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FORMULA FOR ACCURATE DETERMINATIONS.
The following data are given here in order to show the derivation of a formula for use in more accurately determining the flow of gas through a pipe than by means of the table given on page 38. According to the well-known formula,
Then when h is known the velocity of gas (in feet per second) is given by the formula,
Multiplying through by A,
h=velocity head in feet of gas.
W=weight of water in pounds per cubic inch.
h-velocity head in feet of gas.
g=acceleration of gravity=32.16 feet per second.
A cross-sectional area, in square feet, of the pipe from which the gas is flowing. Q-quantity of gas in cubic feet per minute.
Substituting in 2 the value of h we have:
X=specific gravity of gas times the weight of 1 cubic foot of air,
weight of 1 cubic foot of airXspecific gravity of gas
The latter equation is rather similar to that used by Rowse." It requires the determination of the following values: The specific gravity of the gas at a certain temperature and pressure; the weight of a cubic foot of air under the same conditions; the weight of water in pounds per cubic foot at the same temperature; the determination of the differences in inches of the water levels in the gage glass, and the cross-sectional area, in square feet, of the pipe from which the gas is flowing.
a Rowse, W. C., op. cit., p. 1372.
In figure 6 are shown the weights of 1 cubic foot of air at various temperatures, with a constant pressure of 30 inches of mercury."
In figure 7 are shown the weights of water, in pounds per cubic inch, at different temperatures.
Below are tabulated the cross-sectional areas of pipes of various diameters:
EXAMPLES SHOWING ACCURACY OF FORMULA.
The authors have worked out the following examples in order to show the variation in the results from using the more accurate formula given on page 41, as compared with the results obtained by using the table given on page 39.
Suppose the atmospheric pressure to be 14.65 pounds per square inch, the temperature 60° F., the water-gage reading 2 inches, the diameter of the pipe 6 inches, and the specific gravity of the gas 0.60.
From the formula
weight of 1 cubic foot of air-specific gravity of gas.
Square feet. 0.0668 .0872
.1363 . 1963
From figure 7 the weight of water (W) in pounds per cubic inch at 60° F. is found, and from figure 6 the weight of 1 cubic foot of air at 60° F. and 14.65 pounds per square inch is determined.
From the table above the area (A) in cubic feet for a 6-inch pipe is found. H, the inches of water, is read from the gage. Substitution of these values gives:
=1428.17 cubic feet per minute.
Q=555.4 cubic feet of gas per minute.
=799,800 cubic feet per 24 hours.
or 2,056,564 cubic feet of gas in 24 hours.
Using the same data but referring them to the approximate values given in the table on page 39, one finds the quantity of gas to be 2,103,185 cubic feet in 24 hours. The difference is 46,621 cubic feet, or 2.3 per cent of the first value.
Suppose a water-gage reading of 0.3 inch on a 6-inch pipe at 60° F. and 14.65 pounds per square inch, the specific gravity of the gas being 0.6. Proceeding as in the first example, according to the formula:
By referring the given data to the table on page 39 one obtains a result of 740,448 cubic feet. The difference is 59,352 cubic feet, or 7.4 per cent of the first value.
a Rowse, W. C., op. cit., p. 1379.
b Rowse, W. C., op. cit., p. 1380.
WEIGHT OF AIR IN POUNDS PER CUBIC FOOT AT 14.0 POUNDS PER SQUARE INCH PRESSURE (TOTAL) 0.073 0.0725 0.072 0.0715 0.071 0.0705 0.070 0.0695 0.069 0.0685 0.068
0.067 0.0665 0.066
0 per cent humidity
14.1 14.2 14.3 14.4 14.8 TOTAL PRESSURE ON AIR IN POUNDS PER SQUARE INCH FIGURE 6.--Weights of 1 cubic foot of air at various temperatures, pressure being constant at 30 inches of mercury.
AT 14.0 POUNDS PER SQUARE INCH
CORRECTION FOR PRESSURE TO BE ADDED TO WEIGHT OF AIR
Suppose a water-gage reading of 0.3 inch on a 1-inch pipe at 60° F. and 14.65 pounds per square inch, the specific gravity of the gas being 0.60.
From the table on page 39 the cubic feet of gas per 24 hours is found to be 20,568. If the more exact formula be used, the quantity of natural gas per 24 hours is found to be 21,824. The difference is 1,256, or 5.8 per cent.
These three examples will serve to show the errors involved in gas measurement by means of the Pitot tube when the static pressure of the gas is not measured. As regards the measurement of a gas flow on a lease for the purpose of determining the quantity available for gasoline making, the use of the more simple form of Pitot tube appears to be satisfactory.
TEMPERATURE IN DEGREES FAHRENHEIT
The Pitot tube proves most satisfactory when an especially designed instrument is permanently installed. It can then be made an instrument of considerable precision. The use of the accurate form described by the authors is not advisable for field work, unless a device is attached whereby the tube can be rigidly held in place when the readings are made.
Rowse sums up his experiments by saying that the results obtained
peratures, pounds per cubic inch.
FIGURE 7.—Weights of water at different tem- in measuring gases by an absolutely correct Pitot tube may vary 1 per cent, more or less, from the correct results when the static pressure is correctly obtained and when all readings are taken with a reasonable degree of refinement.
GENERAL COMMENTS ON USE OF
0.0362 0.0361 0.0360 0.0359 0.0358 WEIGHT OF WATER IN POUNDS PER CUBIC INCH
NECESSITY OF ALLOWING A WELL TO VENT FREELY BEFORE PITOTTUBE READINGS ARE MADE.
The authors know of a gasoline plant that failed because the gas flow from a well was not accurately measured before the plant equipment had been installed. Many wells on the lease had been open for some time and did not produce enough gas to warrant the installation of a plant. One well that had been closed, on measurement with the Pitot tube, registered a flow of gas of 200,000 cubic feet per 24 hours. A plant was installed against the advice of the
a Rowse, W. C., op. cit., p. 1341.
company that sold the machinery and without its knowledge of the true condition of affairs. After the first day's operation of the plant there was not enough gas left to run the gas engine, and finally the flow practically stopped. The plant, which had cost $7,000, was a failure. This example illustrates the necessity of allowing wells to vent their gases freely before measurements are made, so that the operator may be assured that the quantity measured represents the quantity that will be available for operation of a gasoline plant. Some wells should be open for at least 24 hours before their flow is measured.
In the rush to install gasoline plants in the early days of the industry operators made great blunders. The authors know of one plant that was installed to work upon gas that had not been tested as to quality. The gas proved to be "dry" and the plant was a failure. The authors have heard of other similar mistakes.
INTERPRETATION OF RESULTS OF TESTS.
Considerable experimenting with plant operation on a large scale was necessary before results could be obtained from laboratory tests that could be used as a guide in making plant installations. The Bureau of Mines and different testing laboratories have at present records of the absorption results, specific gravities, and analyses of different natural gases from which gasoline is commercially produced. Reference is made to those results in the examination of new samples.
Many experiments have shown that gasoline may be obtained from natural gas having a specific gravity of 0.80 and higher (air=1). Some inconsistencies have been noted, however, so that the authors would hesitate to recommend the installation of a plant to handle a gas that tests showed to have a specific gravity as low as 0.80 or to have an absorption percentage of 30.0 (Bureau of Mines test), although the gas might be all right for the purpose, especially if it were from wells in a field where other gases of low specific gravity were already producing gasoline. The authors do believe, however, that a gas with a tested specific gravity as high as 0.95 and an absorption percentage as high as 40 might warrant an installation.
Natural gases differ much in composition. A so-called "wet" gas might, for instance, contain a very large proportion of methane, with little ethane, propane, or butane, but enough of the gasoline hydrocarbons to warrant a plant installation. Such a gas when subjected to comparatively low pressures would deposit the gasoline vapors. Another gas of the same specific gravity might contain a comparatively small proportion of methane and ethane and a large proportion of propane and butane, but not enough of the gasoline hydrocarbons to warrant plant installation. Therein lies the reason why specificgravity, solubility, or combustion tests can not always be relied on.