INDUSTRIAL AND ENGINEERING CHEMISTRY
1324
(12) Jones, G. W., and Meighan, M. H., J. IND.E m . CHEM.,11, 311-16 (1919). (13) Merry, E. W., J.Intern. SOC.Leather Trades' Chem., 16, 239-53, 358-77,489-504 (1932). (14) Parr, S. W., and Straub, F. G., Univ. 111. Eng. Expt. Sta., Bull. 177,45-6 (1928); Straub, F. G., Ibid., 216, 79-81 (1930).
Vol. 26, No. 12
(15) Partridge, E. P., Univ. Mich., Eng. ResearchBuZZ. 15 (1930). (16) Wherry, E. T., and Chiles, G. S., Eng Mag., 45, 518-23 (1913).
RECEIVED J u n e 29, 1934. Presented before the Division of Water, Sewage, a n d Sanitation Chemistry at the 88th Meeting of the American Chemical Society, Cleveland, Ohio, September 10 t o 14, 1934.
Rate of Solution of Methane in Quiescent Liquid Hydrocarbons. I1 E. S. HILLAND W. N. LACEY,California Institute of Technology, Pasadena, Calif. INCE its first commercial success in 1912, repressuring of oil formations with natural gas has been considered
S
and used. Repressuring has been done both for the purpose of recovering more oil and for the storage of gas. There has been a need for information on the rate at which the gas dissolves in the oil in the formation and on the quantity of the gas that will dissolve. Before the rate of solution of a natural gas can be predicted from its analysis, it is necessary to study the rate of solution of the pure constituents. The principal constituent of most natural gases is methane, which has therefore been investigated first. It has been shown by Pomeroy and co-workers in the first paper of this series ( I ) that the Fick proposition integrated for the case of a cylinder of infinite length gives a satisfactory means of calculating the diffusion constant from the data on the rate of solution of methane obtained with the apparatus described in the same article. The integrated equation is:
Q
where Q A C,
= = =
t
=
D
=
any deviation from the original assumption beyond the experimental error. Two determinations of a preliminary character were made a t 2000 pounds per square inch (136 atmospheres), with the apparatus which has been described ( 2 ) for phase-equilibrium studies, showing a small but hardly significant increase in the diffusion constant for the rate of solution of methane in kerosene as compared to determinations made a t lower pressures. Hence it is concluded that these assumptions are valid for somewhat higher pressures than those used in the determination.
MATERIALS CSED The methane used in the determinations made at 113' and 140" F. (45' and 60" C.) was prepared from natural gas in the same way as that which had been used formerly (1) The
4;
~-
I -
2C,A quant,ity of gas which has passed a given point area at right angles t o the direction of flow final equilibrium concn. of gas in s o h . time diffusion constant =
VISCOSITV
O F ORIGINAL O I L IN CENTIPOISES
OF SOLUBILITY OF METHANE FIGURE 2. RELATION TO VISCOSITY OF OIL
FIGURE1. RELATIONOF SOLUBILITYOF METHANE TO SPECIFICGRAVITY OF OIL
Certain assumptions were made in obtaining this solution of the Fick proposition which limited its application. It was verified ( I ) that these assumptions were valid for the rate of solution of methane for partial pressures up to 300 pounds per square inch (20.4 atmospheres). Nothing in the additional data obtained for methane and here reported indicates
purity was not as good as desired, and a better method of preparation was devised. The treatment of the natural gas with activated charcoal was improved so that the ethane content of the gas was reduced to 0.36 per cent. After treatment with charcoal, the methane was passed through a steel bomb surrounded by liquid air. The pressure inside this bomb was maintained at 40 mm. of mercury. At this temperature and pressure most of the methane dropped out of the gas stream as a solid, The remaining nitrogen and similar gases were constantly removed by a vacuum pump connected to the bomb. The vapor pressure of solid methane is about 20 mm. a t liquid air temperatures, depending somewhat on the composition of the cooling medium. By this method, in which the methane is condensed as a solid from a gas space
December, 1934
1325
L N D U S T R I A L 4 N D E N G I N E E R I N G CHEMlS'l'ttY
TABLE I. DATAON HYDROCARBONS MOLE M O L . WT. OF
SP. GR. GRAVITY VISCOSITY LIQCID
NO.
4 5 6
7
6
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
Isopentane Pentane n-Hexane Cyclohexane Benzene n-Hiptine 2,2,4-Trimethylpentane Kerosene Spray oil Petrolatum Rosecrans. Calif. Lima Ohio Bartlksville, Okla. Sugarland, Texas Ventura, Calif. Smackover. Ark Bradford, Pa. Bradford. P a .
0,6098 0 6164 0.6526 0.7689 0.8681 0.6751 0.6841 0.7944 0.8617 0.8771 0.8274 0.8238 0.8515 0.8829 0.8710 0.9241 0.793 0.783
0.777
0.773 0.818 0.808 0.8519 0.8418 0.7837 0,7730
A . P . I. Cenll'poises 0.208 95.0 0.210 92.8 0,307 80.8 0 797 49.8 0 561 29.6 0.368 74.0 0.448 71.4 1.417 44.2 13.45 30.7 99.0 28.0 2.75 37.4 4.68 38.1 7.06 32.7 11.28 26.9 12.56 29.1 76.8 20.0 2.65 44.5 I .99 1.72 .. 1.56 2.05 37:4 I.. 60 7.85 30:7 5.09 1.245 44:2 0.897
FHACTION
TEMP. O F.
72.1 72.1 86.1 84.1 78.1 100.1 114.1 167 287 449 181 228 232 244 236 322 186
...
...
...
181
...
287 Spray oil ... Spray oil 167 Kerosene Kerosene 5 G a s and oil volumes measured a t 60' F. a n d 30 inches of meraury. b Gas volume measured a t 60' F. and 30 inches of mercury. 6 Extrapolated from Figure 3.
..
...
in Thich the nitrogen pressure is very small, the degree of separation should be good. The solid methane mas then alloffed to rise in temperature and vaporize into a storage bomb. 'C'nfortunately the analysis of this purified methane for the small amount of nitrogen present has not been satisfactorily completed. However, all indications pointed t o the conclusion that the nitrogen content had been reduced to less than 0.5 per cent. This methane which was used in the 86" F. (30" C.) determinations was superior in purity to that used in the determinations made at the higher temperatures.
86 86 86 86 86 86 86 86 86
86 86 86
86 86 86 86 86
113.0 129.2 140.0 113 140 113 140 113 140
SO
cs b
24.38 23.32 19.58 14.91 11.15 17.19 17.32 10.86 7.79 6.78 10.05 9.23 8.60 8.07 8.36 6.65 10.11 9.57 8.73
22.45 21.62 18.38 14.25 1 0 . 78 16.26 16.37 10.49 7.59 6.62 9.74 8.95 8.37 7.86 8.14 6.51 9.75 9.15 8.28 8.22 8.43 7.95
8.67
8.79 8.40 7.11 6.81 10.08 0.51
6.87
6.51 9.60 8.94
OF
CH4 IN
INCREASE VOL. OF
IN
L I Q ~ I D LIQUID
% 0.1068
0.1016
0.1098 0.0638 0,0403 0.0960 0.1074 0.09% 0.0981 0.1152 0.0830 0.0966 0.0895 0,0856 0.0868
0,0886 0.0883 0.0846 O,Oi79 0.0777 O.Oi34 0,0703 0,0895 0.0861 0.0800 0.0760
6.15 5.43 4.45 3.14 2.26 3.74 3.83 2.15 1.46 1.23C 1.91 1.77 1.60 1.5lC 1.5ic 1.2OC 2.11 1.84 1.89 1.68 1.73 1.74 1.41 1.37 1.96 1.91
DIFFUSION CONSTANT Sp. /t./hr. Sq. cm./sec. 51.5 13.3 13.2 51.2 39.4 10.2 18.2 4.70 21.2 5.47 32.4 8.36 28.0 7.22 1;,9 3.33 3.80 0.98 1.47 0.38 2.72 10.5 2.16 8.4 1.71 6 .6 4.3 1.11 5.; 1.47 0.71 2.8 11.7 3.03 14.7 3.79 17.6 4.55 18.7 4.83 3.88 15.0 19.7 5.07 6.24 1.61 8.22 2.12 17.4 4.50 5.38 20.9
The physical constants of these materials are given in Table I. Specific gravities are a t the temperature of the determination referred to mater a t maximum density (39.1' F. or 3.95" C,). The A. P. I. gravities are corrected to 60' F. (15.5' C.), The absolute viscosity is given in centipoises a t the temperature of the determination.
A~PARATUS The general method of making the rate-of-solution determinations has been described in the earlier article ( I ) , but a number of changes have been made to improve the accuracy of the results: The bronze-tube reservoir gage was replaced with a gage equipped with a stainless steel tube having a smaller volume. The difference between successive calibrations of this gage at considerable time intervals did not exceed 0.5 per cent. A finelined, uniformly graduated scale was used on this gage instead of the original scale. The test gage used t o measure the pressure of the determinations was equipped with a 1OX magnifying lens. Suitable connections were made t o the apparatus so that this gage could be calibrated at the end of each run t o 0.1 pound per square inch. 00026,
FIGURE 3.
~ I V C R E A S E IN
VOLUMEOF LIQUIDD ~ J E TO O F METH.4NE
SOLUTION
The oils used for these determinations consisted of pure individual compounds, refined oils, and crudes (Table I). The isopentane analysis (in per cent) was: 0.20 n-butane, 99.73 isopentane, and 0.07 n-pentane. The pentane analysis FIGURE4. RELATIONBETWEEN INCREASE IN was: 0.7 isopentane and 99.3 pentane. The isopentane and LIQGIDVOLUMEPER USIT OF G.4s DISSOLVED US NU pentane were obtained from the Philgas Company. %-HexTHE SOLUBILITY ane, cyclohexane, benzene, n-heptane, and 2,2,4-trimethylThe glass apparatus used t o determine the increase in volume pentane Tere obtained from the Eastman Kodak Company. of the liquid phase was carefully annealed in a furnace for 8 hours The purity of these oils was satisfactory, as indicated by their and used up to. higher pressures-namely, over 300 pounds per narrow boiling point ranges of one degree or less and their square inch (20.4 atmospheres). The absorpt.ion cell was removed from its former rigid support density, except in the case of hexane which contained a small and placed in a weighted, triangular support mounted on rubber amount of material with a somewhat higher boiling point. stoppers, four high, with suitable leveling devices. This proved The crude oils are representative samples from the respective t o be a sat.isfactory means of eliminating vibrations from out,side sources. fields.
1326
IXDUSTRIAL AND ENGIYEERING CHEMISTRY
A new cell was constructed for determining the rates of solution in the crudes and the more viscous refined oils. The area was approximately three times that of the cell used for the light,er oils and described by Pomeroy (1). The depth of the new cell was 2.500 inches (6.350 cm.) and the diameter 2.492 inches (6.330 cm.). This cell, with a larger area,, required proportionately larger amount,s of gas for determining low rates of solution nith a resulting increase in the accuracy of their determination with the same reservoir as before. Determinations
I Q2J O
o,M
o.!o SPECIFIC G R A V I T Y
,do
1, J0
J
OF O R I G I N A L O I L
FIGURE 5 . EFFECT OF SOLVENT UPON APPARENT SPECIFIC GRAVITY OF DISSOLVED METHANE of t>herat>eof solution of methane in the same oil at the same temperature and pressure made in the two different cells gave the same diffusion constant. The viscosity of the oils was measured with an Ostwald type viscometer. A fused quartz instrument with a water t,ime of 580 seconds at 86" F. (30" C.) was calibrated with water and used for the less viscous oils, while a similar instrument of Pyrex glass, with a larger capillary tube, was used for the more viscous materials. The viscositv measurements are considered reliable to 0.5 per cent. The average molecular weights of the crude oils, kerosene, spray oil, and petrolatum were determined by the method depending upon the freezfng point lowering of benzene.
Vol. 26, No. 12
cosity of the original oil. A somewhat better correlation of the crude oils is obtained than with the specific gravity plot. When methane dissolved in the oils used in these measurements, the volume of oil was increased as shown in Figure 3, in which this increase has been plotted for all the oils a t 86" F. and 300 pounds per square inch as a function of the volume of gas dissolved in a unit volume of solution a t equilibrium a t this temperature and pressure. The increases in volume for petrolatum, and the Sugarland, Ventura, and Smackover crude oils could not he run satisfactorily in the glass apparatus because of their high viscosity. Values for these oils were taken from Figure 3. From these data, the increase in volume of the liquid per unit volume of gas dissolved, e, has been calculated and is shown in Figure 4. This value of e for a given oil is independent of the pressure, over the range in which it has been studied. The accuracy of measurement was not sufficient to detect any small changes due to compressibility. The apparent specific gravity of the dissolved gas shown in Figure 5 was also calculated from the data on the increase in volume of the liquid shown in Figure 3 and plotted as a function of the specific gravity of the original oil. The apparent specific gravity of the dissolved gas is defined as the weight of dissolved gas per unit of volume increase of the resulting solution divided by the weight of the same unit volume of water a t its maximum density. Benzene shows the greatest divergence from a line through the points. The primary object of this work was the determination and correlation of the diffusion constants. These have been calculated from the experimental data for the rate of solution
EXPERIMENTAL RESULTS The rates of solution of methane in seventeen oils were measured a t 86" F. (30" C.) and in four of these oils a t 113' to 140" F. Temperatures were controlled t o within 0.1 " F. The data from these determinations are given in Table I. The experimental plots were similar in character to those previously shown (1) and are, therefore, not reproduced here. Only the final values of the diffusion constant, the saturation values, and the expansion of the liquid phase are reported. All of the measurements were made a t partial pressures within a few pounds of 300 pounds per square inch and corrected to this pressure, which was the highest that could be used satisfactorily in the apparatus. Searly half of the determinations reported are the average of two or more runs. The final equilibrium concentration, or solubility 005 01 0.5 5 IO 50 value, has been reported as volume of gas per unit roliime V I SC 0 SI T Y IN C L 4!t T I PO I5 E S/( t - 6O)m of initial oil is),as volume of gas per unit volume of soluFIGURE6. RELlTION BETWEEN DIFFUSIONCONSTANT AND A N EMPIRICAL FUNCTION OF \rIsCOSITY AND TEMPERITURE tion ( C s ) ,and as mole fraction of methane in the liquid Bhase. The solubilitv value., C,., which must be used in the equation for calculating the quantity of gas diffusing in of methane. Various correlation curves can be drawn for a given time, is the final equilibrium volume of gas dissolved the diffusion constants in the several oils. ,4n investigation in a unit volume of solution. All gas measurements have been of the literature has failed t o reveal any laws that can be used to explain satisfactorily and predict the diffusion constants calculated to 60" F.and 30 inches of mercury. A plot of the solubility values in cubic feet of gas per culic from this data. A plot as a function of the specific gravity foot of solution per 100 pounds per square inch a t 86" F. as a of the oil left benzene far from a line near the points for the function of the specific gravity of the original oil is given in other oils. When the diffusion constant is shown on a logFigure 1 and shows a fair correlation, with the exception of log plot as a function of the viscosity of the original oil, the benzene and cyclohexane. Each point on this curve is for a points lie near a straight line. However, when the temperadifferent oil, the numbers corresponding to those in Table I. ture is increased, a line through the constants for a given oil Although this correlation is not perfect, it furnishes a simple a t different temperatures is steeper than it is for several oils a t means of approximating the C, value for a crude from its the same temperature. In order to take care of the effect of temperature on the diffusion constant, the temperature was specific gravity. I n Figure 2 the solubilities of methane in the various oils introduced into an empirical relation between the diffusion have been plotted on a log-log scale as a function of the vis- constant and the viscosity, as follows:
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 ) .
