Page 251 - Pipeline Rules of Thumb Handbook

238 Pipeline Rules of Thumb Handbook

Know the gas laws

The symbols that will be used in the mathematical expres- information, an arrangement of the formula that would be
sion of the various gas laws are: handy is:

V 1 = volume of the gas in cubic ft with original conditions T 2
V 2 = V 1 ¥ (2)
V 2 = volume of gas in cubic ft under the second set of con-
T 1
ditions
T 1 = initial temperature of the gas in °R (°F + 460) A second part of Charles’ Law is: If the volume of a quan-
T 2 = temperature of gas under second conditions °R tity of gas does not change, the absolute pressure will vary
P 1 = pressure of gas in psia under original conditions directly as the absolute temperature.
P 2 = pressure of gas in psia under second conditions
Expressed mathematically this is:
Any other symbols used in mathematically expressing the
gas laws will be explained at the time of their introduction. P 1 = T 1
P 2 T 2
Boyle’s law. If the temperature remains the same, the
volume of a given quantity of gas will vary inversely as the In this instance, we would probably be more interested in
absolute pressure. This may be expressed mathematically as: the pressure at a second temperature condition which could
be expressed as:

V 1 P 2
=
V 2 P 1 T 2
P 2 = P 1 ¥
(3)
T 1
Inasmuch as in the application of Boyle’s Law we are
generally interested in the volume at a second set of pres-
sure conditions, a rearrangement of the formula more Example. A given weight of gas has a volume of 450 cubic
readily used is: ft when the temperature is 45°F, and the pressure is 10psig.
If the pressure remains the same, but the temperature is
P 1 changed to 90°F, what will be the volume of the gas?
V 2 = V 1 ¥ (1)
P 2
Example. A quantity of gas at a pressure of 42psig has a Table 1
volume of 1,000 cubicft. If the gas is compressed to 100psig, Molecular Weights of Hydrocarbons and Other
what volume would it occupy? Assume the barometric pres- Compounds Associated with Natural Gas
sure to be 14.2psia, and the temperature to remain the same. Atomic Molecular
Substituting in the second arrangement of the formula for Compound Formula Weight
Boyle’s Law above would give:
Methane CH 4 16.043
42 14 2 Ethane C 2 H 6 30.070
.
+
,
V 2 = 1 000 ¥
100 14 2 Propane C 3 H 8 44.097
.
+
Butane C 4 H 10 58.124
.
= 492 1 cubic ft
Pentane C 5 H 12 72.151
Hexane C 6 H 14 86.178
Charles’ law (sometimes called Gay-Lussac’s Law). If the Heptane 100.205
pressure remains the same, the volume of a given quantity of Carbon Dioxide C 7 H 16 44.011
CO 2
gas will vary directly as the absolute temperature. Nitrogen N 2 28.016
This may be expressed mathematically as: Oxygen O 2 32.00
Water H 2 O 18.016
Air 28.967
V 1 T 1
=
V 2 T 2
Note: Molecular weights based on following values of atomic weights:
Hydrogen 1.008, Carbon 12.011, Nitrogen 14.008, Oxygen 16.000, and
Again, since we are usually more interested in the volume Argon 39.944. Air was assumed to consist of 78.09% nitrogen, 20.95%
at a second set of temperature conditions than any other oxygen, 0.93% argon, and 0.03% carbon dioxide.