Intercept theorem - Revision history

en>Wcherowi: Reverted 1 edit by 78.100.226.62 (talk) to last revision by Monkbot. (TW)

2014-12-07T04:13:49Z

Reverted 1 edit by 78.100.226.62 (talk) to last revision by Monkbot. (TW)

← Older revision		Revision as of 06:13, 7 December 2014
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	~~The '''Hubbert Linearization''~~' is a way to plot production data to estimate two important parameters of a [[Hubbert curve]]; the [[Logistic function\|logistic]] growth rate and the quantity of the resource that will be ultimately recovered. ~~The Hubbert curve is the first derivative of a [[Logistic function]], which~~ has been used in modeling [[Oil depletion\|depletion of crude oil]], predicting the [[Hubbert peak]], [[population growth]] predictions<ref name="Roper1">{{cite web \| url = http://arts.bev.net/roperldavid/WorldPop.htm \| title = Projection of World Population \| first = David \| last = Roper}}</ref> and ~~the depletion of finite mineral resources~~.~~<ref name="Roper2">{{cite web \| url = http://www.roperld.com/minerals/metalgon.pdf \| title = Where Have All the Metals Gone? \| first = David \| last = Roper\|format=PDF}}</ref>~~ The ~~technique was introduced by [[Marion King Hubbert]] in his 1982 review paper.<ref name="Hubbert82">"Techniques of Prediction as Applied to the Production of Oil and Gas", in the collection Oil~~ and ~~Gas Supply Modeling, edited by Saul~~ I~~. Gass (published as NBS Special Publication 631)</ref> The geologist [[Kenneth S. Deffeyes]] applied this technique in 2005~~ to make a prediction about the peak production of conventional oil.<ref name="Deffeyes1">{{cite book \|last= Deffeyes \|first= Kenneth \|authorlink=http://www.princeton.edu/hubbert/index.html \|coauthors= \|title=Beyond Oil - The view from Hubbert's peak \|date= February 24, 2005\|publisher= Hill and Wang\|location= \|isbn=978-0-8090-2956-3 }}</ref>		Hello friend. Let me introduce myself. I am Ron but I don't like when individuals use my full name. Interviewing is what she does. Alabama has always been his home and his family loves it. The thing I adore most bottle tops gathering and now I have time to consider on new issues.<br><br>Feel free to visit my web page [http://demonknights.Madrealms.net/index.php?mod=users&action=view&id=13883 http://demonknights.Madrealms.net]

	~~== Principle ==~~

	~~The first step of the Hubbert linearization consists of plotting the production data (P) as a fraction of the cumulative production (Q)~~ on ~~the vertical axis and the cumulative production on the horizontal axis~~. ~~This representation exploits the linear property of the logistic differential equation:~~

	: <~~math~~>~~\frac{dQ}{dt}=P=KQ\left(1 - \frac{Q}{URR}\right) \qquad \mbox{(1)} \!~~<~~/math~~>

	~~where ''K'' and ''URR'' are the logistic growth rate and the Ultimate Recoverable Resource respectively. We can rewrite (1) as the following:~~

	~~: <math>\frac{P}{Q}=K\left(1 - \frac{Q}{URR}\right) \qquad \mbox{(2)} \!</math>~~

	~~[[File:HubbertLin US Lower48.svg\|right\|thumb\|400px\|Example of a Hubbert Linearization on the US Lower-48 crude oil production.]]~~

	The above relation is a line equation in the ''P/Q'' versus ''Q'' plane. Consequently, a [[linear regression]] on the data points gives us an estimate of the slope and intercept from which we can derive the Hubbert curve parameters:
	* the ''K'' parameter is the intercept with the vertical axis.
	* the line slope is equal to ~~''-K/URR'' from which we derive the ''URR'' value.~~

	~~== Examples ==~~

	~~=== US oil production ===~~

	The chart on the right gives an example of the application of the Hubbert Linearization technique in the case of the US [[Continental United States\|Lower-48]] oil production. The fit of a line using the data points from 1956 to 2005 (in green) gives a URR of 199 Gb and a logistic growth rate of 6%.

	~~<gallery caption="Other Examples">~~
	~~Image:HubbertLin_Norway.svg\|Hubbert Linearization on [[w:Norway\|Norway]]'s oil production~~
	~~Image:Hubbert_Norway.svg\|Hubbert curve on [[w:Norway\|Norway]]'s oil production~~
	~~Image:HubbertLin_US_Lower48.svg\|Hubbert Linearization on [[w:US\|US]]'s oil production~~
	~~Image:Hubbert_US_Lower48.svg\|Hubbert curve on [[w:US\|US]]'s oil production~~
	~~</gallery>~~

	~~<!-- === World population ===~~

	~~-->~~
	~~==Alternative techniques==~~

	~~===Second Hubbert linearization===~~
	~~The Hubbert linearization principle can be extended to the second derivatives<ref name="Khebab1">{{cite~~ web ~~\| author=Khebab \| title=A Different Way to Perform the Hubbert Linearization \| publisher=[~~[~~The Oil Drum]] \| date=2006-08-18 \| work= \| url=~~http://~~www~~.~~theoildrum~~.~~com~~/~~story/2006/8/16/102942/337 \| accessdate= }}</ref> by computing the derivative of (2):~~

	~~: <math>\frac{dP}{dt}\frac{1}{P}=K\left(1 - 2\frac{Q}{URR}\right) \qquad \mbox{(3)} \!</math>~~

	~~the left term is often called the decline rate~~.

	~~===Hubbert parabola~~===

	~~This representation was proposed by Roberto Canogar<ref name="Canogar">{{cite web \| author=Canogar, Roberto \| title= The Hubbert Parabola \| publisher=GraphOilogy \| date=2006-09-06 \| work= \| url=~~http://~~graphoilogy~~.~~blogspot~~.~~com/2006/09/hubbert-parabola.html \| accessdate= }}</ref> and applied to the oil depletion problem:~~

	~~: <math>P=KQ-\frac{K}{URR}Q^2 \qquad \mbox{(4)} \!</math>~~

	~~<!-- == See also ==~~
	~~{{Empty section\|date=July 2010}}~~

	~~-->~~
	~~== References ==~~

	~~{{Reflist}}~~

	~~==External links==~~
	* [http://www.theoildrum.com/node/2389 Does the Hubbert Linearization Ever Work?] - [[The Oil Drum]]
	* [http://rutledge.caltech.edu/ Hubbert's Peak, The Coal Question, and Climate Change] - Peak Oil, Peak Coal, Peak fossil-fuels]
	* [http://www.its.caltech.edu/~rutledge/Hubbert%27s%20Peak,%20The%20Coal%20Question,%20and%20Climate%20Change.xls Excel Workbook - Hubbert's Peak, The Coal Question, and Climate Change]

	~~[[Category:Peak oil]~~]

83.179.61.22: Swedish link

2014-01-29T07:50:00Z

Swedish link

← Older revision		Revision as of 09:50, 29 January 2014
Line 1:		Line 1:
	~~Friends call her Claude Gulledge~~. ~~Delaware~~ is ~~our birth~~ location. The ~~thing I adore most bottle tops gathering~~ and ~~now I have time~~ to ~~consider~~ on ~~new things~~. ~~After becoming out~~ of ~~my occupation for many years I grew~~ to ~~become~~ a ~~manufacturing~~ and ~~distribution officer but I plan~~ on ~~changing it~~.<br><br>~~Feel free~~ to ~~visit my~~ web-~~site~~: [http://www.~~Skyperoom~~.com/~~blogs~~/~~post~~/~~9816~~ www.~~Skyperoom~~.~~com~~]		The '''Hubbert Linearization''' is a way to plot production data to estimate two important parameters of a [[Hubbert curve]]; the [[Logistic function\|logistic]] growth rate and the quantity of the resource that will be ultimately recovered. The Hubbert curve is the first derivative of a [[Logistic function]], which has been used in modeling [[Oil depletion\|depletion of crude oil]], predicting the [[Hubbert peak]], [[population growth]] predictions<ref name="Roper1">{{cite web \| url = http://arts.bev.net/roperldavid/WorldPop.htm \| title = Projection of World Population \| first = David \| last = Roper}}</ref> and the depletion of finite mineral resources.<ref name="Roper2">{{cite web \| url = http://www.roperld.com/minerals/metalgon.pdf \| title = Where Have All the Metals Gone? \| first = David \| last = Roper\|format=PDF}}</ref> The technique was introduced by [[Marion King Hubbert]] in his 1982 review paper.<ref name="Hubbert82">"Techniques of Prediction as Applied to the Production of Oil and Gas", in the collection Oil and Gas Supply Modeling, edited by Saul I. Gass (published as NBS Special Publication 631)</ref> The geologist [[Kenneth S. Deffeyes]] applied this technique in 2005 to make a prediction about the peak production of conventional oil.<ref name="Deffeyes1">{{cite book \|last= Deffeyes \|first= Kenneth \|authorlink=http://www.princeton.edu/hubbert/index.html \|coauthors= \|title=Beyond Oil - The view from Hubbert's peak \|date= February 24, 2005\|publisher= Hill and Wang\|location= \|isbn=978-0-8090-2956-3 }}</ref>

			== Principle ==

			The first step of the Hubbert linearization consists of plotting the production data (P) as a fraction of the cumulative production (Q) on the vertical axis and the cumulative production on the horizontal axis. This representation exploits the linear property of the logistic differential equation:

			: <math>\frac{dQ}{dt}=P=KQ\left(1 - \frac{Q}{URR}\right) \qquad \mbox{(1)} \!</math>

			where ''K'' and ''URR'' are the logistic growth rate and the Ultimate Recoverable Resource respectively. We can rewrite (1) as the following:

			: <math>\frac{P}{Q}=K\left(1 - \frac{Q}{URR}\right) \qquad \mbox{(2)} \!</math>

			[[File:HubbertLin US Lower48.svg\|right\|thumb\|400px\|Example of a Hubbert Linearization on the US Lower-48 crude oil production.]]

			The above relation is a line equation in the ''P/Q'' versus ''Q'' plane. Consequently, a [[linear regression]] on the data points gives us an estimate of the slope and intercept from which we can derive the Hubbert curve parameters:
			* the ''K'' parameter is the intercept with the vertical axis.
			* the line slope is equal to ''-K/URR'' from which we derive the ''URR'' value.

			== Examples ==

			=== US oil production ===

			The chart on the right gives an example of the application of the Hubbert Linearization technique in the case of the US [[Continental United States\|Lower-48]] oil production. The fit of a line using the data points from 1956 to 2005 (in green) gives a URR of 199 Gb and a logistic growth rate of 6%.

			<gallery caption="Other Examples">
			Image:HubbertLin_Norway.svg\|Hubbert Linearization on [[w:Norway\|Norway]]'s oil production
			Image:Hubbert_Norway.svg\|Hubbert curve on [[w:Norway\|Norway]]'s oil production
			Image:HubbertLin_US_Lower48.svg\|Hubbert Linearization on [[w:US\|US]]'s oil production
			Image:Hubbert_US_Lower48.svg\|Hubbert curve on [[w:US\|US]]'s oil production
			</gallery>

			<!-- === World population ===

			-->
			==Alternative techniques==

			===Second Hubbert linearization===
			The Hubbert linearization principle can be extended to the second derivatives<ref name="Khebab1">{{cite web \| author=Khebab \| title=A Different Way to Perform the Hubbert Linearization \| publisher=[[The Oil Drum]] \| date=2006-08-18 \| work= \| url=http://www.theoildrum.com/story/2006/8/16/102942/337 \| accessdate= }}</ref> by computing the derivative of (2):

			: <math>\frac{dP}{dt}\frac{1}{P}=K\left(1 - 2\frac{Q}{URR}\right) \qquad \mbox{(3)} \!</math>

			the left term is often called the decline rate.

			===Hubbert parabola===

			This representation was proposed by Roberto Canogar<ref name="Canogar">{{cite web \| author=Canogar, Roberto \| title= The Hubbert Parabola \| publisher=GraphOilogy \| date=2006-09-06 \| work= \| url=http://graphoilogy.blogspot.com/2006/09/hubbert-parabola.html \| accessdate= }}</ref> and applied to the oil depletion problem:

			: <math>P=KQ-\frac{K}{URR}Q^2 \qquad \mbox{(4)} \!</math>

			<!-- == See also ==
			{{Empty section\|date=July 2010}}

			-->
			== References ==

			{{Reflist}}

			==External links==
			* [http://www.theoildrum.com/node/2389 Does the Hubbert Linearization Ever Work?] - [[The Oil Drum]]
			* [http://rutledge.caltech.edu/ Hubbert's Peak, The Coal Question, and Climate Change] - Peak Oil, Peak Coal, Peak fossil-fuels]
			* [http://www.its.caltech.edu/~rutledge/Hubbert%27s%20Peak,%20The%20Coal%20Question,%20and%20Climate%20Change.xls Excel Workbook - Hubbert's Peak, The Coal Question, and Climate Change]

			[[Category:Peak oil]]

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-06T00:27:26Z

ISBNs (Build KC)

New page

Friends call her Claude Gulledge. Delaware is our birth location. The thing I adore most bottle tops gathering and now I have time to consider on new things. After becoming out of my occupation for many years I grew to become a manufacturing and distribution officer but I plan on changing it.<br><br>Feel free to visit my web-site: [http://www.Skyperoom.com/blogs/post/9816 www.Skyperoom.com]