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Many, if not most,  parameters and  measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m³, 100  kPa/bar, 50 miles per hour, 1000 Btu/lb.  Converting from one dimensional unit to another is often somewhat complex and being able to perform such conversions is an important  skill to acquire. The '''factor-label method''', also known as the '''unit-factor method''' or '''[[dimensional analysis]]''', is a widely used approach for performing such conversions.<ref>{{cite book|author=David Goldberg|title=Fundamentals of Chemistry|edition=5th Edition|publisher=McGraw-Hill|year=2006|isbn=0-07-322104-X}}</ref><ref>{{cite book|author=James Ogden|title=The Handbook of Chemical Engineering|publisher=Research & Education Association|year=1999|isbn=0-87891-982-1}}</ref><ref>[http://www.kentchemistry.com/links/Measurements/dimensionalanalysis.htm Dimensional Analysis or the Factor Label Method]</ref> It is also used for determining whether the two sides of a mathematical equation involving dimensions have the same dimensional units.


==Examples==
The [[petroleum industry]] is usually divided into three major components: Upstream, [[midstream]] and [[Downstream (oil industry)|downstream]], though midstream operations are usually included in the downstream category.


The factor-label method is the sequential application of conversion factors expressed as [[Fraction (mathematics)|fraction]]s and arranged so that any dimensional unit appearing in both the [[numerator]] and [[denominator]] of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained.  For example, 10 [[U.S. customary units|miles]] per hour can be converted to [[metre]]s per second by using a sequence of conversion factors as shown below:
== The upstram sector ==


:[[Image:Factor-label 1.png|311px]]
The '''upstream''' oil sector is a term commonly used to refer to the searching for and the recovery and [[Extraction of petroleum|production]] of [[crude oil]] and [[natural gas]]. The upstream oil sector is also known as the ''exploration and production (E&P) sector''.


Thus, when the units ''mile'' and ''hour'' are cancelled out and the [[arithmetic]] is done, 10 miles per hour converts to 4.47 metres per second.
The upstream sector includes the searching for potential underground or underwater oil and gas fields, drilling of exploratory wells, and subsequently operating the wells that recover and bring the [[Petroleum|crude oil]] and/or raw [[natural gas]] to the surface.


As a more complex example, the [[concentration]] of [[nitrogen oxides]] (i.e., NOx) in the [[flue gas]] from an industrial [[furnace]] can be converted to a [[mass]] flow rate expressed in grams per hour (i.e., g/h) of NOx by using the following information as shown below:
== The midstream sector ==


;''NOx concentration''
The '''midstream industry''' processes, stores, markets and transports commodities such as crude oil, natural gas, natural gas liquids (mainly ethane, propane and butane) and sulphur. Midstream operations are sometimes included in the downstream category.
:= 10 [[parts per notation|parts per million]] by volume = 10 ppmv = 10 (volumes of NOx) / (10<sup>6</sup> volumes of flue gas)
;''NOx molar mass''
:= 46 g/[[Mole (unit)|mol]] = 46 [[Kilogram|kg]]/kmol
;''Volumetric flow rate of flue gas (expressed at 0 °C and 101.325 kPa)''
:= 20 cubic metres per minute = 20 m³/min
;''The [[Standard conditions of gas temperature and pressure#molar volume of a gas|molar volume]] of a gas at 0 °C and 101.325 kPa
:= 22.414 m³/kmol''


Using the factor-label method:
== The downstreanm sector ==
The '''downstream''' oil sector is a term commonly used to refer to the [[refining]] of [[petroleum|crude oil]], and the selling and distribution of [[natural gas]] and products derived from crude oil. Such products include [[Liquified petroleum gas|liquified petroleum gas (LPG)]], [[Gasoline|gasoline or petrol]], [[jet fuel]], [[diesel oil]], other [[fuel oil]]s, [[asphalt]] and [[petroleum coke]].


:[[Image:Factor-label 2.png|522 px]]
The downstream sector includes [[Oil refinery|oil refineries]]<ref>{{cite book|author=Gary, J.H. and Handwerk, G.E.|title=Petroleum Refining Technology and Economics|edition=2nd Edition|publisher=Marcel Dekker, Inc|year=1984|isbn=0-8247-7150-8}}</ref>, [[petrochemical]] plants, petroleum product distribution, retail outlets and natural gas distribution companies. The downstream industry touches consumers through thousands of products such as petrol, diesel, jet fuel, [[heating oil]], asphalt, [[lubricant]]s, [[synthetic rubber]], [[plastic]]s, [[fertilizer]]s, [[antifreeze]], [[pesticide]]s, [[pharmaceutical]]s, natural gas and propane.


After cancelling out any dimensional units that appear both in the numerators and denominators of the fractions in the above equation, the NOx concentration of 10 ppmv converts to mass flow rate of 24.63 grams per hour.
=== Byproduct sulphur ===


== Checking equations that involve dimensions ==
Crude oil is a mixture of hundreds of [[hydrocarbon]]s, including many which contain [[sulphur]]. Refining the crude oil includes converting most of that sulphur into gaseous [[hydrogen sulphide]]. Raw natural gas also contains gaseous hydrogen sulphide and sulphur-containing [[mercaptans]], which are removed in [[natural gas processing]] plants before the gas is distributed to consumers. The hydrogen sulphide removed in the refining and processing of crude oil and natural gas is subsequently converted into byproduct elemental sulfur. In fact, the vast majority of the 64,000,000 metric tons of sulfur produced worldwide in 2005 was byproduct sulphur from refineries and natural gas processing plants.<ref>[http://minerals.usgs.gov/minerals/pubs/commodity/sulfur/sulfumcs06.pdf Sulphur production report] by the [[United States Geological Survey]]</ref><ref>[http://www.agiweb.org/geotimes/july03/resources.html Discussion of recovered byproduct sulphur]</ref>
 
The factor-label method can also be used on any mathematical equation to check whether or not the dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of the equation. Having the same units on both sides of an equation does not guarantee that the equation is correct, but having different units on the two sides of an equation does guarantee that the equation is wrong.
 
For example, check the [[ideal gas law]] equation of ''P·V = n·R·T'', when:
* the pressure ''P'' is in pascals (Pa)
* the volume ''V'' is in cubic meters (m³)
* the amount of substance ''n'' is in moles (mol)
* the [[Molar gas constant|universal gas law constant]] ''R'' is 8.3145 Pa·m³/(mol·K)
* the temperature ''T'' is in kelvins (K)
 
:[[Image:Factor-label 3.png|169px]]
 
As can be seen, when the dimensional units appearing in the numerator and denominator of the equation's right hand side are cancelled out, both sides of the equation have the same dimensional units.
 
==Limitations==
 
The factor-label method can convert only unit quantities which have a constant ratio to each other. Most units fit this paradigm.
 
An example for which it cannot be used is the conversion between kelvins and degrees Celsius or between degrees Celsius and degrees [[Fahrenheit]]. Between kelvins and degrees Celsius, there is a constant difference rather than a constant ratio, while between degrees Celsius and degrees Fahrenheit there is both a constant difference and a constant ratio.
 
==References==
{{reflist}}

Revision as of 01:10, 6 July 2009


The petroleum industry is usually divided into three major components: Upstream, midstream and downstream, though midstream operations are usually included in the downstream category.

The upstram sector

The upstream oil sector is a term commonly used to refer to the searching for and the recovery and production of crude oil and natural gas. The upstream oil sector is also known as the exploration and production (E&P) sector.

The upstream sector includes the searching for potential underground or underwater oil and gas fields, drilling of exploratory wells, and subsequently operating the wells that recover and bring the crude oil and/or raw natural gas to the surface.

The midstream sector

The midstream industry processes, stores, markets and transports commodities such as crude oil, natural gas, natural gas liquids (mainly ethane, propane and butane) and sulphur. Midstream operations are sometimes included in the downstream category.

The downstreanm sector

The downstream oil sector is a term commonly used to refer to the refining of crude oil, and the selling and distribution of natural gas and products derived from crude oil. Such products include liquified petroleum gas (LPG), gasoline or petrol, jet fuel, diesel oil, other fuel oils, asphalt and petroleum coke.

The downstream sector includes oil refineries[1], petrochemical plants, petroleum product distribution, retail outlets and natural gas distribution companies. The downstream industry touches consumers through thousands of products such as petrol, diesel, jet fuel, heating oil, asphalt, lubricants, synthetic rubber, plastics, fertilizers, antifreeze, pesticides, pharmaceuticals, natural gas and propane.

Byproduct sulphur

Crude oil is a mixture of hundreds of hydrocarbons, including many which contain sulphur. Refining the crude oil includes converting most of that sulphur into gaseous hydrogen sulphide. Raw natural gas also contains gaseous hydrogen sulphide and sulphur-containing mercaptans, which are removed in natural gas processing plants before the gas is distributed to consumers. The hydrogen sulphide removed in the refining and processing of crude oil and natural gas is subsequently converted into byproduct elemental sulfur. In fact, the vast majority of the 64,000,000 metric tons of sulfur produced worldwide in 2005 was byproduct sulphur from refineries and natural gas processing plants.[2][3]

  1. ↑ Gary, J.H. and Handwerk, G.E. (1984). Petroleum Refining Technology and Economics, 2nd Edition. Marcel Dekker, Inc. ISBN 0-8247-7150-8. 
  2. ↑ Sulphur production report by the United States Geological Survey
  3. ↑ Discussion of recovered byproduct sulphur
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