Page 252 - Pipeline Rules of Thumb Handbook

Gas—General 239

Substitution in the formula for the first part of the Charles’ The ideal gas law. Although expressed in many slightly
Law gives: different arrangements, this law is most frequently expressed
as:
( 90 460)
+
V 2 = 450 ¥ pV = nRT
( 45 460)
+
= 490 cubic ft where p = pressure of the gas
V = volume of the gas
n = number of lb-mols of gas
It is desired to determine what the new pressure would be R = the universal gas constant which varies depend-
for the gas in the above example if the volume remains the ing upon the units of pressure, volume, and tem-
same and the temperature changes from 45°F to 90°F as perature employed
indicated. (Atmospheric pressure is 14.4psia.)
Substitution in the formula gives:
Since the number of lb-mols of a gas would be equal to the
weight of the gas divided by the molecular weight of the gas,
( 90 460) we can express the ideal gas law as:
+
P 2 = ( 10 14 4) ¥
.
+
( 45 460)
+
W
.
= 26 6 p sia or 12.2 psig pV = 10 722. ¥ ¥ T (5)
M
A convenient arrangement of a combination of Boyle’s and where p = pressure of the gas, psia
Charles’ laws which is easy to remember and use can be V = volume of the gas, cubic ft
expressed mathematically as: W = weight of the gas, lb
M = molecular weight of the gas
T = temperature of the gas, °R
PV 1 PV 2
1
2
= (4)
The constant 10.722 is based upon the generally used value
T 1 T 2
for the universal gas constant of 1,544 when the pressure is
One can substitute known values in the combination for- expressed in lb/sqft absolute.
mula and solve for any one unknown value. In cases where This formula can be used in many arrangements. An
one of the parameters, such as temperature, is not to be arrangement which may be used to determine the weight of
considered, it may be treated as having the same value on a quantity of gas is:
both sides of the formula and consequently it can be can-
celled out. MVp
.
W = 0 0933 ¥
T (6)
Avogadro’s law. This law states that equal volumes of all
gases at the same pressure and temperature conditions when the symbols and units are as above.
contain the same number of molecules.
From this it may be seen that the weight of a given volume
of gas is a function of the weights of the molecules and that Example. It is desired to find the weight of a gas in a
there is some volume at which the gas would weigh, in lb, the 1,000-cubic-ft container if the gas is at a pressure of 150psig
numerical value of its molecular weight. and a temperature of 90°F. The molecular weight of the
The volume at which the weight of the gas in lb is equal to gas is known to be 16.816, and the barometric pressure is
the numerical value of its molecular weight (known as the 14.3psia.
“mol-volume”) is 378.9 cubicft for gases at a temperature of Substitution in the formula gives:
60°F and a pressure of 14.73psia. Table 1 gives the atomic
formula and molecular weights for hydrocarbons and other .0933 ¥ 16 .816 ¥ ,000 ¥ (150 14 .3 )
1
+
compounds frequently associated with natural gas. Reference W =
(90 + 460 )
to the table reveals that the molecular weight for methane is
= 468 .7 lb
16.043. Going back to the mol-volume explanation, shows that
378.9 cubicft of methane at 60°F and a pressure of 14.73psia
would weigh 16.043lb. The formula above may be used when the molecular
Avogadro’s law ties in closely with what is usually known as weight of a gas is known; however, at times it is desirable to
the ideal gas law. determine the weight of a given volume of gas when the