It is well known that, if all other things being equal (or in Latin “ceteris paribus or caeteris paribus”), the volume is directly proportional to temperature and inversely proportional to pressure, which are applied to it. Or, in other words, under constant temperature and pressure, the relationship between the volume of gas and the number of moles is direct. This law is known as Avogadro’s Principle or Avogadro’s hypothesis. This hypothesis was first published by Amedeo Carlo Avogadro (1776–1856), an Italian scientist, in the year 1811.
Just for those who prefer a mathematical language, we refer to Avogadro’s original and simple modified equations:
V ÷ n = k, which means that the volume amount fraction will always be the same value if the pressure and temperature remain constant.
Let V1 and n1 be a volume amount pair of data at the commencement of our research. If the amount is transformed to a different value called n2, then the volume will be altered to V2.
As we are aware that V1 ÷ n1 = k and we are acquainted with: V2 ÷ n2 = k.
Meanwhile, as k = k, we can determine that V1 ÷ n1 = V2 ÷ n2.
This equation of V1 ÷ n1 = V2 ÷ n2 will be very useful in cracking Avogadro’s Law problems. Here is the Law articulated in fractional form:
And if we emphasize that the temperature should be presented in kelvins (and Celsius degrees) and the pressure – in Pascals (how all the units are accepted in modern chemistry and physics, as well as in the SI, where 0 K = -273.15 °C and 1 Pa = 1 Newton/m2 = 0.00014503773 Psi), then the needed equation looks as follows:
Vx = Vo × (273.15 + Tn) ¸ Po x Pn, where
Vx – a new, sought-for volume,
Vo – an original volume in the same units,
Tn – a new temperature in Celsius degrees,
Po – an original pressure,
Pn – a new pressure in the same units.
Although the Avogadro’s Law relates to an ideal gas (an abstract, theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collision), the above equation is actually good (universal) for any gaseous or liquid hydrocarbons.
There are no such problems with weight measurements but when it comes to volumes, it very important to bear in mind that, say, in the USA, oil/gas and energy business (and, first of all, API, DoE, PRMS and USGS) use now the following set of volume measurements, known as U.S. standard temperature and pressure (or, shortly, STP): 60°F (288.706 K, 15.556°C) and 14.696 psia (1 atm, 1.01325 bar), also named “1 Standard Atmosphere.” At these conditions, the volume of 1 mole of a gas equals 23.6442 liters while 1 cubic foot of a gas does not equal 28.3168 liters (under any similar measurements) but 28.8719 liters (in line with the definition of the STP, used by the International Gas Union (IGU) (15°C and 760 mmHg).
These U.S. conditions are the most commonly used in the USA and, if not specified or unknown, worldwide to define the volume of what is termed “Sm3” (Standard cubic meter). [FYI: the earlier IUPAC (International Union of Pure and Applied Chemistry) definition of the STP (273.15 K and 101.325105 kPa), “is now discontinued worldwide”, as if it was ever used in the States or elsewhere…].
It is noteworthy that the above mentioned “standard” and “normal” indicate that these units are not strict volumes of gas that are flowing but quantities of gas. An SCF corresponds to 1 cubic foot of gas at 60 °F (15.6 °C) and 14.73 psia, while a Nm3 corresponds to 1 cubic meter of gas at 15°C and at 101.325 kPa or 760 millimeters in a mercurial barometer (760 mmHg). This is about 29.9 inches of mercury and represents approximately 14.7 pounds per sq. inch (psi).
Sometimes, other sets of volume-measurement units are utilized – NTP and SATP. In particular, Normal Temperature and Pressure (NTP) are commonly used as a standard condition for testing and documentation of air compressors, blowers and fans capacities: They are defined as 20oC (293.15 K, 68oF) and 1 atm (101.325 kN/m2or kPa, 14.7 psia, 29.92 in Hg, 407 in H2O, 760 torr). A fan that produces a static pressure of 3 in H2O (a good average value) will increase the absolute air pressure by 3 (in H2O).
Currently, the IUPAC defines the NTP as 273.15 K (0°С) of temperature and: 100,000 Pа of pressure, while the NIST (the Gaithersburg-based (Maryland) National Institute for Standards and Technology) – as 293.15 K (20°С) and: 101,325 Pа (760 mmHg).
Worldwide industrial application there have the so-called Standard Ambient Temperature and Pressure (SATP), which are also used in chemistry as a reference: defined as a reference with a temperature of 25oC (298.15 K) and pressure of 101.325 kPa and may be also named “normal conditions.” At these conditions, the volume of 1 mole of a gas is 24.4651 liters.
The Montreal-based (Quebec, Canada) UN’s International Civil Aviation Organization (ICAO) invented “the international standard atmosphere at sea level” (101325 Pа or 760 mmHg with a zero absolute and relative humidity), which is often called “normal pressure” and uses the following measurement conditions: 288.15 K or 15°С and 101,325 Pа or 760 mmHg.
In Europe, Australia, and Latin America, for example, the STP conditions used by the International Organization for Standardization (ISO) (that are 15°C and 101.325 kPa) have been adopted, as a rule, and are used as the base values for defining the standard cubic meter.
In its turn, in Russia 20°C and 760 mmHg, corresponding, in particular, to the U.S. NIST’s NTP and EPA’s STP, are officially used for volume measurements. As a matter of fact, this is almost the biggest difference in temperatures used at present in the oil and gas industry worldwide (20°C and 60°F)3. At the Russian conditions, 1 U.S. cubic foot of a gas does not equal 28.3168 liters but nearly 28.7527 liters or contains almost 1.54 percent more gas, while U.S. oil 42-gallon barrel is not equal to 158.987295 liters but accommodates over 161.4345 liters of oil (again by nearly 1.54 percent more) (Figure1).
No doubt, not a big deal, indeed. But, if taken in absolute physical terms, with gas production standing now in Russia at some 730 bcm a year and that of crude oil and mixed/leased condensate at over 560 mta, this is more than what was actually produced last year in Vietnam (9.6 bcma or 0.93 bcfd) or Peru (6.4 mta or 154 kb/d) or Peru (Table 1).
For its energy balances, Russia officially uses (like the IEA and the PRC) such energy unit as tonne (of) oil equivalent (toe), which net calorific value (NCV) is defined, by convention, as follows:
- 1 toe = 11.63 megawatt-hours (MWh);
- 1 toe = 41.868 gigajoules (GJ);
- 1 toe = 10 gigacalories (Gcal) – using the international steam table calorie (calIT) and not the thermochemical calorie (calth);
- 1 toe = 39,683,207.2 British thermal units (BTU);
- 1 toe = 1.42857143 tonnes of coal equivalent (tce).
A similar energy unit – barrel of oil equivalent (boe) – is often used in the USA for energy comparisons and combinations. This is a unit of energy based on the approximate energy released by burning one barrel (42 U.S. gallons or 158.9873 litres) of crude oil. The BOE is used by oil and gas companies in their financial statements as a way of combining oil and natural gas reserves and production into a single measure, although this energy equivalence does not take into account the lower financial value of energy in the form of gas.
The U.S. Internal Revenue Service (IRS) defines higher heating value (HHV) of the boe as equal to 5.8 million BTU (5.8×106 BTU59°F equals 6.1178632×109 J, about 6.1 GJ or about 1.7 MWh.) The value is necessarily approximate as various grades of oil and gas have slightly different heating values. If one considers the lower heating value instead of the higher heating value, the value for one boe would be approximately 5.4 GJ (see toe above). Typically, 5,800 cubic feet of natural gas or 58 CCF (100 cubic feet) are equivalent to one boe. The USGS gives a figure of 6,000 cubic feet (170 cubic meters) of typical natural gas.
Over the northern border, in Canada, the toe is used by the country’s ministry of energy – National Energy Board (NEB) – and Canadian leading energy companies. NCV of this energy unit is defined as 41.868 gigajoules (GJ) or 10 gigacalories (Gcal) (see above). Besides, for natural gas and NGLs cubic metres (m3) are used measured at 15°C and 101.325 kPa (760 mmHg), which means that Canadian STP fully corresponds to those used in the EU (see above).
In its turn, in Russia and the FSU other countries, the tce (see above) is widely used for energy comparisons. This energy unit is usually called tonne of standard reference fuel (trf), net calorific value of which is defined as 29.3 GJ or 7,000 kcal. In this case, it equals 0.7 toe and is assumingly referred to energy contents of various fuels in the following way (Table 2):
3 To be exact, an even larger difference should be attributed to volumes (of natural gas) exported by Russia to the EU (almost 1.74%).
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