INDUSTRIAL AND ENGINEERING CHEMISTRY
316
glass plates, the sprayed portion was next covered, and then the adjoining section of each plate was sprayed with the same base lacquer blended with a slowdrying thinner. The photomicrographs of Figure 7 indicate not only the similarity of spraying technic, by comparing the films on the left of the dividing line in each photograph, but also the differences between the structures of films of fast-drying and slow-drying lacquers, by comparing the films on either side of the line. The ra*te of evaporation of the thinners used in these tests increases in the order of the numbers. I t is clear that in this
VOL. 28, NO. 3
case thinner with the smallest rate of evaporation has yielded the smoothest film.
Literature Cited (1) Eastlack, H. E., Paint Oil Chem. Rev., 97,No. 9,22 (1935). (2) Heen, de, J. chim. phys., 11, 205 (1913). (3) Hofmann, IND. ENG.CKEM.,24, 135 (1932). (4) Polcioh and Fritz, Brennstqff-Chem.,5, 371 (1924).
RECEIVED September 12, 1935. Presented before the Division of Paint and Varnish Chemistry at the 90th LMeetingof the American Chemical Society, San Francisco, Calif., August 19 to 23, 1935.
RATES OF SOLUTION OF GASES IN OILS‘
E. A. BERTRAM AND W. N. LACEY California Institute of Technology, Pasadena, Calif.
Rate of Solution of Methane in Oils Filling Spaces between Sand Grains
vv
HEN the pressure within a partially depleted petroleum formation has been increased by injection of natural gas to the gas dome above the oil, there is a tendency for some of the gas to dissolve in the oil, thus lowering its viscosity, surface tension, and density. These possible favorable changes resulting from “repressuring” create interest in the rate a t which the gas may be expected to dissolve under different prevailing conditions. Previous experiments (9,3, 6) have shown that the rate of solution of a gas such as methane or propane in a quiescent body of hydrocarbon oil is controlled primarily by the rate of diffusion of the dissolved gas from the gas-oil interface into the body of the liquid. The rate for such a process is given quantitatively, up to half-saturation, by the equation:
where Q = quantity of gas which has passed through surface C, = final equilibrium concentration of gas in solution A = area of liquid, at right angles t o direction of flow D = diffusion constant 1
=time
Methods of predicting, with sufficient\accuracy for engineering purposes, the values of D for methane (2) and for propane ( 3 )in various hydrocarbon oils have been proposed. Petroleum is found in the pore spaces or interstices between closely packed sand or rock particles. These particles are often siliceous but in some cases are calcareous. They are in many cases unconsolidated but in others are cemented firmly together to form hard rocklike masses. It is obvious from geometrical considerations that the rate of solution of a gas in a given oil will be 1 For other artidea on this general subject, Bee literature o i t a tiom S.S,B.
different when the oil is held within and completely fills the interstices of such a sand mass than when it is in the form of an oil body free of sand. The effective cross section will’ be less and the path of diffusion will be longer in carrying dissolved gas to the same depth below the gas-oil interface. It has been suggested ( I ) that the case of oil held in a sand may be complicated by surface effects due to the presence of large amounts of sand-oil interface which might assist the solution process. It was the purpose of the present investigation to develop methods of utilizing the constants for gases dissolving in oils determined by previous experiments, for the more practical case of oils held in unconsolidated silica sands. It was also desired to ascertain whether the effect of the presence of sand was merely geometrical in character.
A study of the rate of solution of gaseous methane in hydrocarbon oils entirely filling the interstices of closely packed silica sands has shown that the process is substantially the same as for the case of quiescent oils in the absence of sand. In the case with sands present, the over-all area at right angles to the path of diffusion must be multiplied by the fraction of the total volume of the sand body which is occupied by the oil and by a constant whose value is 0.82. The constancy of this factor has been experimentally verified only with unconsolidated sands and therefore throughout a relatively narrow range of porosities. Electrical conductance experiments upon copper sulfate solutions held in similar sand bodies gave practically the same value of the constant, indicating that the effect of the sand is only geometrical.
MARCH, 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
Materials The gas used in the studies here presented was methane. It was prepared from natural gas by the method described by Sage and co-workers (7) and consisted of a fractional liquefaction process followed by treatment with activated charcoal. The resulting material was then subjected to partial solidification a t low pressure to remove nitrogen and oxygen (6). The resulting methane contained less than 0.02 per cent of ethane and heavier hydrocarbons and probably not over 0.1 per cent of nitrogen and oxygen. The two oils studied were samples of kerosene and spray oil used by Hill and Lacey ( 2 ) . They were chosen in order to connect the present measurements directly with the results of the earlier work. These two oils had markedly different properties as shown by the values obtained by the earlier authors and reproduced in Table I. The diffusion constant for methane in kerosene was found to be 3.4 times that for methane in spray oil. The sand samples used were screened lots of naturally occurring silica sands. The 20-30 mesh sand (through a 20mesh screen but retained upon a 30-mesh screen) was standard Ottawa sand. The other samples were cuts from sands mined in Nevada. All the samples had densities within 1per cent of each other. TABLEI. PROPERTIES OF OILS Oil sample:
.
S gf. (86' F./39.loF.) &avity OA. P,.I.. (60' F.)
Viscoaith oentipoises AT. mol. 'weight
Kerosene 0.7944 44.2 1.42 167
Spray Oil
0.8617 30.7 13.46 287
Methods Measurements of rates of solution were made with the same apparatus and by substantially the same methods as were reported by Hill and Lacey ( 2 ) . The technic was complicated by the problem of obtaining a densely packed sand body whose interstices were completely filled with the oil samples and contained a minimum of trapped air bubbles. The best method of obtaining uniform and reproducible dense packing was as follows: Ten or fifteen milliliters of the oil were placed in the steel absorption-rate cell, and enough sand was added to take up almost all of the kerosene in its void spaces. The cell was then given a swirling motion t o release trapped air bubbles. Next the cell was vigorously tapped on a heavy wooden block for several minutes. Another similar addition of oil and sand was made, and the process continued until all of the sample of sand had been added. A level upper surface was obtained by placing the cell in a special wooden vise, which held it level, and then tapping the bottom of the cell. The fraction of the total volume of the sand mass which corresponded t o the void spaces between the grains was determined for each size range of sand in the following manner: A known weight of sand was packed into the cell with kerosene as described above, and the depth of the sand layer in the cell was meamred by placing a cylindrical steel slug, whose diameter was slightly less than that of the cell, on top of the sand. Since the total depth of the cell and the length of the slug were accurately known, measurement of the protruding height of the slug furnished the desired information. This measurement was made by taking the average of a number of readings of the height by means of a cathetometer, observing from different points around the cell. From the diameter of the cell, which had been machined accurately cylindrical, and the height of the sand the total volume was calculated. The volume of the sand grains alone was ascertained from weight of sand and its density as determined by the pycnometer method. The volume of voids was given by difference. The values used were in each case the average of several different measurements, the maximum deviation from the mean being in all cases less than 0.8 per cent. All other methods of packing and measurement which were tried proved t o be less reproducible than the one outlined.
317
In making solution rate determinations, 2 to 3 ml. more oil were used than was necessary to fill the void spaces of the sand. This precaution served to insure that the oil level did not drop below the top of the sand when subjected to the higher pressure of the methane gas. Any small bubbles of air entrapped during the packing process would shrink upon the increase of pressure to about 5 per cent of their earlier volume. More satisfactory experimental results were obtained when no wetted sand was exposed above the surface of the oil. The thin layer of oil above the sand level, together with the wetted interior surface of the bomb walls above the liquid level, produced more rapid solution rates during a few minutes a t the start of a run but these films soon became practically saturated and thereafter the rate of solution depended only on the rate of diffusion of dissolved gas through oil in the sand mass. These rapid earlier rates in no way interfered with later measurements. After the charge of sand and oil in the steel c d was prepared, the cell was closed and connected to the methane measuring and supply system. This system and the method of using it were the same, except for minor improvements, as were described by Hill and Lacey (2). In the runs with sand the air present above the oil was not evacuated from the cell because preliminary trials showed that this operation resulted in disturbing the sand packing to such an extent as to render results unreliable. It was therefore necessary to use the partial pressure of methane rather than the total pressure of gas in the cell for purposes of the calculations. I n all the determinations here reported, the partial pressure of methane was close to 300 pounds per square inch and the temperature was 86.0" F. (30" C.). The experimental runs were carried far enough to establish definitely the slope of the straightline obtained by plotting the amount of gas dissolved against the square root of the time. The runs were carried in most cases to approximately 40 per cent of saturation of the oil.
Experimental Results In order to be sure that materials and experimental technic were comparable to those used in the earlier work, runs were made using the kerosene and the spray oil without sand. In each case values of C. and of D were obtained which agreed with the values reported by Hill and Lacey (2) for 86" F. well within the experimental error. In the diffusion equation given, area A , in the case when no sand is present, is equal to the a.rea of the cell cross section. When sand is present, the mean effective liquid area through which diffusion takes place will be dependent upon the crosssectional area of the cell, upon the percentage of void spaces in the sand body, and upon the deviation of path around sand grains. In this case, A'=AVB where A = cross-sectional area of cell V = fraction voids in sand mass B = constant for conversion of mean horizontal liquid area to mean effective area for diffusion Substituting this expression for A in the diffusion equation, putting in m (corrected slope) for Q/2/
