66.0 203.4 13.77 140 BB 53.4 0 00363 Gas a n d oil volumes measured at 60' F. a n d 30 inches of mercury. b Gas volume measured a t 60' F . a n d 30 inches of mercury.
20.80
19.28
0.2271
0.583
48.08 136.41 12.04 11.86 58.70 107.54 10.80 10.50 51.85 144.50
40.62 92.01 11.30 11.13 47.18 75.72 10.04 9.75 42.23 91.00
0.4045 0.6601 0.1451 0.1434 0.4532 0,602Q 0.1322 0.1292 0.4227 0.6711
0 : 5if3
....
....
....
0.537 0.538 0.534 0.501 0.511 0.505 0.478 0,508 0.495
3.90 10.96 10.86
31.63 2.78 2.74 15.49 28.25 2.83 2.78 14.61 41.67
INDUSTRIAL AND ENGIKEERING CHEMISTRY
1330
Vol. 26, Uo. 12
amount of ga.- di>*olving when there nab no expansion and when there was expansion gave the amount of gas dissolving due to the expansion of the liquid. The additional amount dissolving due to the expansion has been plotted as a function of the expansion in Figure 6, ildditional points were not considered necessary because the curve was practically a straight line, and the amount of solution due to an expansion of the liquid of 100 per cent was only about twice the error of the experimental determinations of the rate of solution. The deviation due to the small error in this assumption ( c ) does not explain the large variation in the values of the diffusion constant. However, correction of the values of the apparent diffusion constant for the effect of expansion was made by the aid of the easily derived relation:
D = K(l - 8)' = diffusion constant corrected for expansion K = apparent or uncorrected diffusion constant 6 = fraction of gas dissolving on account of expansion,
where D
obtained from Figure 6
I
1 60
I 80
I
I
I n Figure 7 the corrected values of D have been plotted as a function of the C, values. The points lie on straight lines for FIGURE 4. VARIATION IN PROPERTIES OF each oil a t each temperature, but the diffusion constant varies SPRAYOIL DUE TO DISSOLVED PROPANE greatly with saturation concentration which is closely related the liquid to one of condensation of the gas, followed by diffu- to the changes in the character of the solution as diffusion prosion of liquid propane into the heavier oil from a layer of ceeds. This indicates that assumption 6 is invalid for the case liquid propane. I n this latter case the rate of condensation of very soluble gasef, except a t very low partial pressures. w o u l d b e independent of The linear i n c r e a s e of D the diffusion process. with solubility holds u p to Assumption c was that the solubilities correspondthe gas moved through the ing to 67 per cent of the 601 l i q u i d o n l y b y diffusion. v a p o r p r e s s u r e of p u r e Since the density of the soluliquid propane. It is possition was less than that of ble that there is very little the original oil as shown in deviation from this relation :,,, before the solubility correFigure 4 and the tempera: sponding to the vapor presture was kept accurately ; qure of pure liquid propane constant, the possibility of 5 300 transference of gas by coni i reached, becauze the gas 8 must diffuse into the liquid vection currents was elimi8oo hefore more can be absorbed nated. However, Figures 1 and 2 show a large increase a. long as the pressure is in the liquid volume when below the vapor pressure of the propane dissolves. I n pure liquid propane a t the the apparatus used for these particular temperature. measurements, the bottom 0 O S 20 Khen the lines of Figure 7 S 9 U A R E R O O T OF T H E T I M E MINUTES and sides of the oil column are extended to very small were fixed and this eXpanFIGCRE 5. E X P E R I M h \ T A L CURVESFOR DETER1lnIV6 R4TES VdUeS Of c,, corresponding OF SOLUTIOV sion necessarily took place in t o the solubility of propane an upward direction. After a t very small partial a run had progresfed for some time, the propane down in the pressure, the re,-ulting rxtrapolated values (Do) of D are a liquid had not had to pass through as long a liquid column as linear function of the temperature for each 011, as shown the propane just entering the liquid surface would have to pass in Figure 8. A correlation of the diffusion constants a t inthrough before it reached the same place. The result of this was that there was more gas in solution than there would have been if expansion had not occurred. The effect of the expansion tended to increase the rate of absorption of gas since the expansion produced an effect corresponding to movement of 2 5 the solute away from the surface. 2 8 4 An analysis of the problem of unsteady state diffusion into a medium which expanded as the concentration increased 2 3 was made by the integration of the Fick proposition for a slab of material with an expanding volume. The solution : 2 was not as simple as for the case without expansion and was 0 evaluated by the graphical integration of the area under the distribution curve of the concentration of gas diffusing below I the surface in the case of a cylinder of liquid of infinite depth, IO 20 30 40 50 (10 90 when there was 10 per cent expansion or increase in volume PER C E N T of the liquid phase, and Then there was 50 per cent expansion OF THE INCREASING VOLUMEOF FIGURE6. EFFECT LIQUIDUPON SOLUTIOV RATE of the liquid a t equilibrium. The difference between the 20
PARTIAL
PRESSURE
do
OF
100 PROPANL IN POUNDS PER SQUARE iNcn
N
$
1
40
1NCREASE
IN L Q U I D
10 VOLUME
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
December, 1934
1331
0
a
2s
w 20
w
< 15
z
